(Part 2) Best science & math books according to redditors
We found 24,037 Reddit comments discussing the best science & math books. We ranked the 8,905 resulting products by number of redditors who mentioned them. Here are the products ranked 21-40. You can also go back to the previous section.
For a fun read, I love The Disappearing Spoon.
For a while, I've been meaning to read Salt which is another fun read.
I also just love the Periodic Table of Videos YouTube channel for other fun stuff.
Textbook-wise, you can't beat Stumm and Morgan or Metcalf and Eddy for your water chemistry/water treatment needs.
Oh? Really? Refraction is easy peasy, eh?
You may have heard that the speed of light slows down depending on the density of the material through which it passes.
But in reality, light sniffs out every possible path, then chooses the least resistant.
Every photon, trillions upon trillions upon trillions of them, considers every possible path through space! When you start to think about "how could such a thing even be possible?" then you get really mindblown.
Check out QED by Feynman for some mindbending. I'd recommend reading the book, but you could watch the lectures.
EDIT: For the truly curious, you can read Chapter 2 of the book here. It's the most accurate refraction ELI5 that exists (or probably will ever exist). It's probably impossible to simplify the explanation any further.
They have already tried to establish their own "facts" with Conservapedia.
For example, Conservapedia suggests that the Theory of Relativity is not supported by evidence, and in fact, says "Claims that relativity was used to develop the Global Positioning System (GPS) are false." ... This assertion by Conservapedia is itself just plain false.
Chris Mooney goes into much more depth with this and other examples in his book "The Republican Brain: The Science of Why They Deny Science - and Reality", worth checking out.
EDIT: I just checked out a few entries in Conservapedia. The following are good for a laugh:
Global Warming
Dinosaurs
Mammoth
Counterexamples to an Old Earth
Well here's how it went down.
But I still love physics. I read QED for fun. I just can't handle anything beyond Taylor and Maclaurin series without someone at my back yelling at me I guess. Also I hated memorizing integrals.
On the tests I would get all the bonus questions right (which tested actual understanding of the concepts) and I'd fail on the actual test due to lack of time (because that part of the test really tested how often you had seen that problem or one similar before).
The answer is "virtually all of mathematics." :D
Although lots of math degrees are fairly linear, calculus is really the first big branch point for your learning. Broadly speaking, the three main pillars of contemporary mathematics are:
You might also think of these as the three main "mathematical mindsets" — mathematicians often talk about "thinking like an algebraist" and so on.
Calculus is the first tiny sliver of analysis and Spivak's Calculus is IMO the best introduction to calculus-as-analysis out there. If you thought Spivak's textbook was amazing, well, that's bread-n-butter analysis. I always thought of Spivak as "one-dimensional analysis" rather than calculus.
Spivak also introduces a bit of algebra, BTW. The first few chapters are really about abstract algebra and you might notice they feel very different from the latter chapters, especially after he introduces the least-upper-bound property. Spivak's "properties of numbers" (P1-P9) are actually the 9 axioms which define an algebraic object called a field. So if you thought those first few chapters were a lot of fun, well, that's algebra!
There isn't that much topology in Spivak, although I'm sure he hides some topology exercises throughout the book. Topology is sometimes called the study of "shape" and is where our most general notions of "continuous function" and "open set" live.
Here are my recommendations.
Analysis If you want to keep learning analysis, check out Introductory Real Analysis by Kolmogorov & Fomin, Principles of Mathematical Analysis by Rudin, and/or Advanced Calculus of Several Variables by Edwards.
Algebra If you want to check out abstract algebra, check out Dummit & Foote's Abstract Algebra and/or Pinter's A Book of Abstract Algebra.
Topology There's really only one thing to recommend here and that's Topology by Munkres.
If you're a high-school student who has read through Spivak in your own, you should be fine with any of these books. These are exactly the books you'd get in a more advanced undergraduate mathematics degree.
I might also check out the Chicago undergraduate mathematics bibliography, which contains all my recommendations above and more. I disagree with their elementary/intermediate/advanced categorization in many cases, e.g., Rudin's Principles of Mathematical Analysis is categorized as "elementary" but it's only "elementary" if your idea of doing math is pursuing a PhD. Baby Rudin (as it's called) is to first-year graduate analysis as Spivak is to first-year undergraduate calculus — Rudin says as much right in the introduction.
I'll stick to recommending science communication books (those that don't require a deep background on biological concepts):
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For books that everyone studying biology ends up reading, my candidate would be Lehninger's Principles of Biochemistry, by Nelson & Cox but that's a textbook.
Here's my rough list of textbook recommendations. There are a ton of Dover paperbacks that I didn't put on here, since they're not as widely used, but they are really great and really cheap.
Amazon search for Dover Books on mathematics
There's also this great list of undergraduate books in math that has become sort of famous: https://www.ocf.berkeley.edu/~abhishek/chicmath.htm
Pre-Calculus / Problem-Solving
Calculus
Linear Algebra
Differential Equations
Number Theory
Proof-Writing
Analysis
Complex Analysis
Functional Analysis
Partial Differential Equations
Higher-dimensional Calculus and Differential Geometry
Abstract Algebra
Geometry
Topology
Set Theory and Logic
Combinatorics / Discrete Math
Graph Theory
P. S., if you Google search any of the topics above, you are likely to find many resources. You can find a lot of lecture notes by searching, say, "real analysis lecture notes filetype:pdf site:.edu"
Three minor corrections:
If anyone is interested in an accessible introduction to this material, read Richard Feynman's QED.
I started from scratch on the formal CS side, with an emphasis on program analysis, and taught myself the following starting from 2007. If you're in the United States, I recommend BookFinder to save money buying these things used.
On the CS side:
On the math side, I was advantaged in that I did my undergraduate degree in the subject. Here's what I can recommend, given five years' worth of hindsight studying program analysis:
Final bit of advice: you'll notice that I heavily stuck to textbooks and Ph.D. theses in the above list. I find that jumping straight into the research literature without a foundational grounding is perhaps the most ill-advised mistake one can make intellectually. To whatever extent that what you're interested in is systematized -- that is, covered in a textbook or thesis already, you should read it before digging into the research literature. Otherwise, you'll be the proverbial blind man with the elephant, groping around in the dark, getting bits and pieces of the picture without understanding how it all forms a cohesive whole. I made that mistake and it cost me a lot of time; don't do the same.
Mathematics: Its Content, Methods and Meaning by A. D. Aleksandrov, A. N. Kolmogorov, M. A. Lavrentev.
Personally read only the first chapter, but the book is praised by lots of people. I bet Mr. Nikolaevich has read it.
You can find it on Amazon https://www.amazon.com/Mathematics-Content-Methods-Meaning-Volumes/dp/0486409163
THe book "Biological Exuberance: Animal Homosexuality and Natural Diversity" is what you need.
https://www.amazon.com/Biological-Exuberance-Homosexuality-Diversity-Stonewall/dp/031225377X/ref=sr_1_1?ie=UTF8&qid=1536733270&sr=8-1&keywords=Biological+Exuberance%3A+Animal+Homosexuality+and+Natural+Diversity.
It lists over 190 in chapter 2 alone and states that Bagemihl's research shows that homosexual behavior, not necessarily sex, has been documented in about 500 species as of 1999, ranging from primates to gut worms. Across all the chapters, it compiles
more than two centuries of observations of homosexual behavior, pair bonding, and coparenting in more than 400 species.
All the peer reviewed statistics and data sources are included in the book for those skeptics.
(Though let's face it, if Anti-vaxxers can ignore hundreds of peer-reviewed scientific documents and focus on the one discredited idiot who stated that vaccines cause autism, then people will cherry pick from this too).
>Metropolitan Anthimos of Thessaloniki, Greece’s second largest city used his pulpit just days before the vote in Greek parliament to suggest that “not even animals” have these tendencies.
Too bad "Biological Exuberance: Animal Homosexuality and Natural Diversity" hasn't been translated into Greek. Because this person needs to read it...
https://www.amazon.com/Biological-Exuberance-Homosexuality-Diversity-Stonewall/dp/031225377X
As someone who has studied dynamical systems for years, I'm pleased to see so many redditors getting interested in them through the double pendulum system. If you're a student and want to learn more, take a course in dynamical systems. If you're not a student, consider reading this book, which is my favorite math book of all time, and I'm far from alone in that sentiment.
If you want to learn a modern (i.e., dynamical systems) approach, try Hirsch, Smale and Devaney for an intro-level book and Guckenheimer and Holmes for more advanced topics.
> a more Bourbaki-like approach
Unless you already have a lot of exposure to working with specific problems and examples in ODEs, it's much better to start with a well-motivated book with a lot of interesting examples instead of a dry, proof-theorem style book. I know it's tempting as a budding mathematician to have the "we are doing mathematics here after all" attitude and scoff at less-than-rigorous approaches, but you're really not doing yourself any favors. In light of that, I highly recommend starting with Strogatz which is my favorite math book of all time, and I'm not alone in that sentiment.
I've had a similar experience with wanting to continue my math education and I've really enjoyed picking up Schaum's Outlines on topics I've been exposed to and ones that I have not. There's also a really fun textbook Non-Linear Dynamics and Chaos which I'm enjoying right now. I find looking up very advanced problems like the Clay Institute Millennium Prize Problems and trying to really understand the question can be very revealing.
The key thing that took me a while to realize about recreating that experience is forcing yourself to work as many problems as you have time to work, even (read: especially) when you don't really feel like it. You may not get the exact same experience and it's likely you won't be able to publish (remember, it takes a lot to really dig deeply enough into a field and understand what has already been written to be able to write something original), but you'll keep learning! And it will be really fun!
> Make no mistake, the gay community needs to file for divorce with the trans community. They are no longer working toward the same goals ... Unlike members of the trans community, who are working against their biology and trying to change who they are physically, gay or lesbian people are trying to be nobody but themselves. They are not seeking surgery or hormone treatments. They love the same gender; they don’t want to be a different gender.
This. This so much.
We have biological evidence that throughout the animal kingdom homosexuality and bisexuality are totally normal and seen in a variety of species. https://www.amazon.ca/Biological-Exuberance-Homosexuality-Natural-Diversity/dp/031225377X
While Bruce Bagemihl also writes about and catalogues evidence of transgenderism in the animal kingdom in the sense of gender-non-confirming behaviour in animals as well as evidence of intersexuality/hermaphrodism. Exact gender roles and expression of those roles vary in species as well as in individuals, but all animals have to accept that biology is immutable. Sexual reassignment surgery is cosmetic and doesn't change one's gender. By being in denial about biology, this current wave of trans identity politics is essentially butting heads with reality. It won't end well.
I know this will be buried, but:
just to be clear, psychologists do not have a clear understanding of the mechanism behind motivated reasoning. all of the persuasion resistance strategies mentioned in the reference you provided are really downstream of the process, they are strategies that result from this motivated reasoning.
it's sort of like asking how Lionel Messi is so good at scoring goals (or LeBron James and basketball or whatever), and answering, "he uses such and such strategies" but that still doesn't answer why he scores all those goals as opposed to other people. it's part of the answer, yes, but not a complete answer. when does he use which strategies? how does he make the decision what strategy to use? when are they more or less effective? there are lots of questions remaining in addition to the critical one of determining the exact mechanism(s).
I'm also surprised you didn't cite the most complete account of motivated reasoning in a journal format, which is Kunda, Z. (1990) in Psychological Bulletin, p. 108.
edit:changed a 'why' to a 'how'. also, for a good recent treatment of this, Chris Mooney, a journalist, as a book The Republican Brain: The Science of Why They Deny Science and Reality which doesn't actually answer those gaps I have brought up, but is a good intro into some of the science nonetheless.
Have you ever read this book? This reminds me of it very much.
It should also be noted that simpler subjects and introductory texts tend to be common knowledge to the point that citation is often not needed. You don't need to cite that water is wet, not even on Wikipedia.
Journals and modern texts about modern subjects tend to be very well cited, because they're building heavily on other sources of information.
When you don't do this, you have to have an enormous amount of backgrounding. For instance, check out this algebra text. It's 944 pages because it doesn't tend to cite much of exposition and instead states it all directly. It includes an enormous amount of information -- it's meant to be used as fundamental education material. It's not just high level conclusions that could fit in 20-50 pages.
So the amount of citation depends a great deal on the purpose of the text and how close it is to common knowledge. However, Anita's criticism is clearly not common knowledge because nobody but her sees it the way she does. Therefore, she should be explaining how she comes to her conclusions, and citing information. She should also be citing the direct quotes she uses, because it's plagiarism otherwise (and we have huge volumes of evidence that she outright plagiarizes a great deal). Plagiarism in academia is something that ends your career.
Start by picking a guide for your area and reading it thoroughly, especially focusing on the anatomy of a mushroom. Go hunting a lot bringing back what you find, take spore prints and work though the IDs. Also joining a NAMA affiliated club will help tremendously.
Regional guides
Alaska
Common Interior Alaska Cryptogams
Western US
All The Rain Promises and More
Mushrooms of the Pacific Northwest
Midwestern US
Mushrooms of the Midwest
Edible Wild Mushrooms of Illinois and Surrounding States
Mushrooms of the Upper Midwest
Southern US
Texas Mushrooms: A Field Guide
Mushrooms of the Southeastern United States
Midwestern US
Mushrooms of the Midwest
Edible Wild Mushrooms of Illinois and Surrounding States
Mushrooms of the Upper Midwest
Eastern US
Mushrooms of West Virginia and the Central Appalachians
Mushrooms of Northeast North America (This was out of print for awhile but it's they're supposed to be reprinting so the price will be normal again)
Mushrooms of Northeastern North America
Macrofungi Associated with Oaks of Eastern North America(Macrofungi Associated with Oaks of Eastern North America)
Mushrooms of Cape Cod and the National Seashore
More specific guides
Psilocybin Mushrooms of the World
North American Boletes
Tricholomas of North America
Milk Mushrooms of North America
Waxcap Mushrooms of North America
Ascomycete of North America
Ascomycete in colour
Fungi of Switzerland: Vol. 1 Ascomycetes
PDFs
For Pholiotas
For Chlorophyllum
For parasitic fungi, Hypomyces etc "Mushrooms that Grow on other Mushrooms" by John Plischke. There's a free link to it somewhere but I cant find it.
Websites that aren't in the sidebar
For Amanita
For coprinoids
For Ascos
MycoQuebec: they have a kickass app but it's In French
Messiah college this has a lot of weird species for polypores and other things
Books that provide more info than field Mycology
The Kingdom of Fungi Excellent coffee table book has nice pictures and a breif guide to Fungal taxonomy and biology.
The Fifth Kingdom A bit more in depth
Introduction toFungi Textbook outlining metobolic, taxonomic and ecological roles of fungi. Need some level of biochemistry to have a grasp for this one but it's a good book to have.
> I think there must be some sort of primordial fear mechanism that Fox/Roger Ailes know how to exploit.
tl;dr Strong correlation between "being conservative" and "brain that tends to respond more strongly to fear, with bigger fear-handling brain parts [the amygdala]".
> What they found is that people who have more fearful disposition also tend to be more politically conservative, and less tolerant of immigrants and people of races different from their own. As [Brown University researcher Rose] McDermott carefully emphasizes, that does not mean that every conservative has a high fear disposition. "It's not that conservative people are more fearful, it's that fearful people are more conservative," as she puts it.
> Darren Schreiber, a political neuroscientist at the University of Exeter in the United Kingdom, first performed brain scans on 82 people participating in a risky gambling task, one in which holding out for more money increases your possible rewards, but also your possible losses. Later, cross-referencing the findings with the participants' publicly available political party registration information, Schreiber noticed something astonishing: Republicans, when they took the same gambling risk, were activating a different part of the brain than Democrats.
> Republicans were using the right amygdala, the center of the brain's threat response system. Democrats, in contrast, were using the insula, involved in internal monitoring of one's feelings. Amazingly, Schreiber and his colleagues write that this test predicted 82.9 percent of the study subjects' political party choices—considerably better, they note, than a simple model that predicts your political party affiliation based on the affiliation of your parents.
> There is a growing body of evidence that conservatives and liberals don't just have differing ideologies; they have different psychologies. How could the rejection of mainstream science be growing among Republicans, along with the denial of expert consensus on the economy, American history, foreign policy, and much more? Why won't Republicans accept things that most experts agree on? Why are they constantly fighting against the facts? Increasingly, the answer appears to be: it's just part of who they are.
> Mooney explores brain scans, polls, and psychology experiments to explain why conservatives today believe more wrong things; appear more likely than Democrats to oppose new ideas; are less likely to change their beliefs in the face of new facts; and sometimes respond to compelling evidence by doubling down on their current beliefs.
> The answer begins with some measurable personality traits that strongly correspond with political preferences. For instance, people more wedded to certainty tend to become conservatives; people craving novelty, liberals. Surprisingly, openness to new experiences and fastidiousness are better predictors of political preference than income or education. If you like to keep your house neat and see the world in a relatively black and white way, you're probably going to vote Republican. If you've recently moved to a big city to see what else life has to offer, you're probably going to vote Democrat. These basic differences in openness and curiosity, Mooney argues, fuel an "expertise gap" between left and right that explains much of the battle today over what is true.
> We found that greater liberalism was associated with increased gray matter volume in the anterior cingulate cortex, whereas greater conservatism was associated with increased volume of the right amygdala. These results were replicated in an independent sample of additional participants. Our findings extend previous observations that political attitudes reflect difference in self-regulatory conflict monitoring and recognition of emotional faces by showing that such attitudes are reflected in human brain structure. Although our data do not determine whether these regions play a causal role in the formation of political attitudes, they converge with previous work to suggest a possible link between brain structure and psychological mechanisms that mediate political attitudes.
A) homosexuality has been common in our species long before overpopulation was an issue
B) same sex sexual activity is common among mammals, reptiles and birds as well as many arthropods. Source Its prevalence seems to be uncorrelated with population density of any species.
I doubt that you're going to find everything you're looking for in a single book.
I suggest that you start with Axler's Linear Algegra Done Right. Despite the pretentious name it does a good job of introducing linear algebra in a general form.
But Axler doesn't do any applications and almost completely ignores determinants (which I like, but it sounds like you want more of that) so I would supplement with Strang's MIT Lectures and any one of his books.
My main hobby is reading textbooks, so I decided to go beyond the scope of the question posed. I took a look at what I have on my shelves in order to recommend particularly good or standard books that I think could characterize large portions of an undergraduate degree and perhaps the beginnings of a graduate degree in the main fields that interest me, plus some personal favorites.
Neuroscience: Theoretical Neuroscience is a good book for the field of that name, though it does require background knowledge in neuroscience (for which, as others mentioned, Kandel's text is excellent, not to mention that it alone can cover the majority of an undergraduate degree in neuroscience if corequisite classes such as biology and chemistry are momentarily ignored) and in differential equations. Neurobiology of Learning and Memory and Cognitive Neuroscience and Neuropsychology were used in my classes on cognition and learning/memory and I enjoyed both; though they tend to choose breadth over depth, all references are research papers and thus one can easily choose to go more in depth in any relevant topics by consulting these books' bibliographies.
General chemistry, organic chemistry/synthesis: I liked Linus Pauling's General Chemistry more than whatever my school gave us for general chemistry. I liked this undergraduate organic chemistry book, though I should say that I have little exposure to other organic chemistry books, and I found Protective Groups in Organic Synthesis to be very informative and useful. Unfortunately, I didn't have time to take instrumental/analytical/inorganic/physical chemistry and so have no idea what to recommend there.
Biochemistry: Lehninger is the standard text, though it's rather expensive. I have limited exposure here.
Mathematics: When I was younger (i.e. before having learned calculus), I found the four-volume The World of Mathematics great for introducing me to a lot of new concepts and branches of mathematics and for inspiring interest; I would strongly recommend this collection to anyone interested in mathematics and especially to people considering choosing to major in math as an undergrad. I found the trio of Spivak's Calculus (which Amazon says is now unfortunately out of print), Stewart's Calculus (standard text), and Kline's Calculus: An Intuitive and Physical Approach to be a good combination of rigor, practical application, and physical intuition, respectively, for calculus. My school used Marsden and Hoffman's Elementary Classical Analysis for introductory analysis (which is the field that develops and proves the calculus taught in high school), but I liked Rudin's Principles of Mathematical Analysis (nicknamed "Baby Rudin") better. I haven't worked my way though Munkres' Topology yet, but it's great so far and is often recommended as a standard beginning toplogy text. I haven't found books on differential equations or on linear algebra that I've really liked. I randomly came across Quine's Set Theory and its Logic, which I thought was an excellent introduction to set theory. Russell and Whitehead's Principia Mathematica is a very famous text, but I haven't gotten hold of a copy yet. Lang's Algebra is an excellent abstract algebra textbook, though it's rather sophisticated and I've gotten through only a small portion of it as I don't plan on getting a PhD in that subject.
Computer Science: For artificial intelligence and related areas, Russell and Norvig's Artificial Intelligence: A Modern Approach's text is a standard and good text, and I also liked Introduction to Information Retrieval (which is available online by chapter and entirely). For processor design, I found Computer Organization and Design to be a good introduction. I don't have any recommendations for specific programming languages as I find self-teaching to be most important there, nor do I know of any data structures books that I found to be memorable (not that I've really looked, given the wealth of information online). Knuth's The Art of Computer Programming is considered to be a gold standard text for algorithms, but I haven't secured a copy yet.
Physics: For basic undergraduate physics (mechanics, e&m, and a smattering of other subjects), I liked Fundamentals of Physics. I liked Rindler's Essential Relativity and Messiah's Quantum Mechanics much better than whatever books my school used. I appreciated the exposition and style of Rindler's text. I understand that some of the later chapters of Messiah's text are now obsolete, but the rest of the book is good enough for you to not need to reference many other books. I have little exposure to books on other areas of physics and am sure that there are many others in this subreddit that can give excellent recommendations.
Other: I liked Early Theories of the Universe to be good light historical reading. I also think that everyone should read Kuhn's The Structure of Scientific Revolutions.
The lectures are $2 on the used market. Well worth the price.
He also covers the dual slit experiment and provides a framework in which the results make sense.
Besides the Napkin Project I mentioned, which is a genuinely good resource? I got a coordinate-free treatment of linear algebra in my school's prelim. abstract algebra course. We used Dummit and Foote, which must be prescribed by law somewhere because I haven't yet seen a single department not use it. However, in reviewing abstract algebra I instead used Hungerford, which I definitely prefer for its brevity. But really, you can pick any graduate intro algebra text and it should teach this stuff.
I would guess that career prospects are a little worse than CS for undergrad degrees, but since my main concern is where a phd in math will take me, you should get a second opinion on that.
Something to keep in mind is that "higher" math (the kind most students start to see around junior level) is in many ways very different from the stuff before. I hated calculus and doing calculations in general, and was pursuing a math minor because I thought it might help with job prospects, but when I got to the more abstract stuff, I loved it. It's easily possible that you'll enjoy both, I'm just pointing out that enjoying one doesn't necessarily imply enjoying the other. It's also worth noting that making the transition is not easy for most of us, and that if you struggle a lot when you first have to focus a lot of time on proving things, it shouldn't be taken as a signal to give up if you enjoy the material.
This wouldn't be necessary, but if you like, here are some books on abstract math topics that are aimed towards beginners you could look into to get a basic idea of what more abstract math is like:
Different mathematicians gravitate towards different subjects, so it's not easy to predict which you would enjoy more. I'm recommending these five because they were personally helpful to me a few years ago and I've read them in full, not because I don't think anyone can suggest better. And of course, you could just jump right into coursework like how most of us start. Best of luck!
(edit: can't count and thought five was four)
I had to deal with the no internet thing for some time.
Find some place with free wi-fi(you are using phone?).
Download ebook/pdf reader, FBreader + PDF plugin is good (Assuming that you are using Android phone).
Install Firefox and this add-on Save Page WE, it also work for phones (tested with Android).
Then you can save pages from some of these web sites or Wikipedia:
Poor man's library:
http://gen.lib.rus.ec/
http://b-ok.org/
https://archive.org/
Some books:
[Harold Jacobs - Elementary Algebra] (https://www.amazon.com/Elementary-Algebra-Harold-R-Jacobs/dp/0716710471) (that's the most friendly and still not bullshit introduction I was able to find)
[Basic Mathematics by Serge Lang] (https://www.amazon.com/Basic-Mathematics-Serge-Lang/dp/0387967877) - Make sure that you understand the first 100-150 pages from the first book if you want to start this one.
Precalculus by David Cohen - Lang's Basic Mathematics is harder (and much more interesting) than this...
Use the three web sites written above to download them. PDF for better performance (and some times quality) on cheap phone, epub/djvu for the smaller size.
I think that free wi-fi will be easy to find. Reading books wouldn't be like watching videos but you will actually learn more. Compass, straightedge and protractor would be really useful.
"Don't Sleep, there are snakes" by Dan Everett - it's a fascinating book about a linguist/missionary who went to work with a tribe of Piraha speakers in the Amazon. Loses his religion, and discovers a language that doesn't really fit into the orthodox view of linguistics and is causing a whole lot of debate.
The Drunkard's Walk - is a great book on how misconceptions of probability rule your life. It's a fun introduction to probability theory and has all sorts of WTF moments in it.
Edit: oh and possibly my favorite book I've read all year is David Attenborough's autobiography A life on air - it's full of all sorts of amazing, hilarious, and insightful anecdotes of Attenborough's 40-odd years of making nature documentaries, and contains lots of interesting info about the state-of-the art in TV making over time (e.g. "we could only run that type of camera for 20 seconds, or it would overheat and catch fire"). Great stuff.
Off the top of my head, I would recommend The Structure of Scientific Revolutions by Thomas Kuhn and The Demon-Haunted World by Carl Sagan.
The former is an excellent summary/treatise of how science works and what brings scientific revolutions about. The latter is an excellent intro to critical thinking. It's quite anti-religious, though, so that may turn you off.
Why Evolution is True by Jerry Coyne is the book I read for the same reason. It is concise, factual, and easy to understand. I recommend it to everyone in your position.
> That's how Dawkins became famous after all, if it wasn't for his open and active anti-theism nobody outside of the academic circles would know about him.
Actually, I understood it was for meme theory, though I might be mistaken. I enjoy Newton's laws of physics, though I don't agree with his views on alchemy. I appreciate genetics, but I don't care for Watson's views on race. That being said, if you really can't stomach Dawkins, then Jerry Coyne's Why Evolution is True might be more up your alley.
> It proposes an explanation yes, but for the application of biology into vital areas such as medicine, species conservation, genetic manipulation etc. you only need to know the how and what happens if - and you discover those things by applying scientific method of observation >> theory >> experiment >> successful repetition of the same results over and over.
This approach will only show you facets of the underlying theory, without understanding the mechanisms that tie it all together. Moreover, it's far easier to learn the underlying theory than it is to learn all the implications of the theory. You could watch a hundred thunderstorms and photograph all sorts of lightning behaviour in super-slow motion, but without an understanding of electricity, all those pieces of evidence don't fit together.
If you're not familiar with the practical applications of evolution, I suggest you read this. I suspect this list will also continue to grow as we find more applications.
> Tuntuu kuitenkin, jopa tästä kirjoituksesta, että on painetta painottaa esimerkiksi sellaisia väitteitä, joissa homoseksuaalisuus olisi adaptaatio, eikä esimerkiksi patogeenin aiheuttama.
Todennäköisemmin syy etsiä adaptaavista selitystä homoseksuaalisuuteen tulee siitä, että homoseksuaalisuutta on havaittu käytännössä kaikilla tutkituolla selkärankaisilla.
Lisäksi, jos havaitaan että homoseksuaallisuus on perinnöllistä tietyissä suvuissa, ja tämä on havaittavissa niin eläimissä kuin ihmisissä, niin evoluution teorian perusteella voidaan tehdä hypoteesi, että tällä ilmiöllä olisi jokin suvunjatkamista edistävä ominaisuus, vaikka se silloin tällöin johtaisi geneettiseen umpikujaan yksilöiden tasolla. Samalla tavalla kuin sirppisoluanemien kohdalla. Sirppisoluanemie johtuu yhdestä pistemutaatiosta, ja jos henkilöllä on kaksi kappaletta näitä geenejä, hän todennäköisesti kuolee jo lapsena (kyseessä on resessiivinen geeni). Jos yksilöllä on vain yksi vioittunut geeni, hänellä on tavallista parempi vastustuskyky malariaa vastaan. Tästä johtuen tämä sirppisolianemiaa aiheuttava geeni on päässyt yleistymään etenkin Afrikassa, mutta vain alueilla joissa esiintyy malariaa.
Onko kyseessä siis adaptaatio vai patogeeni? Joissain tapauksissa tämä voi johtaa yksilön kuolemaan (geneettinen umpikuja), mutta jos geenin antama hyöty populaatiolle ovat suuremmat kuin haitat, se voi silti levitä populaatiossa ja olla näin ollen adaptiivinen alleeli. Käsitykseni mukaan homoseksuaalisuus on samantapainen tapaus. Homoseksuaalisuus on haitallista yksilön geneettiselle jatkumolle, mutta sen aiheuttama(t) geeni(t) voivat olla populaation kannalta edullisia.
Potholer54 teki asiaan liittyen erinomaisen videon, joka kannattaa ehdottomasti vilkaista, jos et ole sitä jo nähnyt:
How to confuse a creationist -- Homosexuality, Evolution and the Bible
If any of you are interested in learning more about the table, I highly enjoyed this book
Actually it's way worse than that. Emotional reasoning affects people of all I.Q.s, they can be completely able to make rational decisions as long as they are not emotionally invested in it. As soon as it is something emotional, their reasoning goes to shit. The more intelligent they are, the better they are at defending the emotional position to themselves. And no, this isn't a false equivalence argument , there is a ton of evidence that the right wing are way worse, plus fox etc use it deliberately and always lead with something fear or anger inducing so they can get their bullshit in while logic is effectively switched off. Good sources, https://www.amazon.com/Republican-Brain-Science-Science-Reality/dp/1118094514
And
https://www.amazon.com.au/d/ebook/Know-What-Isnt-Fallibility-Human-Reason-Everyday/B001D1SS2M/ref=sr_1_6?s=digital-text&ie=UTF8&qid=1496189722&sr=1-6&keywords=Reasoning+everyday
I recommend reading the book; The Fabric of the Cosmos by Brian Greene, numerous people have reported that they don't feel depressed or (as depressed/anxious) after reading it.
Here's a link to buy it on amazon
https://www.amazon.com/Fabric-Cosmos-Space-Texture-Reality/dp/0375727205/ref=sr_1_1?ie=UTF8&qid=1502668682&sr=8-1&keywords=fabric+of+the+cosmos
Ordinary Differential Equations from the Dover Books on Mathematics series. I Just took my final for Diff Eq a few days ago and the book was miles better than the one my school suggested and is the best written math textbook I have encountered during my math minor. My Diff Eq course only covered about the first 40% of the book so there's still a TON of info that you can learn or reference later. It is currently $14 USD on amazon and my copy is almost 3" thick so it really is a great deal. A lot of the reviewers are engineering and science students that said the book helped them learn the subject and pass their classes no problem. Highly Highly recommend. ISBN-10: 9780486649405
​
https://www.amazon.com/gp/product/0486649407/ref=ppx_yo_dt_b_asin_title_o08_s00?ie=UTF8&psc=1
Along the same line, Jerry Coyne's "Why Evolution is True" is fantastic.
"Anyone who doesn't believe in evolution is stupid, insane, or hasn't read Jerry Coyne" - Richard Dawkins
bperki8 is right. Most Young Earth Creationists (YEC) I know have a very poor understanding of evolution, and I don't blame them for not accepting it. What they describe as evolution is utter trash, promoted throught the intellectual dishonesty of the Discovery Institute, Ben Stein, and the likes. Please read Why Evolution is True. I ruthlessly implore anyone with doubts to read this book. YECs are in the same boat as those hundreds of years ago who believed the Earth the center of the solar system, and anything else is against God.
You can try something like Artin or Dummit & Foote.
Harvard’s Benedict Gross gave a course using Artin’s textbook with lectures available on youtube.
No matter what his interests may be, this wonderful survey will cover it, Mathematics: Its Contents, Methods, and Meaning. It was written by a team of prominent Russian mathemations, and became a classic. It's now a single Dover edition, but if possible, find it used in the original MIT 3-volume hardcover edition -- it demands that kind of respect!
Of course efforts like this won't fly because there will be people who sincerely want to can them because it's "computerized racial profiling," completely missing the point that, if race does correlate with criminal behavior, you will see that conclusion from an unbiased system. What an unbiased system will also do is not overweight the extent to which race is a factor in the analysis.
Of course, the legitimate concern some have is about the construction of prior probabilities for these kinds of systems, and there seems to be a great deal of skepticism about the possibility of unbiased priors. But over the last decade or two, the means of constructing unbiased priors have become rather well understood, and form the central subject matter of Part II of E.T. Jaynes' Probability Theory: The Logic of Science, which I highly recommend.
There is a recent book about just this phenomena.
The Republican Brain: The Science of Why They Deny Science- and Reality
The answer to this is much, much deeper than any of the comments so far. The answer to "How does" is not "4%". The answer is in Quantum Electrodynamics.
I have to run to work, and Richard Feynman is much better at explaining things than me, so I'll point you to his book QED which is dedicated to answering this question as a way to explain QED.
Sorry to have to run because this is fascinating, but to give an accurate answer that really hits on the principles behind it, takes about 20 pages from one of the smartest men who ever lived. I couldn't recommend the book more - it is accessible to anyone of reasonable intelligence willing to read it carefully, and unlocks one of the great mysteries of nature in an entertaining and exciting way.
My favorite science-related leisure reading is Derek Lowe's blog In The Pipeline. He covers new developments in chemistry/biology, the drug discovery industry, and occasionally some other stuff. He writes it in a way would be interesting to anyone that like chemistry and biology regardless of their level of education. I always look forward to reading it over lunch.
​
If you are looking for a book, The Disappearing Spoon is a great set of true short stories about chemistry that is a really fun read.
Sagan and Tyson aren't even in the same league. Sagan's Cosmos is much better, scientifically, educationally, and from an entertainment perspective.
However, if you're interested in cosmology specifically, neither series will get you very far. They cover a range of topics, some of which are prerequisites for cosmology (like relativity), others which aren't really cosmology (e.g. astronomy, astrophysics, other kinds of physics.)
Some books that are good for an accessible introduction to issues in cosmology are:
For the very basics (and more), I can highly recommend you Professor Leonard on YouTube.
>What books would you recommend?
How about doing your own research?
Google.com -> book site:reddit.com/r/learnmath
Anyways, take a look at Basic Mathematics by Serge Lang. This is what I'm learning with right now, it's really great.
Mathematics, a learning map
Edit:
Ehm, or take a look at your own thread from a year ago.
https://www.reddit.com/r/learnmath/comments/46xdpp/learning_math_from_scratch_all_by_myself/
There are essentially "two types" of math: that for mathematicians and everyone else. When you see the sequence Calculus(1, 2, 3) -> Linear Algebra -> DiffEq (in that order) thrown around, you can be sure they are talking about non-rigorous, non-proof based kind that's good for nothing, imo of course. Calculus in this sequence is Analysis with all its important bits chopped off, so that everyone not into math can get that outta way quick and concentrate on where their passion lies. The same goes for Linear Algebra. LA in the sequence above is absolutely butchered so that non-math majors can pass and move on. Besides, you don't take LA or Calculus or other math subjects just once as a math major and move on: you take a rigorous/proof-based intro as an undergrad, then more advanced kind as a grad student etc.
To illustrate my point:
Linear Algebra:
Linear Algebra Through Geometry by Banchoff and Wermer
3. Here's more rigorous/abstract Linear Algebra for undergrads:
Linear Algebra Done Right by Axler
4. Here's more advanced grad level Linear Algebra:
Advanced Linear Algebra by Steven Roman
-----------------------------------------------------------
Calculus:
Calulus by Spivak
3. Full-blown undergrad level Analysis(proof-based):
Analysis by Rudin
4. More advanced Calculus for advance undergrads and grad students:
Advanced Calculus by Sternberg and Loomis
The same holds true for just about any subject in math. Btw, I am not saying you should study these books. The point and truth is you can start learning math right now, right this moment instead of reading lame and useless books designed to extract money out of students. Besides, there are so many more math subjects that are so much more interesting than the tired old Calculus: combinatorics, number theory, probability etc. Each of those have intros you can get started with right this moment.
Here's how you start studying real math NOW:
Learning to Reason: An Introduction to Logic, Sets, and Relations by Rodgers. Essentially, this book is about the language that you need to be able to understand mathematicians, read and write proofs. It's not terribly comprehensive, but the amount of info it packs beats the usual first two years of math undergrad 1000x over. Books like this should be taught in high school. For alternatives, look into
Discrete Math by Susanna Epp
How To prove It by Velleman
Intro To Category Theory by Lawvere and Schnauel
There are TONS great, quality books out there, you just need to get yourself a liitle familiar with what real math looks like, so that you can explore further on your own instead of reading garbage and never getting even one step closer to mathematics.
If you want to consolidate your knowledge you get from books like those of Rodgers and Velleman and take it many, many steps further:
Basic Language of Math by Schaffer. It's a much more advanced book than those listed above, but contains all the basic tools of math you'll need.
I'd like to say soooooooooo much more, but I am sue you're bored by now, so I'll stop here.
Good Luck, buddyroo.
Why Evolution is True by Jerry Coyne: Buy it on Amazon
A quality online resource for you would be the free online archive of MIT's class "Human Origins and Evolution"; check it out here: MIT OCW 3.987 EDIT: This would actually only be appropriate as a guide for further study on your own. The course materials provided are primarily syllabi and the like, but does provide an extensive list of books and other sources of information that may be up your alley.
Much more technical options are also available from their biology department: MIT OCW Bio
Nonlinear Dynamics and Chaos by Strogatz is supposed to be good.
This is an awesome and very readable textbook on the subject:
Non-Linear Dynamics and Chaos, by Steven Strogatz.
At the moment, psychology is largely ad-hoc, and not a modicum of progress would've been made without the extensive utilization of statistical methods. To consider the human condition does not require us to simply extrapolate from our severely limited experiences, if not from the biases of limited datasets, datasets for which we can't even be certain of their various e.g. parameters etc..
For example, depending on the culture, the set of phenotypical traits with which increases the sexual attraction of an organism may be different - to state this is meaningless and ad-hoc, and we can only attempt to consider the validity of what was stated with statistical methods. Still, there comes along social scientists who would proclaim arbitrary sets of phenotypical features as being universal for all humans in all conditions simply because they were convinced by limited and biased datasets (e.g. making extreme generalizations based on the United States' demographic while ignoring the entire world etc.).
In fact, the author(s) of "Probability Theory: The Logic of Science" will let you know what they think of the shaky sciences of the 20th and 21st century, social science and econometrics included, the shaky sciences for which their only justifications are statistical methods.
_
With increasing mathematical depth and the increasing quality of applied mathematicians into such fields of science, we will begin to gradually see a significant improvement in the validity of said respective fields. Otherwise, currently, psychology, for example, holds no depth, but the field itself is very entertaining to me; doesn't stop me from enjoying Michael's "Mind Field" series.
For mathematicians, physics itself lacks rigour, let alone psychology.
_
Note, the founder of "psychoanalysis", Sigmund Freud, is essentially a pseudo-scientist. Like many social scientists, he made the major error of extreme extrapolation based on his very limited and personal life experiences, and that of extremely limited, biased datasets. Sigmund Freud "proclaimed" a lot of truths about the human condition, for example, Sigmund Fraud is the genius responsible for the notion of "Penis Envy".
In the same century, Einstein would change the face of physics forever after having published the four papers in his miracle year before producing the masterpiece of General Relativity. And, in that same century, incredible progress such that of Gödel's Incompleteness Theorem, Quantum Electrodynamics, the discovery of various biological reaction pathways (e.g. citric acid cycle etc.), and so on and so on would be produced while Sigmund Fraud can be proud of his Penis Envy hypothesis.
Why Evolution is True - By Jerry Coyne
The author specifically and purposefully avoids all talk of religion and morality, and very simply and concisely lays out the evidence and logic behind evolutionary theory.
Anyone who reads this book and continues denying evolution is not approaching the subject honestly, or has other reasons (religious) for rejecting evolution.
It's only a couple hundred pages, and certainly is no longer than 'Life How Did It Get Here-By Evolution or By Creation', which I am nearly 100% certain is what he will be giving you. (For a fun game, take a shot every time you read a blatant lie or intentional misstatement of fact, or quote mine you find in that book. Just be sure you don't need to drive for the next couple of days.)
He may give you the new Creationism tract they introduced this summer, which is nothing more than excerpts from the larger book.
I agree that some sort of reason is required to make a leap of faith, but I still call it a leap because such a reason would be more social/psychological (What is my motivation to do this?) or aesthetic (does this provide a more elegant perspective of the universe) but since neither of those are based on logic or induction, I can't really call them rational reasons. They're simply explanatory reasons.
As I mentioned elsewhere in this thread, my personal epistimology here is highly influenced by Concluding Unscientific Postscript and Philosophical Fragments (Kierkegaard) as well as the Structure of Scientific Revolutions by Thomas Kuhn.
I'd recommend A Short History of Nearly Everything by Bill Bryson. This book is great because it covers so many of the most scientifically important events throughout history, rather than just being a layman's introduction to a specific branch of science.
If you're at all interested in statistics and how misleading they can be, check out The Drunkard's Walk.
>Why do you think homosexuality exists?
Simple. Humans are animals. Animals have an urge to hump things.
Although, it could be have a social role in nature.
>What caused the writers of the Bible to hate on homosexuality?
A lot of misunderstanding about the universe, such as hyenas used to be thought to be able to change sex.
>Is there evidence that there were homosexual cave men and women?
It is very difficult to find evidence of social behavior in cultures without writing.
---
I have no problem with homosexuality or transgender issue, mostly because I am not religious. However, because of Christian Dominionism (think Sharia Law for Christians), this has become a bigger issue that it needs to be.
I took a grad course on the history of chemistry and we used The Development of Modern Chemistry by Ihde.
Another comprehensive (but style-wise a little hard to read) is
Crucibles:The Story of Chemistry from Ancient Alchemy to Nuclear Fission.
I have yet to read The Disappearing Spoon, a pop-sci read on the history and stories behind discoveries of elements.
I recommend some books to you:
http://www.amazon.com/Consciousness-Explained-Daniel-C-Dennett/dp/0316180661
http://www.amazon.com/Am-Strange-Loop-Douglas-Hofstadter/dp/0465030785
http://www.amazon.com/The-Minds-Fantasies-Reflections-Self/dp/0465030912
Your sense of self, your "I", your mind, is produced by your brain, which is a physical structure that is not destroyed and remade during sleep. This is why you remember what happened yesterday. "You" are a pile of grey goo in a skull.
I really good textbook is probably what you want. Good math textbooks are engaging and have lots of interesting problems. They have an advantage (in pure math) that they don't have to worry about teaching you specific tools (which IMO can make things boring). Lots of people love this one: https://www.amazon.com/Nonlinear-Dynamics-Chaos-Applications-Nonlinearity/dp/0738204536
Also here is a really good lecture series (on a different topic): https://www.youtube.com/watch?v=7G4SqIboeig&list=PLMsYJgjgZE8hh6d6ia2dP1NI0BKNRXbiw
Also if you have a bit of a programming bent or want to learn a little bit of programming, you might like Project Euler:https://projecteuler.net/
Hi. The book Basic Mathematics by Serge Lang covers high school math in a way that is similar to most texts on higher mathematics, with theorems and proofs. As such, I think it would make a great stepping stone to higher maths, and some reviewers on Amazon agree. It gives you a solid foundation, and a little bit of an idea what's in store for you if you choose to pursue math. I think it would be a great place to start.
