(Part 2) Top products from r/theydidthemath

Human ability to reproduce may not really be the limiting factor to consider. How well agricultural practices were able to support a given population and that rapid of a growth rate, for example, might be more informative. And were there even 19.3 million people in 2300-1800 BCE?

There should also be some evidence of an origination point where these 19 million Noachian people originated and immigrated outward from--hypothetically some indication of higher densities of population during that era from which individuals and groups began to steadily move away from, toward better prospects and less competitive environments.

(EDIT: McEvendy and Jones, authors of the Atlas of World Population History, estimate 27 million people in 2000 BCE.)

I am going to strongly recommend that you read a book that might help you deal with the scale of the universe, and that is The Five Ages of the Universe, which takes you from the inconceivable tininess of the beginning to the unfathomable immensity of the far future, and imparts a sense of wonder and hope to the whole thing: it is possible that, no matter how big it gets, how far apart everything is, how dim the lights become, complex life can still exist and thrive. The book is like $10 for your Kindle and it's glorious.

First, I'm going to say that I'm glad this is the actual question. I was really hoping, when I clicked, that it was about dropping Mt. Everest, and not something as boring as falling from Mt. Everest. Give your kid a high-five for me.

Second, I'm going to make a simplifying assumption: that air resistance can be ignored. I provide no math to justify this assumption, but do so on the grounds that a) Mt. Everest is on the same order of size as the Chicxulub asteroid (the one that killed the dinosaurs), and b) the math that other, smarter people did about that asteroid impact suggests that for an object that big, going that fast, air resistance is entirely unimportant.

This kind of shafts your kid's question, since the whole concept of "terminal velocity" depends on air resistance actually mattering. Which is true, but as a concept, terminal velocity also only really applies within the realm of human(ish)-scale objects. For you, or a giraffe, or a schoolbus, or a space shuttle, then sure. Calculate terminal velocity. But for a mountain? Meh. Just not going to matter.

Thus, I will re-interpret your kid's question as "how fast would Mt. Everest be going when it hit?"

To answer that, I'm going to make what is possibly an obvious observation, but one which greatly eases the problem: how fast it's going when it hits depends on how high up you drop it from.

If you drop it from a distance of 1 meter, then we can calculate the impact speed as:

1 meter = 1/2*a*t^2

where a = 9.8 m/s^(2), and t is the time it takes to fall. Solving for t, we get:

t = sqrt(2 / a)

This, we can substitute into the formula for speed under constant acceleration, v = a*t, to get:

v = a*sqrt(2 / a)

And after moving the first a inside the square root and simplifying, we get:

v = sqrt(2a)

Plugging in 9.8m/s^2 for a, we find that the impact speed after dropping Mt. Everest from a height of 1 meter is 4.42 meters per second.

(And please, point out to your kid that being able to answer questions like this is why it's important to learn algebra. It may sound frivolous, but yes, the reason some internet weirdo can answer your kid's goofball question is because I paid attention in algebra class.)

But your kid doesn't care about dropping a mountain from a measly 1 meter high. From your kid's choice of object to drop, I can tell that your kid is looking for an extreme answer. Your kid wants to know about the maximum impact speed. As any right-thinking kid would.

For that, we're going to have to take Mt. Everest out into space. Waaaay out into space. So far out, that the gravitational acceleration is not 9.8 meters/second^2 anymore. So far out, that we can't use the above formula to figure out the speed anymore, because the acceleration is no longer constant. (Not that it was constant before, strictly speaking, but it was close enough not to care.)

If you take Mt. Everest infinitely far away, Earth's gravitational pull becomes infinitely weak. The farther we go, the weaker it gets, but never quite reaches zero. This means that the further we take the mountain, the faster it will go, but the amount more faster it goes diminishes rapidly. After a while, (like, a million kilometers or whatever), it's just not worth the bother to take it the next million kilometers. Sure, it'll go a little bit faster, but not much.

Mathematically, there is a limit to how fast the mountain will go (stay awake during algebra-2, kid, to learn about limits). You can approach this limit by taking the mountain further and further away, but you'll never quite reach it.

Doesn't mean you can't calculate what it would be, though. However, as limits are your gateway drug to calculus, it's not surprising that calculus is what you need to properly calculate the limiting speed.

Now, while I did pay attention in calculus, I can't say that I paid attention well enough to whip the correct integral out of my pants on the spur of the moment, especially not at 11 on a Saturday night, when by all rights I should really be in bed partying with a good book.

Fortunately, I don't have to. Because gravity is symmetric. Meaning, gravity doesn't care which direction you're moving. It pulls on you just as hard, at some given distance, whether you're moving towards the earth or away.

