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Conterintuitive facts in mathematics, CS, and physics

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Re: Conterintuitive facts in mathematics, CS, and physics

#21

Post by lotsofpulp »

jgtrosh wrote: post #18
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…

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.

Re: Conterintuitive facts in mathematics, CS, and physics

#22

Post by mint2 »

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…

I really don’t like that example because it makes no sense. In no logical circumstance could the potatoes dehydrate so quickly when left out over a single night.

Re: Conterintuitive facts in mathematics, CS, and physics

#23

Post by clon »

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.

It was implied that the correct answer is 4.

Re: Conterintuitive facts in mathematics, CS, and physics

#24

Post by IainIreland »

pishpash wrote: post #20

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.

The correct answer was not provided as a multiple choice option, which means by definition that 0% of test takers selected it.

Re: Conterintuitive facts in mathematics, CS, and physics

#25

Post by lapetitejort »

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

Re: Conterintuitive facts in mathematics, CS, and physics

#27

Post by pishpash »

rumpelstilz18 wrote: post #7
jancsika wrote: post #6

> Knowing just slightly more about the value of your car than a potential buyer can make it impossible to sell it: https://en.wikipedia.org/wiki/The_Market_for_Lemons From that Wikipedia page: > This means that the owner of a carefully maintained, never-abused, good used car will be unable to get a high enough price to make selling that car worthwhile. This is bullshit-- the word "enough" was sneaked in there without…

> Knowing just slightly more about the value of your car than a potential buyer can make it impossible to sell it > This means that the owner of a carefully maintained, never-abused, good used car will be unable to get a high enough price to make selling that car worthwhile. Both statements are a wrong understanding of the phenomenon. The market collapses because the transactions happen outside of the market. Somethi…

Under this model, if the transaction of quality goods happened anywhere, some buyer reached information symmetry. But among the assumptions in the article is that sellers have no alternate market (they just "leave", whatever that means) and there is no credible way to provide information on the quality of goods. But then how do buyers know to lower their prices with what's left in the market?

There're a lot of unreasonable assumptions and maybe that's why the paper was rejected 3 times. You can also run the thought experiment backwards: lemons should be removed from the market first since, as stated, those are the ones that sell, but then you should be left with a market full of peaches.

Re: Conterintuitive facts in mathematics, CS, and physics

#28

Post by School-Cotton »

Causality1 wrote: post #16

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."

Of course Gabriel’s horn doesn’t exist in physical reality, but it’s still interesting that such a thing exists in a mathematical theory that is normally a pretty good model of physical reality.

Re: Conterintuitive facts in mathematics, CS, and physics

#30

Post by bpodgursky »

niccl wrote: post #26

Missing one that still makes no sense to me: The Ramanujan Summation: 1 + 2 + 3 + ⋯ + ∞ = -1/12 https://en.wikipedia.org/wiki/1_+_2_+_3_+_4_+_%E2%8B%AF

> where the left-hand side has to be interpreted as being the value obtained by using one of the aforementioned summation methods and not as the sum of an infinite series in its usual meaning
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