Reddit reviews The Road to Reality: A Complete Guide to the Laws of the Universe

> What proof have we that mathematics exist?

My favorite defense of the existence of mathematics comes from Roger Penrose.

The short version of his argument (which you can read more of with greater detail in the book linked above) is that mathematics contains truth that seems to be independent of human minds.

For example, let's take pythagorean's theorem. The proof of this theorem goes back at least as far as Pythagoras in ancient Greece. And yet, unlike changing political views and fashion trends since ancient Greece, this proof and theorem has been just as valid in every generation and culture. The exact same proof works no matter where or who you are. In fact, one could argue that these mathematical truths would be true even if there were no humans to consider them. Does man really have to exist for a^2 + b^2 = c^2 to be a true statement for triangles?

Also, there are examples of mathematical theorems that have been independently arrived at which suggests further there is something independent of man that different humans are discovering. The odds of someone coming up with the same play as Shakespeare is incredibly low as Shakespeare's plays are products of his mind. But in the case of math, theorems do get arrived at independently as if the truth of the theorem is something real to be discovered independent of the mind of the mathematician.

Again, read Penrose for a better explanation but I hope you get the point.

Not OP, just helping out with some formatting (and links!) because I like these suggestions.

> 1) The Magic Of Reality - Richard Dawkins
>
> 2) The Selfish Gene - Richard Dawkins
>
> 3)A Brief History Of Time - Stephen Hawking
>
> 4)The Grand Design - Stephen Hawking
>
> 4)Sapiens - Yuval Noah Harari (Any Book By Daniel Dennet)
>
> 5)Enlightenment Now - Steven Pinker
>
> 6)From Eternity Till Here - Sean Caroll (Highly Recommended)
>
> 7)The Fabric Of Cosmos - Brian Greene (If you have good mathematical understanding try Road To Reality By Roger Penrose)
>
> 8)Just Six Numbers - Martin Reese (Highly Recommended)

Buy a book by Roger Penrose called The Road To Reality. He explains pretty much our current understanding of the universe, and spends the first third of the book explaining the mathematics.

http://www.amazon.com/Road-Reality-Complete-Guide-Universe/dp/0679776311/ref=sr_1_1?ie=UTF8&s=books&qid=1256747531&sr=8-1

http://en.wikipedia.org/wiki/Roger_penrose

It's worth looking at before you spend seven years (as I did) at university studying physics.

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:

• Mr. Tompkins in Paperback
  
  • A super fast read that spends less time looking at the "how" but focused instead on the ramifications and impacts. Covers both GR as well as QM but is very high level with both of them. Avoids getting into the details and explaining the why.
    
    
• Einstein's Relativity and the Quantum Revolution (Great Courses lecture)
  
  • This is a great intro to the field of non-classical physics. This walks through GR and QM in a very approachable fashion. More "nuts and bolts" than Mr. Tompkins but longer/more detailed at the same time.
    
    
    Deeper Pop-sci Dives (probably in this order):
    
    
• Quantum Theory: A Very Brief Introduction
  
  • Great introduction to QM. Doesn't really touch on QFT (which is a good thing at this point) and spends a great deal of time (compared to other texts) discussing the nature of QM interpretation and the challenges around that topic.
    
• The Lightness of Being: Mass, Ether, and the Unification of Forces
  
  • Now we're starting to get into the good stuff. QFT begins to come to the forefront. This book starts to dive into explaining some of the macro elements we see as explained by QM forces. A large part of the book is spent on symmetries and where a proton/nucleon's gluon binding mass comes from (a.k.a. ~95% of the mass we personally experience).
    
• The Higgs Boson and Beyond (Great Courses lecture)
  
  • Great lecture done by Sean Carroll around the time the Higgs boson's discovery was announced. It's a good combination of what role the Higgs plays in particle physics, why it's important and what's next. Also spends a little bit of time discussing how colliders like the LHC work.
    
• Mysteries of Modern Physics: Time (Great Courses lecture)
  
  • Not really heavy on QM at all, however I think it does best to do this lecture after having a bit of the physics under your belt first. The odd nature of time symmetry in the fundamental forces and what that means with regards to our understanding of time as we experience it is more impactful with the additional knowledge (but, like I said, not absolutely required).
    
• Deep Down Things: The Breathtaking Beauty of Particle Physics
  
  • This is not a mathematical approach like "A Most Incomprehensible Thing" are but it's subject matter is more advanced and the resulting math (at least) an order of magnitude harder (so it's a good thing it's skipped). This is a "high level deep dive" (whatever that means) into QFT though and so discussion of pure abstract math is a huge focus. Lie groups, spontaneous symmetry breaking, internal symmetry spaces etc. are covered.
    