And since an integral is really just a fancy way of adding up an infinite number of tiny increments, and since addition doesn't care what order you add stuff up in, you're free to add up the increments in order towards the earth or in order away from the earth. (Strictly speaking, you need to pick a sign convention and put a minus sign in front of those integrals, but whatever. We don't actually care about direction, only magnitude, so we can ignore the sign of the result.)

The net result of all this is that the limit of Mt. Everest's falling speed when it hits the earth is exactly the same as the speed you would have to throw it if you wanted to throw the mountain completely off the earth never to return.

And that speed goes by another, more familiar name: escape velocity.

Put another way: the fastest you can ever go by falling towards a planet is exactly the same as how fast you need to be going to get away from the planet.

So the ultimate reason I don't have to worry about pulling an integral out of my pants on a Saturday night, is because I can just google Earth's escape velocity, and that's the same answer as your kid is looking for: 11.2 kilometers per second

Just don't do it, kid, or you'll wipe us out just like the dinosaurs.

This is an interesting question and comes with many answers depending on how you define certain things like "poverty". IMO, the best answer is given by Jeffery Sachs in this book. He says that if we used $175 billion per year for 20 years, we could end extreme poverty.

With regards to the blog post:

Your point was to create a distinction between students and working social scientists, which is unfounded given the highlighted segment of the post.

With regards to using personal experience as evidence:

I brought it up once, to meet you half on your emphasis on personal experiences. It was not intended as evidence or proof or anything of that sort.

I am not so foolish as to think my own experiences are inherently generalizable.

With regards to having no sources:

At the moment I have three, and to counter I have "No, I've seen different".

But alright, if you wish more:

http://www.amazon.ca/Third-Culture-Beyond-Scientific-Revolution/dp/0684823446

https://www.dukeupress.edu/Science-Wars/index-viewby=author&lastname=Aronowitz&firstname=Stanley&middlename=&sort=newest&aID=1472866.html

http://www.amazon.com/Consilience-Knowledge-Edward-Osborne-Wilson/dp/067976867X

Anyway, this discussion has clearly become pointless. You refuse to acknowledge any evidence that doesn't fit into your personal narrative and keep attempting to assert what I'm saying is ridiculous to dismiss my point.

But on the plus side, your argumentation has fully convinced me you're a social scientist.

Let's assume to describe a 'thing' that Jesus did, it requires 1 verse of a Bible (it's Easter, why not use Bibles). According to Wikipedia, there are 31102 verses in the Bible. This NKJV Bible on Amazon is 7.9"×5.2"×0.9", or 605.86253 mL. Let's assume "the world would not have room" means that the things would not fit within the atmosphere of earth. Assuming perfectly spherical earth with radius 6,371 km, and "within the atmosphere" means up to the Karman line (100 km up), we have

4×π/3 × (6471km)^3 = 4π/3 × (6371km)^3 + b × 605.86253 mL

Where b is the number of Bibles. Plug it into Wolfram we get b=9.903×10^(22) things. Assuming 40 years of life, he did 7.851×10^(13) things per second, or 78.5 trillion things per second.

Don't fret!

Calc and the higher maths are like a video game on paper.

This is a good intro and quite the stirring read.

There are technically 11 wizarding schools worldwide! There's all this background lore not directly mentioned in the series, but in the other littler stories like Tales of Beetle & The Bard (the children's book left to Hermione by Dumbledore that contained the story about the Deathly Hollows).

It would be way too much space.

Let's use a novel as an example. On [Gutenberg] (https://www.gutenberg.org/ebooks/1399), depending on the file format you use, Anna Karenina ranges from 1.1-3.9 MB. According to [Wikipedia] (https://en.wikipedia.org/wiki/Anna_Karenina) and [Amazon] (https://www.amazon.com/Anna-Karenina-Penguin-Classics-Hardcover/dp/014119961X/ref=tmm_hrd_swatch_0?_encoding=UTF8&qid=1481515083&sr=8-1), it's 864 pages long.

If we assume Anna Karenina is representative of all books, this means that your flash drive can hold between 14 to 50 million pages.

Even with the caveat that other written media probably can vary significantly from Anna Karenina, the variations will not be severe enough to make it a readable amount of books.

The holocaust museum in Washington DC does a very good job of this. The World Must Know is a very good but very depressing coffee table book that's a photo journal of the museum.

At the museum they have things like a pile of shoes that were found in the camps, or photos of the victims that were provided by family.

Or you can just read House of Leaves.

There's actually a story about somebody meeting a decimal child in this nonfiction book.

