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Conterintuitive facts in mathematics, CS, and physics

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Re: Conterintuitive facts in mathematics, CS, and physics

#111

Post by zbaxrl »

umvi wrote: post #99
pessimizer wrote: post #61

Earlier quoted context omitted.

> > 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. Comes up a lot lately because of vaccine effectiveness e.g. 95% is twice as effective as 90%.

Wait, how is 95% effective twice as effective as 90%?

90% is 1 in 10, 95% is 1 in 20.

Re: Conterintuitive facts in mathematics, CS, and physics

#112

Post by dlubarov »

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?

In the literature [*], the "proof" is an actual proof, but that's not what the prover sends to the verifier. Rather, the verifier queries random pieces of the proof, eventually convincing themselves that with high probability, the prover knows a valid proof.

[*] At least in most of the older literature descending from the PCP literature. Modern papers sometimes abandon that distinction and just use "proof" and "argument" interchangeably.

Re: Conterintuitive facts in mathematics, CS, and physics

#113

Post by pvg »

duxup wrote: post #103
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…

16 is like the money hall problem. I understand the answer, the answer makes sense to me. And yet but when I think of it how I think of it initially ... it still makes no sense.

The limit case can be helpful here, a strawberry made of 100% water can be dehydrated to practically nothing and is still made of 100% water.

Re: Conterintuitive facts in mathematics, CS, and physics

#114

Post by d_burfoot »

Here is one of my favorites. Take a light source and shine it at a filter that is polarized up/down that is in front of a filter that is polarized left/right. None of the light will get through: the first filter removes all of the L/R components of the light, and the second filter removes all the remaining light.

Now add a third filter, between the two, which is polarized at 45 degrees. Now some of the light goes through!

If this doesn't surprise you, imagine there was a man firing a machine gun at a pair of walls. The two walls are thick enough that they absorb all the bullets. But when you add a third wall in between them, some of the bullets go through.

Re: Conterintuitive facts in mathematics, CS, and physics

#115

Post by moralestapia »

hinkley wrote: post #59
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

I believe Veritasium covered this: spinning at relativistic speeds generates centripetal forces that overcome the nuclear force. There is no material you can use to test this paradox, and there can be no such material because your device would atomize - or worse - in the attempt. Effectively there are g-forces so high that you end up with subatomic particles.

It's mean to be a thought experiment but some people (like Veritasium) can't get around this simple realization.

Like, "I wonder what could be happening inside of a black hole?"

"Oh we would never know, because if we send a camera it would break. Also suppose we MaaaAaAKKeee aa cCAaaMeerra with ThE STROooonngGEEstt Material In the UUunniveersssee, so it wouldn't break, you would find that there's no wifi in there so how would you transmit your findings ;)"

I hate this kind of "smart" people.

Re: Conterintuitive facts in mathematics, CS, and physics

#116

Post by Kranar »

eruleman wrote: post #17
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.

I thought you were right until I decided to look into it myself, turns out we were both wrong. Zero-knowledge proofs are probabilistic and contain a soundness error which is the probability of guessing the correct answer. This can, in some but not all cases, be brought down arbitrarily close to 0, but it can never be 0 exactly.

https://en.wikipedia.org/wiki/Zero-knowledge_proof#Definitio...

Re: Conterintuitive facts in mathematics, CS, and physics

#117

Post by d_burfoot »

Surprising fact about the sun: it actually produces less heat per unit volume than a compost pile - this makes sense when you consider that fusion events are very rare.

The reason the sun is so hot is that it has an enormous ratio of volume to surface area. Heat emission due to radiative cooling is proportional to the surface area, but heat creation due to fusion is proportional to the volume.

Re: Conterintuitive facts in mathematics, CS, and physics

#118

Post by yongjik »

moralestapia wrote: post #115
hinkley wrote: post #59

Earlier quoted context omitted.

I believe Veritasium covered this: spinning at relativistic speeds generates centripetal forces that overcome the nuclear force. There is no material you can use to test this paradox, and there can be no such material because your device would atomize - or worse - in the attempt. Effectively there are g-forces so high that you end up with subatomic particles.

It's mean to be a thought experiment but some people (like Veritasium) can't get around this simple realization. Like, "I wonder what could be happening inside of a black hole?" "Oh we would never know, because if we send a camera it would break. Also suppose we MaaaAaAKKeee aa cCAaaMeerra with ThE STROooonngGEEstt Material In the UUunniveersssee, so it wouldn't break, you would find that there's no wifi in there so…

(Disclaimer: I am not a physicist.)

I think it's actually a pretty reasonable description? Sounds like it's a paradox because we assume a rigid body, but nothing in real life is a perfect rigid body. So the situation simply becomes a bunch of particles following circular orbits. If you measure distance along one direction (while constantly accelerating in relativistic speed) you get one number; if you measure distance in another direction you get a different number. But that's what relativity does.

In other words, it's similar to the simpler question: "If I have a perfectly rigid rod that can reach the moon, and I push it, then the other end pushes the moon immediately. But speed of information cannot exceed speed of light. How come?" Answer: There's no perfectly rigid rod.

Re: Conterintuitive facts in mathematics, CS, and physics

#120

Post by robocat »

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

Spin the observer at the centre of the disc, and keep the disc stationary... now what happens?
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