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Conterintuitive facts in mathematics, CS, and physics

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Re: Conterintuitive facts in mathematics, CS, and physics

#91

Post by p1necone »

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…

You're being overly pedantic (and I would argue actually incorrect). Kilograms and pounds are both referred to as "weight" in general conversation and nobody is going to be confused by this.

Go to any supermarket in a country that uses the metric system, potatoes will be sold by the kilogram - it's the natural way to phrase this outside of America.

In a physics context the definition of kilogram might be specifically mass, with newtons referring to weight/force. But words can have different meanings outside of technical contexts.

If you go to a metric country, and ask someone how much they "weigh", approximately zero people will say "x newtons", they will say "x kilograms" (or "x pounds" still in a lot of commonwealth countries if we're being pedantic).

Re: Conterintuitive facts in mathematics, CS, and physics

#92

Post by wnoise »

pdonis wrote: post #45
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."

> Considering spacetime, matter, and energy are all quantized First, we don't know that spacetime is quantized; that's a plausible speculation but we have no theory of quantum gravity. Second, "quantized" is not the same as "discrete". A free particle in quantum theory is "quantized" but the spectrum of all of its observables is continuous.

It's not even a plausible speculation; all of the best models we have, quantum mechanics, special relativity, quantum field theory, general relativity, and string theory have a fully continuous space-time. The one notable exception is loop quantum gravity.

Re: Conterintuitive facts in mathematics, CS, and physics

#93

Post by Jensson »

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.

Relativistic speed rotations means that you are close to trapping light, meaning your force is similar to being very close to the event horizon of a black hole.

And what is one of the properties of gravity wells like black holes? Well, their circumference isn't equal to 2 pi times radius, since the space has enough curvature to not be flat, similar to how circumference isn't 2 pi times radius if your space is a 2d sphere. So the paradox is correct, you would get that effect, at least if you used a black hole to cause the fast rotation. Although I'm not sure if the maths adds up to be the same.

Re: Conterintuitive facts in mathematics, CS, and physics

#94

Post by adenadel »

campital wrote: post #87

How is 27 counterintuitive? > Let alpha = 0.110001000000000000000001000..., where the 1's occur in the n! place, for each n. Then alpha is transcendental. (Calculus, 4th edition by Michael Spivak) Nearly all infinite sums involving factorial are transcendental.

In fact, almost all numbers are transcendental (algebraic numbers have measure zero).

Re: Conterintuitive facts in mathematics, CS, and physics

#95

Post by enthdegree »

Great list.

The statement “causation does not imply correlation”, while true in some contrived settings, is obstructive as a heuristic in my opinion. It is an anti-productive and unimportant diversion in any setting I can imagine it coming up.

Causation does indeed imply correlation, by tautology, using a very reasonable definition causation in the context of linear correlations.

Re: Conterintuitive facts in mathematics, CS, and physics

#98

Post by adenadel »

londgine wrote: post #86

> There are as many whole positive numbers as all fractions According to a specific non-colloquial definition of "as many".

Hm, I'm not so sure that just because the definition of a bijection is technical that it is not intuitive.

I'll start an enumeration of the rationals

1 1/3

2 1/4

3 1/5

...

If you can prove that you can do this, is that really so non-colloquial? It is certainly what we mean by "as many" for all finite sets, so what is wrong with doing this for infinitely many sets?

Re: Conterintuitive facts in mathematics, CS, and physics

#99

Post by umvi »

pessimizer wrote: post #61
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. 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%?
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