Here you are

https://www.amazon.com/Son-Also-Rises-Surnames-Princeton/dp/0691168377

http://www.amazon.com/gp/aw/d/0751304263?pc_redir=1411020142&robot_redir=1
"The complete book of self sufficiency" by John seymour. This picture is his "one acre family farm" from chapter one. We are using the five acre variation except that it's 28 acres.

Using this statistic from Guiness World Records, it is estimated there is about 5 billion copies of the Bible in circulation.

I'll use the New American Standard Bible here for reference. It's, according to the seller's information, 1 inch thick.

That's 5 billion inches, or about 78 914 miles, or 127 000 kilometres. With the Earth's width of 40 075 kilometres, that's enough to circle the world 3 times over.

If we laid all those bibles side by side face down, they'd make a total surface area of 221.4 billion square inches, 55.15 square miles, or 142.8 square kilometres. With that much pavement, you could encircle the world with a road 1.2 yards (1.1 metres) across.

You've perhaps heard confusion about the correct answer - it depends on precisely how the question is phrased/assumptions.

"...it can't be proven mathematically" is incorrect, it's trivial to show, and you don't even need to use mathematics - just enumerate the tree of possible decisions and count outcomes.

There is a nicely done book The Monty Hall Problem: The Remarkable Story of Math's Most Contentious Brain Teaser that goes over the genesis of the problem, the machinations that various persons went through, the mathematics of the answer(s), and variations therein.

Very inexpensive book, and probably at your local library, highly recommended if you want the Full Monty treatment...

I think that a major problem in your estimate is that it isn't including the cost of solar and battery dropping over time.

There is an interesting assertion from Tony Seba regarding fossil fuels and nuclear going obsolete. He's saying that solar & battery are technologies and will continue to drop in price, like they have done for the last 30 years, and that the cost of fossil fuels will continue to be static or rise. When the cost of solar & battery drops below 6c/KWH, it will be cheaper for many people to produce their own power than to buy off the grid, because the cost of delivery of electricity over the grid is around 6c/KWH. There is still a place for utility generation and the main method of production will be solar & battery.

His book [Clean Disruption of Energy and Transportation: How Silicon Valley Will Make Oil, Nuclear, Natural Gas, Coal, Electric Utilities and Conventional Cars Obsolete by 2030] (http://www.amazon.com/Clean-Disruption-Energy-Transportation-Conventional/dp/0692210539?ie=UTF8&keywords=clean%20disruption&qid=1462589361&ref_=sr_1_1&sr=8-1 ) discusses this in detail.

Here is a [Short presentation] (https://www.youtube.com/watch?v=0L0JAnACdyc) and
a [long presentation] (https://www.youtube.com/watch?v=Kxryv2XrnqM) .

Useful: Nuclear has a negative learning curve for the past 30 years - The more we research and deploy the technology, the more expensive the technology gets. Not sure if Thorium or new technologies are going to change this assertion, or if they can do so before Solar eclipses them completely. Tony lays it out here
Actually, if you have 4 minutes, you can watch this shorter presentation. Deutsche Bank predicts that solar (without battery I think) will be at grid parity by end 2017 - another projection, but very relevant to our discussion.

I'm right now in the middle of this book Thinking, Fast and Slow that breaks down exactly what is going on in our minds here.

Basically, there's two different systems at work, the fast one and the slow one, and we're the arbiter between. The fast one is lazy. It reads that the store owner gave up $100 and then gave back $30 and lazily reports the loss of $130 (or maybe some other number).


The brain is very accepting of the fast answer. The slow system needs to not only blow a whistle and let us know something is off but then has the job of isolating the numbers, doing the math and figuring out not only where the problem is, but what the right answer is. Making things worse, the slow part is very fragile. If we are tired, sick, or in a bad mood, we're even less likely to bother with the slow thinking.

So it is a riddle because it's trying to get you to trust your fast system over anything else.

Here's some reading for you.

And ignoring the oversimplified and outright false accusation that "so many black men abandon their children", what else is wrong? You learn how to be a father from your father. And if your father didn't have the opportunity to learn from his father because they were property? Well, there's another difficulty, isn't there? And it's a difficulty that's not going to go away in one generation in the best of circumstances.

And why is it so far away from being "the best of circumstances"? Well, you could read Slavery by Another Name and The New Jim Crow to see how slavery actually lasted well past its abolishment and how the for-profit prison complex is preventing black people from simply "working past it". It's really such a complicated, horrible web... It's too much for me to try to discuss in one post.

But put simply: No other enslaved group, not the Irish, not the Japanese, not any other group of people has faced the same level of obstruction while attempting to rise up to equality. And if you think that these issues aren't part of the cause rather than the result of crime and drug use and poverty which results in black fathers being taken from their families... well, you're wrong.