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Conterintuitive facts in mathematics, CS, and physics

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Re: Conterintuitive facts in mathematics, CS, and physics

#61

Post by pessimizer »

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%.

Re: Conterintuitive facts in mathematics, CS, and physics

#62

Post by guerrilla »

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."

I think you're taking things too seriously (and in one case not seriously enough): These are all conclusions that are true if their premises are true. Some of their premises can obviously be satisfied, others obviously can't and many others are in between (unknown or debatable.) They're all counterintuitive results though.

Re: Conterintuitive facts in mathematics, CS, and physics

#64

Post by treebog »

lotsofpulp wrote: post #35
version_five wrote: post #33

Earlier quoted context omitted.

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.

In engineering school (in the US), we used pounds mass (lbm) as the unit of mass, and pounds force (lbf) as the unit of force.

Re: Conterintuitive facts in mathematics, CS, and physics

#65

Post by api »

I love “causation does not imply correlation.”

We still reason so much from the implicit premise that correlations are meaningful. It’s so intuitive, but wrong. The thing that finally got me to wrap my mind around it was this:

https://tylervigen.com/spurious-correlations

Re: Conterintuitive facts in mathematics, CS, and physics

#66

Post by pcmonk »

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?

That's why it's sometimes called an "argument" or specifically a "cryptographic proof". You can construct the statement such that it can be "proven" in a traditional sense by adding qualifiers such as "with probability more than 1-1/(2^256)". You'll generally need an assumption like knowledge-of-exponent or at least hash soundness.

Re: Conterintuitive facts in mathematics, CS, and physics

#67

Post by db_admin »

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 cryptography you prove security through showing that an adversary has a negligible [1] chance of winning a game of guess the secret.

[1] https://crypto.stackexchange.com/questions/5832/what-exactly...

Re: Conterintuitive facts in mathematics, CS, and physics

#68

Post by nighthawk454 »

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…

Yes, it doesn't explicitly state the rate or distribution of events. But it is a good reminder of what happens when your whatevers/second are pretty high - see the famous "One in a million is next Tuesday" [1]. "Rare" is soon if you roll the dice fast enough.

Any time your service has a high TPS, your API gets a lot of calls, a button in your app gets pressed a lot, ... this applies.

Critically, "a lot" is defined relative to your failure tolerance. It may actually be very fast or a lot, or not particularly fast but it really really needs to work.

It highlights the fallacy of equating "low probability" and "won't happen".

[1] https://docs.microsoft.com/en-us/archive/blogs/larryosterman...

Re: Conterintuitive facts in mathematics, CS, and physics

#69

Post by hinkley »

kristjansson wrote: post #40
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 - i…

Without the math:

Radius is always proportional to circumference, so a circle twice the size is twice as big around.

Take the case of two identical circles. To move a point on the first circle from 12 o'clock back to 12 o'clock, it only goes halfway around the other circle, which you can prove to yourself by imagining you've wrapped a string around the circle and marked it at 12 and 6 o'clock. If you unwrap half of the string and wrap it around the other circle, then the end of the rope is at 6 o'clock. To roll the string back up by moving the circle, the top of the circle will be pointing upward again when it reaches the bottom. 1 full revolution. Now wrap the other half of the string around the other side, 6 has to go back to the bottom again to roll the string back up. 2 revolutions.

Re: Conterintuitive facts in mathematics, CS, and physics

#70

Post by db_admin »

kristjansson wrote: post #40
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 - i…

You could also argue that it is a matter of perspective. From the perspective of either circle, A will only revolve 3 times.

Only by introducing a larger frame of reference, a grid or in the video a table, you gain an outside perspective. From this outside perspective you redefine a revolution according to some new orientation and end up with n+1 revolutions.

Or maybe the argument is backwards and I just try to justify answering 3.

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