Send me a PM if you need help obtaining (a digital version of) the book.
Mathematics, its Content, Methods, and Meaning - an amazing survey of analytic geometry, algebra, ordinary and partial differential equations, the calculus of variations, functions of a complex variable, prime numbers, theories of probability and functions, linear and non-Euclidean geometry, topology, functional analysis, and more.
Tenenbaum and Pollard's ODE book made the subject come quite easily when all my $150 textbook did was confuse me.
> when you're looking for it to happen, it does.
Okay, straight off, you've impressed me. Most people find themselves unable to figure this out.
> I recently started watching the TV show Heroes.
I like it too - but big warning - almost all hollywood 'science' is utterly bogus. It's fine that it got you thinking though.
> According to Evolutionary theory, as far as I know, mutations are the cause of the "advancement" of a species, or transition, however you say it (not an expert on the subject at all).
Well, mutations are a source of variation. But it's not mutation that leads to change at the population-level (which is what evolution is). Individuals changing isn't evolution.
Basically, you need heritable variation, leading to differences in survival or reproduction (and differences in survival matter because you can't reproduce if you're dead). Natural selection is the primary mechanism by which beneficial versions of genes are retained and the frequency of 'bad' ones reduced.
> The school taught me to retaliate the argument with "give me one example of a positive mutation."
Actually, that's easy: here's two
> If my understanding is correct, mutations aren't beneficial.
Not quite. Frequently mutations are bad - which is why we have mechanisms to prevent them. Often, mutations are relatively neutral - you carry several mutations not present in either of your parents yet here you are. Sometimes mutations are actually beneficial.
One example of a usually-fairly-neutral kind of mutation that is important in evolution is gene-duplication. This is important because you end up with an extra copy of a gene. The extra copy is free to change without any loss of function in the original copy.
> They're meant to wipe a species out,
No, mutations aren't 'meant' to do anything. They are simply there.
The main resistance a population has to a bad mutation is simply this: its carriers leave fewer offspring behind than non-carriers.
> Like cancer: in [x] amount of years, humans should theoretically be immune to cancer if we let it run its course
Cancer has been around hundreds of millions of years. Its present throughout the animal kingdom. All animals should be 'immune to cancer', by this reasoning. There are a variety of reasons why this is not so. You should probably research cancer a bit more deeply, after you've done some learning on evolution.
> If someone could give me some more misconceptions the Christians have about Evolutionary theory,
Actually, in many parts of the world, a majority of Christians accept evolution.
Your first step should be to read about what evolution is. Perhaps start here:
http://en.wikipedia.org/wiki/Introduction_to_evolution
or here:
http://evolution.berkeley.edu/evosite/evo101/IIntro.shtml
.
Some of the misconceptions about evolution:
http://www.talkorigins.org/indexcc/list.html
.
Evidence for evolution: Why Evolution Is True, Jerry Coyne.
Evidence for common descent: http://www.talkorigins.org/faqs/comdesc/
Examples of speciation: http://www.google.com/search?q=examples+of+speciation
(e.g. see the second and third link in particular, but many of the others are also good)
I was hard core TBM, I would believe just about anything, which is why Dirk Gently's Holistic Detective Agency by Douglas Adams is so much funnier to me now that I am an atheist, than when I read it back when I was TBM. http://www.youtube.com/watch?v=qJq8QjLI-so
I also knew when I was TBM that if God exists then anything is possible, ergo the church was true because it made the strongest claim to the truth then any other religion (when I say "truth claim" I am not referring to a logical and rational claim of truth by the church, I am referring to the standard "I know God lives and loves me" sort of truth claim). But I also reasoned that if I were to find sufficient cause to be an atheist, any difficulty of rejecting the LDS church and all other churches is rendered moot.
My biggest hurdle to stop believing in God was the fact that I was raised in an extremely religious environment growing up, even before my family joined the LDS church when I was 13 years old. My mom enrolled my brothers and in private christian schools growing up and we attended church services religiously growing up. My belief in God was such that it never even occurred to me to question his existence in spite of the fact I was keenly interested in science, I was also aware of the concept of atheism, but I could not comprehend why anyone would want to do something stupid like rejecting God.
It took me a long time to go from from fully believing in God, to completely rejecting the notion of God, I accomplished this through reason and science, I taught myself, with help from others how to think and reason. Atheism is not an easy choice for some, for others it is not so hard, it was a big fucking deal for me for me to reject everything I had ever understood about the universe and it scared the hell out of me when I did. There is no point in me telling you exactly why I am an atheist, it's complicated, and it is a very personal road of discovery.
However, for starters I would suggest reading Jerry Coyne's Why Evolution Is True http://www.amazon.com/Why-Evolution-True-Jerry-Coyne/dp/0670020532
and Richard Dawkins The Magic of Reality, How We Know What's Really True
http://www.amazon.com/s/ref=nb_sb_noss?url=search-alias%3Dstripbooks&field-keywords=majic+of+reality&x=0&y=0
Here are some of my most favorite Christopher Hitchens quotes.
>“That which can be asserted without evidence, can be dismissed without evidence.”
>“Our belief is not a belief. Our principles are not a faith. We do not rely solely upon science and reason, because these are necessary rather than sufficient factors, but we distrust anything that contradicts science or outrages reason. We may differ on many things, but what we respect is free inquiry, open-mindedness, and the pursuit of ideas for their own sake.”
>“The only position that leaves me with no cognitive dissonance is atheism. It is not a creed. Death is certain, replacing both the siren-song of Paradise and the dread of Hell. Life on this earth, with all its mystery and beauty and pain, is then to be lived far more intensely: we stumble and get up, we are sad, confident, insecure, feel loneliness and joy and love. There is nothing more; but I want nothing more.”
And my favorite Richard Dawkins quotes.
>“The total amount of suffering per year in the natural world is beyond all decent contemplation. During the minute that it takes me to compose this sentence, thousands of animals are being eaten alive, many others are running for their lives, whimpering with fear, others are slowly being devoured from within by rasping parasites, thousands of all kinds are dying of starvation, thirst, and disease. It must be so. If there ever is a time of plenty, this very fact will automatically lead to an increase in the population until the natural state of starvation and misery is restored. In a universe of electrons and selfish genes, blind physical forces and genetic replication, some people are going to get hurt, other people are going to get lucky, and you won't find any rhyme or reason in it, nor any justice. The universe that we observe has precisely the properties we should expect if there is, at bottom, no design, no purpose, no evil, no good, nothing but pitiless indifference.”
>“We admit that we are like apes, but we seldom realize that we are apes.”
>“Evolution could so easily be disproved if just a single fossil turned up in the wrong date order. Evolution has passed this test with flying colors.”
Evolution threatens Christianity
http://www.washingtonpost.com/blogs/on-faith/post/evolution-threatens-christianity/2011/08/24/gIQAuLVpbJ_blog.html
Read the QED lectures by Feynman, you won't get a better, more accessible explanation than that
Eh, first you have to read up on quantum mechanics and get a decent understanding of quantum mechanical spin and quantum numbers in general. Something like Shankar - Principles of Quantum Mechanics, though there are tons of textbooks on it. You won't really get into particle physics, but should read at least to the point of understanding addition of angular momentum and spin (typically in context of hydrogen atom).
Then a text on particle physics like Griffiths' Intro To Elementary Particle Physics. (You could also start Griffiths' Intro to QM).
You could also consult free resources like the particle data group, but their reviews will be largely gibberish if you don't understand the basics of QM / particle physics / group theory. (Articles like Quark Model, or Naming Scheme for Hadrons).
If you are looking at hobby-level interest without getting into any math/textbooks, the best I can suggest is Feynman's QED but it won't talk about isospin or hadrons or particle naming conventions but is a great layman introduction to quantum electrodynamics.
Random selection of some of my favorites to help you expand your horizons:
The Demon-Haunted World by Carl Sagan is a great introduction to scientific skepticism.
Letter to a Christian Nation by Sam Harris is a succinct refutation of Christianity as it's generally practiced in the US employing crystal-clear logic.
Augustus: The Life of Rome's First Emperor by Anthony Everitt is the best biography of one of the most interesting men in history, in my personal opinion.
Travels with Herodotus by Ryszard Kapuscinski is a jaw-dropping book on history, journalism, travel, contemporary events, philosophy.
A Short History of Nearly Everything by Bill Bryson is a great tome about... everything. Physics, history, biology, art... Plus he's funny as hell. (Check out his In a Sunburned Country for a side-splitting account of his trip to Australia).
The Annotated Mona Lisa by Carol Strickland is a thorough primer on art history. Get it before going to any major museum (Met, Louvre, Tate Modern, Prado, etc).
Not the Impossible Faith by Richard Carrier is a detailed refutation of the whole 'Christianity could not have survived the early years if it weren't for god's providence' argument.
Six Easy Pieces by Richard Feynman are six of the easier chapters from his '63 Lectures on Physics delivered at CalTech. If you like it and really want to be mind-fucked with science, his QED is a great book on quantum electrodynamics direct from the master.
Lucy's Legacy by Donald Johanson will give you a really great understanding of our family history (homo, australopithecus, ardipithecus, etc). Equally good are Before the Dawn: Recovering the Lost History of Our Ancestors by Nicholas Wade and Mapping Human History by Steve Olson, though I personally enjoyed Before the Dawn slightly more.
Memory and the Mediterranean by Fernand Braudel gives you context for all the Bible stories by detailing contemporaneous events from the Levant, Italy, Greece, Egypt, etc.
After the Prophet by Lesley Hazleton is an awesome read if you don't know much about Islam and its early history.
Happy reading!
edit: Also, check out the Reasonable Doubts podcast.
Strogatz's Nonlinear Dynamics and Chaos (https://www.amazon.ca/Nonlinear-Dynamics-Chaos-Applications-Engineering/dp/0738204536) is a good book to introduce applications of differential equations. It's an easy read that focuses on concepts and motivation rather than rigour.
Differential equations describe how things change based on what state they are in. An easy example is that the larger a population is the faster is grows. Or the more predators and the less food it has, the slower it grows. One can build a system that takes all variables thought to be relevant and construct a system that describes how all these things affect each other's growth rate, and then see how this system changes in time. Other examples include chemical reactions, as the rate of change of the ingredients depends on how much of each ingredient is in the mixture. Economics: the change of a market depends on the state of all other relevant markets. Physics: the change in velocity of a satellite depends on its position relevant to a large body. The change in weather depends on the pressure, temperature, and air velocity all over the earth (this is getting into PDEs, but the basic motivation remains).
Of course, the connection of such models to the real world depends on how well the model is constructed and how well it can be analyzed. It's a matter of balancing robustness and usability with accurateness, and there are reasons to explore either side of that spectrum based on what your goals are. Many times we may not even bother to solve them, but rather focus on qualitative properties of the model, such as whether or not an equilibrium is stable, the existence of periodic solutions or chaos, whether a variable goes to zero or persists, etc. Differential equations is probably the largest field in applied math, and in my opinion probably the most important use of math in science other than maybe statistics and probability.
Paul Stamets, the mycologist, offers this one.
just some of my standard answers.
The Disappearing Spoon- yes, it's chemistry but I found it very interesting.
Abraham Lincoln's DNA- if you have a good background in genetics you might already know many of these stories. Read the table of contents first.
New Guinea Tapeworms and Jewish Grandmothers- disease based biology. There is a follow up book if it turns out you like it.
Stiff- more than you wanted to know about dead bodies.
And by the same author but space based... Packing for Mars.
I hope these help... Cheers.
It can be explained, though not simply, nor accessibly. Luckily, I'm not just an atheist, I'm also a theoretical physics student. Keep in mind that this of course can not be demonstrated empirically (science is the study of our Universe, so we obviously can't study things outside it in time or space).
Lets go back to before the Universe exists. Let's call this state the Void. It's important to note that no true void exists in our Universe, even the stuff that looks empty is full of vacuum fluctuations and all kinds of other things that aren't relevant, but you can investigate in your own time if you want. In this state, the Void has zero energy, pretty much by definition. Now, the idea that a Void could be transforms into a Universe is not really controversial; stuff transforms by itself all the time. The "problem" with a Universe arising from a Void is that the Universe has more energy than the Void, and it there's not explanation for where all this energy came from. Upon further investigation, we'll actually see that the Universe has zero net energy, and this isn't actually a problem.
Now, let's think about a vase sitting on a table. One knock and it shatters, hardly any effort required. But it would take a significant amount of effort to put that vase back together. This is critically important. Stuff has a natural tendency to be spread out all over the place. You need to contribute energy to it in order to bring it together. We're going to call this positive energy.
Gravity is something different though. Gravity pulls everything together. Unlike the vase, you'd need to expend energy in order to overcome the natural tendency of gravity. Because it's the opposite, we're going to call gravity negative energy. In day to day life, the tendency of stuff to spread out overwhelms the tendency of gravity to clump together, simply because gravity is comparatively very weak. There's quite a few more factors at play here, but stuff and gravity are the important ones.
Amazingly, it turns out that it's possible for the Universe to have exactly as much negative energy as it does positive energy, which means that it would have zero total energy, meaning that it's perfectly possible for it to pop out of nowhere, by dumb luck, because no energy input is required. Furthermore, we know how to check if our Universe has this exact energy composition. And back in 1989, that's exactly what cosmologists did. And it turns out it does. We can empirically show, to an excellent margin of error, that our Universe has zero net energy. Think about that for a second. Lawrence Krauss has a great youtube video explaining the evidence for this pretty incredible claim.
The really incredible thing is, given that our Universe has zero net energy, it's not only possible that it could just pop into existence on day, it's inevitable. It's exactly what we'd expect. Hell, I'd be out looking for God's fingerprints if there wasn't a Universe, not the opposite.
If you want to read more about it, by people who've spent far more time investigating this than I have, I suggest The Fabric of the Cosmos by Brian Greene, and A Universe From Nothing: Why There Is Something Rather Than Nothing by Lawrence Krauss. Both go into detail about the subject, and don't require any prior physics knowledge.
tl;dr The Universe didn't need a "first cause". PHYSICS!
These:
How to Read the Solar System: A Guide to the Stars and Planets by Christ North and Paul Abel.
A Short History of Nearly Everything by Bill Bryson.
A Universe from Nothing: Why There is Something Rather than Nothing by Lawrence Krauss.
Cosmos by Carl Sagan.
Pale Blue Dot: A Vision of the Human Future in Space by Carl Sagan.
Foundations of Astrophysics by Barbara Ryden and Bradley Peterson.
Final Countdown: NASA and the End of the Space Shuttle Program by Pat Duggins.
An Astronaut's Guide to Life on Earth: What Going to Space Taught Me About Ingenuity, Determination, and Being Prepared for Anything by Chris Hadfield.
You Are Here: Around the World in 92 Minutes: Photographs from the International Space Station by Chris Hadfield.
Space Shuttle: The History of Developing the Space Transportation System by Dennis Jenkins.
Wings in Orbit: Scientific and Engineering Legacies of the Space Shuttle, 1971-2010 by Chapline, Hale, Lane, and Lula.
No Downlink: A Dramatic Narrative About the Challenger Accident and Our Time by Claus Jensen.
Voices from the Moon: Apollo Astronauts Describe Their Lunar Experiences by Andrew Chaikin.
A Man on the Moon: The Voyages of the Apollo Astronauts by Andrew Chaikin.
Breaking the Chains of Gravity: The Story of Spaceflight before NASA by Amy Teitel.
Moon Lander: How We Developed the Apollo Lunar Module by Thomas Kelly.
The Scientific Exploration of Venus by Fredric Taylor.
The Right Stuff by Tom Wolfe.
Into the Black: The Extraordinary Untold Story of the First Flight of the Space Shuttle Columbia and the Astronauts Who Flew Her by Rowland White and Richard Truly.
An Introduction to Modern Astrophysics by Bradley Carroll and Dale Ostlie.
Rockets, Missiles, and Men in Space by Willy Ley.
Ignition!: An Informal History of Liquid Rocket Propellants by John Clark.
A Brief History of Time by Stephen Hawking.
Russia in Space by Anatoly Zak.
Rain Of Iron And Ice: The Very Real Threat Of Comet And Asteroid Bombardment by John Lewis.
Mining the Sky: Untold Riches From The Asteroids, Comets, And Planets by John Lewis.
Asteroid Mining: Wealth for the New Space Economy by John Lewis.
Coming of Age in the Milky Way by Timothy Ferris.
The Whole Shebang: A State of the Universe Report by Timothy Ferris.
Death by Black Hole: And Other Cosmic Quandries by Neil deGrasse Tyson.
Origins: Fourteen Billion Years of Cosmic Evolution by Neil deGrasse Tyson.
Rocket Men: The Epic Story of the First Men on the Moon by Craig Nelson.
The Martian by Andy Weir.
Packing for Mars:The Curious Science of Life in the Void by Mary Roach.
The Overview Effect: Space Exploration and Human Evolution by Frank White.
Gravitation by Misner, Thorne, and Wheeler.
The Science of Interstellar by Kip Thorne.
Entering Space: An Astronaut’s Oddyssey by Joseph Allen.
International Reference Guide to Space Launch Systems by Hopkins, Hopkins, and Isakowitz.
The Fabric of the Cosmos: Space, Time, and the Texture of Reality by Brian Greene.
How the Universe Got Its Spots: Diary of a Finite Time in a Finite Space by Janna Levin.
This New Ocean: The Story of the First Space Age by William Burrows.
The Last Man on the Moon by Eugene Cernan.
Failure is Not an Option: Mission Control from Mercury to Apollo 13 and Beyond by Gene Kranz.
Apollo 13 by Jim Lovell and Jeffrey Kluger.
The end
You're not really doing higher math right now as much as you're learning tricks to solve problems. Once you start proving stuff that'll be a big jump. Usually people start doing that around Real Analysis like your father said. Higher math classes almost entirely consist of proofs. It's a lot of fun once you get the hang of it, but if you've never done it much before it can be jarring to learn how. The goal is to develop mathematical maturity.
Start learning some geometry proofs or pick up a book called "Calculus" by Spivak if you want to start proving stuff now. The Spivak book will give you a massive head start if you read it before college. Differential equations will feel like a joke after this book. It's called calculus but it's really more like real analysis for beginners with a lot of the harder stuff cut out. If you can get through the first 8 chapters or so, which are the hardest ones, you'll understand a lot of mathematics much more deeply than you do now. I'd also look into a book called Linear Algebra done right. This one might be harder to jump into at first but it's overall easier than the other book.
Basic Mathematics by Serge Lang.
https://www.amazon.com/Basic-Mathematics-Serge-Lang/dp/0387967877
Do not enroll in a precalculus class until you have a solid grasp on the foundations of precalculus. Precalculus is generally considered to be the fundamentals required for calculus and beyond (obviously), and a strong understanding of precalculus will serve you well, but in order to do well in precalculus you still need a solid understanding of what comes before, and there is quite a bit.
I do not mean to sound discouraging, but I was tutoring a guy in an adult learning program from about December 2017-July 2018...I helped him with his homework and answered any questions that he had, but when he asked me to really get into the meat of algebra (he needed it for chemistry to become a nurse) I found a precalculus book at the library and asked him to go over the prerequisite chapter and it went completely over his head. Perhaps this is my fault as a tutor, but I do not believe so.
What I am saying is that you need a good foundation in the absolute basics before doing precalculus and I do not believe that you should enroll in a precalculus course ASAP because you may end up being let down and then give up completely. I would recommend pairing Basic Mathematics by Serge Lang with The Humongous Book of Algebra Problems (though any book with emphasis on practice will suffice) and using websites like khanacademy for additional practice problems and instructions. Once you have a good handle on this, start looking at what math courses are offered at your nearest CC and then use your best judgment to decide which course(s) to take.
I do not know how old you are, but if you are anything like me, you probably feel like you are running out of time and need to rush. Take your time and practice as much as possible. Do practice problems until it hurts to hold the pencil.
Indeed; you may feel that you are at a disadvantage compared to your peers, and that the amount of work you need to pull off is insurmountable.
However, you have an edge. You realize you need help, and you want to catch up. Motivation and incentive is a powerful thing.
Indeed, being passionate about something makes you much more likely to remember it. Interestingly, the passion does not need to be a loving one.
A common pitfall when learning math is thinking it is like learning history, philosophy, or languages, where it doesn't matter if you miss out a bit; you will still understand everything later, and the missing bits will fall into place eventually. Math is nothing like that. Math is like building a house. A first step for you should therefore be to identify how much of the foundation of math you have, to know where to start from.
Khan Academy is a good resource for this, as it has a good overview of math, and how the different topics in math relate (what requires understanding of what). Khan Academy also has good exercises to solve, and ways to get help. There are also many great books on mathematics, and going through a book cover-to-cover is a satisfying experience. I have heard people speak highly of Serge Lang's "Basic Mathematics".
Finding sparetime activities to train your analytic and critical thinking skills will also help you immeasurably. Here I recommend puzzle books, puzzle games (I recommend Portal, Lolo, Lemmings, and The Incredible Machine), board/card games (try Eclipse, MtG, and Go), and programming (Scheme or Haskell).
It takes effort. But I think you will find your journey through maths to be a truly rewarding experience.
The Disappearing Spoon is a Brysonesque look at the history of the Periodic Table.
I like pretty much anything Brian Greene writes. He's a layman's physicist, and is very good at explaining exactly what you are asking for. Try The Fabric of the Cosmos. In fact, I think there was a PBS Nova series of the same name that he hosted.
I'd like to give you my two cents as well on how to proceed here. If nothing else, this will be a second opinion. If I could redo my physics education, this is how I'd want it done.
If you are truly wanting to learn these fields in depth I cannot stress how important it is to actually work problems out of these books, not just read them. There is a certain understanding that comes from struggling with problems that you just can't get by reading the material. On that note, I would recommend getting the Schaum's outline to whatever subject you are studying if you can find one. They are great books with hundreds of solved problems and sample problems for you to try with the answers in the back. When you get to the point you can't find Schaums anymore, I would recommend getting as many solutions manuals as possible. The problems will get very tough, and it's nice to verify that you did the problem correctly or are on the right track, or even just look over solutions to problems you decide not to try.
Basics
I second Stewart's Calculus cover to cover (except the final chapter on differential equations) and Halliday, Resnick and Walker's Fundamentals of Physics. Not all sections from HRW are necessary, but be sure you have the fundamentals of mechanics, electromagnetism, optics, and thermal physics down at the level of HRW.
Once you're done with this move on to studying differential equations. Many physics theorems are stated in terms of differential equations so really getting the hang of these is key to moving on. Differential equations are often taught as two separate classes, one covering ordinary differential equations and one covering partial differential equations. In my opinion, a good introductory textbook to ODEs is one by Morris Tenenbaum and Harry Pollard. That said, there is another book by V. I. Arnold that I would recommend you get as well. The Arnold book may be a bit more mathematical than you are looking for, but it was written as an introductory text to ODEs and you will have a deeper understanding of ODEs after reading it than your typical introductory textbook. This deeper understanding will be useful if you delve into the nitty-gritty parts of classical mechanics. For partial differential equations I recommend the book by Haberman. It will give you a good understanding of different methods you can use to solve PDEs, and is very much geared towards problem-solving.
From there, I would get a decent book on Linear Algebra. I used the one by Leon. I can't guarantee that it's the best book out there, but I think it will get the job done.
This should cover most of the mathematical training you need to move onto the intermediate level physics textbooks. There will be some things that are missing, but those are usually covered explicitly in the intermediate texts that use them (i.e. the Delta function). Still, if you're looking for a good mathematical reference, my recommendation is Lua. It may be a good idea to go over some basic complex analysis from this book, though it is not necessary to move on.
Intermediate
At this stage you need to do intermediate level classical mechanics, electromagnetism, quantum mechanics, and thermal physics at the very least. For electromagnetism, Griffiths hands down. In my opinion, the best pedagogical book for intermediate classical mechanics is Fowles and Cassidy. Once you've read these two books you will have a much deeper understanding of the stuff you learned in HRW. When you're going through the mechanics book pay particular attention to generalized coordinates and Lagrangians. Those become pretty central later on. There is also a very old book by Robert Becker that I think is great. It's problems are tough, and it goes into concepts that aren't typically covered much in depth in other intermediate mechanics books such as statics. I don't think you'll find a torrent for this, but it is 5 bucks on Amazon. That said, I don't think Becker is necessary. For quantum, I cannot recommend Zettili highly enough. Get this book. Tons of worked out examples. In my opinion, Zettili is the best quantum book out there at this level. Finally for thermal physics I would use Mandl. This book is merely sufficient, but I don't know of a book that I liked better.
This is the bare minimum. However, if you find a particular subject interesting, delve into it at this point. If you want to learn Solid State physics there's Kittel. Want to do more Optics? How about Hecht. General relativity? Even that should be accessible with Schutz. Play around here before moving on. A lot of very fascinating things should be accessible to you, at least to a degree, at this point.
Advanced
Before moving on to physics, it is once again time to take up the mathematics. Pick up Arfken and Weber. It covers a great many topics. However, at times it is not the best pedagogical book so you may need some supplemental material on whatever it is you are studying. I would at least read the sections on coordinate transformations, vector analysis, tensors, complex analysis, Green's functions, and the various special functions. Some of this may be a bit of a review, but there are some things Arfken and Weber go into that I didn't see during my undergraduate education even with the topics that I was reviewing. Hell, it may be a good idea to go through the differential equations material in there as well. Again, you may need some supplemental material while doing this. For special functions, a great little book to go along with this is Lebedev.
Beyond this, I think every physicist at the bare minimum needs to take graduate level quantum mechanics, classical mechanics, electromagnetism, and statistical mechanics. For quantum, I recommend Cohen-Tannoudji. This is a great book. It's easy to understand, has many supplemental sections to help further your understanding, is pretty comprehensive, and has more worked examples than a vast majority of graduate text-books. That said, the problems in this book are LONG. Not horrendously hard, mind you, but they do take a long time.
Unfortunately, Cohen-Tannoudji is the only great graduate-level text I can think of. The textbooks in other subjects just don't measure up in my opinion. When you take Classical mechanics I would get Goldstein as a reference but a better book in my opinion is Jose/Saletan as it takes a geometrical approach to the subject from the very beginning. At some point I also think it's worth going through Arnold's treatise on Classical. It's very mathematical and very difficult, but I think once you make it through you will have as deep an understanding as you could hope for in the subject.
If you like logic and the scientific method, I recommend E. T. Jaynes' Probability Theory: The Logic of Science. You can buy it here:
http://www.amazon.com/Probability-Theory-The-Logic-Science/dp/0521592712/
or read a PDF here:
http://shawnslayton.com/open/Probability%2520book/book.pdf
I would highly recommend anyone interested in the details at a level the layman can understand pick up Richard Feynman's QED: The Strange Theory of Light and Matter
http://www.amazon.com/QED-Strange-Princeton-Science-Library/dp/0691125759
It is IMO the best physics book aimed at the layman I've ever encountered. It gives a very lucid and detailed explanation of why light behaves the way it does in our everyday world, given the quantum mechanical rules it operates under.
Anything by Feynmann are great reads. For upper division instrumental analysis, spectroscopy, and quantum I wholly recommend QED: The Strange Theory of Light and Matter by Richard P. Feynman et al. It describes all the concepts in the book in layman's terms in a brilliant narrative of chemistry. I recommend it to anyone that wants to learn about the strangeness of physics and chemistry. It is easy to digest.
The Feynman Lectures on Physics, although pricey helped me survive physics (I have the paperbacks). It seems you can read the entirety online at that site.
If you choose to do a lot of organic chemistry laboratory work then Advanced Practical Organic Chemistry is a really great resource. It covers just about everything you need to know to be very competent and safe in the lab. I found a used copy of the second edition that has served me well. I don't know what has been updated in the third edition.
I agree with /u/lmo2th Pauling has written albeit old but definitive books on chemistry. Although it can be very difficult to read and knowledge of differential equations is required, Introduction to Quantum Mechanics with Applications to Chemistry by Linus Pauling et al. was the most succinct book on the nitty gritty math of QM I found.
I recently graduated with a B.S. in Chemistry, it was difficult, but I loved every minute I spent in the lab doing research and can't imagine doing anything else. Edit: QED and Feynmann Lectures are great reads for lower division classes. Save the second two for if you decide on chemistry.
Chris Mooney's The Republican Brain has some interesting things to say related to this. As does John Dean's Conservatives Without Conscience.
I found this to be a fairly decent book on the subject, it involved a lot of neuroscience and cogsci studies.
I studied with this book on abstract. It's authoritative and brutal.
It's hard to give an objective answer, because any sufficiently advanced book will be bound to not appeal to everyone.
You probably want Daddy Rudin for real analysis and Dummit & Foote for general abstract algebra.
Mac Lane for category theory, of course.
I think people would agree on Hartshorne as the algebraic geometry reference.
Spanier used to be the definitive algebraic topology reference. It's hard to actually use it as a reference because of the density and generality with which it's written.
Spivak for differential geometry.
Rotman is the group theory book for people who like group theory.
As a physics person, I must have a copy of Fulton & Harris.
Take my recommendation as a grain of salt as i didn't take my formal math education further than where you're currently at, but I felt the same way after similar classes learning the mechanics but not the motivations. Mathematics: Its Content, Methods and Meaning was recommended to me by a friend and I think it help fills the gaps in motivation and historical context/connecting different fields not covered in classes.
An Introduction to Ordinary Differential Equations - $7.62
Ordinary Differential Equations - $14.74
Partial Differential Equations for Scientists and Engineers - $11.01
Dover books on mathematics have great books for very cheap. I personally own the second and third book on this list and I thought they were a great resource, especially for the price.
Imagine you have a dataset without labels, but you want to solve a supervised problem with it, so you're going to try to collect labels. Let's say they are pictures of dogs and cats and you want to create labels to classify them.
One thing you could do is the following process:
(I'm ignoring problems like pictures that are difficult to classify or lazy or adversarial humans giving you noisy labels)
That's one way to do it, but is it the most efficient way? Imagine all your pictures are from only 10 cats and 10 dogs. Suppose they are sorted by individual. When you label the first picture, you get some information about the problem of classifying cats and dogs. When you label another picture of the same cat, you gain less information. When you label the 1238th picture from the same cat you probably get almost no information at all. So, to optimize your time, you should probably label pictures from other individuals before you get to the 1238th picture.
How do you learn to do that in a principled way?
Active Learning is a task where instead of first labeling the data and then learning a model, you do both simultaneously, and at each step you have a way to ask the model which next example should you manually classify for it to learn the most. You can than stop when you're already satisfied with the results.
You could think of it as a reinforcement learning task where the reward is how much you'll learn for each label you acquire.
The reason why, as a Bayesian, I like active learning, is the fact that there's a very old literature in Bayesian inference about what they call Experiment Design.
Experiment Design is the following problem: suppose I have a physical model about some physical system, and I want to do some measurements to obtain information about the models parameters. Those measurements typically have control variables that I must set, right? What are the settings for those controls that, if I take measurements on that settings, will give the most information about the parameters?
As an example: suppose I have an electric motor, and I know that its angular speed depends only on the electric tension applied on the terminals. And I happen to have a good model for it: it grows linearly up to a given value, and then it becomes constant. This model has two parameters: the slope of the linear growth and the point where it becomes constant. The first looks easy to determine, the second is a lot more difficult. I'm going to measure the angular speed at a bunch of different voltages to determine those two parameters. The set of voltages I'm going to measure at is my control variable. So, Experiment Design is a set of techniques to tell me what voltages I should measure at to learn the most about the value of the parameters.
I could do Bayesian Iterated Experiment Design. I have an initial prior distribution over the parameters, and use it to find the best voltage to measure at. I then use the measured angular velocity to update my distribution over the parameters, and use this new distribution to determine the next voltage to measure at, and so on.
How do I determine the next voltage to measure at? I have to have a loss function somehow. One possible loss function is the expected value of how much the accuracy of my physical model will increase if I measure the angular velocity at a voltage V, and use it as a new point to adjust the model. Another possible loss function is how much I expect the entropy of my distribution over parameters to decrease after measuring at V (the conditional mutual information between the parameters and the measurement at V).
Active Learning is just iterated experiment design for building datasets. The control variable is which example to label next and the loss function is the negative expected increase in the performance of the model.
So, now your procedure could be:
Or you could be a lot more clever than that and use proper reinforcement learning algorithms. Or you could be even more clever and use "model-independent" (not really...) rewards like the mutual information, so that you don't over-optimize the resulting data set for a single choice of model.
I bet you have a lot of concerns about how to do this properly, how to avoid overfitting, how to have a proper train-validation-holdout sets for cross validation, etc, etc, and those are all valid concerns for which there are answers. But this is the gist of the procedure.
You could do Active Learning and iterated experiment design without ever hearing about bayesian inference. It's just that those problems are natural to frame if you use bayesian inference and information theory.
About the jargon, there's no way to understand it without studying bayesian inference and machine learning in this bayesian perspective. I suggest a few books:
Is a pretty good introduction to Information Theory and bayesian inference, and how it relates to machine learning. The Machine Learning part might be too introductory if already know and use ML.
Some people don't like this book, and I can see why, but if you want to learn how bayesians think about ML, it is the most comprehensive book I think.
More of a philosophical book. This is a good book to understand what bayesians find so awesome about bayesian inference, and how they think about problems. It's not a book to take too seriously though. Jaynes was a very idiosyncratic thinker and the tone of some of the later chapters is very argumentative and defensive. Some would even say borderline crackpot. Read the chapter about plausible reasoning, and if that doesn't make you say "Oh, that's kind of interesting...", than nevermind. You'll never be convinced of this bayesian crap.
Wellll I'm going to speak in some obscene generalities here.
There are some philosophical reasons and some practical reasons that being a "pure" Bayesian isn't really a thing as much as it used to be. But to get there, you first have to understand what a "pure" Bayesian is: you develop reasonable prior information based on your current state of knowledge about a parameter / research question. You codify that in terms of probability, and then you proceed with your analysis based on the data. When you look at the posterior distributions (or posterior predictive distribution), it should then correctly correspond to the rational "new" state of information about a problem because you've coded your prior information and the data, right?
WELL let's touch on the theoretical problems first: prior information. First off, it can be very tricky to code actual prior information into a true probability distribution. This is one of the big turn-offs for frequentists when it comes to Bayesian analysis. "Pure" Bayesian analysis sees prior information as necessarily coming before the data is ever seen. However, suppose you define a "prior" whereby a parameter must be greater than zero, but it turns out that your state of knowledge is wrong? What if you cannot codify your state of knowledge as a prior? What if your state of knowledge is correctly codified but makes up an "improper" prior distribution so that your posterior isn't defined?
Now'a'days, Bayesians tend to think of the prior as having several purposes, but they also view it as part of your modeling assumptions - something that must be tested to determine if your conclusions are robust. So you might use a weakly regularizing prior for the purposes of getting a model to converge, or you might look at the effects of a strong prior based on other studies, or the effects of a non-informative prior to see what the data is telling you absent other information. By taking stock of the differences, you can come to a better understanding of what a good prediction might be based on the information available to you. But to a "pure" Bayesian, this is a big no-no because you are selecting the prior to fit together with the data and seeing what happens. The "prior" is called that because it's supposed to come before, not after. It's supposed to codify the current state of knowledge, but now'a'days Bayesians see it as serving a more functional purpose.
Then there are some practical considerations. As I mentioned before, Bayesian analysis can be very computationally expensive when data sets are large. So in some instances, it's just not practical to go full Bayes. It may be preferable, but it's not practical. So you wind up with some shortcuts. I think that in this sense, modern Bayesians are still Bayesian - they review answers in reference to their theoretical understanding of what is going on with the distributions - but they can be somewhat restricted by the tools available to them.
As always with Bayesian statistics, Andrew Gelman has a lot to say about this. Example here and here and he has some papers that are worth looking into on the topic.
There are probably a lot of other answers. Like, you could get into how to even define a probability distribution and whether it has to be based on sigma algebras or what. Jaynes has some stuff to say about that.
If you want a good primer on Bayesian statistics that has a lot of talking and not that much math (although what math it does have is kind of challenging, I admit, though not unreachable), read this book. I promise it will only try to brainwash you a LITTLE.
Intro Calculus, in American sense, could as well be renamed "Physics 101" or some such since it's not a very mathematical course. Since Intro Calculus won't teach you how to think you're gonna need a book like How to Solve Word Problems in Calculus by Eugene Don and Benay Don pretty soon.
Aside from that, try these:
Excursions In Calculus by Robert Young.
Calculus:A Liberal Art by William McGowen Priestley.
Calculus for the Ambitious by T. W. KORNER.
Calculus: Concepts and Methods by Ken Binmore and Joan Davies
You can also start with "Calculus proper" = Analysis. The Bible of not-quite-analysis is:
[Calculus by Michael Spivak] (http://www.amazon.com/Calculus-4th-Michael-Spivak/dp/0914098918/ref=sr_1_1?s=books&ie=UTF8&qid=1413311074&sr=1-1&keywords=spivak+calculus).
Also, Analysis is all about inequalities as opposed to Algebra(identities), so you want to be familiar with them:
Introduction to Inequalities by Edwin F. Beckenbach, R. Bellman.
Analytic Inequalities by Nicholas D. Kazarinoff.
As for Linear Algebra, this subject is all over the place. There is about a million books of all levels written every year on this subject, many of which is trash.
My plan would go like this:
1. Learn the geometry of LA and how to prove things in LA:
Linear Algebra Through Geometry by Thomas Banchoff and John Wermer.
Linear Algebra, Third Edition: Algorithms, Applications, and Techniques
by Richard Bronson and Gabriel B. Costa.
2. Getting a bit more sophisticated:
Linear Algebra Done Right by Sheldon Axler.
Linear Algebra: An Introduction to Abstract Mathematics by Robert J. Valenza.
Linear Algebra Done Wrong by Sergei Treil.
3. Turn into the LinAl's 1% :)
Advanced Linear Algebra by Steven Roman.
Good Luck.
Hrrumph. Determinants are a capstone, not a cornerstone, of Linear Algebra.
https://www.amazon.com/Linear-Algebra-Right-Undergraduate-Mathematics/dp/0387982582
>When university starts, what can I do to ensure that I can compete and am just as good as the best mathematics students?
Read textbooks for mathematics students.
For example for Linear Algebra I heard that Axler's book is very good (I studied Linear Algebra in another language, so I can't really suggest anything from personal experience). For Calculus I personally suggest Spivak's book.
There are many books that I could suggest, but one of the greatest books I've ever read is The Art and Craft of Problem Solving.
Friend asked for a similar list a while ago and I put this together. Would love to see people thoughts/feedback.
Very High Level Introductions:
Deeper Pop-sci Dives (probably in this order):
Blending the line between pop-sci and mathematical (these books are not meant to be read and put away but instead read, re-read and pondered):
> At first black holes were just a concept that was possible.
So, in order to repair your non sequitor, you have translated it to the 18th century. I would suggest that your example might have been improved had you chosen something relevant to modernity (see: M-theory).
> In 2010 a theory was published and peer reviewed that said that black holes could be wormholes to other universes. Scientist do not widely accept this or other alternate theories of black holes. They believe (because they cannot know) that black holes are collapsed stars.
Do you really believe that our understanding of black holes, or any topic of science, is a matter of taste? Do you really know so little of philosophy of science, and the practical establishment of scientific consensus?
> I do see secondary evidence [for theism] such as the universe, DNA, the precise strength of gravity to support life, the precise strength of the strong nuclear force to support life, the nearly unique properties of water.
Surely you can appreciate that a unifying characteristic of cosmogony, abiogenesis, and the origins of physical constants is scientific ignorance. So why are you so eager to connect that trait to your faith? Do you not understand how such a commitment is demonstrably hazardous to scientific literacy?
> My theory is that god exists and much like John Michell and Simon Pierre LaPlace in the 18th century I am waiting for science to catch up.
The mechanism by which science "catches up" is known as experiment.
What experiments could be performed to corroborate the existence of God?
https://www.amazon.com/Biological-Exuberance-Homosexuality-Diversity-Stonewall/dp/031225377X/ref=sr_1_1?ie=UTF8&qid=1542602162&sr=8-1&keywords=biological+exuberance
It's not more common now than it was 500 years ago. We just happen to have a huge population in which the trait can show itself more often. Check out a book called Biological Exuberance by Bruce Baghemihl it does an excellent job telling of the frequency homosexuality is seen in many species.
http://www.amazon.com/Biological-Exuberance-Homosexuality-Diversity-Stonewall/dp/031225377X/ref=sr_1_1?ie=UTF8&s=books&qid=1291778199&sr=8-1
It's likely.
Chemistry is largely based around what the electrons in the outmost shell are doing, and those shells are described by quantum mechanics. So chemistry had this organizational structure built up around experiment then quantum mechanics comes in and gives a full description of why those experiments worked the way they did. In addition to be much harder to work with than chemical laws, quantum mechanics comes with a lot of baggage that people at the time were uneasy about. It meant we lived in a much more probablistic universe than some people wanted to admit, and that the building blocks of the universe were chaotic to some degree. If you are interested in this I suggest checking out The Disappearing Spoon, as it does go into how chemistry and physics intersected.
This is a good introductory essay by Nick Bostrom from The Cambridge Handbook of Artificial Intelligence. And this is a relevant survey essay by Drew McDermott from The Cambridge Handbook of Consciousness.
If folks aren't taking well to the background reading, they might at least do alright jumping to Section 5 from the Descartes' Discourse (they can use this accessible translation). One little snippet:
>I worked especially hard to show that if any such machines had the organs and outward shape of a monkey or of some other animal that doesn’t have reason, we couldn’t tell that they didn’t possess entirely the same nature as these animals; whereas if any such machines bore a resemblance to our bodies and imitated as many of our actions as was practically possible, we would still have two very sure signs that they were nevertheless not real men. (1) The first is that they could never use words or other constructed signs, as we do to declare our thoughts to others. We can easily conceive of a machine so constructed that it utters words, and even utters words that correspond to bodily actions that will cause a change in its organs (touch it in one spot and it asks ‘What do you mean?’, touch it in another and it cries out ‘That hurts!’, and so on); but not that such a machine should produce different sequences of words so as to give an appropriately meaningful answer to whatever is said in its presence—which is something that the dullest of men can do. (2) Secondly, even though such machines might do some things as well as we do them, or perhaps even better, they would be bound to fail in others; and that would show us that they weren’t acting through understanding but only from the disposition of their organs. For whereas reason is a universal instrument that can be used in all kinds of situations, these organs need some particular disposition for each particular action; hence it is practically impossible for a machine to have enough different •organs to make •it act in all the contingencies of life in the way our •reason makes •us act. These two factors also tell us how men differ from beasts [= ‘non-human animals’].
That sets the stage for historically important essay from Turing of Turing-Test-fame. And that essay sets up nicely Searle's Chinese Room thought experiment. Scientific America has two accessible articles: Searle presents his argument here, and the Churchland's respond.
As always, the SEP and IEP are good resources for students, and they have entries with bibliographies on consciousness, the hard problem of consciousness, AI, computational theories of mind, and so on.
There are countless general introductions to philosophy of mind. Heil's Philosophy of Mind is good. Seager's introduction to theories of consciousness is also quite good, but maybe more challenging than some. Susan Blackmore's book Conversations on Consciousness was a very engaging read, and beginner friendly. She also has a more textbook-style Introduction that I have not read, but feel comfortable betting that it is also quite good.
Searle's, Dennett's and Chalmer's books on consciousness are all good and influential and somewhat partisan to their own approaches. And Kim's work is a personal favorite.
(sorry for the broad answer--it's a very broad question!)
Differential Equations, Linear Nonlinear, Ordinary, Partial is a really decent book, he explains loads of details in it and gives a fair few examples, I would also strongly recommend Strogatz, he gives really decent explanations on dynamical systems.