• The Elegant Universe: Superstrings, Hidden Dimensions, and the Quest for the Ultimate Theory
  
  • This is your desert after working through everything above. Had to include something about string theory here. Not a technical book at all but best to be familiar with QM concepts before diving in.
    
    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):
    
    
• A Most Incomprehensible Thing: Intro to GR
  
  • Sorry, this is GR specific and nothing to do with QM directly. However I think it's a great book acting as an introduction. Definitely don't go audible/kindle. Get the hard copy. Lots of equations. Tensor calculus, Lorentz transforms, Einstein field equations, etc. While it isn't a rigorous textbook it is, at it's core, a mathematics based description not analogies. Falls apart at the end, after all, it can't be rigorous and accessible at the same time, but still well worth the read.
    
• The Theoretical Minimum: What You Need to Know to Start Doing Physics
  
  • Not QM at all. However it is a great introduction to using math as a tool for describing our reality and since it's using it to describe classical mechanics you get to employ all of your classical intuition that you've worked on your entire life. This means you can focus on the idea of using math as a descriptive tool and not as a tool to inform your intuition. Which then would lead us to...
    
• Quantum Mechanics: The Theoretical Minimum
  
  • Great introduction that uses math in a descriptive way AND to inform our intuition.
    
• The Road to Reality: A Complete Guide to the Laws of the Universe
  
  • Incredible book. I think the best way to describe this book is a massive guidebook. You probably won't be able to get through each of the topics based solely on the information presented in the book but the book gives you the tools and knowledge to ask the right questions (which, frankly, as anybody familiar with the topic knows, is actually the hardest part). You're going to be knocking your head against a brick wall plenty with this book. But that's ok, the feeling when the brick wall finally succumbs to your repeated headbutts makes it all worth while.

Roger Penrose holds the Platonist view. He discusses it in this ever interesting book The Road to Reality.

http://www.amazon.com/gp/aw/d/0679776311/

Yes, there is such a place: the internet’s collection of academic papers has a very handy search engine at http://scholar.google.com/, plus an illegal download service at http://sci-hub.bz/

It’s going to take you several lifetimes to read it all, but that shouldn’t be too big a problem, right?

Even learning the baby-step basics is going to take years of hard work. You’ll have an easier time of this if you enroll in a full-time degree program in math or physics at a good university. You can’t really learn these subjects unless you do the work – just reading a webpage isn’t going to cut it – and it’s hard to stay motivated to do the work if you’re on your own.

• • *
    
    If you want one book though, you could try Penrose’s: https://amzn.com/0679776311

Someone on Reddit (I wish I could remember who so I could credit them, because it's both true and funny) recently said that General Relativity is bad differential geometry; and Quantum Mechanics is bad functional analysis.

What they meant by bad is that physics isn't math, so you get kind of a physics-ized math instead of the real thing. But still, those are the two branches of math you want to know for physics.

You might take a look at a popular book by Penrose called The Road to Reality. It's a huge book that basically describes all the math you need to understand most of modern physics, and then explains the physics. It's an awesome book.

I got the new millennium edition. While I was researching which one to get , a lot of people mentioned that millenium edition was glossy and had smaller print which made it harder to read. I must say it looks fine. I don't have any problems so far. The reason i picked the latest is because it was relatively cheaper (140ish vs 300+) and had over 900 erratas fixed with respect to older editions.

Bonus: Another book I started reading in tandem is Road to Reality by Penrose which is equivalent in excitement, inspiration and quality of material and gives a nice overview of math required for physics and relation between math and physics. Highly recommend.

You have a lot of work ahead of you for sure, but this is not an impossible task. First off, I wouldn't worry too much about the Nambu-Goto action right now. Instead, you're going to need to develop quite a bit of background knowledge and mathematical tools.

Sites like Brilliant, and Youtube lectures are valuable resources, but if you're going to be successful in this endeavour, I'd recommend that you put some serious effort into learning from textbooks. The ability to learn from a textbook does not come naturally to most people, but it is a skill that can be developed and will be necessary for you to make much progress in this direction. In fact, I'd say that perhaps the most valuable thing I gained in my undergraduate degree was the ability to sit down and actually learn from a textbook in a systematic way.

The book on String Theory by Zweibach is probably going to be the best resource for you as it's a quite approachable low level string theory book designed for advanced undergraduate students. In order to read and understand it, you'll need to first gain at minimum a popular level, hand-wavy understanding of general relativity and quantum field theory and a mathematical understanding of special relativity, quantum mechanics and electromagnetism.

