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Conterintuitive facts in mathematics, CS, and physics

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Re: Conterintuitive facts in mathematics, CS, and physics

#31

Post by syncsynchalt »

lotsofpulp wrote: post #14
6gvONxR4sf7o wrote: post #11

> 16. If you let a 100g strawberry that is 99% water by mass dehydrate such that the water now accounts for 98% of the total mass then its new mass is 50g: https://en.wikipedia.org/wiki/Potato_paradox I really like this one. It's a perfect combo of intuitive from one perspective and mind bending from another. > 18. A one-in-billion event will happen 8 times a month: https://gwern.net/Littlewood This one, on the other…

> https://en.wikipedia.org/wiki/Potato_paradox The Wikipedia link above says: > Fred brings home 100 kg of potatoes, which (being purely mathematical potatoes) consist of 99% water. He then leaves them outside overnight so that they consist of 98% water. What is their new weight? The surprising answer is 50 kg. It annoys me when mass is used interchangeably with force (weight), so I went to the Wikipedia source, and…

> Wonder why the person that wrote the Wikipedia article changed it up when it is supposed to be a direct quote.

They likely changed it from lb to kg because that would be more friendly to an international audience, without realizing that lb is a measure of weight and kg is a measure of mass. Therefore they didn't know to change "weight" to "mass".

Re: Conterintuitive facts in mathematics, CS, and physics

#32

Post by wodenokoto »

dwohnitmok wrote: post #12

29 is not correct as stated and falls prey to logical errors. Hamkins presents a formal take on it here: https://mathoverflow.net/questions/44102/is-the-analysis-as-... His conclusion (which I agree with) is > The claims made in both in your question and the Wikipedia page on the existence of non-definable numbers and objects, are simply unwarranted. For all you know, our set-theoretic universe is pointwise definable…

It’s also terribly phrased.

> The vast majority of real numbers can't be described. But it is impossible to give a single example.

If we accept the first sentence and assume the second refers to indescribable numbers, then isn’t it obvious that we have no examples of things we cannot describe?

If the second sentence refers to real numbers in general I can give one example or two.

Re: Conterintuitive facts in mathematics, CS, and physics

#33

Post by version_five »

lotsofpulp wrote: post #21
jgtrosh wrote: post #18

Earlier quoted context omitted.

In this situation, the mass and weight are proportional and irrelevant to the problem. Other than proper respect of units, why would it really matter? I would agree that using mass+kg would remain correct and be less unusual, but it doesn't matter a lot.

It does not matter, it is just a pet peeve of mine. Might be due psychological trauma from when I was a kid and arguing with an older cousin about how pounds and kilograms are not units of the same thing, and the older cousin "winning" the argument in the eyes of the elders because the cousin was quite a few years older than me and considered to be smart in school.

From what I remember from intro physics, we distinguished between pounds and pounds force, the latter having the 32ft/s^2 multiplied in.

And wikipedia seems to agree with me, see pound (mass) vs pound (force).

Re: Conterintuitive facts in mathematics, CS, and physics

#34

Post by lotsofpulp »

syncsynchalt wrote: post #31
lotsofpulp wrote: post #14

Earlier quoted context omitted.

> https://en.wikipedia.org/wiki/Potato_paradox The Wikipedia link above says: > Fred brings home 100 kg of potatoes, which (being purely mathematical potatoes) consist of 99% water. He then leaves them outside overnight so that they consist of 98% water. What is their new weight? The surprising answer is 50 kg. It annoys me when mass is used interchangeably with force (weight), so I went to the Wikipedia source, and…

> Wonder why the person that wrote the Wikipedia article changed it up when it is supposed to be a direct quote. They likely changed it from lb to kg because that would be more friendly to an international audience, without realizing that lb is a measure of weight and kg is a measure of mass. Therefore they didn't know to change "weight" to "mass".

Oh yes, that would make sense.

Re: Conterintuitive facts in mathematics, CS, and physics

#35

Post by lotsofpulp »

version_five wrote: post #33
lotsofpulp wrote: post #21

Earlier quoted context omitted.

It does not matter, it is just a pet peeve of mine. Might be due psychological trauma from when I was a kid and arguing with an older cousin about how pounds and kilograms are not units of the same thing, and the older cousin "winning" the argument in the eyes of the elders because the cousin was quite a few years older than me and considered to be smart in school.

From what I remember from intro physics, we distinguished between pounds and pounds force, the latter having the 32ft/s^2 multiplied in. And wikipedia seems to agree with me, see pound (mass) vs pound (force).

Oh wow, learning a lot today. I was taught in the US that pounds are a measure of force, and that is how it was always used in physics problems.

Re: Conterintuitive facts in mathematics, CS, and physics

#36

Post by reidjs »

lapetitejort wrote: post #25

My favorite paradox in physics: what happens when you spin a disk at relativistic speed? The circumference should contract, since it's parallel to the direction of motion, but the radius is perpendicular, and thus should not contract. https://en.wikipedia.org/wiki/Ehrenfest_paradox

Relativistic paradoxes are the most insane. Twin paradox, ladder paradox, grandfather paradox, things get so mindbendingly weird at very large, very fast, and very small scales.

Re: Conterintuitive facts in mathematics, CS, and physics

#38

Post by joombaga »

antognini wrote: post #9

Here is one of my favorites: The specific heat of a star is negative. (This also applies to a galaxy or any other gravitationally bound object.) As a star loses energy, it heats up. If you inject it with energy, it cools down. It's a trivial corollary from the virial theorem, but it leads to counterintuitive behavior (like the gravothermal catastrophe).

So what happens to a star inside a "perfect" Dyson sphere?

Re: Conterintuitive facts in mathematics, CS, and physics

#39

Post by reidjs »

whiterock wrote: post #2

very cool collection - truly something to pick from at a party. should have much more upvotes imho.

I have actually told this one at a party (well, not exactly a rager) "Two 12 Inch Pizzas have less Pizza than one 18 inch pizza."

and we did the math to prove it to ourselves. Blew our minds... an actual valid use for middle school math.

Re: Conterintuitive facts in mathematics, CS, and physics

#40

Post by kristjansson »

hodgesrm wrote: post #13

> 0% selected the right answer on this SAT question: Circle A has 1/3 the radius of circle B, and circle A rolls one trip around circle B. How many times will circle A revolve in total? That's fun. I of course immediately selected 3 which means I could have a bright career in test preparation ahead of me.

That one got me good, so my future at College Board is as bright as yours. However, I don't think the argument by demonstration in that video is particularly convincing.

Instead, I think's its easier to note that that the _center_ of a circle of radius r travels 2 * pi * r distance over one rotation. In the problem, the center of the smaller circle has to travel further than the circumference of the bigger circle - it traces a circle whose radius is the sum of the two radii.

So, if 3 * r_small = r_big, the center of the small circle has to travel 2 * pi * (r_s + r_b) = 4 * 2 * pi * r_s, then divide by 2 * pi * r_s per rotation to get 4 rotations.

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