QED: The Strange Theory of Light and Matter, Richard P. Feynman (Princeton Science Library)
http://www.amazon.com/QED-Strange-Theory-Light-Matter/dp/0691024170
To start, you need to you learn that eveything is made from complex waves of probability and that is the only way the math works. This short and inexpensive book is a work of art, accessible by the "intelligent layman". Then google the amazing Feynman!
Recently I've read Feynman's The Strange Theory of Light and Matter. It's a nice "introduction" to the world of quantum physics. ((Also available online on certain sites.))
This book literally changed my life. I was all set to start a career as an experimental condensed matter physicist. After taking a course based on this book, I realized that theory and modelling were my true calling. Now I work in mathematical physics and computational physics.
Definitely Strogatz! Out of the books I have read, IMO, here is the order of readability: Strogatz, Meiss, Perko, Hartman. The italicized books are the ones I would recommend, but Perko and Hartman are really good too.
Strogatz: http://www.amazon.co.uk/Nonlinear-Dynamics-Chaos-Applications-nonlinearity/dp/0738204536
Meiss: http://www.amazon.co.uk/Differential-Dynamical-Systems-Mathematical-Computation/dp/0898716357/ref=sr_1_1?s=books&ie=UTF8&qid=1369504121&sr=1-1&keywords=meiss+dynamical+systems
Perko: http://www.amazon.co.uk/Differential-Equations-Dynamical-Systems-Mathematics/dp/0387951164/ref=sr_1_1?s=books&ie=UTF8&qid=1369504149&sr=1-1&keywords=perko+dynamical+systems
Hartman: http://www.amazon.co.uk/Ordinary-Differential-Equations-Classics-Mathematics/dp/0898715105/ref=sr_1_1?s=books&ie=UTF8&qid=1369504196&sr=1-1&keywords=hartman+differential+equations
If you’d like a physical textbook, I’d recommend Basic Mathematics by Serge Lang, a celebrated mathematician and teacher. It’s an oldie but a goodie. https://www.amazon.com/dp/0387967877/
If you progress past that and want to refresh your calculus, it’s hard to go wrong with James Stewart’s Calculus. https://www.amazon.com/dp/B00YHKU50E/
Linear algebra is an essential tool in many areas of mathematics. Computations with matrices aren't always that important; far more important are the concepts of vector space and linear transformation. Pretty much any time you work with coordinates, dimension, changes of coordinates, vectors, linear relations, or anything like that, you're going to need some linear algebra.
If you're interested, I recommend taking a look at Axler's Linear Algebra Done Right. Axler has very clear exposition and proofs, and if you've only seen the computational aspect of linear algebra, it'll provide a different, more abstract and conceptual perspective.
Some of my favorites:
Brian Greene -- The Fabric of the Cosmos, The Elegant Universe, and The Hidden Reality. Greene is, to my mind, very similar to Hawking in his ability to take complex subjects and make them understandable for the physics layman.
Hawking -- I see you've read A Brief History of Time, but Hawking has a couple of other books that are great. The Grand Design, The Universe in a Nutshell, and A Briefer History of Time.
Same thing applies to Brian Cox. Here's his Amazon page.
Leonard Susskind -- The Black Hole Wars. Here's the basic idea behind this book. One of the basic tenets of physics is that "information" is never lost. Stephen Hawking delivered a presentation that apparently showed that when matter falls into a black hole, information is lost. This set the physics world on edge. Susskind (and his partner Gerard T'Hooft) set out to prove Hawking wrong. Spoilers: they do so. And in doing so, they apparently proved that what we see as 3 dimensions is probably similar to those 2-D stickers that project a hologram. It's called the Holographic Principle.
Lee Smolin -- The Trouble with Physics. If you read the aforementioned books and/or keep up with physics through pop science sources, you'll probably recognize that string theory is pretty dang popular. Smolin's book is a criticism of string theory. He's also got a book that's on my to-read list called Three Roads to Quantum Gravity.
Joao Magueijo -- Faster Than the Speed of Light. This is another physics book that cuts against the prevailing academic grain. Physics says that the speed of light is a universal speed limit. Nothing can travel faster than the speed of light. Magueijo's book is about his theory that the speed of light is, itself, variable, and it's been different speeds at different times in the universe's history. You may not end up agreeing with Magueijo, but the guy is smart, he's cocky, and he writes well.
For Calculus:
Calculus Early Transcendentals by James Stewart
^ Link to Amazon
Khan Academy Calculus Youtube Playlist
For Physics:
Introductory Physics by Giancoli
^ Link to Amazon
Crash Course Physics Youtube Playlist
Here are additional reading materials when you're a bit farther along:
Mathematical Methods in the Physical Sciences by Mary Boas
Modern Physics by Randy Harris
Classical Mechanics by John Taylor
Introduction to Electrodynamics by Griffiths
Introduction to Quantum Mechanics by Griffiths
Introduction to Particle Physics by Griffiths
The Feynman Lectures
With most of these you will be able to find PDFs of the book and the solutions. Otherwise if you prefer hardcopies you can get them on Amazon. I used to be adigital guy but have switched to physical copies because they are easier to reference in my opinion. Let me know if this helps and if you need more.
Khan Academy and Professor Leonard on YouTube will cover up to Calculus 3. From there you can use this Mathematical Methods book to cover the rest of what you would need for an undergraduate physics major. Then you can start learning the physics.
For a brief overview of the scope of math and physics, look at these two videos.
I want to emphasize that learning the math and the physics up to and especially including the theory of relativity is very difficult and time consuming. General Relativity itself is quite beyond undergraduate level physics.
I suggest if you are curious about topics like relativity that you check out Paul Sutter's Ask a Spaceman! podcast. He breaks down what the math says and explains complex subjects in a way that is easy to understand.
I also recommend watching Richard A. Muller's physics for presidents course, which is another great resource for learning about physics without the math getting in the way of understanding the concepts.
Actually have a read of this
http://www.amazon.com/The-Republican-Brain-Science-Science/dp/1118094514
just as a starting point.
how does this pair up to Psilocybin Mushrooms of the World: An Identification Guide
Stamets, Paul ?
​
better/ worse?
If you're doing both applied and pure abstract algebra rather than elementary algebra, then you'll probably need to learn to write proofs for the pure side. I recommend Numbers, Groups, and Codes by J. F. Humphreys for an introduction to the basics and to some applied abstract algebra. If you need more work on proofs, the free Book of Proofs can help, and Fraleigh's A First Course in Abstract Algebra is a good book for pure abstract algebra. If you want something more advanced, I recommend the massive Abstract Algebra by Dummit and Foote.
Learn Algebra, arguably the most important math subject (of course, I may be biased). Dummit and Foote is a fantastic intro if you have proof experience etc.
Hi there,
For all intents and purposes, for someone your level the following will be enough material to stick your teeth into for a while.
Mathematics: Its Content, Methods and Meaning https://www.amazon.com/Mathematics-Content-Methods-Meaning-Volumes/dp/0486409163
This is a monster book written by Kolmogorov, a famous probabilist and educator in maths. It will take you from very basic maths all the way to Topology, Analysis and Group Theory. It is however intended as an overview rather than an exhaustive textbook on all of the theorems, proofs and definitions you need to get to higher math.
For relearning foundations so that they're super strong I can only recommend:
Engineering Mathematics
https://www.amazon.co.uk/Engineering-Mathematics-K-Stroud/dp/1403942463
Engineering Mathematics is full of problems and each one is explained in detail. For getting your foundational, mechanical tools perfect, I'd recommend doing every problem in this book.
For low level problem solving I'd recommend going through the ENTIRE Art of Problem Solving curriculum (starting from Prealgebra).
https://www.artofproblemsolving.com/store/list/aops-curriculum
You might learn a thing or two about thinking about mathematical objects in new ways (as an example. When Prealgebra teaches you to think about inverses it forces you to consider 1/x as an object in its own right rather than 1 divided by x and to prove things. Same thing with -x. This was eye opening for me when I was making the transition from mechanical to more proof based maths.)
If you just want to know about what's going on in higher math then you can make do with:
The Princeton Companion to Mathematics
https://www.amazon.co.uk/Princeton-Companion-Mathematics-Timothy-Gowers/dp/0691118809
I've never read it but as far as I understand it's a wonderful book that cherry picks the coolest ideas from higher maths and presents them in a readable form. May require some base level of math to understand
EDIT: Further down the Napkin Project by Evan Chen was recommended by /u/banksyb00mb00m (http://www.mit.edu/~evanchen/napkin.html) which I think is awesome (it is an introduction to lots of areas of advanced maths for International Mathematics Olympiad competitors or just High School kids that are really interested in maths) but should really be approached post getting a strong foundation.
http://www.amazon.com/Mathematics-Its-Content-Methods-Meaning/dp/0486409163
Learn math first. Physics is essentially applied math with experiments. Start with Calculus then Linear Algebra then Real Analysis then Complex Analysis then Ordinary Differential Equations then Partial Differential Equations then Functional Analysis. Also, if you want to pursue high energy physics and/or cosmology, Differential Geometry is also essential. Make sure you do (almost) all the exercises in every chapter. Don't just skim and memorize.
This is a lot of math to learn, but if you are determined enough you can probably master Calculus to Real Analysis, and that will give you a big head start and a deeper understanding of university-level physics.
Ok, it's kinda expensive (~$60), but it's on amazon:
http://www.amazon.com/Probability-Theory-Logic-Science-Vol/dp/0521592712/ref=sr_1_1?ie=UTF8&s=books&qid=1252600006&sr=8-1
*edit for link pwnage.
https://www.amazon.com/Probability-Theory-Science-T-Jaynes/dp/0521592712
Bayes is the way to go: Ed Jayne's text Probability Theory is fundamental and a great read. Free chapter samples are here. Slightly off topic, David Mackay's free text is also wonderfully engaging.
I read this novel about statistics and found it really digestible and interesting. If you read it you will basically understand how a normal distribution works, which makes you more knowledgeable about stats than 95% of the world.
https://www.amazon.com/Drunkards-Walk-Randomness-Rules-Lives/dp/0307275175
Also this book is probably the most famous "pop stats" book ever written. People reference the book and its author all the time in basically every quantitative field.
https://www.amazon.com/Visual-Display-Quantitative-Information/dp/1930824130
>1.8% чистиx гeїв сeрeд чоловiкiв в США.
Это чистых геев, только среди мужчин, только в религиозно покусанном США, да. Но вот всех ЛГБТ в США - таки 3.8%.
Иллюстративно распределение по штатам, низкие 1.9%-2.9% в правоверных мачожопенях типа Северной Дакоты, Теннесси, Миссиссипи; высокие 4.9-5.1% в расслабленных местах типа Орегона, Вермонта, Гавайев (10% в Коламбии, но там чисто один город, популяция ЛГБТ нетипично высока).
А теперь возьмем сводку по недавним опросам по ряду развитых стран. Просто просмотрите. Франция, Великобритания - около 6% опрошенных говорят, что они ЛГБТ. Бразилия и Польша Вас очень порадуют.
В среднем получаем примерно 6% ЛГБТ (~3% чистых геев/лесбиянок и ~3% би) при отсутствии сильного культурного прессинга.
P.S. Точные цифры так легко пристрастно выдирать из контекста и презентовать в гордом одиночестве. По-аглицки то, что Вы делаете, называется cherry-picking. В статистике и науке за это бьют подсвечниками. Правильно смотреть на сводки множественных опросов, и на всё распределение данных.
>Майжe нiякиx пiддтeрджeнь гомосeксуальної оріентаціі серед тварин немає. Є деякі моменті, коли тварини однієї статі одна з іншою бавяться, але це не означає, що їх протилежна стать не цікавить. Вони вважають, що всi отi корови, що у стадi друг на друга залaзять - вони вжe лeсбiянки.
Ловите 450 видов животных. Не знаю, есть ли перевод. Да, речь очень часто идёт о долговременных отношениях (где в небольшом, где в большом % особей).
>Цe маячня в кубi та нeрозумiння що такe норма.
Если важно, норма или нет, то про бимодальные и мультимодальные распределения слышали? Какого пола нормальный человек? Или норм может быть больше чем одна? 6% это много, если что.
Вообще не должно быть важно, норма или нет, если поведение не нарушает прав и свобод других граждан. "Права не видеть как праативные целуются" в нормальных (скорее вменяемых) государствах нет.
See the book "Biological Exuberance" for dozens of examples of long-term same-sex relationships in the animal kingdom. The name of the book is the code phrase used by researchers to mean "gay" back in the dark times when being gay was considered a mental illness.
https://www.amazon.com/Biological-Exuberance-Homosexuality-Diversity-Stonewall/dp/031225377X
The Disappearing Spoon: And Other True Tales of Madness, Love, and the History of the World from the Periodic Table of the Elements by Sam Kean
Kean borrows from Mendeleev, the Father of the Period Table, and structures his book based on the table itself. Using it as a map, each chapter is centered on a group of common elements - "The Poisoner's Corridor", "The Galapagos of the Periodic Table" - and peeks at some aspect of their backstory. Where one chapter examines the competition between scientists to find a specific element, another exposes the history of those used as medicine, giving the book a great sense of variety. I wrote a little bit more about the book on my blog.
Purchase: The Disappearing Spoon on Amazon
This is a great book on why this happens
http://www.amazon.com/The-Disappearing-Spoon-Periodic-Elements/dp/0316051632
and about a million other remarkable trivia
If you're into chemistry, or even slightly interested in the subject, I'd highly recommend picking up a copy of The Disappearing Spoon.
It's like a year's worth of chemistry TIL's in a book, with full explanations and anecdotes that will put you on the floor in your own personal chemistry-laughter coma.
Are you open to doing some reading?
​
"Behave" by Robert Sapolsky
​
This book is an amalgamation of scientific research, referencing study after study that demonstrates how different aspects of our biology play key roles in our demeanor, our emotions and how we think and behave. Our gut flora, for instance, plays key roles in mood and perhaps even our social interactions [1] [2] [3]. That's just one example of the many dozens of lines of evidence that the book describes.
​
Now, it does look as though you've done some research into the philosophy of human subjective experiences, specifically qualia. I'm sure you're aware, but there are other philosophers who explain that qualia doesn't exist at all. Even one of the larger proponents of qualia, John Searle, doesn't ascribe it to a soul, or substance dualism, but to property dualism. Interestingly, Searle and Dan Dennett (a denier of qualia) had a published exchange on this very topic some 20 years ago. I'm not versed enough on the topic to actively engage in a debate on it, but it seems that, at second glance, qualia isn't necessarily all it's cracked up to be. Time will tell, of course.
​
With that said, there are vast amounts of data that thoroughly link our emotions, feelings, behaviors, etc. specifically to certain function of our biology. There is certainly more to be discovered in this field, but "Behave" spells out all of the nitty gritty details and compiles years and years worth of research. If you're actually interested in reading a thorough hypothesis coupled with the multiple lines of evidence to support it, I have a pdf copy of this book I'd be willing to share. Simply PM me your email address.
Actually, rhetoric of science is a rather burgeoning field. Check out Alan Gross's The Rhetoric of Science and Thomas Kuhn's The Structure of Scientific Revolutions.
Also, honorable mentions for Latour's Science in Action and Sontag's Illness as Metaphor,
Some of my favorite (non-textbook) economic books:
And this last one isn't necessarily economic, but it should be required reading for anyone going into any mathematic or scientific field:
Read The Drunkards Walk. Sounds like it might be up your alley. As I recall, although its been quite a while, it has some interesting analysis of how the way we perceive how and why things happen in business or other areas of our lives.
Like movie execs who would get brought in to revitalize the studio, they would green-light a bunch of projects that would get added to the production pipeline and then a year or two later they would be removed from their position because the situation of the studio hadn't changed. Only then a year later the movies they had put into production would get released, like Titanic, make a billion dollars and they would get no credit for being the ones who chose to make that movie as someone else already has their job.
Fascinating read.
Biological Exuberance
Not to instigate an argument, but it's kinda sorta common. Or at least more common than I originally thought. Definitely still a minority though. Good book on the subject.
The Disappearing Spoon: And Other True Tales of Madness, Love, and the History of the World from the Periodic Table of the Elements
I will recommend The Disappearing Spoon if you have a serious interest. It was a fantastic read and gives a brief account of the history or relevance of each (most?) element and the race to discover and name them.
How about The Disappearing Spoon and The Violinist's Thumb by Sam Kean. They are great books about chemistry and genetics.
The New Kings of Nonfiction is a collection of longform journalism edited by This American Life's Ira Glass.
I'm currently reading The Immortal Life of Henrietta Lacks. It's really interesting, here's part of the synopsis:
>Her name was Henrietta Lacks, but scientists know her as HeLa. She was a poor Southern tobacco farmer who worked the same land as her slave ancestors, yet her cells—taken without her knowledge—became one of the most important tools in medicine. The first “immortal” human cells grown in culture, they are still alive today, though she has been dead for more than sixty years. If you could pile all HeLa cells ever grown onto a scale, they’d weigh more than 50 million metric tons—as much as a hundred Empire State Buildings. HeLa cells were vital for developing the polio vaccine; uncovered secrets of cancer, viruses, and the atom bomb’s effects; helped lead to important advances like in vitro fertilization, cloning, and gene mapping; and have been bought and sold by the billions.
>Yet Henrietta Lacks remains virtually unknown, buried in an unmarked grave.
The Disappearing Spoon is about fascinating stories from the history of the periodic table of elements.
I'm reading this right now: http://www.amazon.com/Consciousness-Explained-Daniel-C-Dennett/dp/0316180661/ref=sr_1_1
It's really quite good, at least to my marginally-educated-about-such-things opinion. :-)
Here's a good read on that fenomenon https://www.amazon.com/Republican-Brain-Science-Science-Reality/dp/1118094514
The scary part is that the more educated they are, the more susceptible they are to that kind of nonsense.
9/11 is one of the major things that made it took a turn for the worse.
Experimental psychology has consistently shown existential risk and a culture of fear drives a turn to the right politically.
I highly recommend the book The Republican Brain for the full story, but this article shares the basic point and a podcast with the author of the book is here.
For a good overview of what the differences between the right and the left are which might help you think about why people move to the right in times of uncertainty, I recommend this infographic.
>You'll need to think of a better ad hominem.
I addressed the position you've taken and the reasons why you see things that way. If you found that offensive, i'm sorry but that is a personal problem. Insulting you was not the point or the totality of what i said.
>And you probably think NYT is unbiased also.
Strawman
>"conservative christian right" hasn't been a boogey man since 1997
Are you serious? Have you watched any of the red debates? Its like 90% theocrats.
Since Nixon/Reagan and the merging of religion and politics the right has gone so much further right and into science and fact denial that it's ridiculous to anyone that isn't brainwashed by it, and repeatedly told to dismiss any dissenting information on any desperate and falsified grounds they can find
Id like to give you some homework.
http://www.amazon.com/The-Republican-Science-Chris-Mooney/dp/0465046762
http://www.amazon.com/The-Republican-Brain-Science-Science/dp/1118094514
The first is more about ideological factors driving the detachments from reality
The second is more about psychological factors driving those same detachments.
"Reality has a well known 'liberal bias' " - Stephen Colbert
This may not be what you are looking for, but Feynman was a master of explanations. He wrote a wonderful book on quantum electrodynamics that you should absolutely check out called QED: The Strange Theory of Light and Matter. It will give you a pretty intuitive look at some of the ideas in QED.
Lang's Basic mathematics might cover what you need.
The Art of Problem Solving has algebra books that focus a bit more on learning through problem solving than your average textbook. Also, Serge Lang's Basic Mathematics is a book about high school math written at a fairly high level.
I agree that there's an unfortunate tendency toward "cookbook mathematics" out there. On the topic you brought up, note that there isn't a general method of factoring polynomials by hand, so there isn't necessarily anything they could teach you that would subsume all other knowledge. However, I'd say learning by solving problems rather than memorizing unmotivated algorithms is better when possible.
A First Course in Graph Theory by Chartrand and Zhang
Combinatorics: A Guided Tour by Mazur
Discrete Math by Epp
For Linear Algebra I like these below:
Lecture Notes by Tao
Linear Algebra: An Introduction to Abstract Mathematics by Robert Valenza
Linear Algebra Done Right by Axler
Linear Algebra by Friedberg, Insel and Spence
Axler's Linear Algebra Done Right is something you might enjoy looking at; since his basic point of view is that linear algebra is generally done wrong.
http://www.amazon.com/Linear-Algebra-Right-Undergraduate-Mathematics/dp/0387982582
This is a compilation of what I gathered from reading on the internet about self-learning higher maths, I haven't come close to reading all this books or watching all this lectures, still I hope it helps you.
General Stuff:
The books here deal with large parts of mathematics and are good to guide you through it all, but I recommend supplementing them with other books.
Linear Algebra: An extremelly versatile branch of Mathematics that can be applied to almost anything, also the first "real math" class in most universities.
Calculus: The first mathematics course in most Colleges, deals with how functions change and has many applications, besides it's a doorway to Analysis.
Real Analysis: More formalized calculus and math in general, one of the building blocks of modern mathematics.
Abstract Algebra: One of the most important, and in my opinion fun, subjects in mathematics. Deals with algebraic structures, which are roughly sets with operations and properties of this operations.
There are many other beautiful fields in math full of online resources, like Number Theory and Combinatorics, that I would like to put recommendations here, but it is quite late where I live and I learned those in weirder ways (through olympiad classes and problems), so I don't think I can help you with them, still you should do some research on this sub to get good recommendations on this topics and use the General books as guides.
Hey! I am a math major at Harvey Mudd College (who went to high school in the Pacific NW!). I'll answer from what I've seen.
End: Also, if you wanna learn something cool, I'd check out Discrete math. It's usually required for both a math or CS major, and it's some of the coolest undergraduate math out there. Oh, and, unlike some other math, it's not terrible to self-teach. :)
Good luck! Math is awesome!
65207
Wow. Have you read this book? It's my favorite!
The Elegant Universe by Brian Greene.
Math
You have to know those three pretty well to start. You pick up some more math along the way as needed, but that's the bulk of it.
Physics
More Math
More physics
Some books
I come from a physics background so I'm familiar with a lot of this stuff. I'll let people better in the know suggest the relevant math books.
It's a long road but well worth it in my opinion. Good luck.
A good reference book is Mathematical Methods in the Physical Sciences by Mary Boas
Amazon link
Get a decent book in Mathematical Methods, it will teach you basically everything you need for physics up to a good point. Boas is good.
I'm only part way through it myself, but here's one I've been recomended in the past that I've been enjoying so far:
Probability Theory: The Logic of Science by E.T. Jaynes
http://www.amazon.com/Probability-Theory-The-Logic-Science/dp/0521592712
http://omega.albany.edu:8008/JaynesBook.html
The second link only appears to have the first three chapters in pdf (though it has everything as postscript files), but I would be shocked if you couldn't easilly find a free pdf off the whole thing online with a quick search.
Jaynes: Probability Theory. Perhaps 'rigorous' is not the first word I'd choose to describe it, but it certainly gives you a thorough understanding of what Bayesian methods actually mean.
I'm soon starting my trek through every problem in the algebra text that Harvard's PhD prelim recommends for study:
Abstract Algebra by Dummit and Foote
I've started the first section of the first chapter, but that was only in a few hours of spare time. I'll be posting solutions by chapter soon and post my stories/insights on Hacker News. Here's section 1.1 (except the last problem, 36):
http://therobert.org/alg/1.1.pdf
Comments are appreciated. Better now than when I start the real journey. :)
Well, Hardy & Wright is the classic book for elementary stuff. It has almost everything there is to know. There is also a nice book by Melvyn Nathanson called Elementary Methods in Number Theory which I really like and would probably be my first recommendation. Beyond that, you need to decide which flavour you like. Algebraic and analytic are the big branches.
For algebraic number theory you'll need a solid grounding in commutative algebra and Galois theory - say at the level of Dummit and Foote. Lang's book is pretty classic, but maybe a tough first read. I might try Number Fields by Marcus.
For analytic number theory, I think Davenport is the best option, although Montgomery and Vaughan is also popular.
Finally, Serre (who is often deemed the best math author ever) has the classic Course in Arithmetic which contains a bit of everything.
If you are asking for classics, in Algebra, for example, there are(different levels of difficulty):
Basic Algebra by Jacobson
Algebra by Lang
Algebra by MacLane/Birkhoff
Algebra by Herstein
Algebra by Artin
etc
But there are other books that are "essential" to modern readers:
Chapter 0 by Aluffi
Basic Algebra by Knapp
Algebra by Dummit/Foot
I learned it out of Dummit and Foote originally, and I thought that was a pretty good book.
I know that in the long run competition math won't be relevant to graduate school, but I don't think it would hurt to acquire a broader background.
That said, are there any particular texts you would recommend? For Algebra, I've heard that Dummit and Foote and Artin are standard texts. For analysis, I've heard that Baby Rudin and also apparently the Stein-Shakarchi Princeton Lectures in Analysis series are standard texts.
I recommend this:
https://www.amazon.com/Mathematics-Content-Methods-Meaning-Volumes/dp/0486409163
Unlike most professional mathematical literature, it is aimed at novices and attempts to communicate ideas, not details. Unlike most popular treatments of mathematics, and in particular unlike the YouTubers you mention, it is written by expert mathematicians and is about advanced mathematical topics. I got a hardcover set from a used bookstore when I was young and enjoyed it very much. It's well worth your time.
Not quite encyclopaedic, but this gives a good overview of most topics you might encounter in an undergraduate course. The first section also gives a very good defense of the need for basic research into mathematics.
There's a lot of ground to cover in math, but completely doable. I'm going to recommend a dense book, but I truly think it's worth the read.
Let me leave you with this. You understand how number work correct? 1 + 1 = 2. It's a matter of fact. It's not up for debate and to question it would see you insane.
This is all of math. You need to truly understand
1 + 1 = 2
a + a = b everything is a function. There are laws to everything, even if people wish to deny it. If we don't understand it, it's easier to state that there are no laws that govern it, but there are. You just don't know them yet. Math isn't overwhelming when you think of it that way, at least to me. It's whole.
Ask yourself, 'why does 1 + 1 = 2 ?' If you were given 1 + x = 2, how would you solve it? Why exactly would you solve it that way? What governing set of rules are you using to solve the equation? You don't need to memorize the names of the rules, but how to use them. Understand the terminology in math, or any language, and it's easier to grasp that language.
The book Mathematics
https://www.amazon.com/gp/product/0486409163/ref=ya_st_dp_summary
This does not specifically target game programmers. However, it's not just specific categories of math that is important to game programmers. It's EVERYTHING math related. And knowing the meaning of it and understanding is more important than just a formula.
The book I just linked is an amazing book. It is well written, and avoids academia where possible. It's balance between math and explination is just right where it can effectively get the point across, and even help you understand more complex explinations.
This book features three volumes, and each volume goes over a wide array of topics in depth.
I'm a particular fan of Tenenbaum and Pollard. It's both really well-explained and cheap.
Try this book
Tenenbaum.
Definitely split up the load and take classes over the summer. I often hear people say Calculus II is the hardest of the EPIC MATH TRILOGY. I certainly agree. If you've done well in Calc I and II and have a notion of what 3d vectors are (physics should of covered this well) then you'll have no problem with Calc III (though series' and summations can be tough).
Differential equations will be your first introduction to hard "pure"-style math concepts. The language will take some time to understand and digest. I highly recommend you purchase this book to supplement your textbook. If you take notes on each chapter and work through the derivations, problems, and solutions, you'll be golden.
In my experience, materials is not math heavy for ME's. All of my tests were multiple choice and more concept based. It's not too bad.
Thermodynamics and Engineering Dynamics will be in the top three as far as difficulty goes. Circuits or Fluids will also be in there somewhere. Make sure you allow plenty of time to study these topics.
Good luck!
I used Tenenbaum. One of my favorite undergrad books. Only downside that it doesn't use any Linear Algebra
The second book that gerschgorin listed is very good, though a little old fashioned.
Since you are finishing up your math major, I'd recommend Hirsch & Smale & Devaney, an excellent book if you have a little bit of mathematical background.
There is also a video series I'm making meant to be a quick overview of many of the key topics. Maybe useful, maybe not. Also, the MIT lectures are excellent.
Casella & Berger is the go-to reference (as Smartless has already pointed out), but you may also enjoy Jaynes. I'm not sure I'd say it's quick but if gaps are your concern, it's pretty drum-tight.
it most certainly is! There's a whole approach to statistics based around this idea of updating priors. If you're feeling ambitious, the book Probability theory by Jaynes is pretty accessible.
If you can find this at your library, I suggest you pour over it in the weekend. You will not regret it.
I've always liked Why Evolution is True by Jerry Coyne.
I have been googling for the past hour and I think they are absorbed, but they are emitted with more-or-less the same wavelength, resulting in more-or-less the same image.
Photons travel at c between the atoms, but the absorption and emission causes an average slower speed, and thus a bend in its path. From the linked article:
> By "absorption" I mean that the energy of the photon causes an electron of
the atom to be kicked to a higher energy level, and the photon ceases to
exist. Then, after a very small time delay, the electron goes back to its
original (usually ground state) energy and "emits" a photon of the same
energy (and thus same frequency and thus same wavelength) as the original
"absorbed" photon.
So to answer your question, yes, refraction is absorption->emission. The article in OP sorta glosses over this, ("This is not due to gravity, but refraction as the lens of our air slants its path before its final plummet to the nighttime country-side below.") perhaps to keep the theme of following one photon on its journey. From what I've read online, a good resource for more info on this is QED: The Strange Theory of Light and Matter by Richard Feynman.
I think my original question is more of philosophical identity (is it really the "same" photon?) than of physics.
Thanks for asking these questions, because I learned a lot in researching the answers lol. All this info made the original article seem even less science-based, but I still think it illustrates the awesome forces at work in this stellar hobby.
I think the best answer is: since photons don't come with nametags, there's no way to tell, but in most cases, the light behaves as if it's the same photon. There are however some properties of light (diffraction, for instance) where thinking of each point in space as a source of new photons is useful.
For extra credit: the same is true of matter.
Not 100% related, but for more on this sort of thing check out Richard Feynman's short book "QED: The Strange Theory of Light and Matter". It's intended for ordinary laypeople, which says a lot about Feynman's confidence in laypeople, but it's great for the dedicated reader.
Indeed yes, there isn't so much absorbtion and reemission of quanta as i understand it as does the substance act like a matrix or diffraction grating. Then within the substance you have lots of little broken up waves all interacting with each other, canceling each other out in parts and bolstering each other in others. The 'super wave' made up of all these interactions propagates at slower than light speed, and potentially at an angle. Come out the other side (into a vaccum again) and there's no diffraction, no 'super wave' but back to light propagating at 'light speed again'.
There's probably a good quantum analogy too, but I don't recall it.
The thing to always remember is that these forces aren't quantum particles or idealized waves, those are just the best models we have for something we don't fully understand.
Read Feynman's QED, its short, written for the layman and completely awesome. It will also blow your freaking mind.
> If you want to involve photons in this picture, you can, but it won't help you very much.
I beg to differ. I only really understood what “electricity” is, including said guitar-amp phenomenon, when I got photons in the picture , thus creating a very different model than the one presented by most textbooks on transistor electronics. The stuff that moves at the speed of light when you turn a switch on? Photons. The stuff that actually transfers electromagnetic energy, including wire “electricity”, from a battery/source to charge? Photons. Stuff that binds electrons to protons? Photons. Stuff that get stored in capacitors? Photons. Hell the photon↔electron interaction goes well beyond “light” or “electricity” and do most things in the universe! (except gravity and nuclear phenomena). I don’t feel qualified to explain it all in quantum terms but I got the better picture from Richard Feynman’s QED, which I heartily recommend to any curious layman. (Also, this page).
Feynman's QED
Asimov's non-fiction is good
Godel, Escher, Bach
Einstein's original book
Maxwell's book (lots of math)
Confrontational atheism: Testament: Memoir of the Thoughts and Sentiments of Jean Meslier
>"Know, then, my friends, that everything that is recited and practiced in the world for the cult and adoration of gods is nothing but errors, abuses, illusions, and impostures. All the laws and orders that are issued in the name and authority of God or the gods are really only human inventions…."
>"And what I say here in general about the vanity and falsity of the religions of the world, I don’t say only about the foreign and pagan religions, which you already regard as false, but I say it as well about your Christian religion because, as a matter of fact, it is no less vain or less false than any other.
Softer (much less confrontational) atheism: 50 Reasons People Give for Believing in a God
>This unique approach to skepticism presents fifty commonly heard reasons people often give for believing in a God and then raises legitimate questions regarding these reasons, showing in each case that there is much room for doubt. Whether you're a believer, a complete skeptic, or somewhere in between, you'll find this review of traditional and more recent arguments for the existence of God refreshing, approachable, and enlightening.
Favorites non-fiction (or at least mostly non-fiction as time will tell) and not directly related to atheism: Hyperspace: A Scientific Odyssey Through Parallel Universes, Time Warps, and the 10th Dimension and The Illustrated A Brief History of Time and the Universe in a Nutshell
Favorites fiction (also not directly atheist related): Treasure Island, and Hogfather: A Novel of Discworld
Atheism book I've tried to read and found to be over my head that's supposed to be the end-all-be-all: The Miracle of Theism: Arguments For and Against the Existence of God
***
Currently reading and while enjoyable it's a bit tough to get, I've found myself re-reading pages regularly: QED: The Strange Theory of Light and Matter
If you're interested in physics, I'd check out Richard Feynman's QED.
It's a short book adapted from a series of lectures he gave on quantum electrodynamics. It's written and explained in such a way that someone with no physics or math background can get a huge amount out of the book.
Quantum electrodynamics explains it using probability amplitudes. Rather than treating light as a particle that bounces off at a point where angle of incidence equals angle of reflection, it approaches it using a quantum mechanical approach incorporating the idea that light is also a wave.
Each point on the mirror acts as an absorption and emission surface, and each point can absorb light from the source and emit light towards the detector (angles don't have to be equal). Taking into wave-like nature of light though, there will be constructive and deconstructive interference between adjacent points. It turns out that there is greatest constructive interference for lights of all wavelength at the point where angle of incidence equals angle of reflection.
Since interference is wavelength dependent, you can selectively choose which colours would be preferred over others at certain angles by modifying the mirror surface - this is how diffraction grating works.
You can read more about it in Feynman's QED: The Strange Theory of Light and Matter.
Nonlinear Dynamics And Chaos: With Applications To Physics, Biology, Chemistry, And Engineering by Steven H. Strogatz is an excellent book on nonlinear dynamical systems and you definitely don't need any probability or statistics to study it, just a good knowledge of multivariable calculus and linear algebra. Chaos theory actually doesn't have anything to do with randomness since one of the defining features of a chaotic system is that it is deterministic.
Edit: There is a freely available course by Strogatz on YouTube.
There seems to be some fuzziness around that term. The text I used defines a strange attractor as an attractor with sensitive dependence on initial conditions. This is clearly not the same definition used by the wikipedia page.
This one by Steven Strogatz is by far the most popular to my knowledge anyways. There is also an accompanying lecture series on youtube if you search the authors name.
Here are some suggestions :
https://www.coursera.org/course/maththink
https://www.coursera.org/course/intrologic
Also, this is a great book :
http://www.amazon.com/Mathematics-Birth-Numbers-Jan-Gullberg/dp/039304002X/ref=sr_1_5?ie=UTF8&qid=1346855198&sr=8-5&keywords=history+of+mathematics
It covers everything from number theory to calculus in sort of brief sections, and not just the history. Its pretty accessible from what I've read of it so far.
EDIT : I read what you are taking and my recommendations are a bit lower level for you probably. The history of math book is still pretty good, as it gives you an idea what people were thinking when they discovered/invented certain things.
For you, I would suggest :
http://www.amazon.com/Principles-Mathematical-Analysis-Third-Edition/dp/007054235X/ref=sr_1_1?ie=UTF8&qid=1346860077&sr=8-1&keywords=rudin
http://www.amazon.com/Invitation-Linear-Operators-Matrices-Bounded/dp/0415267994/ref=sr_1_4?ie=UTF8&qid=1346860052&sr=8-4&keywords=from+matrix+to+bounded+linear+operators
http://www.amazon.com/Counterexamples-Analysis-Dover-Books-Mathematics/dp/0486428753/ref=sr_1_5?ie=UTF8&qid=1346860077&sr=8-5&keywords=rudin
http://www.amazon.com/DIV-Grad-Curl-All-That/dp/0393969975
http://www.amazon.com/Nonlinear-Dynamics-Chaos-Applications-Nonlinearity/dp/0738204536/ref=sr_1_2?s=books&ie=UTF8&qid=1346860356&sr=1-2&keywords=chaos+and+dynamics
http://www.amazon.com/Numerical-Analysis-Richard-L-Burden/dp/0534392008/ref=sr_1_5?s=books&ie=UTF8&qid=1346860179&sr=1-5&keywords=numerical+analysis
This is from my background. I don't have a strong grasp of topology and haven't done much with abstract algebra (or algebraic _____) so I would probably recommend listening to someone else there. My background is mostly in graduate numerical analysis / functional analysis. The Furata book is expensive, but a worthy read to bridge the link between linear algebra and functional analysis. You may want to read a real analysis book first however.
One thing to note is that topology is used in some real analysis proofs. After going through a real analysis book you may also want to read some measure theory, but I don't have an excellent recommendation there as the books I've used were all hard to understand for me.
Nearly everyone on this subreddit recommends Strogatz. However, I've never read this book myself. The one I'm familiar with is Jordan and Smith, which I definitely can recommend, with the caveat that there are a lot of typos in it.
I bought it off of Amazon:) Psilocybin Mushrooms of the World: An Identification Guide https://www.amazon.com/dp/0898158397/ref=cm_sw_r_cp_apa_hZYFAbAMTCCKC
Theres a book https://www.amazon.com/Psilocybin-Mushrooms-World-Identification-Guide/dp/0898158397
Do more than just 'a bit'. If you are serious, make a serious effort. Nobody 'plans' on getting anyone killed, but it happens.
Paul Stamets has an excellent book on active mushroom identification if that's your interest:
https://www.amazon.com/Psilocybin-Mushrooms-World-Identification-Guide/dp/0898158397
But you will also want to become familiar with other types, as you don't want to risk confusing one type for another.
Well considering that taking 2.5g dry (or ~30g fresh) completely prevents migraines and cluster headaches for six weeks at a time (some people experience up to six months' relief but I assume they're taking a full dose - I've only ever consumed enough to trip once), I don't really need to worry about it. Even eating food with lots of soy protein (that's most processed foods) doesn't trigger the headaches for me. (I'm soy intolerant and soy protein is my worst migraine trigger)
And yes, everything people claim about cluster headaches is true. When I get them the last for up to 12 hours (often accompanied by projectile vomiting, and wishing and praying for death because the pain really is that bad), then I usually get 2-3 rebound headaches hours later and each lasts equally long. The only thing that gets me through them is knowing the headache will eventually end.
It's better losing ~5 hours every month to month and a half high on shrooms than 1-3 days a week to these headaches.
What do I do during winter? Cannabis tincture or vaping (which doesn't cure the headaches but makes them tolerable), or if friends have any, I take dried shrooms. They're nasty dried (fresh out in the woods they're kind of like a "gamey" shitake mushroom) so I follow it up with an orange soda chaser. :)
I'm going to eventually relocate to the PNW for easy access to shrooms as azurecens is ubiquitous there, and there is over a dozen other psilocybe species which grow throughout the area. Here we have only six species, they're not terribly common, and they're oyster/shelf-shaped varieties which look very similar to poisonous species so you need to take it very slow, making a spore print and bruise them and inspect them for a membrane before consumption (the first two characteristics is nearly 100% guarantee it's a psilocybe species and therefore edible, the latter you should still check for insurance because there may be a non-psilocybe, toxic species which drops purple-brown spores and bruises blue which hasn't been identified yet). When I move to the PNW I will probably collect a bunch and will have rhododendron or other laurel species shrubbery with a dress bark apron to encourage azurecens grow in my yard since they are a wood-loving species and are symbiotic with laurel-family trees.
I bring one of Paul Stamets' field guides with me ( http://www.amazon.com/Psilocybin-Mushrooms-World-Identification-Guide/dp/0898158397/ref=sr_1_5?ie=UTF8&qid=1464358847&sr=8-5&keywords=paul+stamets ) when I go foraging for visual identification then I do the additional tests to verify. :)
I wish I had known about this property of these fungi sooner - I've lost months of my life bedridden with these agonizing headaches and could have cured them just going out for a walk in the woods. I believed the propaganda about these wonderful species, and believed the lies about cannabis. The government did a huge disservice to The People by pandering to logging and pharmaceutical lobbyists. The stoners were right all along. :-(
Psilocybin Mushrooms of the World by Paul Stamets.
I cannot recommend this enough. All identification features are explained in length, and there are pictures of many, many different psilocybes all over the world. It is not exactly about homegrowing, but a fantastic resource for learning about the amazing genus Psilocybe, and our friends psilocybin, psilocin, and baeocystin. It's a little technical, but it will give you the background to understand many issues faced by growers.
Psilocybin Mushrooms of the World: An Identification Guide https://www.amazon.com/dp/0898158397/ref=cm_sw_r_cp_apa_i_D3z2Cb5XHQ78W
By far the best, hands down:
https://www.amazon.com/Psilocybin-Mushrooms-World-Identification-Guide/dp/0898158397
There's a bit of a learning curve to learn the lingo, and you may need a microscope to differentiate certain species in your area, but it will get you closer than most other resources.
Available on Amazon. The ereader versions pay the content creators nearly nothing so I suggest getting the physical book as the author gets the best royalty this way. Need the wonderful kind intelligent fungi evangelist Paul Stamets to get his. For this book there are two paperback types as the only formats.
https://www.amazon.com/Psilocybin-Mushrooms-World-Identification-Guide/dp/0898158397?SubscriptionId=AKIAILSHYYTFIVPWUY6Q&linkCode=xm2&camp=2025&creative=165953&creativeASIN=0898158397
https://www.amazon.com/Psilocybin-Mushrooms-World-Identification-Guide/dp/0898158397
People will forage for as long as mushrooms continue to grow in the wild. You could probably order them too through the dark net, but I’d be more inclined to order 4-aco-DMT personally. You can also grow them yourself at home. For the record I live in Oakland and have no clue where to buy mushrooms so I wouldn’t suggest coming here for that purpose.
Good post. I must say i follow a similar train of thought considering most matters you have discussed. It seems scientific thought plays a big role, and hence would be wise to understand the philosophical stance of science, or at least the attempts that have been made to understand it. A book i haven't read yet, but will embark on soon is titled What is this thing called science which as far as i'm aware is the go to introduction to philosophy of science text, also among universities. Also there is a good series on youtube that i've watched which covers some of the main ideas in philosophy of science such as inductivism, deductivism, paradigm theory and systematicity. That's a good watch, ~ 12 lectures that go for about an hour or so each. I can give you the lecture slides if you want. Also in relation to philosophy of science, The Structure of Scientific Revolutions is also very popular in which Kuhn puts forth paradigm theory.
Well... yes and no. When your views/findings contradict the views and findings of the vast majority of the rest of the scientific community you tend to have a hard time getting traction, yes. That's part of how it works. The other part, however, is that ultimately the truth is in the data. If the data is good it will win out in the end. Others will come along and check your results, usually with the intent to get you to shut up and move on to helping address what almost everyone else says is important. Then, sometimes... not real often, but sometimes they find out the unpopular weirdo thing that crazy guy was talking about actually is true/works.
Read Thomas Kuhn's The Structure of Scientific Revolutions for an in-depth look at this topic. Oftentimes it takes the old-guard literally dying off for the new model to truly take hold, but ultimately science is about the data and whatever construct best fits the available data is the one that will be used.
