Conterintuitive facts in mathematics, CS, and physics • Hacker News Board

Re: Conterintuitive facts in mathematics, CS, and physics

#11

Post by 6gvONxR4sf7o » Tue, Oct 05, 2021, 10:27 PM UTC

> 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 hand, I don't like. Depending on a whole bunch of subjective definitions, a one-in-billion event can happen a million times a second or practically never or whatever else you choose.

Re: Conterintuitive facts in mathematics, CS, and physics

#12

Post by dwohnitmok » Tue, Oct 05, 2021, 10:29 PM UTC

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, and every object is uniquely specified by a property.

Despite arguments about countability, which ignore how difficult it is to pin down "what is definable," it is possible (although not necessary) for all real numbers to be describable/definable in ZFC.

Re: Conterintuitive facts in mathematics, CS, and physics

#13

Post by hodgesrm » Tue, Oct 05, 2021, 10:33 PM UTC

> 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.

Re: Conterintuitive facts in mathematics, CS, and physics

#14

Post by lotsofpulp » Tue, Oct 05, 2021, 10:36 PM UTC

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 the source is accurate in using units of force throughout.

https://web.archive.org/web/20140202214723/http://www.davidd...

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

Re: Conterintuitive facts in mathematics, CS, and physics

#15

Post by brrrrrm » Tue, Oct 05, 2021, 10:38 PM UTC

a couple more:

- at any time while stirring a cup of coffee, there will be a point on the top that is right where it started. (if we pretend coffee stirring is 2-dimensional, Brouwer's Fixed Point theorem)

- a drunk man will eventually make it home, unless he can fly. in which case he only has a 34% chance. (if we assume the man is walking/flying on a grid, Pólya's recurrence theorem)

Re: Conterintuitive facts in mathematics, CS, and physics

#16

Post by Causality1 » Tue, Oct 05, 2021, 10:40 PM UTC

Considering spacetime, matter, and energy are all quantized, why is something like Gabriel's Horn significant? I don't see how it has any more relation to reality than phrases like "negative surface area" would.

Also, it's patently absurd someone would include Fitch's Paradox, a piece of philosophy, on a list of "counterintuitive facts."

Re: Conterintuitive facts in mathematics, CS, and physics

#17

Post by eruleman » Tue, Oct 05, 2021, 10:42 PM UTC

tunesmith wrote: post #5

Remedial question about zero-knowledge proof. Isn't "proof" a misnomer since the concept is about just making it incredibly likely to be true?

No — the word 'proof' is accurate, it establishes with certainty that you know the value of x.

Re: Conterintuitive facts in mathematics, CS, and physics

#18

Post by jgtrosh » Tue, Oct 05, 2021, 10:43 PM UTC

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…

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.

Re: Conterintuitive facts in mathematics, CS, and physics

#19

Post by MatteoFrigo » Tue, Oct 05, 2021, 10:44 PM UTC

The list is missing one of the most astonishing discoveries of all time: if you reflect the universe in a mirror, you can tell whether you are in our universe or in the mirror because the laws of physics are different in the mirror. See https://en.wikipedia.org/wiki/Wu_experiment

Re: Conterintuitive facts in mathematics, CS, and physics

#20

Post by pishpash » Tue, Oct 05, 2021, 10:48 PM UTC

The most counterintuitive fact, er... fib is this nugget:

"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?"

You know how hard it is to get 100% of the people to do something? Don't insult our intelligence like that, or of SAT test takers in general.