One book I can't recommend enough to non-professionals wanting to get a semi-serious mathematical understanding of modern physics is The Road to Reality by Roger Penrose. In my opinion, the book is a masterpiece. He starts off with "what is a number", and by the end of the first half of the book has given a serious account of fibre bundles using only the ideas introduced in the book. His explanations are lucid, engaging and very deep. The second half then uses the mathematics introduced in the first half to describe much of modern physics. He has a section where he talks about String Theory, but he isn't much of a fan of it so doesn't spend a lot of time on the topic. However, the mathematics he introduces in the first half are invaluable for understanding quantum mechanics, relativity, quantum field theory and string theory. Roger is a bit of a maverick and has some 'cooky' ideas and opinions that would make many professional physicists blush with embarrassment, but throughout the book he is very careful to clearly say when he is making a controversial statement.

I think if you pick of the Road to Reality, and manage to seriously read the first 15 chapters while also reading (or watching) introductory books / lecture series on quantum mechanics and special relativity and electromagnetism you'll be in a great place to try and get into the basics of string theory.

These are a number of my favorite books, and all of which are great reads.

• Philosophy: The Golden Chain of Homer is probably one of the most important books ever written in the field of Alchemy, which delves very deep into Philosophical territory.
  
  
• Business/ Economics/ Finance: The Economic Way of Thinking is always held in high regards as an excellent book in presenting basic economics. It presents the subject in a clear, and concise way, and meant to develop a new way of thinking for those new to economics.
  
  
• Non-Fiction/ Technology/ Science: The Road to Reality has a very nice overview of the essential mathematics of modern physics, and goes into a nice discussion of quantum mechanics and string theory.
  
  
• Current Affairs: A Sociology of Mental Illness is a great insight into current issues in the field of mental illness. You'll never see mental illness in the same way ever again after reading this book.
  
  
• Specialized Topic: Traditional Blacksmithing is probably one of my favorite books of all time. This is as good a discussion and instruction into traditional blacksmithing as you will find, as well as good advice into how a blacksmith ought to conduct himself to live a well rounded lifestyle.

Six Easy Pieces and Six Not So Easy Pieces are good places to start.

You could also try Roger Penrose's The Road to Reality

If your goal is to understand basic concepts without the math, then a highschool physics book would most likely be the best place to start, as the highest math used is usually Algebra/Pre-calc.

That being said, without at least a calculus background it's hard to grasp some of the concepts beyond basic kinematics. Wikipedia might get you somewhere so it's a good place to start, but it could also lead you through a rabbit hole to pages upon pages of background.

I'd say if you want to tackle more advanced physics concepts then you need at least some background in math, so I'd try Mathematical Methods in the Physical Sciences by Mary Boas, a book that explains the physics and math somewhat side by side, or The Road to Reality: A Complete Guide to the Laws of the Universe by Roger Penrose. Neither is a light read, if you don't have a head for math don't even try Penrose as he uses arguments that assume a reasonable mathematical background. The Boas book is technically a mathematics textbook, so you would do well to supplement it with a College Physics textbook (I used one by Tipler in my university courses).

Amazon Links Below:
Penrose: http://www.amazon.com/Road-Reality-Complete-Guide-Universe/dp/0679776311/ref=sr_1_1?s=books&ie=UTF8&qid=1404248577&sr=1-1&keywords=the+road+to+reality+roger+penrose

Boas: http://www.amazon.co.uk/Mathematical-Methods-Physical-Sciences-Mary/dp/0471365807/ref=sr_1_1?s=books&ie=UTF8&qid=1404248599&sr=1-1&keywords=boas

Tipler: http://www.amazon.co.uk/Physics-Scientists-Engineers-Modern/dp/1429202653/ref=pd_sim_sbs_b_1?ie=UTF8&refRID=1NX3QE9FG7XGKWQ15NQ4

Hope this helps, good luck!

http://www.amazon.com/gp/product/images/0679776311/ref=dp_image_0?ie=UTF8&n=283155&s=books

To be honest it's really hard to learn without doing the coursework. But yes such books exist; for example http://www.amazon.com/Road-Reality-Complete-Guide-Universe/dp/0679776311. You'll have to supplement with other things, but that should be a good backbone. There is also this list: http://www.staff.science.uu.nl/~hooft101/theorist.html.

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

You are experiencing modern angst. If you had lived only 100 years ago these feelings [for the most part] would not have had a chance to have arisen in the form you are expressing [stardust, universe experiencing itself] - be grateful you can do do it at all [I'm not saying people didn't have these feelings, like Camus, Neitzche, Descartes and others but that most average people didn't have the chance to worry like this, in the information laden way you are spitting it, since most people were busy feeding themselves and their families by farming etc]. So, yes, you are alive and it's all so crazy to think about.