If you're interested in statistics as it relates to many aspects of our lives--including the law--in often unintuitive ways, I highly recommend reading "The Drunkard's Walk" http://www.amazon.com/The-Drunkards-Walk-Randomness-Rules/dp/0307275175/
There's a generally well liked book on this subject called "Biological Exuberance". I thought it got a little creepy at times, not in content, but tone.
When my ex-husband came out, his mom was worried about how his elderly Midwestern grandmother would take it. She needn't have been since what grandma said was "oh please, I grew up on a farm! Spend some time with barnyard animals and you'll never doubt that homosexuality is a natural variation."
> The only times homosexuality has been observed in non-Homo Sapiens animals are when such animals are IN CAPTIVITY
Wrong, one look at the Wikipaedia article on this shows multiple examples of homosexual behaviour in the wild. Further examples here and here and an article on Fox news that specifically acknowledges it. Also for specific examples- gorillas, sumatran orangutans, gibbons
Ant then theres a book, Biological Exuberance: Animal Homosexuality and Natural Diversity which lists another 450 species in which it has been observed in the wild. I have that book
Not sure about the number, but lions are totally gay. It's probably a lot more than 8%. This is from the book biological exuberance
To add another dimension to /u/franlyfran's "joke gift" idea. Is it possible to think of shows, scenes, sketches, stand-up specials, skits and stuff you like that involve the toy in question? And then to say that you and this "friend's" shared appreciation for [insert thing] provided the context for which it would be sort of funny but not sexual, for the "friend" to give you such a gift.
This idea only came to me because a friend of mine gave me this book on animal homosexuality, a friend with which I share such a bond (which is a love of all things Gervais) that makes it OK! Although, as nosy as my mother is too, she's yet to find it!
Hope it works out.
Not in any orifice.
I knew I know that face from somewhere.
Homosexuality among animals is well documented. If you're too snooty for Wikipedia, try a book: https://www.amazon.com/Biological-Exuberance-Homosexuality-Diversity-Stonewall/dp/031225377X
So if you find this even mildly interesting, you must read “The Disappearing Spoon”. It’s basically the stories behind the elements and their discovery. Before you yawn and move along, it reads like a badass Indiana Jones novel and is a page turner. The name is from Gallium which was used in a tea party and shaped like spoons. When the patrons stirred their tea the spoon disappeared and everyone was delighted (health concerns?). Anyways, you’ll never look at elements the same way:
The Disappearing Spoon: And Other True Tales of Madness, Love, and the History of the World from the Periodic Table of the Elements https://www.amazon.com/dp/0316051632/ref=cm_sw_r_cp_api_i_XCUVDbVXGT9JM
The Disappearing Spoon?
A great book that mentions this and many other interesting facts regarding discoveries is The disappearing Spoon.
It covers the discovery of each of the elements in the periodic table. It is truly a fascinating collection of stories.
See a gallium spoon melt. It would seem to disappear in black coffee.
Read Consciousness Explained by Dan Dennett.
As /u/Das_Erlebnis said, there's tons of literature in the philosophy of mind. Check out some books, e.g. Chalmer's [The Conscious Mind] (https://www.amazon.com/Conscious-Mind-Search-Fundamental-Philosophy/dp/0195117891/ref=asap_bc?ie=UTF8) and Dennett's [Consciousness Explained] (https://www.amazon.com/Consciousness-Explained-Daniel-C-Dennett/dp/0316180661/ref=pd_bxgy_14_img_2?_encoding=UTF8&psc=1&refRID=MK07ERGEZ7B8NBW6JBS1).
Edit: I'll add Nagel's essay [What is it like to be a bat?] (http://organizations.utep.edu/portals/1475/nagel_bat.pdf) to the list.
Where did he claim atheists are (more) intelligent? Do you think he claimed it with this part?
>Atheists see religious people as idiots...
When a believer and an atheist come to different conclusions on a moral issue, both sides logic behind the argument should be scrutinized, however one side wins easily when the other side usually only come up with "because I said so" or "because someone said so".
When people in disputes (like theists and atheists) through different ways come to agree on some part of an issue that's called common ground, and that is generally sought after, but you don't seem to want that, or think one couldn't come to the same conclusions for different reasons.
>Oh please don’t claim religion.
Yet you claim atheists to be the hypocritical ones?
Still, I can also quote random people unnecessarily ;)
>It is impossible to begin to learn that which one thinks one already knows.
– Epictetus
>The old argument from design in nature, as given by Paley, which formerly seemed to me so conclusive, fails, now that the law of natural selection has been discovered. There seems to be no more design in the variability of organic beings and in the action of natural selection, than in the course which the wind blows.
– Charles Darwin
Actually, the fields of psychology and sociology do have things to say about evolution of consciousness, free will, behavioral analysis and morality. Although everything is not known yet, at least some are trying. Here's a few interesting articles/books on the subject:
The Evolution of Ethics by Francisco Ayala
The Moral Landscape by Sam Harris, on Google Books
Consciousness Explained by Daniel C. Dennett
Edit: formatting
You need to read Daniel Dennett's Consciousness Explained (1991). That is the best treatment I've ever read about it.
Consciousness Explained by Dan Dennett
If you think you can read an undergraduate textbook Ryden is a standard.
However, if you think that may be too advanced, start with some popular books on the subject such and The Fabric of the Cosmos by Brian Greene, Parallel Worlds by Michio Kaku or the classic by Hawking A Brief History of Time.
If after reading those you want something more advanced but still not a textbook try The Road to Reality by Penrose. It reads like a popular book but he actually works through math (and the real stuff with like tensors etc...) to make his points so it is more advanced. Also, the Dummies Books are also a more intermediate step and are often decently good at teaching the basics on a lower technical level than a textbook.
Here you go: Brian Greene's The Fabric of the Cosmos
Greene's The Fabric of the Cosmos is also really quite good for General Relativity. Even if I personally don't find the appeal in string theory.
The question isn't whether or not they have both, which they certainly do, so much as it is the proportions they occupy in their respective bubbles of conversation.
Also I'm drawing from themes from Chris Mooney's Republican Brain, which I think is a decent starting point for a lot of summarized research on the matter.
If you really believe that conservatives aren't biased you're really only giving evidence that conservatives aren't any less biased then anyone else. But, since you asked, here's a well-known book on the topic. I don't endorse the book or the slant it uses to discuss the issue, but it's the most famous popular work on the topic and sources a whole wealth of science to support the fact that everyone has cognitive biases.
The most important concept here isn't that conservatives are biased or that liberals are biased, it's that the difference between liberal and conservative is essentially the difference between two different sets of cognitive bias.
Saved you a click: Emmett Rensin
Try this one instead: The Republican Brain: The Science of Why They Deny Science- and Reality
The Republican brain
There ya go.
The claim that "time is exactly like space" is not true. Time is treated as a dimension in Special Relativity (SR) and General Relativity (GR), but it is very different from the "usual" spatial dimensions. (It boils down to "distance" along the time direction being negative, but that statement doesn't really mean anything out of context.) The central idea of relativity is that while the entire four dimensional "thing" (spacetime) just is (is invariant), different observers will have different ideas about which way the time direction points; it turns out to be convenient for our description of nature to respect the natural "democratic" equivalence of all hypothetical observers.
I can point you to a couple of good resources:
This
is a very good, book about SR, and some "other stuff". It's pretty mathematical, and I wouldn't recommend it to someone who isn't totally comfortable with college level intro physics and calculus.
This
is the "standard" text for undergraduate SR; it's less demanding than the above, but uses mathematical language that won't translate immediately if you go on to study GR. (I have not read this myself.)
This is the book that I learned from; I thought it was pretty good.
This is Brian Greene's famous popularization of String Theory. It has chapters in the beginning on SR and Quantum Mechanics that I think are quite good.
This is Einstein's own popularization, only algebra required. All the examples that others use to explain SR pretty much come from here, and sometimes it's good to go right to the source.
This is a collection of the most important works leading up to and including relativity, from Galileo to Einstein, in case you'd like to take a look at the original paper (translated). The SR paper requires more of a conceptual physical background than a mathematical one; the same can't be said of the included GR paper.
I don't know what your background is--the first three options above are textbooks, and that's probably much more than you were hoping to get into. The last three are not; the book by Brian Greene and the collection (edited by Stephen Hawking) are interesting for other reasons besides relativity as well. For SR, though, another book by Greene might be a bit better: this.
There are some really good books that you can use to give yourself a solid foundation for further self-study in mathematics. I've used them myself. The great thing about this type of book is that you can just do the exercises from one side of the book to the other and then be confident in the knowledge that you understand the material. It's nice! Here are my recommendations:
First off, three books on the basics of algebra, trigonometry, and functions and graphs. They're all by a guy called Israel Gelfand, and they're good: Algebra, Trigonometry, and Functions and Graphs.
Next, one of two books (they occupy the same niche, material-wise) on general proof and problem-solving methods. These get you in the headspace of constructing proofs, which is really good. As someone with a bachelors in math, it's disheartening to see that proofs are misunderstood and often disliked by students. The whole point of learning and understanding proofs (and reproducing them yourself) is so that you gain an understanding of the why of the problem under consideration, not just the how... Anyways, I'm rambling! Here they are: How To Prove It: A Structured Approach and How To Solve It.
And finally a book which is a little bit more terse than the others, but which serves to reinforce the key concepts: Basic Mathematics.
After that you have the basics needed to take on any math textbook you like really - beginning from the foundational subjects and working your way upwards, of course. For example, if you wanted to improve your linear algebra skills (e.g. suppose you wanted to learn a bit of machine learning) you could just study a textbook like Linear Algebra Done Right.
The hard part about this method is that it takes a lot of practice to get used to learning from a book. But that's also the upside of it because whenever you're studying it, you're really studying it. It's a pretty straightforward process (bar the moments of frustration, of course).
If you have any other questions about learning math, shoot me a PM. :)
I think Basic Mathematics is basically a precalculus text. I can't stand normal textbooks, everything is disconnected and done for you. This is written by one of the best mathematicians and will provoke thought and understanding. He knows his audience too, he's good with kids, check out his book Math! Encounters with High School Students. He's also written a 2-volume calculus text that I know has been used well in high school settings.
What class were you previously in? What class are you going to now? Honestly, if you just practice an hour a day going through a textbook like Lang's Basic Mathematics, then you'll be fine. The summer is a great time to not only review but to get ahead. Bored of your previous material? Go learn something new!
I've read some good reviews of Basic Mathematics by Serge Lang. It should prepare the reader for calculus.
Otherwise, many online and free books are already available. Here you find a list of free books approved by the American Institute of Mathematics.
If you want to understand the WHY, then you need to read proofs and at least be familiar with basic concepts of logic. I've found this site really helpful. It's a source for definitions and proofs.
https://www.amazon.fr/gp/product/0387967877/ref=ppx_yo_dt_b_asin_title_o09_s03?ie=UTF8&psc=1
Il part vraiment de 0 et présente la construction des mathématiques à partir d'éléments très simples. Il faut comprendre l'anglais par contre, il y a peut-être des traductions.
If you're dislike of linear algebra comes from using the determinant and matrix calculations, you would love Axler's Linear Algebra Done Right.
I learned a lot from getting a copy of Rudin (however, this book is very challenging and probably not the best to self study from. I was able to get to about continuity before taking my analysis course and it was challenging, but worth while). You can probably find it online somewhere for free.
A teacher lent Introduction to Analysis to me and suggested I use it instead of the book by Rudin. It was a well written book and had exercises which were much more approachable (although it included very difficult ones as well). The layout of this book (and I'd bet many others) is quite similar to that of Rudin. It was nice to be able to read them together.
For linear algebra, I can't speak to the quality of many books, but there are plenty which can fairly easily be found online. You will likely be recommended Linear Algebra Done Right however I found it a bit challenging as a first introduction to linear algebra and never got quite far.
My university course used Larson, Falvo Linear Algebra and it was enjoyable and helps you learn the computations very well and gives a decent understanding of proofs.
I learned lin. alg. from Axler's Linear Algebra Done Right. I found it extremely readable, with exercises that were not too hard to get through quickly.
I'd suggest Probability, Linear Algebra, Convex Optimization and ML in that order.
As for study materials, I'd suggest
That should keep you busy for a while.
I think you should read this book to get a clear idea about everything related to string theory : https://www.amazon.com/Elegant-Universe-Superstrings-Dimensions-Ultimate/dp/039333810X
When it comes to QM and String Theory, Brian Greene wrote a great book on the subjects.
Really great setup! Saw the kind of books you like and I recommend The Elegant Universe if you haven't read it already
I heard he's doing a layman's overview of string theory, general relativity, and quantum mechanics, which is similar to what he did in his book The Elegant Universe.
The Elegant Universe is outstanding
https://www.amazon.com/gp/aw/d/039333810X/ref=mp_s_a_1_1?ie=UTF8&qid=1485491203&sr=8-1&pi=AC_SX236_SY340_QL65&keywords=the+elegant+universe&dpPl=1&dpID=510wznJPd3L&ref=plSrch
Linear algebra, calculus, multivariable calculus, differential equations, probability and statistics, complex numbers, Fourier transforms.
This book covers every topic and you can buy the solutions manual as well.
Boas Mathematical Methods in the Physical Sciences has a lot of useful math, although it is mostly focused on DEs and complex analysis.
As a poster mentioned above, Stewart's Multivariable Calculus, and [Boas' Mathematical Physics](http://www.Mathematical.com/ Methods in the Physical Sciences https://www.amazon.com/dp/0471198269/ref=cm_sw_r_cp_apa_6zeYAbQ5R5KB6) are excellent sources for the required math background.
Similarly, McQuarrie Physical Chemistry may be helpful.
At my school, pchem was divided into a first semester which covered the quantum chemistry of individual atoms/molecules, and a second semester which used some of these quantum ideas (but mostly statistics and thermo) to talk about the statistical mechanics of collections of particles. I believe that McQuarrie's Physical Chemistry covers both, but note that the "mathematical review" sections are just brief interludes. For a more thorough treatment of math methods for physical scientists, consider the Mary Boas book. This book mostly focuses on physics applications, but from my experience in pchem, I would argue that it's just a very "applied" or "specific" version of quantum (or thermal, E&M, etc.) physics.
Also, for quantum chem, it is of utmost importance to be familiar with matrices, vectors, and ideally some of the more fancy portions of a first course in linear algebra, like bases and diagonalization. Although the relative importance of calculus/DE vs. linear algebra might depend on whether your course follows a "Schrodinger" vs. "Heisenberg" (not the Walter White one) approach, respectively.
Math, math and more math. If you don't feel comfortable with differential equations, or if you're like I was after freshman year you don't know what a differential equation really is, then that's where you should start. Quantum Mechanics basically starts with an awesome differential equation and then goes from there.
Learning the math of this level of Physics on your own would be challenging to say the least, but if you want to dive in I'd suggest Mathematical Methods in the Physical Sciences by Boas. Pairing that with Introduction to Quantum Mechanics by Griffiths might be fun.
Nuclear theory goes into statistical mechanics, classical mechanics is multivariable calc/linear algebra, quantum field theory combines those two with differential equations and sprinkles in a bunch of "whoa that's weird" just to keep you on your toes. But it's really important that you know the math (or more likely you fake your way through the math enough to gain some insight to the Physics).
Physics is very cool and awe-inspiring - I’ve always had a big interest in it as well! Since people have already supplied you with some answers to your question, I thought I’d give you a book suggestion: Fabric of the Cosmos by Brian Greene https://www.amazon.com/Fabric-Cosmos-Space-Texture-Reality/dp/0375727205/ref=asc_df_0375727205/?tag=hyprod-20&linkCode=df0&hvadid=266033622375&hvpos=1o2&hvnetw=g&hvrand=2170571332209706386&hvpone=&hvptwo=&hvqmt=&hvdev=m&hvdvcmdl=&hvlocint=&hvlocphy=9019289&hvtargid=pla-436179468378&psc=1. This book changed the way I look at the world. Brian Greene does an incredible job at explaining complex topics in an understandable and exciting way (not like a textbook - actually feels like you are reading a story). And there is even pretty extensive notes if you want to take a deeper dive. His TED Talks are great as well - and so are his other books!
I actually see a lot of parallels between your situation and where I found myself at your age. It was 14 or 15 that I really developed an interest in science, because before that I hadn't really been properly exposed before that. Fast forward 6 or 7 years, I'm now a third year university student studying physics and I love it; I'll be applying to PhD programs next fall.
Like you, astronomy (by which I broadly mean astronomy, astrophysics, cosmology, etc.) was what really caught my attention. In school, I liked all the sciences and had always been good at math (calculus was by far one of my favorite high school courses because the science can be pretty watered down).
If you're interested in learning more about astrophysics, I would recommend any one of a number of books. The first book on the topic that I read was Simon Singh's Big Bang; I read a couple Brian Greene books, namely The Elegant Universe and Fabric of the Cosmos; I read Roger Penrose's Cycles of Time, and finally Bill Bryson's A Short History of Nearly Everything. Also, I bought a book by Hawking and one by Michio Kaku that, to this day, sit on a shelf at my parents' house unread. I would recommend Singh's book as a nice book that should be at your level, and in fact it was the one recommended to me by some professors who I bugged with questions about the universe when I was around your age. Also, Bryson's book is a good survey look at a lot of different scientific topics, not just astrophysics/cosmology specific; I enjoyed it quite a lot.
As far as reaching out to people, I would recommend trying to connect with some scientists via email. That's what I did, and they were more responsive than I expected (realize that some of the people will simply not respond, probably because your email will get buried in their inbox, not out of any ill-will towards you).
At this point, I'll just stop writing because you've more than likely stopped reading, but if you are still reading this, I'd be more than happy to talk with you about science, what parts interest(ed) me, etc.
Audio Books are your friend, like seriously pick up something to listen to.
Surely You're Joking, Mr. Feynman! (Adventures of a Curious Character) by Richard P. Feynman
The Pleasure of Finding Things Out: The Best Short Works of Richard P. Feynman
"What Do You Care What Other People Think?": Further Adventures of a Curious Character
The Elegant Universe: Superstrings, Hidden Dimensions, and the Quest for the Ultimate Theory by Brian Greene
The Fabric of the Cosmos: Space, Time, and the Texture of Reality by Brian Greene
The Hidden Reality: Parallel Universes and the Deep Laws of the Cosmos by Brian Greene
Physics of the Impossible: A Scientific Exploration by Michio Kaku
Einstein's Cosmos: How Albert Einstein's Vision Transformed Our Understanding of Space and Time: Great Discoveries by Michio Kaku
The Black Hole War: My Battle with Stephen Hawking to Make the World Safe for Quantum Mechanics by Leonard Susskind (This one I recommend on the highest degree, personally I have read it 3 times)
A Brief History of Time by Stephen Hawking
The Theory of Everything: The Origin and Fate of the Universe by Stephen W. Hawking
Pale Blue Dot: A Vision of the Human Future in Space by Carl Sagan
Contact by Carl Sagan
Billions & Billions: Thoughts on Life and Death at the Brink of the Millennium by Carl Sagan
All these books I've listened to or read, and I recommend all of them some more then others, I have tons more about Quantum Mechanics, Physics, Biology, Cosmology, Astronomy, Math etc. But I'm to lazy to list all of them here.
You might like The Fabric of the Cosmos. Greene is a string theorist but this covers a lot of quantum mechanics and various modern physics ideas in a fairly easy to read manor for the layman.
> Those analogies do not correspond to any actual scientific concepts.
Those analogies does correspond to actual scientific theories. Read this book
http://www.amazon.com/The-Fabric-Cosmos-Texture-Reality/dp/0375727205
and watch this
http://www.pbs.org/wgbh/nova/physics/fabric-of-cosmos.html
That series does the best job of explaining it to non-scientists.
Brian Greene is a pretty well known name in the world of Physics
Eh, he should have said that their is a negligible, however non-zero, probability that one of the electrons in his body is elsewhere.
Uncertainty Principle
Try this book like this for the information to be distilled in a more understandable fashion.
Serge Lang's Basic Mathematics is probably the place to start if its been 8 years.
Basic Mathematics by Serge Lang is one. Not free, though.
I assume you mean this book? It's a good option.
Nothing else written by Lang is a good option for a high school student, though, so I'm not sure what you mean about a decision.
I like to reccommend Basic Mathematics by Serge Lang. It will take you exactly from addition and subtraction to a prepared state for calculus and beyond. Don't let the name fool you though, it is a rigorous study, but with an honest effort you will do well.
hey i found something you need
Since you hope to study mathematics more seriously, I would look into this book link.
It's an excellent book that treats high school/basic college mathematics in an "adult" way. By adult I mean in the way that mathematicians think about it.
(The fun thing about Lang is that you can read only his books and get pretty much a high school through advanced graduate education).
Honestly, I think you should be more realistic: doing everything in that imgur link would be insane.
You should try to get a survey of the first 3 semesters of calculus, learn a bit of linear algebra perhaps from this book, and learn about reading and writing proofs with a book like this. If you still have time, Munkres' Topology, Dummit and Foote's Abstract Algebra, and/or Rudin's Principles of Mathematical Analysis would be good places to go.
Roughly speaking, you can theoretically do intro to proofs and linear algebra independently of calculus, and you only need intro to proofs to go into topology (though calculus and analysis would be desirable), and you only need linear algebra and intro to proofs to go into abstract algebra. For analysis, you need both calculus and intro to proofs.
Linear Algebra can be of different levels of difficulty:
I've never taught the course, but a couple of my colleagues are very fond of Linear Algebra Done Wrong and would willingly teach from it if (1) the title wouldn't immediately turn students off of it and (2) the school would be okay with sacrificing some income from students having to purchase a book.
If you're curious, the book title is a play on the title of another well-known linear algebra book.
Linear algebra is about is about linear functions and is typically taken in the first or second year of college. College algebra normally refers to a remedial class that covers what most people do in high school. I highly recommend watching this series of videos for getting an intuitive idea of linear algebra no matter what book you go with. The book you should use depends on how comfortable you are with proofs and what your goal is. If you just want to know how to calculate and apply it, I've heard Strang's book with the accompanying MIT opencourseware course is good. This book also looks good if you're mostly interested in programming applications. A more abstract book like Linear Algebra Done Right or Linear Algebra Done Wrong would probably be more useful if you were familiar with mathematical proofs beforehand. How to Prove it is a good choice for learning this.
I haven't seen boolean algebra used to refer to an entire course, but if you want to learn logic and some proof techniques you could look at How to Prove it.
Most calculus books cover both differential and integral calculus. Differential calculus refers to taking derivatives. A derivative essentially tells you how rapidly a function changes at a certain point. Integral calculus covers finding areas under curves(aka definite integrals) and their relationship with derivatives. This series gives some excellent explanations for most of the ideas in calculus.
Analysis is more advanced, and is typically only done by math majors. You can think of it as calculus with complete proofs for everything and more abstraction. I would not recommend trying to learn this without having a strong understanding of calculus first. Spivak's Calculus is a good compromise between full on analysis and a standard calculus class. It's possible to use this as a first exposure to calculus, but it would be difficult.
It's aight. Just read linear algebra, and mv calculus. Maybe some statistical mechanics, read some thermo and kinetics. Atkins for kinetics and thermo, McQuarrie for stat mech. For linear algebra read get this. You'll still have to take classes on it, so it's cool. The worst you may have to do is take some UG classes to get up to speed.
I'd like to take this opportunity to recommend a great book: The Elegant Universe. The answer to many questions here and more! :)
For a more in-depth look at String Theory I recommend The Elegant Universe.
You undoubtedly already know the part of the theory that posits everything boils down to these fundamental "string" objects, and the way they vibrate (both in terms of the typical wave vibration, but also the way where the whole object moves back and forth) determines how it behaves in the universe. And that's influenced and constrained by the type of space in which the strings can move, etc.
But how might that help resolve QM and GR? Well, because strings have a little bit of length.
When we think about particles, we treat them as points with zero dimensions. That works all right in the framework of QM, but when you apply the equations of GR to those points, you end up with some fun, indeterminate divide by zero issues. Any nonzero length at all, like something on the scale of the Planck Length, can bridge the connection and produce a meaningful result.
Now, that's not to say that's all there is to it or everything has been solved (far from it), but that may shed some light on why it's an attractive theory to pursue. There are then many types of String Theory, which may just be different facets of one larger one, but finding connections between them is difficult. And experimental confirmation of strings is completely out of reach of our current technology. So, much remains to figure out.
I really enjoyed The Elegant Universe by Brian Greene. A nice mid point between layman and post-doc
For people who enjoyed this explanation I highly recommend The Elegant Universe it gives a great ELI5 overview of modern physics from Newton to string theory.
> So, when we look at Andromeda through an ultra-mega-super powerful telescope - we are seeing something that is 3.5 billion years "old"?
Well, 2 million years old. That's how far away it is.
But the galaxy itself (not it's light) will collide with the milky way in 3.5 billion years. Sorry for combining those two facts in a confusing way.
But there are PLENTY of galaxies we can see today that are many billions of light years away. Which means what we see of them is how they were many billions of years ago, which is crazy.
I'm not really sure what I could recommend. I've been poking around and reading about space for a while just reading stuff I come across. If you aren't watching it I'd recommend the TV series Cosmos running right now with Neil Degrasse Tyson. I also really liked a couple books by Brian Greene (here's a link to one, and another.). The first one I really liked and it helped me to get a grasp on some things that always confused me.
Also, as a mod of ELI5 I'm not afraid to say ELI5 is an awesome source, and most any topic you can think about has been covered in depth here. Just type keywords into the search box and go to town. If there's something you can't find a great explanation for, post and ask and you'll get some great responses. /r/askscience is also great, although they are more sticklers for citation and aren't always as focused on layman explanations as ELI5.
As a different idea if you're just interested in the whole dimensions thing, I'd recommend The Elegant Universe. It's mostly about string theory, but a prerequisite for understanding that is that it must teach all about higher level dimensions.
It uses the flatland analogies for a bit. But it's a modern and serious read. It's not exactly an easy read, but it's not a textbook either. Should be good for anyone who enjoyed physics at the high school level.
I found it most interesting for its explanations of relativity, though. That wasn't taught in high school, so I found it mind blowing.
No problem!
Philosophy of time is an enormous area!
Not only are there many distinct positions that attempt to address the scientific and philosophical questions in different ways, there are different positions regarding the very method by which we should attempt to answer these questions! Some of these certainly overlap.
What do I mean by this?
Putting it roughly:
There are those who tend to think that we should use science to answer these questions about time. All we should care about is what observations are made; we should only care about the empirical data. These people might point to the great success of our best scientific theories that refer to 'time', such as those in physics, including; Einstein's Theory of Relativity, Entropy (The Arrow of Time), and even Quantum Theory, but also those in neuroscience and psychology, where our perception of time becomes relevant (such as the Inference Model of Time and the Strength Model of Time). So we have notions of physical/objective time, and subjective/mental time. We may talk about time slowing down around a massive body such as a black hole, or time slowing down when a work-shift is boring or when we're experiencing a traumatic event.
But there are also those who tend to think that we should use not just science, but also uniquely philosophical methods as well. Conceptual analysis is one such method; one that involves thinking very carefully about our concepts. This method is a distinctically a priori method (A priori is just philosophical jargon meaning; "Can be known without experience," for example, the statement "All triangles have three sides"). These people think we can learn a great deal about time by reflecting on our concepts about time, our intuitions about time, and the laws of thought (or logic) and how they relate to time. This philosophical approach to answering questions about time is distinctively metaphysical opposed to the former physical and cognitive theories about time.
Of course there are many who may see the use in all of these different approaches!
Recommendations:
Physics:
Hawking, S 1988, A Brief History of Time: From The Big Bang to Black Holes, Bantam Books, Toronto; New York. [Chapters 2, 9 & 10. Absolute Classic, little dated but still great read]
Gardner, M 1988, Time Travel and Other Mathematical Bewilderments, W.H. Freeman, UK. [Chapter 1]
Greene, B 2010, The Elegant Universe: Superstrings, Hidden Dimensions, and the Quest for the Ultimate Theory, W. W. Norton, New York. [Chapter 2 is a great introduction for Special Relativity]
Physics and Metaphysics:
Dainton, B 2010, Time and Space, 2nd edn, McGill-Queen's University Press, Montreal; Ithaca N.Y. [Chapters 1-8, 18, 19 & 21. This book is incredible in scope, it even has a chapter on String Theory, and it really acknowledges the intimate connection between space and time given to us by physics]
Metaphyics:
Hawley, K 2015, Temporal Parts, The Stanford Encyclopedia of Philosophy <http://plato.stanford.edu/entries/temporal-parts/&gt;. [Discussion of Perdurantism, the view that objects last over time without being wholly present at every time at which they exist.]
Markosian, N 2014, Time, The Standford Encyclopedia of Philosophy <http://plato.stanford.edu/archives/fall2016/entries/time/&gt;.
Hunter, J 2016, Time Travel, The Internet Encyclopedia of Philosophy
<http://www.iep.utm.edu/timetrav/&gt;.
Callender, C & Edney, R 2014, Introducing Time: A Graphic Guide, Icon Books Limited, UK. [Great book if you want something a bit less wordy and fun, but still very informative, having comprehensive coverage. It also has many nice illustrations and is cheap!]
Curtis, B & Robson, J 2016, A Critical Introduction to the Metaphysics of Time, Bloomsbury Publishing, UK. [Very good recent publication that comes from a great series of books in metaphysics]
Ney, A 2014, Metaphysics: An Introduction, Routledge Taylor & Francis Group, London; New York. [Chapters 5 & 6 (Chapter 4 looks at critiques of Metaphysics in general as a way of answer questions and Chapter 9 looks at Free-will/Determinism/Compatiblism)]
More advanced temporal Metaphysics:
Sider, T 2001, Four-Dimensionalism: An Ontology of Persistence and Time, Clarendon Press; Oxford University Press, Oxford New York. [Great book defending what Sider calls "Four-Dimensionalism" (this is confusing given how others have used the same term differently) but by it he means Perdurantism, the view that objects last over time without being wholly present at every time at which they exist.]
Hawley, K 2004, How Things Persist, Clarendon Press, UK. [Another great book: It's extremely similar to the one above in terms of the both content and conclusions reached]
Some good Time travel movies:
Interstellar (2014)
Timecrimes (2007)
Looper (2012)
Primer (2004) [Time Travel on drugs]
12 Monkeys (1995)
Donnie Darko (2001)
The Terminator (1984)
Groundhog Day (1993)
Predestination (2014)
Back To the Future (1-3) (1985-1990)
Source Code (2011)
Edge of Tomorrow (2014)
"An elegant universe" by Brian Greene is a good read. It leans more towards string/superstring theory. "The science of interstellar" also touches on some concepts related to quantum mechanics.
I know that you asked for books but "PBS Spacetime" is a YouTube channel that does a great job explaining quantum mechanics. "Veritasium" is another great channel with a few videos explaining phenomena as well. I posted links below. Physics is dope. Happy hunting!
An elegant universe:
https://www.amazon.com/Elegant-Universe-Superstrings-Dimensions-Ultimate/dp/039333810X
The science of interstellar:
https://www.amazon.com/gp/aw/d/0393351378/ref=mp_s_a_1_1?ie=UTF8&amp;qid=1502885214&amp;sr=8-1&amp;pi=AC_SX236_SY340_FMwebp_QL65&amp;keywords=the+physics+of+interstellar&amp;dpPl=1&amp;dpID=41Ii8OmMy0L&amp;ref=plSrch
PBS Spacetime:
https://m.youtube.com/channel/UC7_gcs09iThXybpVgjHZ_7g
Veritasium:
https://m.youtube.com/user/1veritasium
Most physics undergrads take a class called "Mathematics for Physics" or something similar which uses a book like this. It will help you cut to the chase and is a good reference for the math you haven't studied in detail.
As for where you are right now, you should be okay with ODE, multivariable/vector calc, and linear algebra. Those you probably want to devote considerable time learning.
If you understand and are able to work with this material before learning QM, you'll be in excellent position.
For a more in depth and thorough coverage, grab a math for physicists textbook, like Mary Boas'.
Square one...
You should have a solid base in math:
Introduction to Calculus and Analysis, Vol. 1 by Courant and John. Gotta have some basic knowledge of calculus.
Mathematical Methods in the Physical Sciences by Mary Boas. This is pretty high-level applied math, but it's the kind of stuff you deal with in serious physics/astrophysics.
You should have a solid base in physics:
They Feynman Lectures on Physics. Might be worth checking out. I think they're available free online.
You should have a solid base in astronomy/astrophysics:
The Physical Universe: An Introduction to Astronomy by Frank Shu. A bit outdated but a good textbook.
An Introduction to Modern Astrophysics by Carroll and Ostlie.
Astrophysics: A Very Short Introduction by James Binney. I haven't read this and there are no reviews, I think it was very recently published, but it looks promising.
It also might be worth checking out something like Coursera. They have free classes on math, physics, astrophysics, etc.
Im currently in a mechanics physics course and this is the main text book we use
https://www.amazon.com/Classical-Mechanics-John-R-Taylor/dp/189138922X
I'd say it's pretty good and an easy read as well
We have also been using a math text book to complement some of the material
https://www.amazon.com/Mathematical-Methods-Physical-Sciences-Mary/dp/0471198269
Hope this helps
Read this:
https://www.amazon.com/Mathematical-Methods-Physical-Sciences-Mary/dp/0471198269
The Cambridge Companion to Mathematics is good also.
Here is a path.
Calculus 1,2,3.
Introduction to Proofs.
Real Analysis.
Complex Analysis.
Ordinary Differential Equations.
Partial Differential Equations.
Calculus of Variations.
Linear Algebra.
Fourier Series, Fourier Transforms, Special Functions. Hilbert Space.
Probability and Statistics.
Abstract Algebra/Group Theory.
Most of the topics you mentioned were what I would call algebra or single-variable calculus. I would start learning some linear algebra and multivariable/vector calculus first - the latter should be available in any good calculus text anyways. Besides these, you should at least know some basic probability and maybe a little about complex numbers. With this amount of math you could probably get through most of a "basic" physics degree, but you'll probably want to learn much more math if that's what you're into.
Many people on Reddit have glowing reviews for Boas' mathematical physics text (haven't read it myself though). Looking at the table of contents, I think it's a good overview of topics useful for an undergrad curriculum.
some good resources:
Math for Physics books like Boas and Arfken et al. Here's one in pdf:
http://www.amazon.com/Mathematical-Methods-Physical-Sciences-Mary/dp/0471198269
http://www.goldbart.gatech.edu/PostScript/MS_PG_book/bookmaster.pdf
-----
Cambridge and Oxford have all kinds of notes and study guides online (as do MIT, UCLA, UC-Berkeley etc:
http://www.maths.ox.ac.uk/courses/material
http://www.maths.cam.ac.uk/undergrad/
http://www.maths.cam.ac.uk/studentreps/res/notes.html
---------------
book lists: http://math.ucr.edu/home/baez/books.html
https://github.com/ystael/chicago-ug-math-bib
So, you are gonna be an engineer/scientist, rather than a pure math major which, probably, means techniques will take precedence over ideas and rigor. To that end, you might like:
Engineering Mathematics
Advanced Engineering Mathematics
Numerical Methods for Scientists and Engineers
Mathematical Methods in the Physical Sciences
Basically, you need to put yourself through technical boot-camp that involves Calculus, Applied Linear Algebra, some Stats, Diff. Equations.
Boa's Mathematical Methods for the Physical Sciences will provide you a good foundation in linear algebra and multivariate calculus, completely sufficient math background for a physics student (and a great reference forever). This is the standard math text for physics students at many universities, and it is what people expect physics majors to know when conducting summer research (at least to having the competency to look up and apply without asking). Any high school/intro college calculus text will provide sufficient calculus background to read Boas (Larson; Edwards & Penney; etc.).
Brush up on mathematical methods for physics. Learn Linear Algebra, Ordinary and Partial Differential Equations, Multivariable Calculus, Complex Analysis, and Tensor Analysis. A good book would be this: http://www.amazon.com/Mathematical-Methods-Physical-Sciences-Mary/dp/0471198269/ref=ntt_at_ep_dpi_1
Classical Mechanics: http://www.amazon.com/Mechanics-Third-Course-Theoretical-Physics/dp/0750628960/ref=sr_1_7?s=books&amp;ie=UTF8&amp;qid=1291625026&amp;sr=1-7
E&M: http://www.amazon.com/Electromagnetic-Fields-Roald-K-Wangsness/dp/0471811866/ref=ntt_at_ep_dpi_1
or http://www.amazon.com/Introduction-Electrodynamics-3rd-David-Griffiths/dp/013805326X/ref=sr_1_1?s=books&amp;ie=UTF8&amp;qid=1291625100&amp;sr=1-1
Statistical Mechanics: http://www.amazon.com/Fundamentals-Statistical-Thermal-Physics-Frederick/dp/1577666127/ref=sr_1_1?ie=UTF8&amp;s=books&amp;qid=1291625184&amp;sr=1-1
Quantum Mechanics: http://www.amazon.com/Principles-Quantum-Mechanics-R-Shankar/dp/0306447908/ref=sr_1_4?s=books&amp;ie=UTF8&amp;qid=1291625261&amp;sr=1-4
That's perfect then, don't let me stop you :). When you're ready for the real stuff, the standard books on quantum mechanics are (in roughly increasing order of sophistication)
By the time you get to Shankar, you'll also need some classical mechanics. The best text, especially for self-learning, is [Taylor's Classical Mechanics.] (http://www.amazon.com/Classical-Mechanics-John-R-Taylor/dp/189138922X/ref=sr_1_1?s=books&amp;ie=UTF8&amp;qid=1372650839&amp;sr=1-1&amp;keywords=classical+mechanics)
Those books will technically have all the math you need to solve the end-of-chapter problems, but a proper source will make your life easier and your understanding better. It's enough to use any one of
When you have a good handle on that, and you really want to learn the language used by researchers like Dr. Greene, check out
Aside from the above, the most relevant free online sources at this level are
For introductory physics, I'd recommend Giancoli, Physics for Scientists and Engineers. You may want something in addition to this for deeper math, but Giancoli is fantastic for getting the core ideas and integrating them across different phenomena. After Giancoli, you will understand almost everything a lot better.
After Giancoli, things get a lot rougher. Your next objective is Classical Mechanics. You cannot learn Quantum Mechanics without studying Classical Mechanics in depth. You can try, as I did, but you are in for a world of pain that you won't fully grasp until you take Classical Mechanics seriously. You will especially want to pay attention to periodic and harmonic systems. Giancoli's main disadvantage is a weak treatment of periodic systems. Any Classical Mechanics book will make up for this.
At this point you will also need a companion book to take you through Classical Mechanics and everything that follows (Statistical Mechanics, Electrodynamics, Quantum Mechanics). That book is Mary L. Boas' Mathematical Methods in the Physical Sciences. Frankly, upper level undergraduate physics textbooks assume you have this knowledge. It's a fantastic book and it would have saved me a world of pain if I'd known about it right from the beginning.
Anyhow, after Giancoli you should look at Boas, then you may choose "Classical Mechanics" by Thornton & Marion. This book assumes you have Boas. Then you can plunge into Griffiths' Introduction to Quantum Mechanics, which assumes you have Boas. However, you'll have an easier time of the material if you read Griffiths' E&M book first, which assumes you have Boas. You'll also be well-served with a Statistical Mechanics textbook. Blundell & Blundell (Introduction to Thermal Physics) is a wonderful book conceptually, except that it lacks solutions. The mathematical and conceptual ideas in each of these subjects were fundamental to the development of Quantum Mechanics, and familiarity with the subjects is assumed by QM textbook authors.
Sure, I personally know of many examples; that's why I mentioned it before. Also, your second paragraph did not seem remotely offensive to me; it just sounded like you were trying to clearly articulate your point! In response, I think there might be two helpful things to raise at this point before going into specific examples:
> when I read of how people "question their faith" I see a similarity. I see myself in their words. So far, I haven't seen anything deviate from this.
Two concluding caveats; despite how frequently this point is raised in debate, it is not substantial:
> a dozen religions believe contradictory things
The way this is usually developed to merely criticize religion is like saying "because a dozen philosophies or aesthetic theories or anthropological worldviews believe contradictory things, they are all wrong." Just because two different religious loci make wildly different claims does not mean that they are both equally, wildly incorrect. On the other hand, this is a very good point:
> some of these "self-criticisms" are no better than a person who's in love with someone who is emotionally abusive towards them but they can't bring themselves to leave. Any sort of "evaluating the relationship" is simply a joke. Any example of misconduct is explained away by rationalizing that "but everything else is OK and it feels good on top of that."
I think what we are dealing with here is something that is not specific to religious belief but to any belief that is radicalized in the case of religion. This was part of the point Kuhn so famously made in The Structure of Scientific Revolutions, that there is a strong effect of personal bias and comfort and perceived upheaval in the way that any discipline develops. In other words, I would absolutely grant your point that a lot of religious people are sub-critical and self-deluded when it comes to their reflections on their own religion, but I would attribute this to a condition of humanity in general given its prevalence in other realms of rational endeavor and not just as something particular to religion.
Perhaps this is so obviously prevalent in the case of religion for two reasons:
Nevertheless, I maintain that there are a lot of religious people who are healthily critical of their own beliefs.
Since we are talking about expert based evidence courts use the Daubert test.
Now it still has an element of the bandwagon fallacy, so it's not best for determining actual truth.
Then there is the problem of induction which implies that actual truth from scientific testing may not be obtainable because all science relies on induction.
The next place to go to is The Structure of Scientific Revolutions which I think anyone who is interested in epistemology should read. The take away for this discussion is that scientific consensus is ever changing and while it is not perfect it does give rigorously tested guesses. And as long as a theory can make valid predictions then there is no reason to not accept it, but it should never stop being questioned. Mere skepticism gets you know where besides solipsism. Skepticism with scientific rigor allows you to make predictions that, while flawed, result in cars, computers, rockets, medicine etc. etc.
Physical evidence is derivative of science because the the methods used to test physical evidence are based in scientific theory. So, the same logic applies
My personal approach is a factors test that looks at such things as:
Whether it makes logical sense, Probably the weakest factor, but it helps to weed out logical errors first.
Whether it passes scientific rigor, Scientists do a good job of testing things repeatedly to see whether a theory works practically, in addition to logically. Some areas of science are more trust worthy than others. Always check what bias my exist in the scientist. Always follow the money.
How many other assumptions do I have to make to get to? This is a variation on Occam's razor. The more assumptions I have to make to get to the conclusion the less likely I am to believe it.
I don't believe I have perfect knowledge. I do believe I have practical/working knowledge. And if something happens in the next five minutes that changes my assumptions then I'll change what I believe.
I took a class in college called "Scientific Revolutions" about the shifts in scientific paradigm throughout history. One of the textbooks in the course was The Structure of Scientific Revolutions by Thomas S. Kuhn. It was rather enjoyable and extremely informative. I wish I kept my copy. Amazon has a bunch of related suggestions as well.
(https://www.amazon.com/Structure-Scientific-Revolutions-Thomas-Kuhn/dp/0226458083)
Perhaps this will spark some ideas?
*SNAP* Yep, this one's going in my cringe compilation.
\>Cherry picking studies and datasets to fit an agenda under a thin facade of academia certainly takes some brain power.
Accuse the enemy of what you already do yourself, a classic. Left-leaning/Leftist academics selectively publish/approve articles that conform to their worldview regardless of the veracity.
https://quillette.com/2018/10/01/the-grievance-studies-scandal-five-academics-respond/
Also, you have not cited anything; your argumentation is entirely based on emotions. Pathos, quite literally pathetic.
Continue to reject scientific data that does not conform to your worldview; it is normal.
Pick up a copy of The Structure of Scientific Revolutions. It is the foundation for the widely cited and accepted notion that science is not a progressive act in the way it is commonly perceived. Even scientists will reject or fight with data that does not match their existing narrative about the world.
P.S. I've got another common part of reality for you to reject.
Dogs and other animals can be selectively breed to produce specific behavioral traits. Humans are animals with close ties to other mammals (you do not seem to be a creationist to me). In this study a group of wild foxes were domesticated within roughly 40 years. There is nothing shocking about groups of humans that have reproduced separately for several hundred to thousands of years having different traits.
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In case anyone was too lazy to look it up.
It's fairly cheap too!
Check out The Structure of Scientific Revolutions by Thomas Kuhn. It is a great book and would be sure to give you a few topics to write about.
I'm a big fan of The Drunkard's Walk. Also, the author Leonard Mlodinow (PhD in physics from Berkeley) has a number of other really good books on different scientific fields.
> that random stock algos can beat pros. That just doesn't seem right.
It makes sense if you look at investing as a game of chance rather than a game of skill. It's not like darts, it's like roulette. There's just too much randomness involved in the game to win when betting on single numbers/stocks.
Maybe you keep track of the table operators and realize that Joe lands mostly on low, even numbers, and hey! -- Jane has hit 21 red three times in the last quarter. And if she set up the wheel in the exact same position and launched the ball in the exact same way as those last three times you'd be a winner for betting on 21 red. But she won't, because she can't, even if she tries to. Someone sneezed nearby, there was an earthquake, her fingers are a little oily. There's just too much interference in the real world.
However, there is a winning strategy. Turns out betting (variable amounts) on all options wins you enough to keep playing. A little more, a little less, but the longer you play the better your prospects.
For another interesting book about a walk, see The Drunkard's Walk by Leonard Mlodinow.
I have another possible explanation for bad days at the gym, as well as good days. They can be eplained by NOTHING. They are simply the result of random chance.
In The Drunkard's Walk: How Randomness Rules Our Lives, the author explains this issue, and how misunderstanding it can lead to bad behavior, for training in particular.
A bad day (or a good day) is a rare event. Two bad days in a row is a very rare event. It's quite likely you'll do better during your next practice for no reason at all. And for many people, they'll incorrectly attribute this improvement to something that they did.
In training, it's well knows that rewarding people for doing well is more effective than punishing people for doing poorly. But when trainers see their students have a bad day, and they yell at them, they see improvement the next day! "Swearing at my students causes them to improve." Similarly when a student has a very good day, and the trainer compliments them, they see them getting worse the next day. "Complimenting my students makes them get worse!"
People can end up making a lot of bad decisions by not accounting for the effects of random chance. I'm not saying that's the case here, it's just something to keep in mind when you're evaluating your own performance.
If you multiply the probability of winning times the payoff, you find that each entry, assuming you wouldn't have to share it and you get the full $400 million, is worth $1.74. Since it costs $2 to play and there are other things that reduce the winning amount, it is not a good bet.
Source: page 77 of this book.
In 1992 the Virginia Lottery had a game in which the value of the ticket was a little over $3, but they charged $1 per ticket. So investors got together and bought a lot of tickets, and won doing it.
should try and read the book then;
http://www.amazon.com/Biological-Exuberance-Homosexuality-Diversity-Stonewall/dp/031225377X
how does the nurture theory explain the homosexuality documented in hundreds of other species?
edit: pick up Biological Exuberance for a thought provoking read.
As someone that lived in Utah valley at the age of 14-15, let me tell you that reality is very different there then Mormons anywhere else in the world. I'm sure you are familiar with the cliques that form to show how righteous they are. I really got tired of people thinking it was the most righteous place on earth. (Even more so than SLC because of the worldly influence there).
The reason why I bring this up is anyone accepting you as you are has to admit there is a flaw in Mormonism. Since one of the basic premises of Mormonism is that the prophet can not have any flaws, you must be wrong. They will try to change you to save their own faith.
I say this with the idea that you already recognize that there is a discordance between what you have been taught and your own personal reality. So let me introduce you to the concept of religion and the concept of church. For example, it is OK to be Catholic, but think the Pope is wrong. You can believe in the religion and disagree with the church, in the same way that you would not worship the UPS man for delivering you something you really wanted.
(As a side note, there will be people that tell you that you are not natural, and your feelings are not natural. The perfect rebuttal is to mention that the rate of the population that show homosexual tendencies is 1.5% to 3% across all mammals. Here is the reference Mormonism says animals can not sin - therefore being gay can not be a sin.)
tl;dr God created gay animals, therefore you're normal, Utah Valley isn't
Homosexuality is well documented and been known for a long time (source: Biological Exuberance: Animal Homosexuality and Natural Diversity (Stonewall Inn Editions (Paperback)) https://www.amazon.com/dp/031225377X/ref=cm_sw_r_cp_api_i_prkBDbH4HMXTB ).
The problem is (and I speak on both sides of the political spectrum) people only care about the statistics that support what they already want to believe.
Hm.
Toss in something about homosexual animals...
http://www.amazon.com/Biological-Exuberance-Homosexuality-Diversity-Stonewall/dp/031225377X
There are virtually no attributes of humans that are not shared to some degree with animals, which is unsurprising since humans are animals. I have no idea whether human homosexuality is one thing or many, but as exhaustive studies have shown, it's a trait shared by animals. See Biological Exuberance: Animal Homosexuality and Natural Diversity . It's thought that having non-reproductive males in a group assists its survival, and those males pass on their genes by proxy, as they are near relations with other other members of the group.
Actually, homosexuality absolutely is natural. It's not a matter of politics, and hasn't been for a long time. It is a fact.
Homosexual behaviour is documented in hundreds of animal species, including guinea pigs (my own pets actually did this... or at least, one did it to the other), bonobos, several species of dolphin (who fuck each others' blowholes), hedgehogs, penguins, ducks, sheep, cassowaries, sunfish, char, salmon, etc. I could go on for a long time and mention animals you've never even heard of.
There's actually a delightful book on the subject that I'd recommend to anyone with a slightly unhealthy interest in it. It even has lovingly-drawn illustrations of lesbian hedgehog cunnilingus!
Homosexuality has been observed in over 450 animal species. Homophobia has only been observed in 1. So tell me now, which is more unnatural?
Your reaction is totally normal. Pretty much everyone in the LGBT world has gone through a period of self-loathing. Society tells us we're worthless, but those claims are based on fear and ignorance. All evidence points to the fact that our sexuality is innate... and there's nothing wrong with it. There's nothing wrong with you! Don't beat yourself up for your mere capacity to love someone of the same sex. If there's anything the world needs more of -- it's love!
Have patience, LOSTnhope! There are lots of us out here rooting for you in your long, tough road of self-discovery. hugs
"The Disappearing Spoon!"
It's a wonderful and engrossing read about all the elements from the periodic table! What each one is and does, where they were found/discovered, what for and how they are used in the world today.
I would say many of the stories about many of the elements beginnings in society are so entertaining that they could be turned into a film!
This book is engrossing.
Hey, girl in chemistry here. First I wanted to comment on the beaker glasses idea. If you do get something like that, go with a beaker mug and try to pick something with thicker glass. Regular beakers heat up easily and if she pours hot beverage, it will get too hot to hold in a few minutes even if there is a handle (this was tested out in a field by many chemists). Does she like to read? If so, get her The Disappearing Spoon by Sam Kean (http://www.amazon.com/Disappearing-Spoon-Madness-Periodic-Elements/dp/0316051632/ref=sr_1_1?ie=UTF8&amp;qid=1417607692&amp;sr=8-1&amp;keywords=disappearing+spoon). It's a book full of true, fun and sometimes weird stories about many elements. Any chemist would appreciate that. Also, anything periodic table will be appreciated, in addition to shower curtain idea there are fridge magnets. T-shirts are tough since most of them are really cheesy. Recently I came across this one which is not bad http://www.amazon.com/Never-Everything-Science-Unisex-T-shirt/dp/B00HWEHM6M/ref=pd_sim_a_32?ie=UTF8&amp;refRID=09FK7M4D48KR5RD8K80H. Anything with moles and avogadro will do, example http://www.amazon.com/CafePress-Mole-Problems-Mug-Multi-color/dp/B00INLA6RU/ref=sr_1_8?ie=UTF8&amp;qid=1417609281&amp;sr=8-8&amp;keywords=avogadro+number. Can't really think of anything else right now, but if you want to run a specific idea by me, feel free to do it.
The Invisible Gorilla - about how our perception and memory can deceive us.
The Disappearing Spoon - stories about the periodic table of elements.
You beat me to it. As soon as I saw the question, I thought of that book. Another good one might be The Disappearing Spoon: http://www.amazon.com/gp/product/0316051632/ref=oh_details_o06_s00_i01?ie=UTF8&amp;psc=1
Here are some of my favorite popular books by academic researchers about consciousness:
And for more of an inside-out view, I'd recommend a book on meditation by a former neuroscientist: The Mind Illuminated by Robert Yates
>Since when is the concept of free will unprovable?
A lot of other people responded, but your question was addressed to me.
I will assume that you aren't being purposefully dense, and that you really aren't aware of the debate surrounding whether free will is real or an illusion. Unfortunately this is not a debate that can be summed up in a reddit comment. There are worse places to start researching than wikipedia:
http://en.wikipedia.org/wiki/Free_will
But if these questions actually intrigue you and you are willing to challenge your preconceptions, I highly recommend this book:
http://www.amazon.com/Consciousness-Explained-Daniel-C-Dennett/dp/0316180661
>If you do not believe in a higher power, do you not have free will by default?
This is called an "either-or" fallacy, or a false dilemma. I've read a number of books by apologists, and I'd say this is their favorite fallacy (although arguments from ignorance and arguments from authority are close behind).
The answer is no, you don't have to believe in free will if you don't believe in a deity. Whatever gave you that idea?
I personally don't know if free will exists or not. For one thing, there is currently no empirically testable definition of free will. All existing definitions aren't falsifiable.
I would caution you about Dennett because, while he is a well-respected and important philosopher, he also write books for a popular audience that are less philosophical in nature.
So I would stay clear of his new atheism stuff, stay away from his beef with Sam Harris (who isn't a philosopher), and try to find lectures where he talks about consciousness (which is his main topic in philosophy).
So I would recommend starting with Daniel Dennett's TED talks, which are much easier and accessible. Here's a good introductory lecture:
https://www.youtube.com/watch?v=cYh0lAWCnpI
https://www.ted.com/speakers/dan_dennett
Next, I would try to watch this lecture and see if you can follow it (it's a bit more complicated, but it outlines the debates around consciousness in a similar way to what you might find on the SEP):
https://youtu.be/JoZsAsgOSes
Finally, his book Consciousness Explained outlines his basic approach to consciousness. While not for a general audience, he does clarify and explain his positions well, so it might be worth looking into:
https://www.amazon.com/Consciousness-Explained-Daniel-C-Dennett/dp/0316180661/ref=sr_1_1?ie=UTF8&amp;qid=1518209721&amp;sr=8-1&amp;keywords=consciousness+explained
His approach to philosophy of mind and consciousness is "heterophenomenological" (his phrase) and is anti-Cartesian in the sense that it attempts to collapse the mind and body into one physical entity (monism) via appeals to neuroscience and cognitive psychology. Consciousness, Explained is a great place to start.
No.
Read a book. May I suggest:
How the Mind Works
Consciousness Explained
The Crucible of Conscoiusness
The Astonishing Hypothesis
The Blank Slate: the Modern Denial of Human Nature
u/LeeHyori provides a great outline of the main aspects of logical positivism, e.g. the verification principle, so I won't bother addressing the 'what is logical positivism' question in detail. (The only things I would add are things like a general tendency towards: reductionism, formalism, a Wittgensteinian metaphilosophy, support of the sciences and unifying them, etc). What I want to bring up is about the objections to LP and positivists today, like Dennett.
>From my understanding, it was because their main idea seemed contradictory ("only verifiable things can be true" is itself not verifiable).
Aside from the self-refuting nature of the verification principle that you point out here, there were other problems as well, such as the theory-ladenness of observation, consequent problems with logical positivism's reductionism and empiricism (e.g., observation/protocol statements are not purely empirical), the holistic nature of confirmation, the [difficulties defining what an analytic statement is/the circular nature of the concept] (http://www.ditext.com/quine/quine.html), and the apparent irreducibility of the sciences. So you're right that LP suffered tremendously by relying on a self-undermining theory of meaning, but there were other serious problems, which gave rise to a ton of awesome new literature on the subject.
>However, has there been any prominent philosophy that has grown out of logical positivism that is in itself a stronger version of the positivist's philosophy?
I don't think anyone that famous became more positivist, in the sense of embracing a more extreme verification principle, but Dennett has said publicly he is kind of a closet verificationist - examples of which are in [Consciousness Explained] (http://www.amazon.ca/Consciousness-Explained-Daniel-C-Dennett/dp/0316180661). He talks for instance about how his analysis of the inverted qualia argument supports "the shockingly "verifications" or "positivist" view that the very idea of inverted qualia is nonsense--and hence that the very idea of qualia is nonsense" (p.390 in my edition). He also mentioned we're all verificationists in some sense, using the example of impossible-to-detect gremlins in the engine of your car - but here he seems to be more saying the obvious claim that we need evidence to verify hypotheses, not that unverifiable = nonsense.
In any case, Dennett's definitely one of the biggest philosophers still writing today who inherited the positivist tradition, and if we can still use the term I'd say he's one of the most positivist philosophers alive.
Hi there! I love how organised your lists are. I might have to take a leaf out of your book because I'm entirely too disorganised. Annoyingly I have to have a separate Amazon UK wishlist for Blu-Rays because I'm in Australia and the US site has DVD/BRs for the wrong region.
The Origin of Consciousness in the Breakdown of the Bicameral Mind is a fascinating read about how it might have come about. I recently finished reading Consciousness Explained. It was kind of long but also interesting.
Read naturalist explanations of decision-making, the image of the self, how thoughts work, qualia, etc. You probably want to start with I am a Strange Loop, then Consciousness Explained, and work your way to Godel Escher Bach. There are also many essays online about the non-supernatural nature of the mind, this one being one that atheist Redditors link to often. Also see Wikipedia articles about the mind, free will, etc.
Even after I became an atheist, I could not shake the feeling that consciousness could not be just patterns of atoms. Even in a universe that follows rules and that was not deliberately created as part of a plan, I thought that maybe there's some kind of "soul stuff" that interacts with our brains and is responsible for consciousness. But then, if I can tell that I am conscious, then 1) the soul stuff impacts the natural world and is thus observable and not supernatural, and 2) I am no different from a computer that understands itself well enough to say it is conscious. (It helped me to think of AIs from fiction, like HAL and Data, and try to think of what it would be "like" to be them. Books like The Mind's I are full of such thought experiments). So after thinking about it for a while, I was able to shed that last and most persistent bit of supernaturalism and embrace the naturalistic view of the mind.
I love science books. These are all on my bookshelf/around my apt. They aren't all chemistry, but they appeal to my science senses:
I got a coffee table book once as a gift. It's Theodore Gray's The Elements. It's beautiful, but like I said, more of a coffee table book. It's got a ton of very cool info about each atom though.
I tried The Immortal Life of Henrieta Lacks, which is all about the people and family behind HeLa cells. That was a big hit, but I didn't care for it.
I liked The Emperor of all Maladies which took a long time to read, but was super cool. It's essentially a biography of cancer. (Actually I think that's it's subtitle)
The Wizard of Quarks and Alice in Quantumland are both super cute allegories relating to partical physics and quantum physics respectively. I liked them both, though they felt low-level, tying them to high-level physics resulted in a fun read.
Unscientific America I bought on a whim and didn't really enjoy since it wasn't science enough.
The Ghost Map was a suuuper fun read about Cholera. I love reading about mass-epidemics and plague.
The Bell that Rings Light, In Search of Schrödinger's Cat, Schrödinger's Kittens, The Fabric of the Cosmos and Beyond the God Particle are all pleasure reading books that are really primers on Quantum.
I also tend to like anything by Mary Roach, which isn't necessarily chemistry or science, but is amusing and feels informative. I started with Stiff but she has a few others that I also enjoyed.
Have fun!
The Fabric of the Cosmos by Brian Greene. http://www.amazon.com/Fabric-Cosmos-Space-Texture-Reality/dp/0375727205/ref=ntt_at_ep_dpi_2
Woo!
Friendly info:
"College Algebra" = Elementary Algebra.
College Level Algebra = Abstract Algebra.
Example: Undergrad Algebra book.
Example: Graduate Algebra book.
If you can read through gallian's book, I consider dummit and foote's book (http://www.amazon.com/Abstract-Algebra-3rd-David-Dummit/dp/0471433349) as the best math textbook i've ever read. tons of examples, thorough treatment of material, and tons of exercises.
There's no single book that's right for everyone: a suitable book will depend upon (1) your current background, (2) the material you want to study, (3) the level at which you want to study it (e.g., undergraduate- versus graduate-level), and (4) the "flavor" of book you prefer, so to speak. (E.g., do you want lots of worked-out examples? Plenty of exercises? Something which will be useful as a reference book later on?)
That said, here's a preliminary list of titles, many of which inevitably get recommended for requests like yours:
Good luck finding something useful!
I am a master's student with interests in algebraic geometry and number theory. And I have a good collection of textbooks on various topics in these two fields. Also, as part of my undergraduate curriculum, I learnt abstract algebra from the books by Dummit-Foote, Hoffman-Kunze, Atiyah-MacDonald and James-Liebeck; analysis from the books by Bartle-Sherbert, Simmons, Conway, Bollobás and Stein-Shakarchi; topology from the books by Munkres and Hatcher; and discrete mathematics from the books by Brualdi and Clark-Holton. I also had basic courses in differential geometry and multivariable calculus but no particular textbook was followed. (Please note that none of the above-mentioned textbooks was read from cover to cover).
As you can see, I didn't learn much geometry during my past 4 years of undergraduate mathematics. In high school, I learnt a good amount of Euclidean geometry but after coming to university geometry appears very mystical to me. I keep hearing terms like hyperbolic/spherical geometry, projective geometry, differential geometry, Riemannian manifold etc. and have read general maths books on them, like the books by Hartshorne, Ueno-Shiga-Morita-Sunada and Thorpe.
I will be grateful if you could suggest a series of books on geometry (like Stein-Shakarchi's Princeton Lectures in Analysis) or a book discussing various flavours of geometry (like Dummit-Foote for algbera). I am aware that Coxeter has written a series of textbooks in geometry, and I have read Geometry Revisited in high school (which I enjoyed). If these are the ideal textbooks, then where to start? Also, what about the geometry books by Hilbert?
If you are enjoying your Calc 3 book, I highly recommend reading Topology, which provides the foundations of analysis and calculus. Two other books I would highly recommend to you would be Abstract Algebra and Introduction to Algorithms, though I suspect you're well aware of the latter.
Dummit and Foote's Abstract Algebra is an excellent book for the algebra side of things. It can be a little dense, but it's chock full of examples and is very thorough.
To help get through the first ten or so chapters, Charles Pinter's A Book of Abstract Algebra is an incredible resource. It does wonders for building up an intuition behind algebra.
Before the Princeton Companion to Mathematics, there were:
What Is Mathematics? by Courant and Robbins
Mathematics: Its Content, Methods and Meaning by Aleksandrov, Kolmogorov, and Lavrent'ev
Concepts of Modern Mathematics by Ian Stewart
Mathematics - Its Content, Methods and Meaning gives you an overview of the major topics covered in university Math curriculum.
Recentemente estive procurando algo interessante pra ler e me deparei com várias recomendações do livro How to solve it: A New Aspect of Mathematical Method.
Um livro extremamente denso mas com muito conteúdo é o Mathematics: Its Content, Methods and Meaning. Comecei a ler esse livro, mas outras atividades me fizeram dar uma pausa. Vou tentar voltar a ele e colocar como meta terminar antes de 2020 rs.
Já li alguns livros explicando a origem dos números. Mas, de todos que li, Os números é imbatível.
Check out:
If you only want one math book, SO said this is it: Mathematics
For those interested in the "abstractness" of non-natural numbers, there's a phenomenal brief introduction in one of my favorite math texts, Mathematics: Its content, methods and meaning. A cold war Russian standard that covers a helluva lot of ground in applied math.
They make the point that the number "1" seems pretty intuitive to humans... you can have "1" of something, or "2" of something. But having "0" of something doesn't really make any sense, and for a long time it was argued whether or not "0" was even a "number". You certainly can't have "1/2" of a thing. If you cut an object in half, you just have 2 things now. And to have negative something is just absurd. There's a blurb about some primitive isolated tribes that have words for the number "1", "2", and "many". The number 1,237,298 is still pretty abstract to a human, because it's not like you can count that or really visualize that many things, but we acknowledge such a quantity can be useful.
Κατ' αρχάς συγχαρητήρια και καλή αρχή. Έχεις επιλέξει φοβερά ενδιαφέρον πεδίο κατά τη γνώμη μου και ζηλεύω λίγο :P
Ήθελα κι εγώ να μάθω σωστά μαθηματικά κάποια περίοδο και είχα ψάξει σε φόρουμ για κάποιο προτεινόμενο βιβλίο που να είναι ολοκληρωμένο και εύκολα κατανοητό. Ήταν πολλοί που πρότειναν αυτό το βιβλίο: https://www.amazon.com/dp/0486409163/?coliid=IFD6IMMG22STW&colid=3J1YAUNLTYQCX&psc=0&ref_=lv_ov_lig_dp_it
Δυστυχώς τελικά δε το αγόρασα επειδή δεν είχα χρόνο να αφιερώσω αλλά τα σχόλια που διάβασα με είχαν πείσει. Ίσως σε βοηθήσει.
Are you thinking of this one?
Mathematics: its Content, Methods, and Meaning by Alexandrov, Kolomogrov, and Lavrent'ev.
Mathematics for the Nonmathematician (very cheap atm - $3.99 )
https://www.amazon.com/Mathematics-Nonmathematician-Morris-Kline/dp/0486248232/ref=sr_1_1?ie=UTF8&amp;qid=1522215994&amp;sr=8-1&amp;keywords=Mathematics+for+the+Nonmathematician
If you get hooked on math later, consider "Mathematics: Its Content, Methods and Meaning (3 Volumes in One)".
https://www.amazon.com/Mathematics-Content-Methods-Meaning-Volumes/dp/0486409163/ref=sr_1_1?ie=UTF8&amp;qid=1522216524&amp;sr=8-1&amp;keywords=kolmogorov+mathematics
or the Princeton companion to mathematics - https://press.princeton.edu/titles/8350.html
Cool youtube channels:
3blue1brown
PBS Infinite Series
patrickJMT
Welch Labs
For your situation I would highly recommend Mathematics: Its Content, Methods and Meaning, which is ~1000 page survey of mathematics topics.
I would also highly suggest the 3 volume set, Mathematical Thought from Ancient to Modern Times by Morris Kline. I'm not finding the words for why I think anyone, but particularly teachers, to have a historical context for mathematics, but I strongly believe it.
It also helps to read about what sort of problems people were interested in when they came up with things such as groups, or sqrt(-1), etc.
Another book that you wouldn't use in a class: "Mathematics: Its Content, Meaning, and Methods"
http://www.amazon.com/Mathematics-Content-Methods-Meaning-Dover/dp/0486409163
For ODEs, I'd seriously suggest buying this. Lots and lots of exercises, and full solutions. Plus, at $15, it hopefully won't break the bank too badly.
this one
i used this book, the one that was required for the class sucked, this one is much better and it's super cheap. Also, answers and steps are included in the sections, so you can actually check if you're doing it correctly or not.
I've never really used MIT OCW however I've used Paul's OMN a lot back when I was studying multivar calc. I do recommend books, though. I have books both on multivar calc and differential equations and they're both well, however, I've moved on from calculus (that is, I don't actively study it anymore) so I can't really say much more.
The books I have:
> https://www.amazon.com/Multivariable-Calculus-Clark-Bray/dp/1482550741/ref=sr_1_3?s=books&amp;ie=UTF8&amp;qid=1500976188&amp;sr=1-3&amp;keywords=multivariable+calculus
> https://www.amazon.com/Ordinary-Differential-Equations-Dover-Mathematics/dp/0486649407/ref=sr_1_1?s=books&amp;ie=UTF8&amp;qid=1500976233&amp;sr=1-1&amp;keywords=differential+equations
There seems to often be this sort of tragedy of the commons with the elementary courses in mathematics. Basically the issue is that the subject has too much utility. Be assured that it is very rich in mathematical aesthetic, but courses, specifically those aimed at teaching tools to people who are not in the field, tend to lose that charm. It is quite a shame that it's not taught with all the beautiful geometric interpretations that underlie the theory.
As far as texts, if you like physics, I can not recommend highly enough this book by Lanczos. On the surface it's about classical mechanics(some physics background will be needed), but at its heart it's a course on dynamical systems, Diff EQs, and variational principles. The nice thing about the physics perspective is that you're almost always working with a physically interpretable picture in mind. That is, when you are trying to describe the motion of a physical system, you can always visualize that system in your mind's eye (at least in classical mechanics).
I've also read through some of this book and found it to be very well written. It's highly regarded, and from what I read it did a very good job touching on the stuff that's normally brushed over. But it is a long read for sure.
Ordinary Differential Equations by Tenenbaum and Pollard is a classic. I thought it explained things well and was more rigorous than some other treatments of subject that I've come across.
15! Well then, you have plenty of time to figure this out. Well, a few years, in any case.
I think what you should do is learn some programming as soon as possible (assuming you don't already). It's easy, trust me. Start with C, C++, Python or Java. Personally, I started with C, so I'll give you the tutorials I learned from: http://www.cprogramming.com/tutorial/c/lesson1.html
You should also try out some electronics. There's too much theory for me to really explain here, but try and maybe get a starter's kit with a book of tutorials on basic electronics. Then, move onto some more complicated projects. It wouldn't hurt to look into some circuit theory.
For mechanical, well... that one is kind of hard to get practical experience for on a budget, but you can still try and learn some of the theory behind it. Start with learning some dynamics and then move onto statics. Once you've got that down, try learning about the structure and property of materials and then go to solid mechanics and machine design. There's a lot more to mechanical engineering than that, but that's a good starting point.
There's also, of course, chemical engineering, civil engineering, industrial engineering, aerospace engineering, etc, etc... but the main ones I know about are mechanical (what I'm currently studying), electrical and computer.
Hope this helped. I wasn't trying to dissuade you from pursuing engineering, but instead I'm just forewarning you that a lot of people go into it with almost no actual engineering skills and well, they tend to do poorly. If you start picking up some skills now, years before college, you'll do great.
EDIT: Also, try learning some math! It would help a lot to have some experience with linear algebra, calculus and differential equations. This book should help.
http://www.amazon.com/Ordinary-Differential-Equations-Dover-Mathematics/dp/0486649407/ref=mt_paperback?_encoding=UTF8&amp;me=
Stay away from Youtube and Khan Academy unless you need reinforcement on a specific topic. Go through this book, page by page, learn the material, and do every problem.
I've used Tenenbaum to teach myself ODEs. Got an A in my class. Arnold is cannon, but you need mathematical maturity so YMMV.
The one and only , if you're willing to dedicate the time
Ordinary Differential Equations (Dover Books on Mathematics)
https://www.amazon.com/dp/0486649407/
FYI, Jaynes actually wrote a whole probability textbook that essentially put together all his thoughts about probability theory. I haven't read it, but many people say it got some good stuff.
Depends what your goal is. As you have a good background, I would not suggest any stats book or deep learning. First, read trough Probability theory - The logic of science and the go for Bishop's Pattern Recognition or Barbers's Bayesian Reasoning and ML. If you understand the first and one of the second books, I think you are ready for anything.
If you want a math book with that perspective, I'd recommend E.T. Jaynes "Probability Theory: The Logic of Science" he devolves into quite a lot of discussions about that topic.
If you want a popular science book on the subject, try "The Theory That Would Not Die".
Bayesian statistics has, in my opinion, been the force that has attempted to reverse this particular historical trend. However, that viewpoint is unlikely to be shared by all in this area. So take my viewpoint with a grain of salt.
You may also enjoy Probability Theory: The Logic of Science by E.T. Jaynes, and Information Theory, Inference and Learning Algorithms by David McKay.
Probability Theory: The Logic of Science
Probability Theory: The Logic of Science. This is an online pdf, possibly of an older version of the book. Science covers knowledge of the natural world, and mathematics and logic covers knowledge of formal systems.
I've heard good things about (but have not read) Probability, the logic of science.
A complete table of contents + the first 3 chapters are available here. This should tell you if it covers the appropriate material and if the explanations are to your satisfaction.
Well if you have the time, there's The Greatest Show on Earth: The Evidence for Evolution by Richard Dawkins and Why Evolution Is True by Jerry A. Coyne. You could check if your local library has one of them.
Also, although this will not teach you evolution, Richard Dawkins notes a flaw in the idea of a designer in that there are clear imperfections that one would not expect from an intelligent designer, but would from evolution.
If she will read a book for this and evolution is a big sticking-point, then actually maybe The God Delusion isn't the best Dawkins for the job.
I'd suggest Climbing Mount Improbable, or The Blind Watchmaker. Surprisingly I don't think The Greatest Show on Earth is the best to start with.
Or, This one :http://www.amazon.com/Why-Evolution-True-Jerry-Coyne/dp/0670020532
>Not familiar as I probably ought to be. I know that there were other homo species -possibly at the same time as humans. I think I heard something about interbreeding at some point, but maybe that was just speculation?
To be honest, I'm not exactly an expert on the specifics. However, Wikipedia provides as always - If the article and the numerous citations are to be believed, they're considered separate species as mitochondria genetic data (that I could explain further if you like) shows little significant breeding. However, there is indeed some evidence of limited interbreeding.
>This is fascinating stuff!
I'm glad you like it!
>To clarify: do all the primates share the same mutation which is different from the mutation in other creatures, ex. guinea pigs?'
Precisely! Mind you, I believe there are a few changes which have accumulated since divergence (since if they don't need the gene once it's "off", further mutations won't be selected against), but the crucial changes are indeed the same within primates - and those within guinea pigs are the same within guinea pigs and their nearby relatives (I believe), but different from those from simians. Amusingly, because mutations occur at a generally steady rate, the number of further divergences between the pseudogenes (no-longer-functional genes which resemble working copies in other organisms) in different species will give hints at how long ago those species had a common ancestor (this, and related calculations, are termed the "genetic clock").
Nifty, isn't it?
>I guess I don't see why it would be demeaning to be patterned after other homo species which were adapted to the environment we would inhabit. Maybe I'm way off here, but it seems like the case for common ancestry could also point to a common creator. (obviously it is outside the bounds of science to consider that possibility, but philosophically, it might have merit?)
I have indeed heard that before; the suggestion of a common creator as opposed to common descent is a fairly common suggestion, pardon the pun. The typical arguments against fall first to traits which can be considered "poor design" in pure engineering terms, even if they're traits that are now needed. I can point to the genetic baggage of the human eye compared to that of the cephelopod (nerve fibers over vs. under the retina), or the human back (not great for walking upright), or further traits along those lines which suggest that we're still closer to our origins. Indeed, we can also look at things like the pseudogene involved with vitamin C above as unnecessary addons; genetic artifacts which hint at our descent.
While this additional argument, I will grant, is better at addressing general creation then special human creation, we can also look at repeated motifs. For example, the same bones that form our hand also form a bird's wing, a whale's flipper, a dog's paw, a horse's hoof, and all the other mammalian, reptile, and avian forelimbs - though sometimes you need to go to the embryo before you see the similarity. When taken alone, that may suggest either evolution or design; it would make sense for a creator to reuse traits. It becomes more stark when you consider examples that should be similar - for example, the wings of the bat, bird, and pterodactyl, despite using the same bones, have vastly different structures, despite all being used for the same purpose (that is, flight).
The way that my evolutionary biology professor phrased this is that "design can explain this, but cannot predict it; evolution both explains and predicts." This idea - that natural observations may be explained or excused (begging your pardon) in a creation model, but are what are expected from an evolutionary model - is the major point I wish to make in this regard. And, I shall admit, perhaps as close as I can get to "disproving" special creation; it tends to approach unfalsifiability, if I understand it correctly.
>If I recall correctly, this is the position of Francis Collins / BioLogos. It's possible, but I have a few concerns. The first being that I think animals do have souls. If that's correct, ensoulment doesn't help make sense of the theology.
Yup; ensoulment as special is less compatible in that case.
>It would also mean that (at least at some point) there were other creatures who were genetically equal to human beings, but didn't have souls. Cue slave trade and nazi propaganda -they're human, but they aren't people. It would have been possible (probable?) that ensouled humans would breed with the soulless humans -and that just seems . . . squicky.
Point taken; even if you were to claim ensoulment for all humans existing at a specific point and thereafter, there can be...negative connotations.
>So, for now, it's a possibility, but it seems to be more problematic than special creation.
To be perfectly frank, I'm not really equipped to argue otherwise. As an atheist, my tendency is to end up arguing against ensoulment, as it's not something we can really draw a line at either. Still, I figured I'd put it out there; I'm a little delighted at your dissection of it honestly, as you brought up things I'd not yet considered.
>Like I said, the genetics is fascinating, and I am naive to much of it. Short of becoming a geneticist, could you recommend a good book on the subject of human genetics and common descent? I took basic genetics in college, so I was able to follow the discussion about chromosomes, telomeres, etc. But I would like to know more about the discoveries that have been made.
Oooh, that's a rough question. Don't get me wrong, it's a wonderful question, but I rarely read books aimed at laymen dealing with my specialty; most of my information comes from text books, papers, and profs, if you take my meaning. Which in the end is a way for me to provide my disclaimer: I can provide recommendations, but I've generally not read them myself; sorry.
Having said that, I'm not about to discourage your curiosity - indeed, I cannot laud it highly enough! - and so I shall do what I can:
I think I'll hold off there for the moment. The latter two are focused more on humans, while the former is about evolution in general. I'm sure there are more books I could recommend - Dawkin's The Greatest Show on Earth has been lauded, for example. I tried to stick with texts which were at a slightly higher level, not merely addressing the basics but delving a little deeper, as you noted you have a measure of familiarity already, and those which were related to humans. I hope they help!
It's not an alternative to books, but Wikipedia does have a fair article on the topic (which I linked near the very top as well). And believe it or not, I do enjoy this sort of thing; you are more then welcome to ask more questions if and when they occur to you.
Or if you want correct answers:
http://www.amazon.com/Why-Evolution-True-Jerry-Coyne/dp/0670020532
which handily demolishes this creationist nonsense over and over.
(This is the rest of my answer, cut off for being too long).
3) I'm beginning to think that we need to skip ahead and talk about evolution, because if you don't understand how DNA could have evolved, you've really never read a single book on evolution. (I'm not criticizing you; you're in good company there). So let's combine your third and fourth points, and allow me to clarify what evolution is, why it explains DNA, and why your micro/macro distinction is, frankly, bullshit.
First principle behind evolution: If something can make copies of itself, there will soon be more of it. It there are lots of competing things that can make copies of themselves, the ones that can do so most efficiently will end up having the most copies.
If that statement strikes you as true, there we go. Evolution.
The first proto-organisms were basically strings of RNA. Under certain conditions, a nucleotide strand would attach complementary bases, and you would have two strands of RNA. Then environmental conditions change and the two strands separate, and both of them can attach to more complementary bases.
Second principle behind evolution: If copies aren't exactly the same as the original, then some changes will increase efficiency. Other changes will decrease efficiency. After enough generations, your population will contain lots of copies of efficient replicators and very few copies of inefficient replicators.
So some of the RNA sequences happen to misplace an adenine instead of a cytosine, and that means that a replication enzyme bonds more tightly to the strand, and this mutant makes more copies of itself than its neighbors do.
And eventually, a nucleotide ends up with a deoxyribose sugar instead of a ribose sugar, and this configuration turns out to be WAY more stable - it can form into a double helix that is less likley to spontaneously collapse, and which can replicate with fewer errors. And this mutant makes more copies of itself than its neighbors do.
And these sequences of DNA/RNA aren't just random collections of letters. Well, some of them are, but others can be interpreted to build proteins that facilitate copying - and the ones with these helpful sequences can make more copies of themselves.
Let this process happen for a couple billion years.
But, you're saying, the probability is so small! You mean all those coincidences just happen to occur? Convenient mutations just happen to come along? If you multpily together the odds of all those things happening, it's tiny!
Well, of course it is. When you have a trillion early replicators hanging around, improbable things happen ALL. THE. TIME. And multiplying together the odds of each mutation is the completely wrong way to look at the problem - it's like looking at all the possible combinations of your parents' sperm and eggs that could have existed and declaring triumphantly that the probability of you existing is one in a gazillion. Of course it is! The question is what the probability of some complex life developing, under the given optimization pressures, and it should be obvious that it's reasonably high. Of those trillions of worlds we talked about earlier, maybe only a couple billion of them got to complex life.
Obviously, this is the grossly oversimplified version. For the whole story, you need to read this or this or this or this or... any of these, actually. But I hope you understand why most atheists feel that the distinction between macro- and micro-evolution is silly. Evolution is just the change in gene pools over time. This change has been observed to lead to one species splitting off into multiple species which can no longer reproduce (the biological definition of speciation). At what point is this process called "macro" evolution? How many genes need to change before you insist that the process "doesn't exist"? Why would evolution push two separate populations to the brink of speciation and then suddenly stop working by the rules we've repeatedly observed? Saying "micro but not macro" is like saying you believe gravity works on people but not on planets. There's just no reason to draw the distinction!
Using techniques called molecular systematics, we can trace the evolutionary relationships between species by mapping the differences in noncoding DNA. And, of course, I'm neglecting the single biggest piece of supporting evidence for evolution: the fossil record. You've probably been fed the lie that we don't have the transitional fossils. Well, we do have the transitional fossils. Overwhelmingly..
Now, ethics. The God of the Bible, if he existed, is a monstrous, selfish, egomaniacal, power-hungry terrifying sociopath. I don't mean to cause offense (though I probably will) but I read the Bible and it nearly made me ill. God tortures everyone who doesn't worship him for all eternity. He had 42 children mauled to death by bears for laughing at a bald man.(II Kings 2:23-24). He murders all the inhabitants of an entire city for being "sinful" (Genesis 19:1-26). He orders his people to commit genocide, over and over again. (Deuteronomy 13:13-16, Numbers 31:12-18, I Chronicles 21:9-14).
He's okay with rape (often, he explicitly orders his followers to commit rape) and treats women as property(Deuteronomy 22:28-29, Deuteronomy 22:23-24, Exodus 21:7-11). He's pro-slavery (I Timothy 6:1-2, Exodus 21:20.) He even claims in Isaiah 45:7 to have created all evil. In short, if we're getting our morals from that guy, we're seriously screwed. This isn't the wise and loving father whose children can't understand his dictates: it's the abusive alcoholic father whose son runs away when he realizes that rape, murder, and incest aren't okay just because Dad says so.
You're about to protest that most of those are Old Testament. But Jesus explicitly endorses the Old Testament and says that he has not come to change the old laws (Matthew 5:17). He endorses what God did in Sodom and Gomorrah and threatens to do even worse to three more cities because their inhabitants were unimpressed with him.(Matthew 11:21-24). He says that any child who curses his parents should be killed as according to Old Testament Law. (Mark 7:10)
I don't think a world where everyone follows their individual conscience could possibly be worse than a world rules by that God. And, in fact, countries that are nonreligious have lower rates of crime, higher standards of living, and higher self-reported happiness.
Interesting debate, thanks!
When it comes to understanding evolution, Why Evolution is True is a very entertaining, easily read introduction. I would also recommend The End of Faith by Sam Harris.
You can get by without enrolling in upper-level courses. There is some great free coursework out there if you want to go that route without paying money. Otherwise there are great introductory texts on the subject, like Why Evolution is True.
Here is a good book for Christians on evolution. It was recommended by Dawkins once for people that didn't like him and would never read his own books.
http://www.amazon.com/Finding-Darwins-God-Scientists-Evolution/dp/0060930497
The author (Miller) is Roman Catholic, and also has several other good books on the topic if you look at the author's page on amazon.
This one by a different author is also very good.
http://www.amazon.com/Why-Evolution-True-Jerry-Coyne/dp/0670020532/ref=pd_bxgy_b_img_b
If you'd like the basics online, here:
http://evolution.berkeley.edu/evolibrary/search/topicbrowse2.php?topic_id=46
Looking on their website it seems as if they do not let outside people borrow from their library, sorry :(.
I know many libraries have "partnerships" for the lack of a better word, where if you try to borrow a book from the library, and they don't have it, they will request it from somewhere else they are partnered with and get it for you.
Some ideas of books:
For my undergraduate astrophysics class I used - Foundations of Astrophysics by Ryden and Peterson, ISBN13: 978-0-321-59558-4
I have also used (more advanced, graduate level) - An Introduction to Modern Astrophysics by Carroll and Ostlie, ISBN13: 978-0-805-30402-2
There are plenty of other undergraduate text books for astrophysics, but those are the only two I have experience with.
Some other books that may be just fun reads and aren't text books:
A Brief History of Time - Hawking
QED: The Strange Theory of Light and Matter - Feynman
Random popular science books:
Parallel Worlds - Kaku (or anything else by him Michio Kaku)
Cosmos - Sagan
Dark Cosmos - Hooper
or anything by Green, Krauss, Tyson, etc.
Videos to watch:
I would also suggest, if you have an hour to burn, watching this video by Lawrence Krauss. I watched it early on in my physics career and loved it, check it out:
Lawrence Krauss - A Universe From Nothing
Also this video is some what related:
Sean Carroll - Origin of the Universe and the Arrow of Time
Hope you enjoy!
Edit: Formatting.
He did, sort of, in his book :)
http://www.amazon.com/QED-Strange-Theory-Light-Matter/dp/0691024170
Also, someone else mentioned Feynman's book, called QED. It's a great read.
Yes, it's an approximation. This is evidenced by effects like the Lamb shift that cannot be explained with classical electrodynamics (e.g. Coulomb's law). One way of putting quantum electrodynamics (QED) is that two charged particles "communicate" with each other by exchanging photons, "telling" each other whether to come closer or farther apart, and by how much. If you're curious, I suggest reading Feynman's layman explanation.
That the universe is governed by rules does not imply that it is determinate. If you think nature is determinate, I suggest you study some quantum mechanics. This book and these lectures on which it is based are great starting points.
I'm just glad I could help. I would recommend for you the book QED: The Strange Theory of Light and Matter, which is a transcription of four lectures by Richard Feynman.
If you don't know who Richard Feynman is, he's one of the people who won a Nobel prize for the formulation of Quantum Electrodynamics (the interaction of photons with charged particles like electrons). But more importantly than that, Feynman was EXCELLENT at talking about science in a manner that laypeople can understand, without actually dumbing down the material. These lectures explain QED in straightforward English. I strongly recommend it, it's definitely worth the $12. Hopefully this book will be a jumping-off point to further learning for you (as it was for me). Enjoy!
Get this book, I think you would enjoy it and it would probably answer most (if not all) of your questions.
At a certain point you have to just accept that electricity behaves the way it does, just because it does. A lot of the way we talk about electricity is convention, or it makes general assumptions about the way electricity behaves that in most cases are well-founded, so you can get away with them. If you really start to dig, stuff can get weird.
If you want a glimpse of how strange reality can get, read this. It is not directly about electrons but it talks about light so there are some similarities. Plus Feynman is a great author.
These reality branches can add together, or even cancel out. This effects the probability of certain events occurring, which can be tested by repeating experiments.
I would try to explain it further, but I am sure I'll mess it up. I recommend QED, which is surprisingly easy to read.
Not something I consult regularly, or really ever, but one text that I actually enjoyed immensely while reading is Nonlinear Dynamics and Chaos by Steven H. Strogatz.
EDIT: I just discovered he has two other books that aren't quite texts, and one is semi-autobiographical with an element of calculus - sounds a lot like my favorite playwright, Tom Stoppard. I know what I'm buying myself for Christmas.