Oh and yes, we do actually understand more than a "spec" of reality.

You say that if I am calm about what your saying then I am missing the point and haven't grasped the full implication of it's meaning. I say truth is relative and the truth of what you're saying is one of many perspectives I can tap into and get lost in. You seem to be hyperventilating only one stream of thought - your existential purpose, validity, meaning.

You seem to want someone to validate your feelings with an equal amount of shock and awe. Well you might get it, so what then? I'm not saying the knowledge you are talking about doesn't lead one to existential angst and confusion, but just remember what the Buddha said about the nature of reality. All is change. All is impermanent. This isn't some lofty metaphysical concept that is impossible to apply to everyday life. On the contrary, it is imminently important to understand so as to get a grip on your situation. If all is impermanent, then your feelings, opinions, knowledge etc.. is all impermanent. You are holding onto the feelings of utter confusion and awe. You have made a mistake unconsciously, that everyone does, when they mistake their immediate phenomenal experience as a permanent "thing" in reality. To be consistent with the Buddha's revelation one must relax, quiet the mind and understand the nature of reality - impermanence.

Read - Buddhism: Plain and Simple and also Zen Mind, Beginner's Mind

Questioning, the kind you seem to be doing, is just spinning your wheels if not tempered with a calm awareness and composure. Do you want to seek contentment and happiness? Do you want to feel resolve? Then shut your mind up for a moment. Listen to the birds chirp. Sit quietly in your room and watch your breathe. Work with your hands and feel reality in all it's textures. Just be aware. Hopefully you will have a long life to ponder these questions you have but for now don't make the mistake that so many neurotics do; mainly the mistake of attaching oneself to a overly anxious perspective while neglecting other modes of thought that are just as easily attachable. You have control over your mind, and your mind is doing all this anxious thinking.

If you want to have these questions turned upside down and be thrown into a different sort of thought then you must read Krishnamurti and his musings about life, love, truth, intelligence, nature.... "A consistent thinker is a thoughtless person, because he conforms to a pattern; he repeats phrases and thinks in a groove." Jiddu Krishnamurti - more quotes here.

“Judge a man by his questions rather than by his answers” - Voltaire

Apply this quote to yourself. Spend time with it. What are you really asking and what answers are you really searching for?

“We are what we think. All that we are arises with our thoughts. With our thoughts, we make the world.” - Buddha

Good luck.

http://www.amazon.com/The-Road-Reality-Complete-Universe/dp/0679776311/ref=sr_1_1?ie=UTF8&qid=1334267314&sr=8-1

Yes indeed (and thank you /u/sleeps_with_crazy for the link below, it looks very helpful. I can actually follow the explanations! Yay.)

Speaking of conceptual clarity, my dream is to someday make it all the way through Road to Reality without glossing over any of the concepts. And I can't do it without supplemental reading, not a chance; he loses me completely halfway in (around n-manifolds and tensors I think). I think this level of explanation is pretty much exactly what I need for that, though! I can't hack the super rigorous stuff, and that's fine.

I need more info regarding his level of knowledge. As someone who went through the same struggles that this student is going through, I can recommend a lot of books but it depends on how much they know. In terms of cheaper books, If they've completed 18.01-18.03 and 18.06 plus 8.01-8.04 then the book "Road to Reality" by Roger Penrose is a good option. It's a huge book so it should keep him busy for a while and gives a very comprehensive treatment of various topics in mathematical physics.
here's the link:http://www.amazon.com/The-Road-Reality-Complete-Universe/dp/0679776311

I quite like this book The Road to Reality: A Complete Guide to the Laws of the Universe. Detailed and excellent explanation. But, you need to have some good basics else it will be a bumpy ride.

Uhm...it's kind of hard for me to answer that, because I feel math-tarded all the damned time, and have to constantly be reminded that most of the population doesn't give a second thought to the math I use on a daily basis. So, I guess the answer is "maybe"? Depends on what level you got up to, and how much math explanations you're willing to put up with. His books are fairly computationally heavy - they kind of have to be, given the subject matter - but he does explain everything in a fair amount of detail, so I think you wouldn't have a problem if you wanted to read them.

Amazon has a lot of his books with the "Look Inside!" feature, and that link shows kind of what I'm talking about (starting in chapter 2. Chapter 1 of that book is a bit..odd). I hope it helps!

some amazing books I would suggest to you are:

• Godel Escher Bach
  
  
• Road to Reality By Roger Penrose.
  