Yes it's a really fascinating subject! I'm doing my PhD in oceanography and work with climate simulations. Of course the climate system is quite chaotic, so the whole subject piqued my interest.
I'm fortunate that I'm taking a class in 'chaotic dynamics' currently on campus. We actually just spent a few weeks with the logistic map equation, cobweb diagrams, etc. so this was good timing.
Here's a good MOOC with videos that you'll learn a lot from: https://www.complexityexplorer.org/courses/79-nonlinear-dynamics-mathematical-and-computational-approaches-fall-2017/segments/6202?summary
Our course textbook is Strogatz's book on chaos which is a great resource: https://www.amazon.com/Nonlinear-Dynamics-Chaos-Applications-Nonlinearity/dp/0738204536 . I believe he also has a lectures series out on Youtube.
If you would like to look at something a bit more applied then there is nothing better than Strogratz
I made a comment in a another thread.
I second /u/ProfThrowawary17's recommendation for Strogatz and also suggest the undergrad text Hale and Kocak. Strogatz is a rare text that delivers both interesting math and well-motivated applications in a fairly accessible manner. I have not systematically read Hale and Kocak, but it also seems to provide a gentle yet rigorous introduction to ODE's from the modern dynamical systems point of view.
Like /u/dogdiarrhea, I also recommend the graduate text Hale. If you have a strong analysis background, working through Hale would be quite worthwhile. It's also a Dover publication! So if Hale doesn't work out for you in a first time reading, it would still be a useful reference later on.
If you want to get into the nitty gritty of it, look to computational modeling of nonlinear systems, specifically the navier-stokes equations and the 4th order runge-kutta method.
Of course that requires a bunch of math and bit of programming. If you're up for it this is an excellent starting point: https://www.amazon.com/Nonlinear-Dynamics-Chaos-Applications-Nonlinearity/dp/0738204536
Yes! Dynamical Systems is awesome...Strogatz wrote one of the best math textbooks I've read, hopefully you'll be using it.
I'd recommend Nonlinear Dynamics and Chaos by Strogatz ( amzn.to/2PEFnvX <--That's an affiliate link that helps support the blog )
https://www.amazon.com/Psilocybin-Mushrooms-World-Identification-Guide/dp/0898158397/ref=asc_df_0898158397/?tag=hyprod-20&amp;linkCode=df0&amp;hvadid=312090128349&amp;hvpos=1o1&amp;hvnetw=g&amp;hvrand=12340258693395792528&amp;hvpone=&amp;hvptwo=&amp;hvqmt=&amp;hvdev=m&amp;hvdvcmdl=&amp;hvlocint=&amp;hvlocphy=9008532&amp;hvtargid=pla-331923859582&amp;psc=1
I have a book, Psilocybin Mushrooms of The World, and in it there's a pic of this woman with a wide brimmed hat that has spore prints all around it. She walks around town spreading billions of spores without a care in the world. I love that kind of initiative.
EDIT: Found it!
First find out if they grow where you live. Then start by "acquiring" books such as this one:
https://www.amazon.com/Psilocybin-Mushrooms-World-Identification-Guide/dp/0898158397
Start here
And DEFINITELY buy other identification guides to cross-reference. Forest-hunting isn't particularly lucrative for psychedelics. Be very careful and deliberate with anything you find, because there are quite a few species (in the fields and forests) that are similar to psilocybin species, but dangerous.
https://www.amazon.com/Psilocybin-Mushrooms-World-Identification-Guide/dp/0898158397
The Republican Brain
As a brief matter of convention, I like that definition of indoctrination and it is functionally very close to the way I intended to use the word in my previous post.
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> Yes ... They have not given up.
All scientific inquiry is driven by a lack of knowledge of a subject that is suspected to be adjacent to either known information or theorized information. Everything beyond that adjacency is speculation and unscientific.
That process can be thought of as the scientist's puzzle drive. To translate your statement into these terms, you're saying an agnostic who claims unknowability can't possibly have a puzzle-drive. This is incorrect.
The agnostics puzzle drive is just one level abstract from the scientist's puzzle drive. The agnostic could be driven by a presumed lack of knowability of a subject that is adjacent to either verifiable evidence or epistemological theory. Everything beyond that adjacency is absurdity and gnostic.
>Well, intensity is a feature of all education ... to attend a regimen of Sunday School and so forth.
>Ideally, we humans would be presented with a proposition ... more likely he is to be persuaded.
That is a lot of discussable/disputable information, but since I agree with most of it, I suggest we save it for a different conversation. Very interesting stuff.
> (1) the relatively automatic filtration by cognitive bias ("your GF is cheating on you." "Impossible! She's much too pretty to cheat on me!") based on previously known information
> (1), and they get better at it as they gather more reference material.
This is called motivated reasoning and it models and predicts the smart idiot^Mooney effect very well. I would definitely be an audience to the argument that there is some overlap with critical thinking (in practice).
> Aside from religion, they become poor marks for conspiracy theories, magical cures, horoscopes, ghost sightings and so on
Again -- have you seen the way popular media co-opts skeptical language to these ends!? Ghost Hunters, popular conspiracy theories etc... these groups draw power from ridiculing religion just like we do. If it's a religious thing, the anecdotal precedence is not readily available to me, and I would feel more comfortable deferring to topical data.
I agree, teaching actual critical thinking skills is vital, but I'm not so sure (read: convinced) the lack of critical thinking skills offers a significant in-religious correlation when you adjust for population. Maybe the subtext here is people are fucking stupid, but I'd rather make that as a global claim than a religious claim. /rant (sorry.)
> Err no, that's most likely type (1) processing, it's more cognitive bias than "real" critical thinking.
I don't completely disagree, but I've got several different models of this to compare it to, so I'm going to challenge it. Can you demonstrate this? What are you thinking of?
Also there's something I call the chaos theory of religious world-view which basically holds the following:
Let me know if you're interested in hearing about that.
> In science education, at least as far as through grade school, any claim can usually be supported, if questioned, by referring to and explaining the historic experiments by which it was arrived at.
But, practically these is superficial regress. You explain the experiments but if the explanation is questioned you can only fall back on the concept. If the concept is rejected, the instructor can't really be expected to demonstrate further. The model still supports fabrication, it just shifts it. Can we demonstrate that it shifts it to a point where fabrication is too difficult? (Maybe... I would argue this is the importance of peer review and try to demonstrate it's relevance.) Your thoughts?
The rest of that paragraph I readily agree with (even if your terms are usually far more graphic than I would use).
> After being made to swallow that the Bible is God's word and therefore necessarily true (that establishes its authority once and for a long time), pretty much the first lesson is "questioning is inappropriate in a religious context."
Again -- this assumes a certain type of Christianity. The kind that is employing this method of inculcating. There are two things here, a cautionary message and a disagreement.
(1) If the religious group was not doing this, then you would need to move goal posts to re-establish their badness or look elsewhere. Don't do that.
(2) The religious groups who aren't doing this are probably not doing this for a reason! Could there be any reasons you would agree with? As a call back to the original discussion, wouldn't that make them sort of viable candidates to being on your side?
> I don't have good backup material for the claim that critical questioning is discouraged in Sunday School. If you have a problem with that claim, I'll have to retract it.
No, it can stay. Just as a matter of contingency, imagine if that factor was removed -- so too would your problem with sunday school. I never get too bent out of shape over contingent conclusions because somewhere, somehow, they won't apply and then I'll need to go back to the drawing board.
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Mooney:
> But it’s not just global warming where the “smart idiot” effect occurs. It also emerges on nonscientific but factually contested issues, like the claim that President Obama is a Muslim. Belief in this falsehood actually increased moreamong better-educated Republicans from 2009 to 2010 than it did among less-educated Republicans, according to research by George Washington University political scientist John Sides.
> The same effect has also been captured in relation to the myth that the healthcare reform bill empowered government “death panels.” According toresearch by Dartmouth political scientist Brendan Nyhan, Republicans who thought they knew more about the Obama healthcare plan were “paradoxically more likely to endorse the misperception than those who did not.” Well-informed Democrats were the opposite—quite certain there were no “death panels” in the bill.
Chris Mooney, The Republican Brain
> Elle a perdu parce qu'elle a été victime d'attaques incessantes contre les démocrates pendant des mois, des attaques infondées et risibles.
Non. Si c'était ça qui faisait perdre une élection aux États-Unis, Obama n'aurait jamais pu être président. Trump non-plus d'ailleurs.
> Est-ce que c'est les démocrates qui écrivent des livres intitulé
Sans dec, tu crois que les démocrates sont des anges ou bien tu viens de découvrir que la politique aux US c'est encore plus violent que chez nous ? Bien-sûr que les démocrates écrivent aussi des horreurs sur les Républicains. Comme The Republican Brain, Idiot America, après l'élection de Trump on a déjà sorti Insane Clown President, Too dumb to fail, et autres bouquins écrit parfois par des élus Démocrates et contenant des illustrations telles que des images "dépeignant les républicains comme des éléphants rouges maléfiques portant une crosstika" (mélange de croix chrétienne et de swastika)...
Si tu crois que les démocrates sont tendres avec les républicains et que seuls les républicains tapent fort sur les démocrates, tu planes à 10 000. Mais tout ça c'est pas grave, ça n'a pas vraiment d'importance : les attaques contre tel ou tel bord politique, ça ne trigger que les militants convaincus de chaque bord. Or c'est pas ceux-là qui font une élection, puisqu'ils votent à peu près toujours pareil.
Le problème des démocrates, c'est pas qu'ils ont attaqué les républicains.
C'est qu'ils ont attaqué des tas de gens qui n'étaient pas spécialement politisés et qui à vrai dire auraient pu pencher du côté démocrate, mais que les élites démocrates méprisaient profondément parce qu'ils avaient le tort de pas penser comme il faut ou de manquer d'éloquence face au titulaire d'un PhD en liberal arts, et que ces petites gens, de dépit, alors qu'ils auraient dû être défendus par les démocrates justement parce que ce sont des petites gens (ce qui ne veut pas forcément dire leur donner raison sur tout hein, mais déjà chercher à les comprendre plutôt que de les traiter de débiles et de racistes/sexistes/homophobes/xénophobes/etc. ça aurait été un bon début) sont allés se réfugier dans les bras des républicains. Qui les ont accueilli à bras ouvert parce qu'ils ont bien compris, eux, que c'était ces gens là qui allaient faire pencher l'élection d'un côté ou de l'autre. Et ça n'a pas manqué.
https://www.amazon.com/Republican-Brain-Science-Science-Reality/dp/1118094514
https://www.amazon.com/gp/aw/d/0898158397/ref=mp_s_a_1_1?ie=UTF8&amp;qid=1519918587&amp;sr=8-1&amp;pi=AC_SX236_SY340_QL65&amp;keywords=psilocybin+mushrooms+of+the+world&amp;dpPl=1&amp;dpID=51YNNfdC6bL&amp;ref=plSrch The Amazon link.
Or you might be able to get it at the libary. I’ve seen it here in WA. That might differ from state to state.
Thank me later. http://www.amazon.com/gp/aw/d/0898158397/ref=redir_mdp_mobile
Well, yes, but certain mushrooms grow in certain areas. Not sure how many woodloving mushrooms ya'll got over there in your Louisiana woods, as they're all over the Pacific North West. Could be.
I'd read up on Psilocybe mushrooms, and recommend Paul Stamets' book Psilocybin Mushrooms of the World. The important thing is not knowing about the blue bruising Psilocybes, but rather the blue bruising lookalikes which are toxic.
This is a great book about that very subject.
It's not that Republicans are mentally wrong, but they do tend to think differently than liberals in many areas. Many of those differences, while they might be useful in certain situations and contexts, are pretty awful when dealing with a modern, free society.
This one?
https://www.amazon.com/Republican-Brain-Science-Science-Reality/dp/1118094514
https://www.scribd.com/doc/114800796/Psilocybin-Mushrooms-of-North-America
https://www.amazon.com/Psilocybin-Mushrooms-World-Identification-Guide/dp/0898158397
https://www.youtube.com/playlist?list=PLbz8EvhqeMxul_huFTjigKQq8DmIUHhpJ
the first two links will give you more of a general overview of identification techniques and psychoactive mushrooms at large . the youtube playlist at the bottom depicts videos of the species that occur in massachusetts. the more research you do, the more confident you will be. especially considering this is your first hunt, make sure to clarify with experienced hunters reports online. please be extra careful my friend, and if you can’t find any locally i’m sure you can find other ways of obtaining the magic. cheers!
Agreed, but according to Chris Mooney (FWIW) conservatives are more likely to stick with their ideology despite evidence to the contrary. The Republican Brain
Hey, you. Yeah, you reading this. Don't think these LBM's (Little Brown Mushrooms) that look an awful lot like the ones growing in your yard are safe. Never, ever, EVER pick and eat mushrooms you find unless you have extensive knowledge of mycology. LBM's are notorious for being difficult to identify, as they have no real phenotypic traits (fancy way of saying that there are few visual cues as to what they are and if they're safe or not).
LBM's usually require spore prints to identify the species, and even then you need a keen eye and lots of experience to use those to identify the mushroom. There are plenty of books to help, but remember that microscopic features can be the difference between a trip and a trip to the hospital.
So, what you're telling me is that you're not biased, don't think it's possible to search for the statistics around the topic at hand, believe that everyone abuses the welfare system, yet when presented with evidence gathered by the federal agency responsible for the welfare program that contradicts your non-biased view of the matter, you dismiss it immediately as preposterous without needing to provide any counter-examples proving that it is indeed preposterous?
There's a book out I think you should read.
It cites all sorts of lovely studies. Studies that "show conservatives more likely to defend their beliefs against new evidence and highly-educated conservatives are even more prone to do so." (Kulinski is the name of the guy who ran the study, but I'm having trouble finding a link to the paper at the moment, and I have to get to work)
But nobody's trying to tell you you're not biased at all. No. I'd never tell you to your face that you're not, in fact, in possession of the truth (big T, or little t - take your pick).
edit - started on a cell phone, and the damned thing thought it was time to post half-way through my comment.
have you read this? disregard the politics it's worthwhile for the psychology.
I'm not projecting, you're just a fucking filthy liar.
The letter is a hoax. You've admitted that is doesn't exist, and yet your somehow still defending it. Here the book that really explain why you do this : http://www.amazon.com/The-Republican-Brain-Science-Science-/dp/1118094514/ref=sr_1_sc_1?ie=UTF8&amp;qid=1404233833&amp;sr=8-1-spell&amp;keywords=the+reblican+mind
Unlike your source, which is just one quake ranting about his political opponents, the author of this book pulls togther study after study after study into neroscience to present his thesis about how cognitively defective and morally deficent right wingers are. Funny enough, it's a branch of study that got started back in the 1950s as people tried to figure out how so many Germans could be made to go along with the Nazis. Turns out, 30% of the population is just evil, right wing filth that really really has a hard time confronting reality.
I just heard there is a new book out about the Republican Brain. About how differently Reps and Dems think. Sounded interesting on the radio review. It may enlighten some.
edit: ok it's due out this week. link
http://www.amazon.com/The-Republican-Brain-Science-Science/dp/1118094514
https://www.amazon.com/Republican-Brain-Science-Science-Reality/dp/1118094514
Bestselling author Chris Mooney uses cutting-edge research to explain the psychology behind why today’s Republicans reject reality—it's just part of who they are.
From climate change to evolution, the rejection of mainstream science among Republicans is growing, as is the denial of expert consensus on the economy, American history, foreign policy and much more. Why won't Republicans accept things that most experts agree on? Why are they constantly fighting against the facts?
Science writer Chris Mooney explores brain scans, polls, and psychology experiments to explain why conservatives today believe more wrong things; appear more likely than Democrats to oppose new ideas and less likely to change their beliefs in the face of new facts; and sometimes respond to compelling evidence by doubling down on their current beliefs.
Goes beyond the standard claims about ignorance or corporate malfeasance to discover the real, scientific reasons why Republicans reject the widely accepted findings of mainstream science, economics, and history—as well as many undeniable policy facts (e.g., there were no “death panels” in the health care bill).
Explains that the political parties reflect personality traits and psychological needs—with Republicans more wedded to certainty, Democrats to novelty—and this is the root of our divide over reality.
Written by the author of The Republican War on Science, which was the first and still the most influential book to look at conservative rejection of scientific evidence. But the rejection of science is just the beginning…
Certain to spark discussion and debate, The Republican Brain also promises to add to the lengthy list of persuasive scientific findings that Republicans reject and deny.
Whoa, great questions, but I think you want a textbook, not a reddit post response. I used Dummit & Foote but it is probably a bit "heavier" than what you want/need at this point.
Griffiths' Quantum Mechanics has a crash course in most of the linear algebra required to do a first course in quantum mechanics. It's not very complicated - you just need basic understanding of vector spaces, linear transformations and functionals, and inner products, with a little bit of practice using dual notation of vectors (not too much, just enough for the Dirac notation which the book explains). Griffiths' also has a good explanation of simple fourier series/transform.
The key thing is being able to do basic linear algebra without matrices since in most of the cases, the vector space is infinite dimensional. But spin is a good example where almost everything can be done with matrices.
Additionally, solving ordinary differential equations and using separation of variables for partial differential equations in 3-d quantum mechanics would help.
Group theory will be of help in more advanced classes. Dummit and Foote or Arton's books on algebra are decent introduction. They are a bit dense though. If you want a real challenge, try Lang's Algebra book. I don't know of any easier books though. My first algebra book was Dummit and Foote which can be done without any real prerequisites beyond matrix algebra, but isn't really well written.
Links to books: Griffiths, Dummit and Foote.
PS: I have ebooks of these two books in particular.
Dummit (or just D&F), Artin, [Lang] (https://www.amazon.com/Algebra-Graduate-Texts-Mathematics-Serge/dp/038795385X), [Hungerford] (https://www.amazon.com/Algebra-Graduate-Texts-Mathematics-v/dp/0387905189). The first two are undergraduate texts and the next two are graduate texts, those are the ones I've used and seen recommended, although some people suggest [Pinter] (https://www.amazon.com/Book-Abstract-Algebra-Second-Mathematics/dp/0486474178) and Aluffi. Please don't actually buy these books, you won't be able to feed yourself. There are free versions online and in many university libraries. Some of these books can get quite dry at times though. Feel free to stop by /r/learnmath whenever you have specific questions
Yes: Dummit and Foote. I used it in my freshman algebra class. It has excellent proofs and exercises. It will teach you the mathematical maturity faster than analysis and will most likely be more useful to you later on.
I'll throw out some of my favorite books from my book shelf when it comes to Computer Science, User Experience, and Mathematics - all will be essential as you begin your journey into app development:
Universal Principles of Design
Dieter Rams: As Little Design as Possible
Rework by 37signals
Clean Code
The Art of Programming
The Mythical Man-Month
The Pragmatic Programmer
Design Patterns - "Gang of Four"
Programming Language Pragmatics
Compilers - "The Dragon Book"
The Language of Mathematics
A Mathematician's Lament
The Joy of x
Mathematics: Its Content, Methods, and Meaning
Introduction to Algorithms (MIT)
If time isn't a factor, and you're not needing to steamroll into this to make money, then I'd highly encourage you to start by using a lower-level programming language like C first - or, start from the database side of things and begin learning SQL and playing around with database development.
I feel like truly understanding data structures from the lowest level is one of the most important things you can do as a budding developer.
If there is something close to an Encyclopaedia Mathematica, but you can read it like a novel, it is these three volumes from Aleksandrov/Kolmogorov/Laurentiev. Amazon
Edit: Ahem, but after reading carefully post0, I would recommend you simply to begin with the textbooks of secondary school or so.
The closest thing I can find to a self-contained series of math courses is this:
https://www.myopenmath.com/info/selfstudy.php
Prealgebra, Algebra, Precalculus, and Trigonometry.
However, I have no guarantee of the quality of this self-contained self-study resource. And it doesn't contain calculus. So, it's not really self-contained, but it's close.
_
Yet another source. Unfortunately the bibliographies may not be comprehensive.
https://www.reddit.com/r/bibliographies/wiki/directory
What is /r/bibliographies?, answered here: https://www.reddit.com/r/bibliographies/wiki/faq
>A bibliography is a text post in this subreddit that has a specific scope and provides a list of sources that, taken together, constitute an introduction to the knowledge within this scope. This subreddit seeks to collect as many high-quality bibliographies as possible that collectively cover anything readers might wish to learn. Within each bibliography is an explanation of the bibliography's scope, suggestions for learning the topic, and a list of resources that cover the scope and give readers a way to get started in their learning. Bibliographies are created and maintained by redditors called "librarians". Anyone is welcome to create a bibliography and become a /r/bibliographies librarian (see "How do I create a bibliography?" below).
&nbsp;
___
Several free/cheap textbooks from Algebra to Calculus approved by the American Institute of Mathematics. I suppose you could possibly use the lists as a self-contained study resource. Lots of exercises for you to do, or "hands on practice".
Here is what AIM uses for its evaluation criteria: https://aimath.org/textbooks/evaluation-criteria/
___
Beginning Algebra from West Texas A&M University:
http://www.wtamu.edu/academic/anns/mps/math/mathlab/beg_algebra/
Intermediate Algebra from West Texas A&M University:
http://www.wtamu.edu/academic/anns/mps/math/mathlab/int_algebra/index.htm
Clark University, Dave's short Trig course:
https://www2.clarku.edu/faculty/djoyce/trig/
Source of all these 3 links: Originally made for physicists, but it works for people who want to relearn the basic maths(mostly algebra and trig)
http://www.staff.science.uu.nl/~gadda001/goodtheorist/primarymathematics.html
____
I'm not sure why I put this here, but here you go.
&nbsp;
Warning: This book is not for people who are learning the basics of math and it's not even about learning math. It's more like discovering the several fields of math and what each field has to offer.
See why here: https://www.quora.com/Is-Mathematics-Its-Content-Methods-and-Meaning-appropriate-for-someone-with-no-mathematical-knowledge
> No, it is not. This is not a book for learning mathematics. Of course it is appropriate for anyone wanting to know more about mathematics, but the question details say you want to “begin learning math”, and this book is not at all suitable for that purpose.
> It's a survey of mathematics for the generally interested reader. It talks a bit about history, a bit about some of the major results and a bit about the methods used in modern math, but you won't learn how to actually do mathematics by reading this book. You won't be able to pass any test or exam in any undergrad course or even most high-school exams.
> If your goal is to educate yourself about some of the main fields of mathematics and what they are about, this is a great book. If, however, you wish to actually learn mathematics, this is not the right book, and in fact no single book will let you do that.
> You'll need to study linear algebra using a good linear algebra textbook with plenty of exercises and have someone help check your proofs. You'll need to study real analysis with a good real analysis textbook, probably a couple of them, and do lots and lots of exercises. The same for complex analysis, field theory, group theory, number theory, probability theory, differential equations and so on.
> Before you do any of that, if you really have “no prior knowledge”, you'll need to absolutely master the basics: school-level algebra, calculus and geometry.
> Of course, if your purpose is to study a narrow part of math for some specific purpose, you can get by with just a subset of the things I've mentioned. But the book in the question won't help you master any of those domains. It's not meant for that.
https://www.amazon.com/Mathematics-Content-Methods-Meaning-Dover/dp/0486409163
Mathematics: Its Content, Methods and Meaning (3 Volumes in One) Paperback – July 7, 1999
Here is a review from Michael Berg about the book itself on the Mathematical Association of America website:
https://www.maa.org/press/maa-reviews/mathematics-its-content-methods-and-meaning
Thanks for your reply. I read positive reviews about this , what do you think?
By Kolmogorov himself: http://www.amazon.ca/Mathematics-Its-Content-Methods-Meaning/dp/0486409163
Thanks! what do you think about Mathematics: Its Content, Methods and Meaning ? from what I searched it can teach a lot a novice like me and quite the wonderful book.
Mathematics Content Methods Meaning
I think this may be what you look for. I have read some chapters of it. It talks about meanings, where theories come from..
I also remembered it when I saw it in my bookshelve. Written by Roger Penrose. Penrose talks about math from numbers to modern physics application of math. Especially Einstein's math of space time can be understood in this book;
The Road to Reality
Aside from The Princeton Companion to Mathematics, you might like to check out What Is Mathematics? An Elementary Approach to Ideas and Methods by Courant and Robbins, and Mathematics: Its Content, Methods and Meaning by three Russian authors including Kolmogorov.
Aleksandrov, Kolmogorov, Lavrent'ev. http://amzn.com/0486409163. Foundations to applicationsl.
Courant, Robbins, Stewart. http://amzn.com/0195105192. Tour of mathematics.
I just bought this for $10. Not all textbook companies are jokes. Just most.
General Advice
Specific Advice
What about the second example that triggers the same domain problem for 0. Do you get the same result?
https://www.amazon.ca/Ordinary-Differential-Equations-Morris-Tenenbaum/dp/0486649407/ref=mp_s_a_1_1?keywords=ordinary+differential+equations&amp;qid=1567534646&amp;s=gateway&amp;sprefix=ordinary+differ&amp;sr=8-1
This is the link for the textbook.
Tenenbaum and Pollard's book is fine. It is cheap too (published by Dover methinks)
https://www.amazon.com/Ordinary-Differential-Equations-Dover-Mathematics/dp/0486649407
That helps a little. I'm not too familiar with that world (I'm a physics major), but I took a look at a sample civil engineering course curriculum. If you like learning but the material in high school is boring, you could try self-teaching yourself basic physics, basic applied mathematics, or some chemistry, that way you could focus more on engineering in college. I don't know much about engineering literature, but this book is good for learning ODE methods (I own it) and this book is good for introductory classical mechanics (I bought and looked over it for a family member). The last one will definitely challenge you. Linear Algebra is also incredibly useful knowledge, in case you want to do virtually anything. Considering you like engineering, a book less focused on proofs and more focused on applications would be better for you. I looked around on Amazon, and I found this book that focuses on applications in computer science, and I found this book focusing on applications in general. I don't own any of those books, but they seem to be fine. You should do your own personal vetting though. Considering you are in high school, most of those books should be relatively affordable. I would personally go for the ODE or classical mechanics book first. They should both be very accessible to you. Reading through them and doing exercises that you find interesting would definitely give you an edge over other people in your class. I don't know if this applies to engineering, but using LaTeX is an essential skill for physicists and mathematicians. I don't feel confident in recommending any engineering texts, since I could easily send you down the wrong road due to my lack of knowledge. If you look at an engineering stack exchange, they could help you with that.
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You may also want to invest some time into learning a computer language. Doing some casual googling, I arrived at the conclusion that programming is useful in civil engineering today. There are a multitude of ways to go about learning programming. You can try to teach yourself, or you can try and find a class outside of school. I learned to program in such a class that my parents thankfully paid for. If you are fortunate enough to be in a similar situation, that might be a fun use of your time as well. To save you the trouble, any of these languages would be suitable: Python, C#, or VB.NET. Learning C# first will give you a more rigorous understanding of programming as compared to learning Python, but Python might be easier. I chose these three candidates based off of quick application potential rather than furthering knowledge in programming. This is its own separate topic, but my personal two cents are you will spend more time deliberating between programming languages rather than programming if you don't choose one quickly.
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What might be the best option is contacting a professor at the college you will be attending and asking for advice. You could email said professor with something along the lines of, "Hi Professor X! I'm a recently accepted student to Y college, and I'm really excited to study engineering. I want to do some rigorous learning about Z subject, but I don't know where to start. Could you help me?" Your message would be more formal than that, but I suspect you get the gist. Being known by your professors in college is especially good, and starting in high school is even better. These are the people who will write you recommendations for a job, write you recommendations for graduate school (if you plan on it), put you in contact with potential employers, help you in office hours, or end up as a friend. At my school at least, we are on a first name basis with professors, and I have had dinner with a few of mine. If your professors like you, that's excellent. Don't stress it though; it's not a game you have to psychopathically play. A lot of these relationships will develop naturally.
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That more or less covers educational things. If your laziness stems from material boredom, everything related to engineering I can advise on should be covered up there. Your laziness may also just originate from general apathy due to high school not having much impact on your life anymore. You've submitted college applications, and provided you don't fail your classes, your second semester will probably not have much bearing on your life. This general line of thought is what develops classic second semester senioritis. The common response is to blow off school, hang out with your friends, go to parties, and in general waste your time. I'm not saying don't go to parties, hang out with friends, etc., but what I am saying is you will feel regret eventually about doing only frivolous and passing things. This could be material to guilt trip yourself back into caring.
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For something more positive, try to think about some of your fun days at school before this semester. What made those days enjoyable? You could try to reproduce those underlying conditions. You could also go to school with the thought "today I'm going to accomplish X goal, and X goal will make me happy because of Y and Z." It always feels good to accomplish goals. If you think about it, second semester senioritis tends to make school boring because there are no more goals to accomplish. As an analogy, think about your favorite video game. If you have already completed the story, acquired the best items, played the interesting types of characters/party combinations, then why play the game? That's a deep question I won't fully unpack, but the simple answer is not playing the game because all of the goals have been completed. In a way, this is a lot like second semester of senior year. In the case of real life, you can think of second semester high school as the waiting period between the release of the first title and its sequel. Just because you are waiting doesn't mean you do nothing. You play another game, and in this case it's up to you to decide exactly what game you play.
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Alternatively, you could just skip the more elegant analysis from the last few paragraphs and tell yourself, "If I am not studying, then someone else is." This type of thinking is very risky, and most likely, it will make you unhappy, but it is a possibility. Fair warning, you will be miserable in college and misuse your 4 years if the only thing you do is study. I guarantee that you will have excellent grades, but I don't think the price you pay is worth it.
LIST OF APPLICATIONS IN MY DIFF EQ PLAYLIST
Have you seen the first video in my series on differential equations?
I'm still working on the playlist, but the first video lists a bunch of applications that you might not have seen before. My goal was to provide a sample of the diversity of applications outside of mathematics, and I chose fairly concrete examples that include applications in engineering.
I don't go into any depth at all regarding any of the particular applications (it's just a short introductory video), but you might find the brief introduction to be helpful.
If you find any one of the applications interesting, then a Google search will reveal more detailed resources.
A COUPLE OF FREE OR INEXPENSIVE BOOKS
Also, off the top of my head, the books below have quite a few applications that you might not see in the more standard textbooks.
I think you can find other legal PDFs of Braun's third edition, too. Pollard and Tenenbaum is an inexpensive paperback from Dover, and I actually found a copy at my local library.
ENGINEERING BOOKS
Of course, the books I listed are strictly devoted to differential equations, but you can find other applications if you look for books in engineering. For example, I used differential equations in a course on signals and systems that I tutored last semester (applications included electrical circuits and mass-spring-damper systems).
NEAT VIDEO (SOFT BODY MODELING)
By the way, here's a cool video of various soft body simulations based on mass-spring-damper systems modeled by differential equations.
Here's a Wikipedia article on soft body dynamics. This belongs to the field of computer graphics, so I'm not sure if you're interested, but mass-spring-damper systems come up a fair amount in engineering courses, and this is an application of those ideas that might open your mind a bit to other possible applications.
Edit: typo
For DEs try:
Ordinary Differential Equations by Tennenbaum
Its a great book with a TON of worked examples and solutions to all the exercises. This text was my holy book during my undergrad engineering courses.
I had a hard time getting through dif eq also, because the book was unreadable (to me). I also hate reading anything by Hibbler. The Munson fluid mechanics book is... barely tolerable. When that happens, I tend to look, with more vigor than usual, for other sources. Dif eq: I was lucky, and our tutoring center has dif eq tutors. Fluids: I found a wonderful lecture series done by UC Irvine OpenCourseWare. Hibbler... well, I've been S.O.L. on that so far. Generally, I also try to find a solutions manual. If I'm having a terrible time with a problem, I work through it and check myself each step of the way. I often try to find a different book, too. The only reason you need the required book is so you know what to look for in your chosen book.
I recently discovered there is a very highly-rated dif eq book available used on Amazon for about $13, so I ordered it in the hopes that it will be readable, as I now need to brush up on dif eq and can't stand the book we used in class.
I enjoyed
Introduction to Probability Theory, Hoel et. al
Also,
Probability Theory, Jaynes
is essential. For probabilistic programming I would also look into
Bayesian Methods for Hackers
I really love Probability Theory: The Logic of Science by Jaynes. While it is not a physics book, it was written by one. It is very well written, and is filled with common sense (which is a good thing). I really enjoy how probability theory is built up within it. It is also very interesting if you have read some of Jaynes' more famous works on applying maximum entropy to Statistical Mechanics.
learn Haskell, learn how to make money, or learn some probability theory
> Honestly, both of our arguments have become circular. This is because, as I have stressed, there is not enough data for it to be otherwise. Science is similar to law in that the burden of proof lies with the accuser. In this case there is no proof, only conjecture.
((Just in case it is relevant: Which two arguments do you mean exactly, because the circularity isn't obvious to me?))
In my opinion you can argue convincingly about future events where you are missing important data and where no definitive proof was given (like in the AI example) and I want to try to convince you :)
I want to base my argument on subjective probabilities. Here is a nice book about it. It is the only book of advanced math that I worked through \^\^ (pdf).
My argument consists of multiple examples. I don't know where we will disagree, so I will start with a more agreeable one.
Let's say there is a coin and you know that it may be biased. You have to guess the (subjective) probability that the first toss is head . You are missing very important data: The direction the coin is biased to, how much it is biased, the material .... . But you can argue the following way: "I have some hypotheses about how the coin behaves and the resulting probabilities and how plausible these hypotheses are. But each hypothesis that claims a bias in favour of head is matched with an equally plausible hypothesis that points in the tail direction. Therefore the subjective probability that the first toss is head is 50%"
What exactly does "the subjective probability is 50%" mean? It means if I have to bet money where head wins 50 cent and tail wins 50 cent, I could not prefer any side. (I'm using small monetary values in all examples, so that human biases like risk aversion and diminishing returns can be ignored).
If someone (that doesn't know more than me) claims the probability is 70% in favour of heads, then I will bet against him: We would always agree on any odds between 50:50 and 70:30. Let's say we agree on 60:40, which means I get 60 cent from him if the coin shows tail and he gets 40 cent from me if the coin shows head. Each of us agrees to it because each one claims to have a positive expected value.
This is more or less what happened when I bet against the brexit with my roommate some days ago. I regularly bet with my friends. It is second nature for me. Why do I do it? I want to be better at quantifying how much I believe something. In the next examples I want to show you how I can use these quantifications.
What happens when I really don't know something. Let's say I have to guess my subjective probability that the Riemann hypothesis is true. So I read the Wikipedia article for the first time and didn't understand the details ^^. All I can use is my gut feeling. There seem to be some more arguments in favour of it being true, so I set it to 70%. I thought about using a higher value but some arguments might be biased by arguing in favour to what some mathematicians want to be true (instead of what is true).
So would I bet against someone who has odds that are different from mine (70:30) and doesn't know much more about that topic? Of course!
Now let's say in a hypothetic scenario an alien, a god, or anyone that I would take serious and have no power over him appears in front of me, chooses randomly a mathematical conjecture (here: it chooses the Rieman hypotheses) and speaks the following threat: "Tomorrow You will take a fair coin from your wallet and throw it. If the coin lands head you will be killed. But as an alternative scenario you may plant a tree. If you do this, your death will not be decided by a coin, but you will not be killed if and only if the Riemann hypothesis is true"
Or in other words: If the subjective probability that the Riemann hypothesis is true is >50% then I will prefer to plant a tree; otherwise, I will not.
This example shows that you can compare probabilities that are more or less objective (e.g. from a coin) with subjective probabilities and that you should even act on that result.
The comforting thing with subjective probabilities is that you can use all the known rules from "normal" probabilities. This means that sometimes you can really try to calculate them from assumptions that are much more basic than a gut feeling. When I wrote this post I asked myself what the probability is that the Riemann hypothesis will be proven/disproven within the next 10 years. (I just wanted to show you this, because the result was so simple, which made me happy, but you can skip that).
And this result is useful for me. Would I bet on that ratio? Of course! Would I plant a tree in a similar alien example? No I wouldn't, because the probability is <50%. Again, it is possible to use subjective probabilities to find out what to do.
And here is the best part, about using subjective probabilities. You said "Science is similar to law in that the burden of proof lies with the accuser. In this case there is no proof, only conjecture." But this rule is no longer needed. You can come to the conclusion that the probability is too low to be relevant for whatever argument and move on. The classic example of Bertrand Russel's teapot can be solved that way.
Another example: You can calculate which types of supernatural gods are more or less probable. One just needs to collect all pro and contra arguments and translate them to likelihood ratios . I want to give you an example with one type of Christian god hypothesis vs. pure scientific reasoning:
In the end you just multiply all ratios of all arguments and then you know which hypothesis of these two to prefer. The derived mathematical formula is a bit more complicated, because it takes into account that the arguments might depend on each other and that there is an additional factor (the prior) which is used to indicate how much you privilege any of these two hypotheses over all the other hypotheses (e.g. because the hypothesis is the most simple one).
I wanted to show you that you can construct useful arguments using subjective probabilities, come to a conclusion and then act on the result. It is not necessary to have a definitive proof (or to argue about which side has the burden of proof).
I can imagine two ways were my argument is flawed.
Jaynes' Probability Theory is fantastic.
All gone now. (05:30 UMT 10 August) LiSP and Probability Theory: The Logic of Science are still in the top two slots, but amazon.ca appears to have sold out of new copies.
> There are some philosophical reasons and some practical reasons that being a "pure" Bayesian isn't really a thing as much as it used to be. But to get there, you first have to understand what a "pure" Bayesian is: you develop reasonable prior information based on your current state of knowledge about a parameter / research question. You codify that in terms of probability, and then you proceed with your analysis based on the data. When you look at the posterior distributions (or posterior predictive distribution), it should then correctly correspond to the rational "new" state of information about a problem because you've coded your prior information and the data, right?
Sounds good. I'm with you here.
> However, suppose you define a "prior" whereby a parameter must be greater than zero, but it turns out that your state of knowledge is wrong?
Isn't that prior then just an error like any other, like assuming that 2 + 2 = 5 and making calculations based on that?
> What if you cannot codify your state of knowledge as a prior?
Do you mean a state of knowledge that is impossible to encode as a prior, or one that we just don't know how to encode?
> What if your state of knowledge is correctly codified but makes up an "improper" prior distribution so that your posterior isn't defined?
Good question. Is it settled how one should construct the strictly correct priors? Do we know that the correct procedure ever leads to improper distributions? Personally, I'm not sure I know how to create priors for any problem other than the one the prior is spread evenly over a finite set of indistinguishable hypotheses.
The thing about trying different priors, to see if it makes much of a difference, seems like a legitimate approximation technique that needn't shake any philosophical underpinnings. As far as I can see, it's akin to plugging in different values of an unknown parameter in a formula, to see if one needs to figure out the unknown parameter, or if the formula produces approximately the same result anyway.
> read this book. I promise it will only try to brainwash you a LITTLE.
I read it and I loved it so much for its uncompromising attitude. Jaynes made me a militant radical. ;-)
I have an uncomfortable feeling that Gelman sometimes strays from the straight and narrow. Nevertheless, I looked forward to reading the page about Prior Choice Recommendations that he links to in one of the posts you mention. In it, though, I find the puzzling "Some principles we don't like: invariance, Jeffreys, entropy". Do you know why they write that?
This one? Damn, it's £40-ish. Any highlights or is it just a case of this book is the highlight?
It's on my wishlist anyway. Thanks.
>All I'm saying is that the origin of a claim contains zero evidence as to that claim's truth.
I had a look back though your other posts and found this, which explains a lot, for me anyway. Most people would put some more options in there - yes, no, im pretty sure, its extremely unlikely etc..
Heres what I think is the problem, and why I think you need to change the way you are thinking - Your whole concept of what is "logical" or what is "using reason" seems to be constrained to what is formally known as deductive logic. You seem to have a really thorough understanding of this type of logic and have really latched on to it. Deductive logic is just a subset of logic. There is more to it than that.
I was searching for something to show you on other forms of logic and came across this book - "Probability Theory - The Logic of Science" Which looks awesome, Im going to read it myself, it gets great reviews. Ive only skimmed the first chapter... but that seems to be a good summary of how science works- why it does not use just deductive logic. Science draws most of its conclusions from probability, deductive logic is only appropriate in specific cases.
Conclusions based on probability - "Im pretty sure", "This is likely/unlikely" are extremely valid - and rational. Your forcing yourself to use deductive logic, and only deductive logic, where its inappropriate.
>You have no way of knowing, and finding out that this person regularly hallucinates them tells you nothing about their actual existence.
Yeah I think with the info you've said we have it would be to little to draw a conclusion or even start to draw one. Agreed. It wouldnt take much more info for us to start having a conversation about probabilities though - Say we had another person from the planet and he says its actually the red striped jagerwappas that are actually taking over - and that these two creatures are fundamentally incompatible. ie. if x exists y can't and vice-versa.
I'd suggest MATP 4600, Probability Theory & Applications. Only prerequisite is Calc if I remember right.
Or if you're confident in your time management, maybe read this textbook on your own; it's pretty accessible: https://www.amazon.com/gp/aw/d/0521592712/
(Neither of these will teach you a bunch of statistical tests, but those are easy to abuse if you don't understand the fundamentals ... and very easy to look up if you do understand the fundamentals.)
> For one, you need a categorical definition by which to justify your "probability" with. What, does each time you tell a god to speak deduct 1%? That's absurdly vague, stupid, and unheard of, so no wonder I never thought you'd actually be arguing this.
I don't happen to know the appropriate decibel-values to assign to E and not-E in this case. But I know the fucking SIGNS of the values.
No, I don't know how many times god needs to appear for me to believe that I wasn't drugged or dreaming or just going crazy. But god appearing is evidence for the existence of god, and him not appearing is evidence against.
Does it really matter if we are talking intervals of 5-seconds versus lifetimes?
3 pages, and you don't even have to go to a library! Check it out:
http://www.amazon.com/reader/0521592712?_encoding=UTF8&amp;ref_=sib%5Fdp%5Fpt#reader
Click on "First Pages" to get to the front.
You can lead a horse to water...
"Bayesian" is a very very vague term, and this article isn't talking about Bayesian networks (I prefer the more general term graphical models), or Bayesian spam filtering, but rather a mode of "logic" that people use in everyday thinking. Thus the better comparison would be not to neural nets, but to propositional logic, which I think we can agree doesn't happen very often in people unless they've had lots of training. My favorite text on Bayesian reasoning is the Jaynes book..
Still, I'm less than convinced by the representation of the data in this article. Secondly, the article isn't even published yet to allow anyone to review it. Thirdly, I'm suspicious of any researcher that talks to the press before their data is published. So in short, the Economist really shouldn't have published this, and should have waited. Yet another example of atrocious science reporting.
My one-stop book recommendation would be Sam Harris's Letter to a Christian Nation. It's a short read, but nearly every paragraph is its own distinct argument, and it covers a lot of territory.
If you're aiming to construct your paper around a set of the most popular arguments, here are some common refutations to arguments for the existence of God. Keep in mind that many of our arguments are in the form of refutation instead of assertion, since the burden of proof is on the claimant:
Ontological Argument (Argument from experience) - We assert that feelings do not equal facts; revelation is not a reliable basis for a factual claim. We also realize that to criticize someone for feelings that are personal can seem like a personal attack. Most of us wouldn't tell someone who claims he/she had a spiritual experience that it didn't happen, but we would try to find a scientific explanation rather than coming to the immediate conclusion that it was God's doing. As a brief example, a friend of mine said he "felt the touch of God" when his daughter was born, but we interpret his feeling as a normal, natural high that most people feel at such an emotional moment.
Teleological Argument (Argument from design) - We accept the evidence for evolution and realize that it is inconsistent with the biblical creation story. For further reading about what proof we have for evolution, I'd personally recommend The Greatest Show on Earth by Richard Dawkins, and he promotes Jerry Coyne's Why Evolution Is True though I haven't read the latter yet.
Cosmological Argument (Causal Argument) - This is a case of people assigning the "God" label to something difficult to comprehend. The best we have to go on so far is the Big Bang Theory, and scientists will continue to test the theory. We don't have evidence that the beginning of the universe was brought about by an omnipotent/omniscient being outside of what is claimed by religious texts, and that goes back to the. We might also ask, "who/what made God?" inviting an infinite loop of "which came first" questions.
Moral Argument - We believe (normal) people are able to tell the difference between right and wrong without religious guidance. In turn, it seems that the Christian Bible teaches, excuses, or condones actions that our enlightened society would deem immoral, such as slavery, killing of children and non-heterosexuals, oppression, rape, and genocide. Interpretations of the Bible differ, of course, and most modern Christians don't believe they should actually kill their disobedient children (or that the laws of the Old Testament no longer apply since the coming of Christ, which is another conversation). Regardless of arguments from the Bible, we believe that science can tell us a lot more about morality than we give it credit for.
Lastly, here is a wikipedia list of lots more arguments in case you'd like to ask about specific ones: link
Good luck, and I hope you enjoy writing your paper. Not that you should necessarily crowd-source coursework, but you'd probably get quite a strong response if you posted up a final draft, too.
> However, addressing your argument about "denying observable reality" is quite insulting.
Your denial of observable reality is quite insulting to those of us who care about observable reality.
> Many people refuse to believe in the literal six day creation or global flood and insist they are just stories
The reason for this is that everything we've observed about the relevant reality indicates that these events simply did not happen.
Read a science textbook. Or this.
Okay - I know...have him read this:
http://www.amazon.com/Why-Evolution-True-Jerry-Coyne/dp/0670020532/ref=sr_1_1?ie=UTF8&amp;s=books&amp;qid=1252105723&amp;sr=8-1
Jerry Coyne has a great book you might want to pick up
Or maybe the one by Dawkins
Or there's always this
Here is a good book for your research in understanding Evolution. It's a nice read with reliable knowledge from an ecology specialist.
In a different vein, I heard that there is a popular science nonfiction Chinese book, called "The Physics of the Three Body Problem Universe,"
I was keen to order it but realized that I probably can't understand it.
But there are several excellent pop-sci books on String Theory, Big Bang that I would have considered abstract, obtuse prior to reading Three Body Problem,
https://www.amazon.com/Elegant-Universe-Superstrings-Dimensions-Ultimate/dp/039333810X/ref=sr_1_6?s=books&amp;ie=UTF8&amp;qid=1486145503&amp;sr=1-6&amp;keywords=Physics
https://www.amazon.com/Fabric-Cosmos-Space-Texture-Reality/dp/0375727205/ref=pd_sim_14_1?_encoding=UTF8&amp;psc=1&amp;refRID=4FS9WM0HGP79QXBRHDBS
https://www.amazon.com/Brief-History-Time-Stephen-Hawking/dp/0553380168/ref=pd_sim_14_3?_encoding=UTF8&amp;psc=1&amp;refRID=1MQ7BXTSH2NJK5E0E02Y
Well, one of the books I read that really got me started in cosmology and physics is Brian Greene's The Fabric of the Cosmos. I think it is his best book and talks a lot about the fundamentals of our universe. Brian Greene studies string theory and those bits are interesting, but just know that the theory is far from complete or proven. This one is definitely the most physics heavy suggestion.
Another book that I really enjoy is A Short History of Nearly Everything by Bill Bryson. It is essentially a history of science, and he covers a lot of topics. Many of which I knew almost nothing about when I read it. It puts into perspective how all the things we know came to be.
The next two recommendations are not books, but they still have a lot of great information in them. This first is a Youtube series called Crash Course Astronomy. The host is Phil Plait, one of the programmers involved with the Hubble Space Telescope. There are a lot of videos, so it would keep you busy and learning for a while.
The last recommendation is as close to the upper level undergraduate astronomy courses that I have taken without actually doing any math. It is a bunch of class lectures from Ohio State University that were recorded and released as a podcast about stellar astronomy and planetary astronomy. I found the lecturer's voice a little whiny at first, but I soon got past that because the content was so good. I kid you not, I listened to this ahead of my ASTRO 346 Stellar Astronomy class at my university, and I felt like the class concepts were almost a review.
All of those recommendations require you to do no math, but you only get a glimpse of the concepts that way. If you want to dive in more, you'll need to take a class or read a textbook on your own.
I hope that helps. Let me know if you have any other questions about astronomy as a subject or as a course of study in school :)
The Elegant Universe, The Fabric of the Cosmos
Also, The Age of Spiritual Machines discusses theoretical and quantum physics. I'm not saying its the book to read to learn physics but thats what originally got me interested.
I teach "Monsters Are Due on Maple Street" every year. My students love it!
This is on the list I keep for my husband. He is kind of a nerd :-)
Pretty much everything that passes by. I love learning new things and expand my knowledge, but here are my biggest passions:
-Music: I'm studying to become a composer and music has been a major part of my life since birth, as I was born into a musical family. It's such a joy when I find a new band or composer and start going through their works and discover many new, exciting works. It's even better when you analyse scores and play then on piano, and everything starts to make sense, the melodies, harmonic structure,... sometimes it gives you the same feeling as when you open your christmas present, except you have been given an insight into a mind of a musical genius from the past.
-Lore: A lot of times I pick up a new game/book/TV series/movie, if I really like it, I go and read as much background lore as possible. The extra information and insight behind the main plot is really interesting to read and I tend to memorize unhealthy amounts of useless information :) So far it spans through Star Wars, Jurassic Park, Harry Potter, Warhammer 40k, Elder Scrolls, and probably a few more I forgot.
-History: It's real life lore :) Big emphasis on Roman empire/Viking culture/WW2.
-Philosophy: Basically discussing everything ranging from old philosophical problems to problems and dilemmas of the today's world.
-Physics: I love reading about space, black holes, wave-particle duality, electricity,... The more experimental it is, the better. I highly recommend this book.
-Motorsports: Rally and F1 mostly, but I love to drive and I am always blown away by the skills these drivers have. Also, the tech behind the cars is amazing and very interesting.
But the best part is if I can explain the above things to somebody else. It's really one of my favorite things to do. I really like to share my enthusiasm with other people and I can go on for hours at the time :)
Here is a good book on trigonometry.
Here is one for algebra.
Here's another
The Serge Lang book looks to be pretty expensive on Amazon, is it worth it?
Thank you for the recommendations, the Gelfand books look like they're worth checking in to!
Okay. So..
You speak of this book I assume. Which is intended to be used by students in H.S. Yet you are familiar with abstract algebra? I understand abstract algebra has many levels to it. But how far did you go? Was it so close that you were touching on topographies or statements?
I'm very confused here. You're concerned about your math. But yet you're reading a calculus prep book?
What is an IT college exactly? Are you a freshman or sophomore at a Uni? And it happens that you are referring to your department? Or are you referring to a technical college / school?
These questions are to satisfy my assumptions. Optional at best.
As a math major with a CS minor in my uni, which is something I'm in the process of. I am required pre-algebra, algebra, pre-calc, calc, calc 1, calc 2, calc 3, abstract algebra, linear algebra, discreet math, some general programming classes involving these prerequisite math courses, and some other math classes I cannot remember.
Abstract algebra, in my opinion is something of a higher level language. So this should explain my confusion here.
First, please make sure everyone understands they are capable of teaching the entire subject without a textbook. "What am I to teach?" is answered by the Common Core standards. I think it's best to free teachers from the tyranny of textbooks and the entire educational system from the tyranny of textbook publishers. If teachers never address this, it'll likely never change.
Here are a few I think are capable to being used but are not part of a larger series to adopt beyond one course:
Most any book by Serge Lang, books written by mathematicians and without a host of co-writers and editors are more interesting, cover the same topics, more in depth, less bells, whistles, fluff, and unneeded pictures and other distracting things, and most of all, tell a coherent story and argument:
Geometry and solutions
Basic Mathematics is a precalculus book, but might work with some supplementary work for other classes.
A First Course in Calculus
For advanced students, and possibly just a good teacher with all students, the Art of Problem Solving series are very good books:
Middle & high school:
and elementary linked from their main page. I have seen the latter myself.
Some more very good books that should be used more, by Gelfand:
The Method of Coordinates
Functions and Graphs
Algebra
Trigonometry
Lines and Curves: A Practical Geometry Handbook
http://www.amazon.ca/Basic-Mathematics-Serge-Lang/dp/0387967877
My two cents
If you want to improve your skills you can do two things in the short term -- read and practice.
I would recommend Basic Mathematics by Lang (it gets mentioned a lot around here). Or if you are interested in higher math look at How to Prove It by Velleman
The great thing is that both include exercises.
The two books already mentioned sound awesome, but if you ever wanted a textbook with a formal approach to mathematics (written by a well-known and respected mathematician), check out Basic Mathematics by Serge Lang.
This is more for anyone reading who would like to continue on to a math or perhaps a physics major. The book takes you from elementary algebra and geometry all through pre-calculus; basically the only book you should need to prepare you for calculus and elementary linear algebra.
I've heard good things about Serge Lang's Basic Mathematics. It's pre-calculus geometry and algebra mainly I think, but it treats you like a grown-up.
Don't skip proofs and wrestle through them. That's the only way; to struggle. Learning mathematics is generally a bit of a fight.
It's also true that computation theory is essentially all proofs. (Specifically, constructive proofs by contradiction).
You could try a book like this: https://www.amazon.com/Book-Proof-Richard-Hammack/dp/0989472108/ref=sr_1_1?ie=UTF8&amp;qid=1537570440&amp;sr=8-1&amp;keywords=book+of+proof
But I think these books won't really make you proficient, just more familiar with the basics. To become proficient, you should write proofs in a proper rigorous setting for proper material.
Sheldon Axler's "Linear Algebra Done Right" is really what taught me to properly do a proof. Also, I'm sure you don't really understand Linear Algebra, as will become very apparent if you read his book. I believe it's also targeted towards students who have seen linear algebra in an applied setting, but never rigorous and are new to proof-writing. That is, it's meant just for people like you.
The book will surely benefit you in time. Both in better understanding linear algebra and computer science classics like isomorphisms and in becoming proficient at reading/understanding a mathematical texts and writing proofs to show it.
I strongly recommend the second addition over the third addition. You can also find a solutions PDF for it online. Try Library Genesis. You don't need to read the entire book, just the first half and you should be well-prepared.
As others mentioned, it is very hard to make progress learning programming without using a computer (think of reading about driving without ever driving a car). Instead, get yourself excited about science and computer science:
Science:
Computer Science (actually math, but this will help change the way you think to be more analytical, and will be useful for programming, vector graphics, etc.):
I think linear algebra is a much more interesting topic without getting bogged down in matrix computations, such as what Axler does with Linear Algebra Done Right. That's just my opinion I suppose.
Apart from that you can also work your way through textbooks, such as Molecular Quantum Mechanics, read popular publications such as A Brief history of time or The Elegant Universe (haven't read those unfortunately).
You can also visit the subreddit /r/Physics, to be up to date, ask questions and such, or even visit 4Chans /sci/ which gives you access to a large science and math guide.
When I was a sophomore in high school, I was just starting to get interested in philosophy. I took an unusual route, but I can sure recommend some good books that will change how you think!
Thanks.
[For the lazy]
(http://www.amazon.com/The-Elegant-Universe-Superstrings-Dimensions/dp/039333810X)
Anything by Brian Greene. His books are aimed at laypeople, and he explains the ideas behind quantum mechanics, relativity and string theory without any mathematics whatsoever.
I would recommend you start with The Elegant Universe and then The Fabric of the Cosmos. These books are easier to follow than Brief History of Time, and explain all of the interesting aspects of physics such as time dilation, warping of space, particles being waves, etc.
To put this in a slightly different light than other commenters, there's one simple answer: the laws of physics should work no matter what you're doing (this is what Einstein focused on). You can't go exactly the speed of light, but even if you blasted off from Earth at 0.999c (very close to it!) your spaceships headlights, disco ball, and christmas light would still beam light away from you at the speed of light. Whaaat? Why?
Speed and velocity are relative. In this case, your ship is moving relative to Earth, and off to Neptune or some dank, misty moon like Titan. If you're in empty space and a spaceship goes floating by, it's difficult to tell if she's the one whizzing past, or you. Inside you're own ship, like when you're in a smoothly cruising car, it's almost like you're standing still. Hence, when you turn on a flashlight, or your headlights, they work just like normal and the light travels at the speed of light. If this seems weird - it is a bit weird! It's where all the cool stuff that happens in relativity comes from (twin paradox time dilation, E= mc^2). To learn more, I seriously recommend checking out shows like Cosmos or books like "The Elegant Universe." Hopefully they will blow your mind like they did mine. :)
One of the best explanations for relativity I've come across is from Brian Greene in "The Elegant Universe," a book I highly recommend if you're interested in physics without having to learn all the math involved. Be warned, the material is dense. Took me about four months to read and digest.
Basically, space and time are different expressions for the same concept, space-time, much like magnetism and electricity are different expressions for the same force, electro-magnetism. Greene says we're always travelling at light speed. When standing in place, we're moving at light speed through time. When we move through space at any speed we're moving a corresponding amount slower through time. The faster we move through space the slower we move through time up until we reach light speed, at which point we've completely stopped moving through time.
So, when travelling at any significant fraction of light speed, our relative speed through time is slower than that of someone standing still. It's kind of a see-saw effect where increasing one side decreases the other side of the equation. This is so fun to think about because it's mind bending and totally counter-intuitive.
The Elegant Universe by Brian Greene did a pretty good job of covering high-level physics concepts up through string theory.
By looking at the gloves. The Centauri look at the gloves in order to deduce the earth glove key.
TBH; I am no expert on this stuff, we are reaching the point where my hackneyed understanding via science writing and metaphor is falling apart. I suggest reading "the elegant universe by brian greene". It is a super cheap book that has a lot of really amazing explanations for stuff with relativity, quantum mechanics and string theory.
https://www.amazon.com/Elegant-Universe-Superstrings-Dimensions-Ultimate/dp/039333810X
For anyone interested in this kind of stuff, I highly recommend The Elegant Universe by Brian Greene (http://www.amazon.com/The-Elegant-Universe-Superstrings-Dimensions/dp/039333810X). I thought it was a great read and relatively easy to understand for someone not in the physics field.
It's VERY well understood. Gravity is concretely understood. We can predict orbits, how fast something will fall, gravitational constants, etc. etc. etc. EVERYTHING on a large scale (talking about anything macroscopic) can be precisely modeled and explained.
The issue that we run into is when we get into the Microscopic scale. Not the size of molecules, but the size of atoms and sub-atomic particles. That's when things get tricky. Scientist and theoretical physicists cannot YET accurately model anything that's smaller than an atom. Hell, we can't even tell where an electron will be in the orbit around the proton. However, this is what Quantum Mechanics is trying to tie together. Because nothing at that level mathematically follows the rules of Macro physics such as gravity. It's been a century long question and once a unifying theory comes around to join Quantum Mechanics and Gravitational theory, then it's going to be monumental.
You're absolutely correct that the theory of gravity doesn't apply to ALL things, because at the very small scale, things get really weird. Theories about 11+ dimensions come into play. No one really knows yet or how to predict it.
Fascinatingly enough, this is what Interstellar was about. At the beginning of the movie, they explain that they finally found the unifying theory that joins gravitational theory and quantum mechanics together.
Rest assured, we know how gravity works. We can accurately predict how planets will move, and how gravity impacts other objects. There are anomalies like black holes and quantum mechanics that we just simply don't know enough about. But I can confidently say, gravity is real, we know what it is (although we can't physically see the force, we can just see how it impacts objects), and the math behind it is very concrete.
Since you seem quite literate, I'd highly recommend reading this book:
https://www.amazon.com/Elegant-Universe-Superstrings-Dimensions-Ultimate/dp/039333810X
It's a tough read, but it's real quite fascinating and eye opening to how bizarre the small world really is.
https://www.amazon.com/Introduction-Quantum-Mechanics-David-Griffiths/dp/0131118927
For the QM
And
https://www.amazon.ca/Mathematical-Methods-Physical-Sciences-Mary/dp/0471198269
For the math.
Edit: I'm rereading both of these over the summer as a refresher. They make a great combo.
Just want to mention that pop sci (which everything you mentioned is) and an actual rigorous study of physics are two very very different things. The romantic image of physics you get from those kind of programs is very different then what is actually involved in learning physics.
I would suggest getting more familiar with the mathematics (calculus, statistics, linear algebra) before diving into the actual physics.
Having the math first will make it much easier to see the actual physics behind the equations instead of sitting there trying to figure out the math and physics at the same time.
To that end I would suggest having Boas mathematical methods next to you at all times during your early studies. Its at about a sophomore (college) level but is easily accessible to most anyone with a basic mathematics background.
(http://www.amazon.com/Mathematical-Methods-Physical-Sciences-Mary/dp/0471198269)
Other than that watch Kahn academy or the MIT online courses.
First you need Algebra and Trig. From this stage you mainly need to be able to manipulate equations (e.g. take x^2 + y^3 + z^2 = k^2 / n^2 and solve for x, it's one of the easier parts of algebra) and to understand exponents/logarithms. From trig you need to know how to break a vector into components, how to find angles, how sines/cosines/etc are defined, and all those nasty trig identities (e.g 1 - sin^2 = cos^2). You don't need to memorize them (usually, some professors are insane) but it helps to be kinda-sorta familiar with them.
If you've mastered all that, you want to study calculus. If you can take derivatives and solve integrals you're probably good enough to start, but the more you understand the better. It's a lot easier to solve physics problems when you're not struggling with the math you need to solve them.
If you get a book like this and work through it you'll get a lot of what you need, but it's not really necessary to go that far-- that is stuff you won't need until your fourth or fifth semester. Some of it is grad school math.
tl;dr: Trig, Algebra, and basic Calculus for sure. That's what you need for year 1. You can go further if you want, but there is no need to kill yourself to learn advanced math before taking intro physics.
I will give you the same answer I give every one of my students, and that one of my mentors gave me: don't think that there is a logical progression to approaching mathematics. The reason that people think there is such a thing as a logical order to mathematics is due to the school system, which teaches things in a particular order before university, and then structures university classes using prerequisites, making you think that, for example, you need trigonometry before you do calculus. This simply isn't true. I could say more about this, but it won't answer your question.
Here is my suggestion. Go to the mathematics section of a library, yank any book off the shelf, and go to town. Most books aimed at advanced undergrad/grad students (which is the level you're looking for) will say in the introduction something to the effect of "there are no real prerequisites for this book other than mathematical maturity," and this is nearly always true. You probably won't have mathematical maturity starting out, which can be frustrating, but you'll develop it over time. You will encounter things that you don't understand in these books, and the correct response to this is to go find another book on that topic. You can't learn mathematics just by compiling a list of theorems and techniques.
So all you really need is a starting point. Looking at what you're interested in, I'd recommend this book, which is extremely practical. You'll find more computational things in there than mathematical things, but it has a pretty broad spectrum of techniques whose theoretical underpinnings you can pursue. This course of action is the only one I can recommend, because it's the one I took. The only math class I took in college was calculus, and now I do research in mathematics in grad school. The frustrating thing about this approach is that there's no quantitative way to measure your progress. On the other hand, you get a real feeling for why and how people came up with various aspects of mathematics, which is a feeling you can't get from a curriculum.
The Structure of Scientific Revolutions by Kuhn. Maybe not the book that has influenced me the most, but definitely one that jumped to mind immediately when I read this thread.
Read "The structure of scientific revolutions" by Thomas Kuhn.
http://www.amazon.com/Structure-Scientific-Revolutions-Thomas-Kuhn/dp/0226458083
The definitive book on academic disagreements, how and why they happen, and what they're good for. You will find it interesting and probably eye-opening: academics disagree all the time, but only when their accepted common beliefs no longer make sense and they've run out of productive research to do together. The book itself is about scientists, but many of his ideas can be applied to other disciplines as well.
You're right: the amount of texts out there is daunting, so it can be hard to find the right area that appeals to you. Maybe a little more about the issues and questions you're interested in would help narrowing the options down a bit.
Two books that might be worth looking at: Proofs and Refutations by Lakatos. It looks at math and advances a thesis about what "proving" in math is really about.
And, Structure of Scientific Revolutions by Kuhn. It looks at the development of science through history and puts forth a provocative thesis about how science develops.
Take a glance at those, and see if they are up your alley. They are not too difficult, but they aren't really intro texts.
In the context of learning, essentially what you are proposing is what Thomas Kuhn proposed as a paradigm shift. If you haven't read "The Structure of Scientific Revolutions" you and everyone should. It's available at amazon https://www.amazon.com/Structure-Scientific-Revolutions-Thomas-Kuhn/dp/0226458083
However, the premise that Kuhn proposed was that it took a generation of scientists to die away before the new ideas had a chance to emerge. When he wrote the book, that was probably true, but in the present, in many disciplines, the ability to change a paradigm has gone from 30 years to 18 months, so it may not be as relevant as it was when written.
As to the premise of I'll believe it when I see it, that seems more to be a license plate slogan, i.e. Wisconsin "Just cows and cheese."
The simple fact of the matter, and my returning to this forum after an absence, is that there is a very high risk now of creating false expectations instead of revolutionary discovery. In my other OP thread, there is commentary showing me to be a defender of test results from a methodological perspective, which ultimately turned out to be subject to falsification.
I am not capable nor qualified to argue the physics side of this. I am absolutely qualified and capable of arguing the social psychology side of this. My simple premise is this. Looking at this from a philosophy of science point of view (it's a real academic discipline), the debate in this forum has gone from wonder and excitement to pathological. The physics doesn't support this. The experimentation doesn't support this. The 7,000 odd subscribers to this forum have to understand that this is approaching a pathological and near theological debate comparable to Scientology or hollow earth beliefs.
There are some competent and highly qualified individuals doing best efforts research into the EMdrive phenomenon, and some of them have the capacity to produce results, if positive, deserve scrutiny. However, IMHO, this reddit forum at this time with the commentaries posted, with the lame debates posted, does not contribute to those who wish to learn and know more.
Essentially, there are no plausible arguments for EMdrive, and no theoretical models that extend beyond crack-pottery. There are some interesting experiments in process that may push for a closer look, but none of them have come to fruition.
I am trying to take the high road and simply state that EVERYONE is entitled to their opinion, and in Physics, EVERYONE is entitled to a poster presentation, however, in the end, data has be replicated and scrutinized and beat to death and is the only thing that contributes to an extension of what we think of as knowledge. EMdrive hasn't yet gone beyond the poster presentation stage.
Things are a bit different for hearing, but the "such and unexplored area" feeling will be the same. For reference, this is what science is.
http://matt.might.net/articles/phd-school-in-pictures/
OH, also read Thomas Khun's, The Structure of Scientific Revolutions only 200 pages, and you'll probably get the point around page 50. Best book on human knowledge ever.
Vetting "good" philosophy sources can be tricky. After my students get a basic idea of some topic from wiki, I usually sent them to Stanford Encyclopedia of Philosophy
For basic terms you might try A Dictionary of Philosophical Terms and Names. But keep in mind that sometimes people use terms rather oddly so sometimes it's best to just ask them to define how they are using them.
Then you might want to read some books related to the topics you are interested in. For example, if you are interested in the history or philosophy of science you might pick up The Structure of Scientific Revolutions or some other works in that area.
Basically dive in and start reading about the things that interests you, then try to bring that knowledge to the table...or use them to ask questions and get more help.
Yes, Einstein didn't like that quantum mechanics could only predict probabilities, and he figured that a deeper understanding would give rise to a more deterministic theory. A lot more research has been done since he said that, and unfortunately he died so there's no way we'll ever know if he would have changed his mind when faced with more evidence. That being said, there are still a lot of unanswered questions and we still don't have a theory of everything so maybe Einstein was right. We don't know.
But we're talking about science, not scientists, and Einstein's opinion on the matter didn't dictate what research showed in the years after his death. Physicists come up with theories and test them, and if they stand up to scrutiny, these ideas are adopted until something better comes along. If a theory isn't supported by the evidence, it's rejected- regardless of what the original proponent of the theory thinks. Therein lies the magic of science. New generations reject ideas that have overwhelming evidence against them.
I don't need to tell you that this doesn't happen with religion. The Bible, for example, directly contradicts itself in countless ways and describes events that we know are physically impossible, but is still considered to be inerrant by conservative Christians who may have been born hundreds of years after a given Biblical assertion was shown to be monstrously implausible.
If you're genuinely curious about how paradigm shifts happen in science, you might like to read Thomas S. Kuhn's The Structure of Scientific Revolutions. It's considered the definitive work on the matter, and it's interesting, easy to read, short, and inexpensive.
http://www.toptenz.net/top-10-most-famous-scientific-theories-that-turned-out-to-be-wrong.php
http://www.psychologytoday.com/blog/psychohistory/201207/group-think
http://www.amazon.com/Structure-Scientific-Revolutions-Thomas-Kuhn/dp/0226458083
http://online.wsj.com/article/SB123655590609066021.html
Thank you for your response and for the citation of the text.
As I argued above from multiple texts across the Old Testament, slaves were to be treated as human beings. To take Leviticus 25:44 which belongs to the same body of work as contradictory to the other texts above (where I also noted that slaves were allowed to be taken in war), due to vesting a modern notion of “being property” into the text is to interpret anachronistically. To point it out from the 10 commandments as you ask:
> “but the seventh day is the Sabbath of the LORD your God. On that day you must not do any work, you, your son, your daughter, your male slave, your female slave, your ox, your donkey, any other animal, or the foreigner who lives with you, so that your male and female slaves, ‘like yourself’, may have rest. Recall that you were slaves in the land of Egypt and that the LORD your God brought you out of there by strength and power. That is why the LORD your God has commanded you to observe the Sabbath day.”
(Deut 5:14–15 NET)
Consider this as well: Israel has the law and knows the true God. If you are a slave there are many harsh places in the world that you could go, but if you go to Israel you have legal protections, and become acquainted with God.
Regarding applying moral notions to God, I wrote above. God doesn’t reserve rights for himself so much as dispense any rights anyone else has. That’s the Creator/Creature distinction.
Regarding DNA and paleontology, draw what conclusions fit with what is authoritative for you according to your worldview. Read Structure of Scientific Revolutions by Thomas Kuhn. For myself, science is great as natural revelation filling in special revelation, but something subject to paradigm shifts is shaky foundation for a philosophical basis.
Regarding Adam & Noah, forgive my simplicity but Jesus believed them (Matt 19:4-5; Matt 24:37-39), and I trust him more than any man’s guesses since he’s God and he made them. I am still in r/Christianity right? This is the right place to post this? If you rather believe that you are assessing science’s assessment of the data correctly (layered as that is from the original data), that’s your decision.
As I said in another comment on this post, once we get off the Christian concept of God what is even the point of considering the OP’s question? I mean if Jesus isn’t God, Adam & Noah aren’t real, the Bible isn’t an accurate account of God, then what does it even matter if God can deceive or not, seeing as such a being likely doesn’t exist anyway?
The question only matters within the context of Scripture: does Scripture present a God who is indistinguishable from the devil? The answer is no. If we are going to be picky about what Scripture we are allowed to inform that interpretation by invoking science, why not just invoke science to disallow the concept of God and be done? If you want to debate the Bible’s reliability there are places for that, but that wasn’t the original question.
Thanks for reading. Let me know if I can clarify
I recommend reading this book https://www.amazon.com/Drunkards-Walk-Randomness-Rules-Lives/dp/0307275175
You're taking two observations and strongly correlating them, without actual evidence.
This is a fast-paced, beautifully written, introduction to the sciences- there's a chapter each devoted to scientific theory, probability, measurement, physics, chemistry, evolutionary and molecular biology, geology, and astronomy. It's written entirely for laymen in an engaging way, and from 2007, so the information is quite current.
For instance, from the evolutionary bio chapter:
> Evolution is neither organized nor farsighted, and you wouldn't want to put it in charge of planning your company's annual board meeting, or even your kid's birthday party at Chuck E. Cheese. As biologists like to point out, evolution is a tinkerer, an ad-hocker, and a jury-rigger. It works with what it has on hand, not with what it has in mind. Some of its inventions prove elegant, while in others you can see the seams and dried glue.
Leonard Mlidinow in A Drunkards Walk makes an extremely compelling argument for why a CEO has no actual effect on a company's growth/success. And that judging a CEO on how successful the company is a lot like judgings a person for being able to predict a the next roll of a die will be a 6.
Read:
> https://www.amazon.com/Drunkards-Walk-Randomness-Rules-Lives/dp/0307275175/ref=sr_1_1?s=books&amp;ie=UTF8&amp;qid=1511077999&amp;sr=1-1&amp;keywords=the+drunkards+walk+how+randomness+rules+our+lives&amp;dpID=41AmTHIRGpL&amp;preST=_SY291_BO1,204,203,200_QL40_&amp;dpSrc=srch
Check out this book http://www.amazon.com/Drunkards-Walk-Randomness-Rules-Lives/dp/0307275175
The Drunkard's Walk was a pretty interesting read about how randomness and our poor psychological understanding of it affects so many things. Its in the same sort of genre as a Freakonomics or Blink type thing I'd say.
The Drunkard's Walk: How Randomness Rules Our Lives
I read this 5 or 6 years ago and really enjoyed it. Has a lot of math, but includes a lot of history and some psychology as well.
From the Amazon page:
"By showing us the true nature of chance and revealing the psychological illusions that cause us to misjudge the world around us, Mlodinow gives us the tools we need to make more informed decisions. From the classroom to the courtroom and from financial markets to supermarkets, Mlodinow's intriguing and illuminating look at how randomness, chance, and probability affect our daily lives will intrigue, awe, and inspire."
Superforecasting has been on my "get to soon" list since I got it last Christmas. It just got a nice nod in the latest CAS magazine.
Along the probability/math lines, other books I've enjoyed are:
Most people don't.
?? Then read some statistics. Even if 100% of these anecdotes was made up, what do you think of this article?
http://blogs.channel4.com/factcheck/factcheck-black-americans-commit-crime/19439
You can debate cause, but there is data on this issue. If you think it's racist to keep track of the data, IMO you're part of the problem.
From the article:
>Judging from online comments, there is a wide spectrum of views on this, from unapologetic racism to militant refusal to blame the problem on anything but historic white racism.
IMO all the people described in that sentence are the problem. Shitty behaviour is shitty behaviour, and even if it's not always going to give you accurate conclusions if you treat anecdotes as data, it's pretty hard to ignore your lived experiences.
See: Drunkard's Walk if you want to see how often we do this.
http://www.amazon.ca/The-Drunkards-Walk-Randomness-Rules/dp/0307275175
Ooohhh! Happy Halloween!
http://www.amazon.com/dp/0307275175/ref=wl_it_dp_o_pC_nS_ttl?_encoding=UTF8&amp;colid=2I3Z7DM97AUY3&amp;coliid=IC5EYSPD87Y2G
Thanks for the contest!
read the drunkards walk and you understand why this is so.
They refer to this in The Drunkard' Walk, but with pilots. (https://www.amazon.com/Drunkards-Walk-Randomness-Rules-Lives/dp/0307275175)
We essentially have a skill level, but there are so many variables that some days you'll perform worse, some days you'll perform better. But overall, you'll tend to be closer to your normal skill level.
The better question to ask is why do you need this in the first place? If you were playing good and running good your mental game would be fine. The only thing that affecting poker player results are playing bad or running bad. Playing bad can be fixed by analyzing hands, reading good poker books and training. The effects of running bad can be lessened by understanding probability and randomness better. Running bad shouldn't really be an issue if you are bank rolled properly because if it is, then you are playing bad.
Most poker players that I know that are always frustrated or constantly tilting are almost always playing at stakes their bankroll doesn't support.
If you are using the 100 times big blind and 25 buyins recommendation, you shouldn't really have a mental game issue because you should be able to absorb the variance.
Mental Game Books
More understanding about probability, randomness and focusing on the present can be helpful. If you understand those more it should help your mental game. I would recommend these books and at least understand their central points:
For further information, the book The Drunkard's Walk: How Randomness Rules Our Lives by Leonard Mlodinow contains a number of good examples of how humans have difficulties recognizing true randomness. For example, iTunes had to make the random play function less random in order to appear more random.
Mathematical Tourist by Ivars Peterson is an entertaining book for math audiences of all levels. Light on depth but lots of breadth into modern math problems.
The Drunkard's Walk by Leonard Mlodinow is a great historical account of the development of probability theory and statistics with lots of interesting examples.
Yeah, I didn't understand that point really correctly until I read The Drunkard's Walk. People vastly underestimate the role of randomness in how things are.
Yes.
Too many examples to mention but the most talked about examples online would include Bonobo Monkeys and Giraffes. If you want more info on the topic I would suggest the book "Biological Exuberance: Animal Homosexuality and Natural Diversity" by Bruce Bagemihl Dont let the title fool you. It covers much more than homosexuality.
> Biologically, homosexual relationships don't work to further a species.
Yes they do. Two male geese, as an example, are far better at raising a brood than a male/female are.
http://www.amazon.com/Biological-Exuberance-Homosexuality-Diversity-Stonewall/dp/031225377X/ref=sr_1_1/187-8590692-7268402?ie=UTF8&amp;qid=1382549797&amp;sr=8-1&amp;keywords=biological+exuberance
Pretty easy to tear down.
First it's always good to start a debate knowing what your arguing against, So the first thing to ask is what their definition of "Natural" and "unnatural" is, The typical definition and the way the word "Natural" is commonly used is:
>Existing in or derived from nature; not made or caused by humankind
If their definition significantly differs to that then you're arguing against a claim that doesn't follow our languages usage or definitions of common words in which case you're just going to end up wasting your time arguing over definitions, So long as their definition fits this criteria you can move on.
Based on that definition all you need to do is prove that homosexuality occurs "naturally" i.e. "without human intervention"
Which oh boy, we already can, You can point them towards This Wikipedia Article or alternatively they can read up the book "Biological Exuberance: Animal Homosexuality and Natural Diversity" written by Canadian biologist Bruce Bagemihl which shows homosexuality occurring in hundreds/thousands of species other than humans.
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Alternatively What I like to do is to humor their initial claim that "Homosexuality is unnatural" and see where that assertion leads.
So for the discussion we can establish a hypothetical scenario in which they're right and that homosexuality only occurs in humans making it for all intents and purposes "unnatural".
Now that we've created our hypothetical scenario what other conclusions can we draw from that information?... The answer is none, Because neither "natural" things or "unnatural" things have any other inherent qualities or properties that you can make assertions or draw conclusions from, The only question you've answered is whether it occurs with or without human intervention...
The argument that "Homosexuality is unnatural" is typically coming from the Naive perspective that "All unnatural things are inherently bad!" which is obviously nonsense because I doubt these same people making this same stupid argument are going to be the ones denying their children life saving medications because the meds are "unnatural" or refusing to drive to work because cars are "unnatural"
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Homosexuality is documented in other animals as well. So yes, it is
> normal like today's society is trying to make it seem
Why are we any different?
Yeah, I think it will shut them up. Another study I saw suggested that the effect was particularly strong in people who had experienced strict, authoritarian parenting so bring that up if they are conservatives.
Edit: This is a major work on animal homosexuality.
Dr Joan Roughgarden is another expert in this field.
The news article linked by OP is a much more current example, but it is worthy to note that a book was written on the subject as well. It's by a Canadian biologist named Bruce Bagemihl:
Biological Exuberance: Animal Homosexuality and Natural Diversity
Stop second-guessing your choice of major. Keep your eyes on what you actually want, and remember that the steps along the way will all build there eventually. Check in on your plans when you're picking classes each semester, to make sure you're still on course and still want that ultimate goal. The REU and some lab time will all help.
Try reading some science-related books, not actual science but stuff about scientists themselves or stories about specific scientific discoveries. Like The Immortal Life of Henrietta Lacks, Double Helix, Eighth Day of Creation, The Disappearing Spoon, and Surely You're Joking Mr. Feynman. Your school should have copies of most of them, and they aren't textbook-heavy (though not quite as light as fiction novels).
Don't forget to stay at least a little rounded. Someone on just about every recruitment weekend for grad school will ask about your hobbies. I'm pretty sure they're required to do so :) Or you'll discover you and your interviewer both do ceramics and can chat about that, leaving a stronger impression than if you were yet another person talking about science. It's good to be done with the requirements, but make sure you keep up something outside your major, even if it's just ultimate frisbee.
If anyone is looking more elemental oddities, [The Disappearing Spoon] (https://www.amazon.com/Disappearing-Spoon-Madness-Periodic-Elements/dp/0316051632?ie=UTF8&amp;*Version*=1&amp;*entries*=0) is a great read for all ages.
http://www.amazon.com/Disappearing-Spoon-Madness-Periodic-Elements/dp/0316051632/ref=sr_1_1?ie=UTF8&amp;qid=1319233233&amp;sr=8-1
I read that over the summer. This was one of the stories in it. If you guys are into nonfiction and science, you might want to check that book out. Full of amazing stories about chemistry. This story was cool, but there are a lot of cool stories in that book.
I dont find "invisible Spoon" is maybe The Disappearing Spoon ( http://www.amazon.com/The-Disappearing-Spoon-Periodic-Elements/dp/0316051632 ) ?
You should read The Disappearing Spoon. Fascinating read on the elements, how they were named, discovered, and the intrigue behind them. It's a lot more interesting than I'm making it sound...
Gallium disappears.
https://www.amazon.com/Disappearing-Spoon-Madness-Periodic-Elements/dp/0316051632
https://www.amazon.com/Disappearing-Spoon-Madness-Periodic-Elements/dp/0316051632 has every thing you listed in a single book. It is a fantastic read that covers the usage of elements and stories of their discoveries and the scientists behind them. I love it and going to finish it while overseeing exams in the coming weeks.
Here is a couple, the first two are Pop-sci and may be more of what you are looking for. The third is probably the most dense.
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https://www.amazon.com/Disappearing-Spoon-Madness-Periodic-Elements/dp/0316051632
http://home.theodoregray.com/bookproducts/the-elements-autographed-copy
https://www.amazon.com/Chemical-Tree-History-Chemistry-Science/dp/0393320685/ref=sr_1_16?keywords=chemistry+history&qid=1574340632&sr=8-16
Reddit's acting wonky and showing me some comments, then removing them. But I thought I would answer your question as best I could.
Basically, they had figured out spectroscopy. If you put a gas in a tube with metal plates at each end you can sent an electric current through it and the gass will glow. You get different colors based on what is glowing. My 7th grade science teacher did this and it was cool as hell. Here's a cool video that shows some gases (it uses a Tesla coil to excite the gas). If you send the light through a prism, you can separate out the colors. Depending how you do it, you either get a rainbow with some parts missing, or just the missing colors. Here's a wikipedia article with the spectral lines of a bunch of elements. Apparently a guy named Fraunhofer did this in 1802.
There was a solar eclipse in 1868 and they did a spectral analysis of the sun. They found some lines that didn't correspond to anything. Meanwhile, Mendelev didn't publish his periodic table until 1869. His table didn't include Helium. There were a decent number of elements and the periodic table went through several revisions. In addition, Helium is a noble gas so it doesn't really react with other elements. It's also pretty rare on earth (although common in the universe). So it took scientist a while to find it on Earth.
Although I don't remember it covering the discovery of Helium, I'd recommend The Disappearing Spoon by Sam Kean that is a fun, but informative, book on the elements.
I enjoyed Krakatoa: The Day the World Exploded by Simon Winchester.
Also, and this one isn't strictly geo, but it's awesome, The Disappearing Spoon by Sam Kean. Basically a history of the periodic table. And it's really funny too.
Consciousness Explained
There's an awesome primer here on how the human mind creates the illusion of experience, if you want to check it out. Dennett's sometimes a bit obtuse, but he's rarely wrong: http://www.amazon.com/Consciousness-Explained-Daniel-C-Dennett/dp/0316180661
Have you read Consciousness Explained ?
We don't know yet.
The brain is so complex, science is just scratching the surface of what consciousness is and how it works.
Daniel Dennett wrote a book called Consciousness Explained. Summary: It's a hard problem.
While it's a bit out of date, "Consciousness Explained" by Daniel C. Dennett can give a good introduction to what we know about how the brain really functions, and the vast difference between directly perceiving the world and the actual action of the brain to filter out most of the world, and translate what's left into an internalized model our consciousness is made aware of. It's a philosophy book, but leans heavily on medical understanding of brain biology, real-world behavior testing, and AI development progress (as of the 1990's).
The biggest aspect of it being out of date has to do with the sections on AI; our neural network architectures in use today are significantly more advanced and more similar to biological systems than what was available in the 1990's. That said, the insights from the state of development at the time (and its failures) are even more prescient in light of the last 10 years of AI development and progress.
Em janeiro, terminei de ler Fundação, do Isaac Asimov. É um livro sensacional; super recomendo. Agora, estou terminando The Foundational Falsehoods of Creationism e Gödel, Escher, Bach: An eternal golden braid. O próximo que eu vou ler provavelmente será Consciousness Explained, do Daniel Dannet.
First off, we are not sure how to define conciousness. It is very difficult to study because it is inherently subjective. To approach conciousness requires integrating information ideas from evolutionary biology, neuroscience, computational science. That said, one of the premier thinkers/writers about conciousness, Daniel C. Dennett, is also a premier thinker about evolution. To boot, he is one of the new atheist writers called the "Four Horsemen of the Apocalypse". His body of work includes the audaciously titled Conciousness Explained. His works are meticulously thought out & thourogh, so be prepared.
http://www.amazon.com/Consciousness-Explained-Daniel-C-Dennett/dp/0316180661/ref=sr_1_1?s=books&amp;ie=UTF8&amp;qid=1412263188&amp;sr=1-1&amp;keywords=consciousness+explained
Other works i can recommend are: Darwin's Dangerous Idea, Freedom Evolves. His theory of conciousness has changed a bit since The Minds "I".
(I know I'm late, but would like to add my 2 cents anyway.)
I'd say the series stays about the same. (But I also loved it to begin with.) I only remember disliking some of the developments with the Deltans storyline (though I did like it again at the end) and perhaps the romance being a bit of a mixed bag for me.
>... the narrative left behind a lot of what I found most intriguing about the story (Cartesian dilemma of soul and body) ...
Do you mean dualism? When exactly was this brought up?
As I understood it, Bob 1 was pondering whether or not he (a computer program) could be considered conscious -- Something living, something of moral significance. I thought this was settled adequately by his extended monologue. He was wondering whether he was a philosophical zombie (i.e. acting as if conscious without actually being conscious.) He was not wondering how his soul interacted with his replicant hardware (or software.)
And I'd say he's revealed himself as a sort a functionalist: "Handsome is as handsome does." Or rather "Bob is as Bob does."
On that subject, one of my favorite philosophy books is Consciousness Explained by Daniel Dennett. It's heavy reading but I still recommend it. Here's a review. Also this preface by Tadeusz Zawidzki about Dennett's corpus :D
Edit: phrasing
Weiskrantz L. - Some contributions of neuropsychology of vision and memory to the problem of consciousness - chapter 8 of "consciousness in contemporary science" edited by Marcel and Bisiach esp pp 186-190
see also
Weiskrantz L. - "Blindsight: A case study and implications"
you might be able to find a pdf..
Referenced in Dennett's "Dismantling the witness protection program - 2. Blindsight: Partial zombiehood?", chapter 11 pp 322-333 of "Consciousness Explained"
I first heard the word "meme" from this book from 1992 :
http://www.amazon.com/Consciousness-Explained-Daniel-C-Dennett/dp/0316180661/ref=sr_1_1?ie=UTF8&amp;s=books&amp;qid=1293749679&amp;sr=8-1
If you like Harris and Pinker's philosophical stuff, check out John Searle, Noam Chomsky, and Dan Dennett (Dennett wrote a harsh review of Harris' book on free will). They're like Harris and Pinker, but better.