  
• Code by
  Charles Petzold.
  
  
• Pi in the Sky by John Barrow.
  
  All of these I would love to read again, if I had the time, but none more so than Godel, Escher, Bach, which is one of the most beautiful books I have ever come across.
  
  Road to Reality is the most technical of these books, but gives a really clear outline of how mathematics is used to describe reality (in the sense of physics).
  
  Code, basically, teaches you how you could build a computer (minus, you know, all the engineering. But that's trivial surely? :) ). The last chapter on operating systems is pretty dated now but the rest of it is great.
  
  Pi in the Sky is more of a casual read about the philosophy of mathematics. But its very well written, good night time reading!
  
  You have a really good opportunity to get an intuitive understanding of the heart of mathematics, which even at a college level is somewhat glossed over, in my experience. Use it!

> 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.

Here are some links for the product in the above comment for different countries:

Link: http://www.amazon.com/The-Road-Reality-Complete-Universe/dp/0679776311

• UK: amazon.co.uk
  
• Spain: amazon.es
  
• France: amazon.fr
  
• Germany: amazon.de
  
• Japan: amazon.co.jp
  
• Italy: amazon.it
  
• China: amazon.cn
  
  
  This bot is currently in testing so let me know what you think by voting (or commenting).

It's great that you want to study particle physics and String Theory! It's a really interesting subject. Getting a degree in physics can often make you a useful person so long as you make sure you get some transferable skills (like programming and whatnot). I'll reiterate the standard advice for going further in physics, and in particular in theoretical physics, in the hope that you will take it to heart. Only go into theoretical physics if you really enjoy it. Do it for no other reason. If you want to become a professor, there are other areas of physics which are far easier to accomplish that in. If you want to be famous, become an actor or a writer or go into science communication and become the new Bill Nye. I'm not saying the only reason to do it is if you're obsessed with it, but you've got to really enjoy it and find it fulfilling for it's own sake as the likelihood of becoming a professor in it is so slim. Then, if your academic dreams don't work out, you won't regret the time you spent, and you'll always have the drive to keep learning and doing more, whatever happens to you academically.

With that out of the way, the biggest chunk of learning you'll do as a theorist is math. A decent book (which I used in my undergraduate degree) which covers the majority of the math you need to understand basic physics, e.g. Classical Mechanics, Quantum Mechanics, Special Relativity, Thermodynamics, Statistical Mechanics and Electromagnetism. Is this guy: Maths It's not a textbook you can read cover to cover, but it's a really good reference, and undoubtably, should you go and do a physics degree, you'll end up owning something like it. If you like maths now and want to learn more of it, then it's a good book to do it with.

The rest of the books I'll recommend to you have a minimal number of equations, but explain a lot of concepts and other interesting goodies. To really understand the subjects you need textbooks, but you need the math to understand them first and it's unlikely you're there yet. If you want textbook suggestions let me know, but if you haven't read the books below they're good anyway.

First, particle physics. This book Deep Down Things is a really great book about the history and ideas behind modern particles physics and the standard model. I can't recommend it enough.

Next, General Relativity. If you're interested in String Theory you're going to need to become an expert in General Relativity. This book: General Relativity from A to B explains the ideas behind GR without a lot of math, but it does so in a precise way. It's a really good book.

Next, Quantum Mechanics. This book: In Search of Schrodinger's Cat is a great introduction to the people and ideas of Quantum Mechanics. I like it a lot.

For general physics knowledge. Lots of people really like the
Feynman Lectures They cover everything and so have quite a bit of math in them. As a taster you can get a couple of books: Six Easy Pieces and Six Not So Easy Pieces, though the not so easy pieces are a bit more mathematically minded.

Now I'll take the opportunity to recommend my own pet favourite book. The Road to Reality. Roger Penrose wrote this to prove that anyone could understand all of theoretical physics, as such it's one of the hardest books you can read, but it is fascinating and tells you about concepts all the way up to String Theory. If you've got time to think and work on the exercises I found it well worth the time. All the math that's needed is explained in the book, which is good, but it's certainly not easy!

Lastly, for understanding more of the ideas which underlie theoretical physics, this is a good book: Philsophy of Physics: Space and Time It's not the best, but the ideas behind theoretical physics thought are important and this is an interesting and subtle book. I'd put it last on the reading list though.

Anyway, I hope that helps, keep learning about physics and asking questions! If there's anything else you want to know, feel free to ask.

Mathematics is intimately linked with physics. I recommend Penrose's book The Road to Reality. Here is a PDF version. It is the best math book I ever bought. By far. Every equation has a purpose for its existence - divorcing math from physics started the demise of American education.