Fair enough. Didn't know that this was where you were coming from.
No, I haven't read Barrow. But pretty much any popularization of physics recently seems to make this very point. From Brian Greene to Lee Smolin seems to make this point.
I think we were both missing what the other was saying. I agree with your point on why, apologies for the bluntness. I didn't fully see your Devil's Advocate position until now. So I guess we agree to agree?
For Quantum Physics I cannot recommend Quantum Physics: A Beginner's Guide it has enough maths to make it worth reading, but the equations etc. are in supplemental boxes with explanations and investigations so you can ignore all the maths if you want. It tends to focus on the applications of quantum physics in semiconductors, superconductors which is good to learn about as it is easier to comprehend than the really tricky philosophical implications.
I would also recommend The Fabric of the Cosmos by Brian Greene, because it has more philosophical stuff in it, and although it is broader and not just about quantum physics but includes relativity and stuff too, it is an awesome book and you won't regret reading it.
For evolutionary biology I would recommend The Blind Watchmaker by Richard Dawkins, it is a Science book so don't worry if you don't like his aggressive atheism as if I recall correctly it doesn't rear it's head in the book at all. It is especially good if you enjoy Computer Science as he makes some analogies between life and programs which are obviously easier to appreciate if you have some experience (Dawkins was a programmer for many years).
I don't know what paleo-anthropology is so unfortunately I can't recommend anything there, but I would be extremely happy if you could enlighten me and perhaps recommend some texts. (Not terribly helpful, I know :P )
You should read The Fabric of the Cosmos: Space, Time, and the Texture of Reality by Brian Greene, he covers many of the major concepts in physics and string theory in an accessible manner.
the fabric of the cosmos by brian greene.
https://imgur.com/a/YDnnlXI
this is the book that got me into the subject when i was a kid. it builds understanding with terms that are understandable and then builds from there.
https://www.amazon.com/Fabric-Cosmos-Space-Texture-Reality/dp/0375727205
and dont worry, if i opened a paper from anything other than my own specific niche id be just as lost!
.... that said, i dont have a better answer than a five hundred page book. its not a simple topic!
As others have pointed out, there really is more to it than can easily be put into a reddit post. You CAN spend a lifetime studying it, and many do.
That being said, I've often linked people to Evolution in a cartoon by Darryl Cunningham. It's long for a cartoon, but short for the amount of information and insight it provides. It's a brief overview and is to be used only as a primer on the topic, not a thorough compendium.
If you find yourself interested in further information, I'd suggest Jerry Coyne's book Why Evolution is True.
As others have noted, Talk Origins is an excellent, comprehensive resource. But it can get a bit technical and wordy for people new to the topic.
Best of luck, enjoy the journey. Let us (me specifically if you'd care to) know if you want to discuss anything further.
I suggest you read a couple of books that present the evidence for evolution very clearly:
Why Evolution Is True
The Greatest Show on Earth: The Evidence for Evolution
Evolution itself is a simple concept, but the evidence for it is broad and detailed across many scientific disciplines, and it all fits together.
Regarding the existence of God, one can't prove that your God doesn't exist, or that any of the other thousands of gods that have been worshiped through the ages don't exist. The real question is whether there is enough evidence to positively prove the existence of any one of those gods.
Evolution is true:
http://www.amazon.com/Why-Evolution-True-Jerry-Coyne/dp/0670020532
Evolution is true and doesn't conflict with religion:
http://www.amazon.com/Finding-Darwins-God-Scientists-Evolution/dp/0060930497
Skepticism:
http://www.amazon.com/Demon-Haunted-World-Science-Candle-Dark/dp/0345409469
Why evolution is true. by Jerry A. Coyne
Pretty much all the evidence you need for evolution there. For information about the origins of life you will have to look elsewhere though.
http://www.amazon.com/Why-Evolution-True-Jerry-Coyne/dp/0670020532
You might try here: http://www.reddit.com/r/askscience/search?q=fact&amp;restrict_sr=on
and then ctr+F for "evolution" for a few previous instances of this question, or here:
http://www.reddit.com/r/askscience/search?q=evolution+fact&amp;sort=top&amp;restrict_sr=on
or other variations thereupon.
Anyways, we don't make a habit of letting these questions out all that often, as they never really do well, and when they do attract attention it's mostly people who don't really understand evolution all that well, trying to explain evolution to people who definitely don't understand it that well, and it just never really winds up being productive (while those of us who do know something about evolution squirm in agony at even attempting to undue all the damage this whole "fact vs theory" thing in a somewhat concise manner).
I'm keeping it spammed (you could also try searching in /r/evolution), but my honest suggestion would be to have her read something like Jerry Coyne's Why Evolution is True, if she's willing to (and perhaps you could sit down and read it yourself first, to be able to give it an honest recommendation). Alternatively Dawkins's The Greatest Show on Earth is supposed to be good (I haven't read it myself), although Coyne's writing style might be more appealing for the non-academic, and some people are allergic to Richard Dawkins, for obvious reasons if you know who he is.
What's her angle. Presumably she is of the faithful? If that's really her angle, then you might be hard pressed to convince her with a short paragraph or two that I could provide.
When you take the position of refusing to learn, nothing can be done to convince you. Why not be curious instead? Why not become interested in the world and how it works? It's fun.
It's not really possible to learn evolution via reddit comments. You need to read a book. For example, Why Evolution is True.
I wouldn't say a damn thing. I'd just point them in the direction of this and this.
Yes. From "The High Frontier", a book on making space colonies, you could deflect meteors - even nonmetallic - from a colony with an electric field. It required a charge of about two gigavolts to be maintained across the whole of it.
This is costly. And any visiting craft would have to be neutralized relative to whatever charge the colony holds.
Just coating a colony in slag is pretty good; sure, spin up will be harder, but... well, reasons previously listed.
I'm reminded of a conversation a friend had with me; a force field is basically something that would repel an object from contact with the field, right? And you'd need some sort of stabilizing element, right? Something spread across the whole field, probable uniformly?
Something like atoms?
What with the nucleus holding it together and the electrons around it providing the desired electric field?
Yeah. A sheet of strong plastic is essentially a force field.
BUT, that's not nearly as cool.
So you could make an electric field strong enough to repel something moving like a meteor, but... well, here's food for thought. Cathode ray TV's and monitors operate at 35Kv or lower. And they are designed to fail if they over voltage, because they shoot beams of electrons through/at a metal screen, and would deliver X-rays to the viewer if they didn't have such circuits.
Why did you think they were made of lead/strontium glass? Rhetorical question, it's to not irradiate the user.
So, having metal buttons on your person may well enough end up giving you cancer. Not so bad if it's your only choice, or you have a short time to live anyway.
Now, maybe if you could entrap differently charged ions in two fields layered over each other, you'd just need like, a mesh to generate and hold the fields, and then when an object passes through the fields, it'd explosively short it. Sorta like ablative armor but... This may still end badly for the user. Layer it, perhaps?
We do have a very good understanding of electricity on the atomic level; Quantum Electro Dynamics. Feynman wrote a really great introduction to it - he was a great teacher, and was one of the inventors of the theory. It's called "QED: The Strange Theory of Light and Matter".
Gravity is also pretty solid; Laplace fixed our understanding of orbital mechanics in the Napoleonic age. Whooole lot of differential equations there.
QED: The Strange Theory of Light and Matter
It's short (less that 200 pages), it's written so a high school student can understand it and for many years I have gained new incite by thinking back on this book.
http://www.amazon.com/QED-Strange-Theory-Light-Matter/dp/0691024170
(I have many others - I just wanted to make certain this book appeared.)
I would recommend reading, Feynman explains modern physics beautifully and tailors his writing to someone with very little math knowledge
Amazon Link
Recommended reading on the subject. Here's my explanation, though this is outside my expertises, and a physics major should offer a more comprehensive answer. But here we go.
When a photon strikes an atom, it causes an electron to jump to its next energy level. The photon is absorbed in the process, and its energy is conserved by an increase in the electron energy level. The atom won't like the configuration, so the electron will soon drop back down to the lower energy level, releasing a photon. This is called reflection.
Now, when you get enough atoms lined up in the right orientation, the image will be conserved. The book I provided offers an awesome explanation of the phenomena. Simply, the light can be considered to be reflected off the front surface and back surface. You know how light is sometimes thought of a wave? It is useful to think of it in this way for this explanation. The reflections from the back and front surface will interfere (two waves taking up the same space). If a peak meets with a valley, the two cancel. If a peak meets with another peak, it will interfere 'constructively', and the light will be preserved.
Now, if the surface is nice and smooth, a clear reflection will be seen as a result of this interaction between the two lights. reflections off glass windows works in this manner. When you are in a bright room at night, the light reflecting off from the room is brighter than the light coming in from outside. This is why you have a hard time seeing through your windows at night, and it helps to shield the glass from the light with your hands. BUT I DIGRESS
Now, you are correct in thinking that the absorption/emission event sends the photon in a random direction. But the waves associated with these random reflections cancel each other out in most cases. The only photon that survives the mass extinction are the ones that reflected with an angle of reflection equal to the angle of incidence.
But really, read the book I linked. It explains this all much better than I can.
Perhaps a lot will be clearer if you get the quantum nature of the measurement of light's polarization. Classically, light is a transverse electromagnetic wave. When one measures a photon's polarization it assumes a definite value, i.e. some orientation. To say that light is unpolarized means that all electric field directions of every photon in a beam will have equal probability to be measured. If the light is polarized then it can be measured in one of only two states. "Circular polarization" means each possible state is described by a plane waves of equal amplitude but differing in phase by 90°. If the light is "elliptically polarized" then it's unmeasured state is described by two simultaneous plane waves of differing amplitude related in phase by 90°. It can also be called elliptically polarized if the amplitudes of the two states are equal but the relative phase is other than 90°. So an unpolarized beam of photons say, or a single photon with a polarization at some angle relative to your measuring polarizer say, is not split into two when sent through a polarizer, rather each photon takes one path or another according to probability.
Concerning your next group of questions about how light propagates through dielectric solids like glass... There is only free propagation, absorption, and scattering. Scattering can be either elastic or inelastic. Scattering theory is a rich subject because materials are so diverse in composition. The most common form of scattering in isotropic media like the atmosphere and dielectric solids composed of small molecules is an elastic form of scattering called Rayleigh scattering. Rayleigh scattering occurs when a photon penetrates into a medium composed of particles whose sizes are much smaller than the wavelength of the incident photon. In this scattering process, the energy (and therefore the wavelength) of the incident photon is conserved and only its direction is changed. Rayleigh scattering has a simple classical origin: the electrons in the atoms, molecules or small particles radiate like dipole antennas when they are forced to oscillate by an applied electromagnetic field. This is not an absorption and re-emission. If the scattering sources are stationary, then this secondary radiation is phase locked to the driving electromagnetic field. So perhaps this is what you mean by "coherent transmission". But even for a truly coherent source of photons, from a laser say, the coherence length is shorted by the presence of the dielectric.
Lastly, your bonus question... You need to read Richard Feynman's, QED: The Strange Theory of Light and Matter. Light propagates as a wave, even single photons. It therefore takes all possible paths, not just the path of least time! It's just that only those paths which arrive at the detector in phase will result in a non-zero amplitude. And for a single ray of light passing from one isotropic medium to another of different index of refraction, there is only one path that satisfies that condition, the path of least time. Anyway, you will love the book and will come away understanding light much better.
The Strange Theory of Light and Matter for an intro to QED.
QED by Feynman
The man that said "if you think you understand when to mechanics, you do not understand quantum mechanics" is Richard Feynman. He also wrote a book that explains quantum mechanics, called QED.
You must realize you are the box and the box is you. With the same instance that you understand your box, your box understands you. This means quantum mechanics may substitute for a cozier box?
On a sidenote however, I understood quatum mechanics at least a little better after reading QED The Strange Theory of Light and Matter I recommend it.
If you want to understand how reflection behaves in a "true" way, read Feynman's QED. Transcripts of popular science lectures. They're not exactly simple to understand, but they were designed to be at least somewhat accessible.
Try reading some of Feynman's lectures - he explains these difficult concepts very well.
Maybe The Strange Theory of Light and Matter would help.
I'm sure you can find a source on the internet pretty easily if you don't want to buy a printed copy.
Here are some links for the product in the above comment for different countries:
Link: QED is the one more relevant to this discussion.
This bot is currently in testing so let me know what you think by voting (or commenting).
> do you mean that they are man-made tools to help picture and calculate and predict?
Yes.
> once we figured out that light is the oscillation of the EM field, that proved to us that fields are actually a real physical... thing.
That's definitely not the case (the second part.) In fact the experiments of Michelson and Morley are usually cited as definitive proof that it's not a real, physical thing.
> If you don't feel confident answering, are there any books you would refer me to?
Check out Feynman's books "6 Not-So-Easy Pieces" and "QED". QED is the one more relevant to this discussion. I would also recommend Roger Penrose's The Road to Reality if you have a lot of spare time and are willing to keep up with it properly.
Are you taking an intro to physics course as an undergraduate? If so, and if you are interested enough to take more coursework on physics, try taking an EMags (Electromagnetic Fields) class in the EE or physics department. 20th century physics (relativity) and a couple of QM (Quantum Mechanics) classes would be helpful as well. After you take a couple of EM and QM courses, you'll really appreciate how god damn hard it is to have any sort of "intuition" about physics, and how important it is to just treat the math like math.
You might consider reading QED: The Strange Theory of Light and Matter, by Richard Feynman. It's a short, inexpensive, book based on 4 lectures he gave for the general public on the subject of light. With all due respect to those who have answered you so far, I think Feynman's explanation is clearer.
The 4 lectures themselves are available in streaming video.
Damn, actually I thought he was suggesting this be our holy book.
http://www.amazon.com/QED-Strange-Princeton-Science-Library/dp/0691125759/ref=sr_1_1?s=books&amp;ie=UTF8&amp;qid=1321740625&amp;sr=1-1
>To answer I guess it would be an unusual intentional altering of normal physical processes by some agent outside those processes. Or something, kind of hard to come up with one that fits everything.
That sounds like a good definition. I still don’t know how we (a) separate a natural event from one caused by an outside agent, whatever that is, and (b) how we can tell if claims of miracles are true or just made up. Like it would be a miracle if David Copperfield really transported himself, but he merely gives the illusion of doing this.
>To answer I guess it would be an unusual intentional altering of normal physical processes by some agent outside those processes. Or something, kind of hard to come up with one that fits everything.
What is the overwhelming evidence? I mean what is your very best bit of evidence? Or top 3, top 5, top 10...
At the end I know you take me up on some other sources, which I will provide, and a key learning of them is that it’s really hard to actually figure out real truths, to be really sure of things, and it’s very easy to fool yourself along the way. Just think that for many people, for a long time, even with overwhelming evidence of it being the case, it would have appeared that the sun/moon/stars moved around the earth, being at the center. But that would have been wrong. This is how careful you need to be before accepting things as true, because it’s very easy to fool yourself.
>Muhammed was the most obvious false prophet in history. Allah is capricious, even to muslims, arbitrarily allowing believers into heaven or not.
So what? How do we know God (if he exists) is even the “good guy”?
>Whether or not I picked the right one, I would not pick one so obviously wrong
What are you basing your notion of “wrong” on? Some subjective personal feeling about how God must be?
>Not all miracles are equivalent, and not all miracle accounts are equivalent.
I agree, some can be made up on the spot, others talking about for centuries. But which ones can you actually demonstrate to be true?
The link you provide gives no evidence outside of a circular argument based on Biblical accounts. Anyone can write down a claim in a book, that is still just a claim, not evidence of the claim.
>There are no physically possible options
You’re claiming to know. And maybe you’re even right, maybe there are no “physically possible” options whatever that means. Maybe there is a non-physical option. But the simple truth is we don’t know what that is (we can only take faith in some version of it, which again, is a horrible way to figure out truth).
>The appropriate answer is that we do know - no natural options are possible, therefore the origin is supernatural.
there are also a whole hell of a lot of “supernatural” options. Could be the Christian God, could be Allah, could be as George Carlin put it, some supernatural force that brought the universe as we know it into existence but doesn’t care about us at all (I think probably the most likely, to assume otherwise is very hubristic): https://www.goodreads.com/quotes/235413-something-is-wrong-here-war-disease-death-destruction-hunger-filth
>You think that the unscientific musings some people use to explain the origin of the laws of physics are somehow so robust that it becomes a scientific certainty that the laws of physics could not have changed since then? Is that what you're saying?
Just show me the evidence that they’ve changed and we can put this to bed.
>So I guess you prefer circular reasoning, or perhaps an infinite regression? Those are the only three options according to baron von munchhausen, so let me know what you choose before attacking axiomatic reasoning.
I already said it’s UNKNOWN. Maybe it’s an unknown supernatural force that set things in motion but isn’t conscious, doesn’t care. Maybe it’s an infinite regress we can’t understand. You are the one using circular arguments to state it must be a certain way. You even seem certain that Mohammed is a false prophet. Please go take your evidence for that to the Middle East because it would solve a lot of problems.
I see you think the Quran is disproven through contradictions. Maybe that’s one reason to question it, but I think the bigger problem is simply that it has not been proven because evidence hasn’t been provided to confirm it’s truth. It has to be accepted on faith that it is the word of God as given to Mohammed. Same problem with the Bible, it has to be taken on faith that it’s portraying real events (like the resurrection of Jesus).
Now for the information I offered, I would start with a short video and a commencement speech; https://m.youtube.com/watch?v=tWr39Q9vBgo
http://calteches.library.caltech.edu/51/2/CargoCult.htm
(He talks about pseudosciences and poor approaches to science, and please just realize that religious claims are like another order of magnitude more absurd when it comes to accepting them as true)
These both deal with the pitfalls we can succumb to and “fool ourselves”, and how difficult it is to really figure something out. If this interests you even slightly, I highly highly suggest this book: https://www.amazon.com/QED-Strange-Theory-Light-Matter/dp/0691125759
Because he is able to describe the known (DEMONSTRATED) behavior of light and quantum mechanics, without using any equations, and tells you how it really is. The purpose of reading this (even just the first couple chapters) is to provide an understanding of the level of depth us humans have been able to go to in understanding the world around us, and help you put Biblical claims into context. The fact that Biblical claims come nowhere remotely close to fitting the most bare bones requirements that would be applied to saying a scientific theory is true, I know most theists dismiss as “well that’s because this is outside the realm of science” - but you’ve never demonstrated that! Again it all comes down to faith, and it not the fault of science that we’ve learned how to really learn things, not just take faith in some story.
https://www.amazon.com/QED-Strange-Theory-Light-Matter/dp/0691125759
https://www.amazon.com/gp/product/1420946331/ref=dbs_a_def_rwt_bibl_vppi_i0
The latter is at gutenberg.org as well. Good idea with some of the simpler and less creative gymnastics.
As far as philosophy's concerned, these two in particular are a bit classic. The less time is spent on dealing with and accepting experiments, the further into lala land of maths you go. None of these newer theories actually offer an answer and are creative proposals that all fall short of a physical description and process. QED by Feynman is entertaining and funny, and you won't find better explanations that doesn't discuss some mathematical idea, which means we've left the realm of philosophy and physics in a classical sense. Because saying the "maths works", so let's justify it with something that sound plausible is really starting to get old.
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So this is perhaps "basic" and what you were asking for. But it may offer a grounding before exploring all the terms and ideas that can be referenced when calculating and wanting to make a prediction. Or a phenomenological argument that has little to do with experiments and well off into the fringes of physics regions. Phenomenology is not philosophy in this sense, it's an subjective argument based on own work and experience and is largely subjective and hinges on whatever idea it revolves around.
https://en.wikipedia.org/wiki/Phenomenology_(physics)
In HEP, predictions come after preliminary data, where application of theories and calculations are the "phenomena" and the experimental results with high statistical significance is the "horse". So to compete here you need a rumour mill and access to let's say 2-4 sigma results. Experiments are cool, hoping for something truly revealing, theory dealing with results and what it means gets boring with these speculations. Good luck finding an article that argues a problem.
I can only find the Amazon Kindle version. :(
http://www.amazon.com/dp/0691125759
QED: The strange theory of light and matter by Richard P. Feynman
http://www.amazon.com/QED-Strange-Princeton-Science-Library/dp/0691125759
Personally, I think you would get great suggestions on /r/physics. But since you're here...
Since you seem like you're just dipping your toes in the water, you might want to start off with something basic like Hawking (A Brief History of Time, The Universe in a Nutshell).
I highly recommend Feynman's QED, it's short but there's really no other book like it. Anything else by Feynman is great too. I found this on Amazon and though I haven't read it, I can tell you that he was the greatest at explaining complex topics to a mass audience.
You'll probably want to read about relativity too, although my knowledge of books here is limited. Someone else can chime in, maybe. When I was a kid I read Einstein for Beginners and loved it, but that's a comic book so it might not be everyone's cup of tea.
If you really want to understand quantum mechanics and don't mind a little calculus (OK, a lot), try the textbook Introduction to Quantum Mechanics by Griffiths. Don't settle for hokey popular misconceptions of how QM works, this is the real thing and it will blow your mind.
Finally, the most recent popular physics book I read and really enjoyed was The Trouble with Physics by Smolin. It's ostensibly a book about how string theory is likely incorrect, but it also contains really great segments about the current state of particle physics and the standard model.
>Man, I've already told you. That answer to that question isn't compressible by me to you.
No, it is. It really is.
> It's Shadows of the Mind. Not the easiest read, but not the hardest either.
I'll pick it up. However from googling I think you have misinterpreted Penrose's quantum gravity.
https://www.scientificamerican.com/article/physicists-eye-quantum-gravity-interface/
It's a hypotheses as to why the wave function decoheres. That's a completely different issue than the effects.
I highly recommend Feynman's QED. If you have any desire to understand Quantum Mechanics, you will understand after reading it. It requires no math.
https://www.amazon.com/gp/aw/ol/0691125759/ref=olp_tab_all
If you have a solid background in calculus, this is a great book that touches on fractals as part of a broader treatment of nonlinear dynamics and chaos theory. You can also learn a lot by messing around with fractal plots (especially the Mandelbrot set) in programs like Winplot and seeing what happens.
You can download the full episodes at:
http://www.radiolab.org/archive/
The podcasts are short, but the full hour-long episodes are available. It's one of my favorite programs. That, and Philosophy Talk.
Radio Lab tends to feature one of my favorite mathematicians, Steven Strogatz, in several episodes (Emergence was great). He has a good presentation style (see YouTube) and I've really enjoyed his book: http://www.amazon.com/Nonlinear-Dynamics-Chaos-Applications-Nonlinearity/dp/0738204536
What kind of nerd am I to have a favorite mathematician? I'm not sure I want to know.
In order to learn about chaos theory, you need to know a little bit about differential equations. If you feel like you have that down, this book is a good place to start for a beginner:
http://www.amazon.com/Nonlinear-Dynamics-Chaos-Applications-Nonlinearity/dp/0738204536/ref=sr_1_1?ie=UTF8&amp;qid=1302645159&amp;sr=8-1
No problem, glad you find it interesting. If you want to know more, Steve Strogatz's Nonlinear Dynamics and Chaos is a good place to start and is generally very accessible. It talks about how to tell what regions of phase space are stable vs unstable, for example, and how chaos arises out of all of this. Overall it is a good read and has a lot of interesting examples (as is typical of a lot of his books).
For more on the Hamiltonian mechanics in particular (albeit at a more advanced level), the classic text is Goldstein's Classical Mechanics. Its definitely more dense, but if you can push through it and get at what the math is saying its a really interesting subject. For example, in principle, you can do a coordinate transformation where you decouple all the generalized momentum - coordinate pairs and do a sort of modal analysis on a system where you would never be able to do so otherwise (these are called action-angle variables)
It's cool that you're interested in complex systems, but your post is a bit vague. I liked Nonlinear Dynamics and Chaos (Strogatz). It is a very easy/friendly intro to the field. Another good book, depending on what you're wanting to do, might be Daniel Gillespie's book on markov processes. In general, you basically need to read some papers, find a type of problem/approach that interests you and then fill in the blanks with supplementary material. Most of what you need to know is in a journal somewhere. Google that shit. If you want to code stuff, learn python & C.
http://www.amazon.com/Nonlinear-Dynamics-And-Chaos-Applications/dp/0738204536/ref=sr_1_2?s=books&amp;ie=UTF8&amp;qid=1335215605&amp;sr=1-2
Strogatz writes in a very easy to understand manner. For those interested in chaos theory and nonlinear dynamics, this is the book to read.
If by ‘good kind’ you mean psilocybin containing, you are dangerously far off. Buy and cherish Paul Stamet’s Psilocybin Mushrooms of the World(https://www.amazon.com/Psilocybin-Mushrooms-World-Identification-Guide/dp/0898158397) if you want to know what to look for.
If by ‘good kind’ you mean edible, then you should read the sticky on how to properly request an ID as you are missing key features used in identification of your mushroom.
Based on the initial picture I would say very likely a no to both possibilities of a good kind.
I used to do the Shroomery quite a bit... grew up some. Not to disparage, but some of them damn kids! Ugh.
Too northern? I'm not sure about that. Season's coming up for winter stuff in northern climates...
Are you asking for a "shroom" guide, or a mushroom guide?
This for the former.
This and this for the latter.
Can you tell me where you are, generally, so that i can help?
This one
Psilocybin Mushrooms of the World: An Identification Guide https://www.amazon.com/dp/0898158397/ref=cm_sw_r_cp_apa_i_D3z2Cb5XHQ78W
The world is your source
Couldn't remember why I knew that name, but then I remembered he did some work with Psilocybin.
https://www.amazon.com/Psilocybe-Mushrooms-Their-Allies-Stamets/dp/0930180038
https://www.amazon.com/Psilocybin-Mushrooms-World-Identification-Guide/dp/0898158397
Richard Feynman's "Strange Theory of Light and Matter" explains why. It's all about probabilities.
I'll recommend QED by Richard P. Feynman. It's not a textbook, and it has no math. Yet it quickly leads to a solid understanding of QM.
&#x200B;
https://www.amazon.com/QED-Strange-Theory-Light-Matter/dp/0691125759/ref=dp_ob_title_bk
'Fabric of the Cosmos' by Brian Greene
Brian Greene's The Elegant Universe gets my recomendation
Rofl! Ron Paul!
Hahahahahahahahahahahahahahahaha
Oh yeah, republitards love science! Remember when they said:http://www.huffingtonpost.com/2012/10/06/paul-broun-evolution-big-bang_n_1944808.html
That was fun!
Here are a few more!
http://www.motherjones.com/blue-marble/2012/03/its-not-your-imagination-republicans-really-dont-science
http://www.salon.com/2013/01/11/scientists_hate_the_gop_for_a_reason/
This book might explain why..:http://www.amazon.com/Republican-Brain-Science-Science-Reality/dp/1118094514
In conclusion
http://i.imgur.com/2cfsJnP.jpg
http://i.imgur.com/8TcwHbx.jpg
Except this idea is just wrong. Suggested readings:
How the laws of physics lie
The Structure of Scientific Revolutions
Realism and the Aim of Science
I'm not here to get into a debate on the philosophy of science, nor do I have any time for revealed religions. But science is an investigative quest, and suffers from its own sociological conundra. And much what science is isn't actually trying to be true, which is fine; an empirically accurate approximation is quite serviceable enough most of the time. But the bottom line of that is there is no reason to believe that in replaying it the same models would have to be produced.
This has been a respectful back and forth, and I appreciate that. This will be my concluding comment.
> Religion has been the single greatest force limiting advancement in human history
>
This is the claim of the likes of Sam Harris. And this was the point that Nassim Taleb tried to make to him, although quite clumsily- religious thought has greatly contributed to building the Western world. For example, much of science has it's foundations in the presumptions produced by a religious worldview. Religion provides answers to existential questions that need to addressed before any scientific inquiry can be made. For example, one must have the presumption that the world is intelligible and comprehensible before engaging in scientific inquiry. If you don't start with that presumption, you cannot do science.
If you're interested in learning more about the philosophical presumptions that form the basis for scientific inquiry, check out The Structure of Scientific Revolutions by Thomas Kuhn
Peace.
We DON"T know that, its just every time we check on them (do experiments) the results come out that in such a way that makes us think that the laws that we have deduced from previous experiments still hold true. The interesting thing about scientific paradigms is that we do something, then see a result and then try to come up with an explination of why that result happened, the better our explanation explains the result and explains other results and survives repeated testing the better our explanation is to determining how the world really works, from which we can do things that build on our explanation.
This in the end does allow false assumptions to exist in science (think phlogistion chemistry) but as the field of science requires more complicated and complicated excuses for why different events happened, they are replaced with a new paradigm that explains the physical world differently.
In the end we may find at some point down the road something that scientists believe an unquestionable rule of physics is actually incorrect because it cannot explain X,Y, or Z but a new explanation comes forth and explains the stuff the first law explained and X,Y, or Z, in a better, cleaner way.
To read more I suggest : The Structure of Scientific Revolutions by Thomas Kuhn
http://www.amazon.com/Structure-Scientific-Revolutions-Thomas-Kuhn/dp/0226458083
Almost anything Malcom Gladwell.
Disappearing Spoon
http://www.amazon.com/The-Disappearing-Spoon-Periodic-Elements/dp/B00401LQ2Q/ref=tmm_aud_title_0
Feynman's Rainbow: A Search for Beauty in Physics and in Life
http://www.amazon.com/Feynmans-Rainbow-Search-Beauty-Physics/dp/044653045X
Euclid's Window : The Story of Geometry from Parallel Lines to Hyperspace
http://www.amazon.com/Euclids-Window-Geometry-Parallel-Hyperspace/dp/0684865246/ref=la_B001IGP3W0_1_7?ie=UTF8&amp;qid=1342497797&amp;sr=1-7
The Drunkards Walk : How Randomness Rules Our Lives
http://www.amazon.com/The-Drunkards-Walk-Randomness-Rules/dp/0307275175/ref=la_B001IGP3W0_1_3?ie=UTF8&amp;qid=1342497797&amp;sr=1-3
Steve Jobs Walter Issacson Book
A Short History of Nearly Everything
Eat That Frog
In Defense of Food
Nullification
The Dictionary of Christianity and Science by Paul Copan, Tremper Longman III, Christopher L. Reese, and Michael G. Strauss. In one volume, you get reliable summaries and critical analyses of over 450 relevant concepts, theories, terms, movements, individuals, and debates on how Christian theology relates to scientific inquiry. It goes over the competing philosophies of science, and asks if they “work” with a Christian faith based on the Bible. Featuring the work of over 140 international contributors, the Dictionary of Christianity and Science is a deeply-researched, peer-reviewed, fair-minded work that illuminates the intersection of science and Christian belief.
Author Gerald L. Schroeder (widely known for converting atheist Anthony Flew to a Deist), Number 5 here was what convinced Flew. It's worth pointing out though that he conforms his theories to the current scientific paradigm of the age of the universe and strives for compatability when it comes to other areas like Pre-Adamite cave men. He is strongly against evolution and lays out why very thoroughly in his books. He is also Jewish.
The Structure of Scientific Revolutions by Thomas S. Kuhn. Kuhn makes a well-reasoned argument that science is not an objective search for "truth," as many people believe. Instead, "normal science" is a problem solving endeavor, solving known problems by known methods. Science only changes the rules by which it operates (its "paradigm" - that over-used and often misused term in contemporary language) only when the current paradigm causes more problems than it solves. This is the real answer to any from any field who say, "The science is settled. There is no room for discussion." Those who make that statement need to re-read Kuhn and come to grips with the reality that all knowledge is inevitably socially constructed.
https://answersingenesis.org/answers/ An excellent resource that looks seriously at natural phenomenon in light of Scriptural revelation. They attempt to meet the skeptics own burden of proof by using established scientific methods. An important claim of theirs is that evidence always has to be interpreted. In the evolution vs. creationism debate for instance, there is no such thing as evidence with big bright letters stating that "this is a transitional fossil". There are not creationist fossils and evolutionist fossils, but there are creationist and evolutionist interpretations of the fossils. Charles Darwin himself made this point. In the introduction to The Origin of Species, he stated, “I am well aware that scarcely a single point is discussed in this volume on which facts cannot be adduced, often apparently leading to conclusions directly opposite to those at which I arrived.” Darwin was willing to admit that interpretation was key to choosing a belief. One scientist might view a particular fact as supportive of naturalism; another scientist might view that same fact as supporting creationism. I'd also point out the difficulty in in defending the young earth stance as it requires you to lay out all the arguments exhaustedly (which answersingenesis has done). Not only do you have to call into question the current scientific viewpoints but you also have to put forward the alternative theories. You have to do all this while your debate opponent can just sit back and appeal to authority and the current scientific consensus.
When Skeptics Ask by Norman Geisler and Ronald Brooks. Contains a good general overview of science and Christianity along with some other great chapters that answer quite a few questions that have been brought up by biblical skeptics.
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Because Reddit leans liberal, and most Christians have not done a deep dive into the philosophy of science, they accept evolution without much thought. That's why you see them promoting people like Christian Francis Collins who created Biologos.com and attempts to reconcile Biblical narrative with evolution. Never mind that the attempts of Dr. Collins are thwarted by Scripture contradicting the evolutionary timeline.
It's important for people to realize that science is based on axiomatic assumptions that requires faith. These assumptions turn into glaring flaws when trying to develop truths about the past like macroevolution and should significantly reduce the certainty one has regarding it.
It's also important to remember that the Bible is not written as a scientific document using the standards of our own recent methodology (the scientific method). Over history what we have seen are Christian's assumptions of the world that we live in by taking (often times vague) verses from Scripture and interpreting them. A good rundown of this is here. http://www.ligonier.org/blog/what-rc-sprouls-position-creation/
For a more exhaustive (but not complete) overview of books related to intelligent design, see this page. It's worth noting though that like Natural Theology, some intelligent design authors get you only half way there (i.e.. Theism). The rest would have to be done by studying comparative religion.
For a brief introduction to the normative narratives in Science read the following: The Structure of Scientific Revolutions.
When you have read that, then the last time you checked Science will have had normative narratives. Then we can continue our conversation.
I am not questioning their methodology, I am questioning their motives. Reading the citations at the end sounds like a reading list for young progressives. I am sorry, but it sounds like AGW believers that conservatives are irrational and here, we have the "hockey stick" (i.e. heart rate) to prove it.
Check out the Republican Brain book which basically says conservatives don't have the empathy gene, so they are emotionally inferior to the morally superior liberals.
It really smacks of 1984 to prove a political point more than research designed to show some innate difference.
Sorry if you wrote the study. Did you base your thinking on the book?
https://www.amazon.com/American-Fascists-Christian-Right-America/dp/0743284461
https://www.amazon.com/Republican-Brain-Science-Science-Reality/dp/1118094514
https://www.amazon.com/Insane-Clown-President-Dispatches-Circus/dp/0399592466
https://www.amazon.com/Idiot-America-Stupidity-Became-Virtue/dp/0767926153
https://www.amazon.com/Republican-War-Science-Chris-Mooney/dp/0465046762
https://www.amazon.com/Anti-Intellectualism-American-Life-Richard-Hofstadter/dp/0394703170
https://www.amazon.com/Better-Off-Without-Manifesto-Secession/dp/145161666X/
https://www.amazon.com/How-Fight-Conservative-Daniel-Kurtzman/dp/140226576X
It took me less than 2 minutes to find all of these
You would do well to read the book The Republican Brain: The Science of Why They Deny Science - and Reality by Chris Mooney. You may be able to find it at your local library. If not, it is worth the price to purchase it, especially if you have lots of Right Wing folks in your family. I learned so much reading this book and cannot recommend it highly enough!
And thanks for the link at the end of your post! I've been laughing my ass off for the last 15 minutes!
>but I will say that most conservatives I know at least understand the liberal position and disagree with it, while lots of people like the redditor above you seem to have trouble grasping the idea.
It's quite undeniably the exact other way around.
What do you believe do I not understand about the right wing position?
You see, understanding a position doesn't mean you agree with it.
Because you commented on my personal position: I understand right wing positions quite perfectly. Which is why I fundamentally disagree with it. I have thorough debates about politics every day. I have a thorough education about these topics. I discuss my views and those of others every day. I constantly improve my views and reject ideological reasoning. If I am confronted with evidence, I will change my views. In fact, I won't even express views that I haven't already seen evidence of.
And one of the problems with right wingers is that they don't do these things. As becomes evident by their type of argumentation and the way they conduct debates alone. If right wingers understood their own position, they would stop supporting it. And if they understood the left wing position (not liberal, by the way) they would start supporting it.
As you might have notice: I am literally am asking people to justify their right wing position. Because that way they themselves have to critically think about the things they believe and have to formulate falsifiable statements so I can be convinced by them or refute them. But it turns out that most of the time they can't even do that. Unlike left wingers they don't even provide falsifiable arguments and aren't really willing to debate in the first place. And it's not that they won't for whatever reason they tell themselves (e.g. "The evil libtards never listen to me or tolerate my valid opinions anyway!"). It's that they simply just can't. Even if you can get them to actually discuss their views, ultimately always abandon rational debate and start blindly dismissing arguments of others or attacking people personally (see: your own comment).
In the meantime: Ever saw a right winger try and understand positions that differ from his/her own? Because I sure didn't. Just look at all the replies I get here. Non of them is actually interested in reasonable conversation or understanding what I said. They just got enraged by my criticism and become defensive and attack me personally or blindly dismiss what I said. No serious questions, no serious attempt to answer mine. They aren't interested in understanding things and choosing what is better based on evidence and arguments. They make their choice first and then spread relativism to justify their position. "My position is just as valid as yours, it's all just different opinion." That's simply not how logical reasoning works.
>For more reading look at research done into confirmation bias, the difference between the values of conservatives vs liberals, and egalitarian communitarianism vs heirarchal individualism.
Yes, please do.
http://rstb.royalsocietypublishing.org/content/367/1589/640.full?sid=95b65067-2a89-4cfa-abbf-a30069789213
http://pss.sagepub.com/content/early/2012/01/04/0956797611421206.abstract
http://personal.lse.ac.uk/kanazawa/pdfs/SPQ2010.pdf
http://edition.cnn.com/2010/HEALTH/02/26/liberals.atheists.sex.intelligence/
http://www.sciencedirect.com/science/article/pii/S0160289609000051
http://www.sciencedirect.com/science/article/pii/S0160289608001049
http://www.sciencedirect.com/science/article/pii/S0160289610001339
http://www.amazon.com/The-Republican-Brain-Science-Science/dp/1118094514
http://www.theatlantic.com/politics/archive/2014/09/liberals-care-more-about-empathy-than-conservatives/380404/
You will notice that left leaning people are far more open to discussing ideas and considering the views of others. They are also more rational and base their opinions on reason and logic rather than emotions and ideology. That doesn't mean they are more accepting of opinions that are evidently bad for society. Which right wing views simply quite often are (if they were evidently good for society, left wingers would immediately adopt them).
You will also notice that there is a positive correlation between the level of intelligence and education and left wing thought. While the dumber and less educated you are the more likely you are to fall for right wing propaganda.
The problem with what you said is that it's flawed based on a very fundamental level of definitions: Left wing politics is inherently open-minded. The entire purpose of left wing politics is to do what's best for society and the people and the planet as a whole. It is based on evidence and reason. It stands directly in contrast to right wing politics, which is based entirely on establishing hierarchy and doing what's best for an elite (e.g. nationalist, religious, economic, etc.).
Research shows us that, on average, left wingers are: Significantly more empathetic, educated, intelligent, open-minded and unbiased. Left wing politics is inherently more evidence based and progressive. These things are thoroughly confirmed through evidence (and, as was already said, are a consequence of the very definitions of these tenets).
Sorry, but reality doesn't support your views and relativism.
Politics isn't about left vs. right and the truth being somewhere in the middle. It's pretty much about the people who care about society as a whole (i.e. the left) fighting against people who put themselves or elitist groups over the general population and the planet (i.e. the right). Centrists are simply people who try and find a middle ground because they implicitly believe the elites in power can't be stopped in their quest to consolidate it and the left wing won't stop defending the interests of the general population and the planet, either, so they "compromise" regardless whether or not one side is objectively superior to the other. Seriously, look up what left and right mean, understanding the definitions of these terms alone should already do away with most of your opinions.
Edit: Notice how right wing apologists are making blind accusations and unsubstantiated claims and when met with evidence of them being wrong and thorough and falsifiable explanations, they just downvote and refuse to even expose themselves? It's always like that. Right wingers are simply never demonstrating reasonable behaviour. I haven't met a single reasonable right winger in my life (if they were reasonable, they wouldn't be right wingers). Yet here we had a person making excuses and actually accusing the left of not being open-minded. What /u/chintzy claimed was effectively a lie and instead of fessing up to it and apologizing or deleting their comments, they keep up their lies. It's impossible to reason with people that display such behaviour and that's why right wing thought keeps existing.
It's relevance is that it educates you about the prehistory of humanity, the neolithic revolution and the beginning of civilization where class society and private property first appear. To understand what Marxism is you must understand the basics first. I would also recommend you the following books if you want to understand the philosophical basis of Marxism, dialectical materialism which is essential:
Quantum Social Science by Emmanuel Haven, Andrei Khrennikov
The Structure of Scientific Revolutions
by Thomas S. Kuhn
Ubiquity: Why Catastrophes Happen by Mark Buchanan
Non of these authors are Marxists as far as I know but they are following in the footsteps of Marx and Engels, who developed the logic of dialectical materialism out of philosophical inquiry into the natural world.
Read something interesting about this recently from The Disappearing Spoon by Sam Keane. Won't answer the question but it's food for thought:
"Every amino acid in every protein in your body has a left-handed twist to it. In fact, virtually every protein in every life form that has ever existed is exclusively left-handed. If astrobiologists ever find a microbe on a meteor or moon of Jupiter, almost the first thing they’ll test is the handedness of its proteins. If the proteins are left-handed, the microbe is possibly earthly contamination. If they’re right-handed, it’s certainly alien life.
[...] All of our carbohydrates have a right-handed twist. Regardless, Pasteur’s main point remains: in different contexts, our bodies expect and can only process molecules of a specific handedness. Our cells would not be able to translate left-handed DNA, and if we were fed left-handed sugars, our bodies would starve."
--The last bit confuses me, I always thought that DNA twisted to the left.. ?
Here's how I was taught, but I was taught in physics not math.
Fourier transforms are more intuitive, so think about how you take a derivative of a FT. You carry the derivative operator into the integral and you just get a factor of 2(pi)ix under the integrand. Logically, if you want a second derivative, just take the FT of the functions transform times x^2 etc. If you want a 1.3^th derivative (yes fractional derivatives exist) then FT the function times x^1.3 etc. This means taking a n^th derivative in real space is the same as multiplying by x^n in transform space. Sounds alot like what logarithms did for multiplication back in the day doesn't it? So now you can turn a differential equation into a polynomial equation if you just take the Fourier transform of it. However, if the diff eq is more complex than just n^th order with constant coefficients, maybe the FT isn't the best transform available for simplifying it? Then use a transform that's tailored for the particular function you have.
If I remember correctly this book has a nice description. I consider this book to be the "readable" version of this one
video makes the same mistake in interpretation you do. impossibility of deterministic forecasts of climate in the terms of weather, say, max and min temperatures on Nov 22 2104 is a given. does not mean that we can not predict a likely distribution of for those max and min temperatures conditioned on some boundary condition change to the climate system.
silly, silly, silly. you should start with strogatz, not with youtube.
Actually this book already defined and explained it quite well, with reasonable scientific evidence that has mostly held up over the years.