Conterintuitive facts in mathematics, CS, and physics
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Conterintuitive facts in mathematics, CS, and physics
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Re: Conterintuitive facts in mathematics, CS, and physics
#2very cool collection - truly something to pick from at a party. should have much more upvotes imho.
Re: Conterintuitive facts in mathematics, CS, and physics
#3very cool collection - truly something to pick from at a party. should have much more upvotes imho.
Agreed, some real mindbenders there!
Re: Conterintuitive facts in mathematics, CS, and physics
#4[deleted]
Re: Conterintuitive facts in mathematics, CS, and physics
#5Remedial question about zero-knowledge proof. Isn't "proof" a misnomer since the concept is about just making it incredibly likely to be true?
Re: Conterintuitive facts in mathematics, CS, and physics
#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 any rationale provided. The most we can say is that a seller-- if they decide to sell-- won't get as high a price as they would if the information assymmetry didn't exist. But that's just a truism.
I'd be willing to agree for the sake of argument that we are representing humans here as some commonly known set of JSON values. But before we go anywhere else from that argument, I'd need to know that the speaker will at some point halt the simulation and come back to Earth with insights into the real world.
Does that happen in this paper? If not, then how does the paper have relevance for the economic transactions among the set of bona fide human beings?
Re: Conterintuitive facts in mathematics, CS, and physics
#7> 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. Something similar has in my opinion happened on the job market. Most good jobs are outside the regular job boards. Most good applicants could not be bothered to apply for a job opening but are asked by recruiters or friends.
Re: Conterintuitive facts in mathematics, CS, and physics
#8Someone asked about #4 then deleted after I typed the response, so here it is.. :)
It's queuing theory in general, related to "utilization". The utilization curve is always shaped the same; 50% utilization always doubles waiting time, and the curve is practically vertical when you get to 99% utilization. That's what explains the difference - 5.8 customers per hour, for a throughput of 6 per hour, shoves the efficiency to the almost-vertical part of the curve, which impacts waiting time.
Re: Conterintuitive facts in mathematics, CS, and physics
#9Here is one of my favorites: The specific heat of a star is negative. (This also applies to a galaxy or any other gravitationally bound object.)
As a star loses energy, it heats up. If you inject it with energy, it cools down. It's a trivial corollary from the virial theorem, but it leads to counterintuitive behavior (like the gravothermal catastrophe).
Re: Conterintuitive facts in mathematics, CS, and physics
#10Great list!
> 33. "...if you flip fair coins to generate n-dimensional vectors (heads => 1, tails => -1) then the probability they're linearly independent is at least 1-(1/2 + o(n))^n. I.e., they're very very likely independent!
Counterintuitive facts about high dimensional geometry could get their own list. A side-1 cube in n dimensions has volume 1 of course, but a diameter-1 sphere inside it has volume approaching zero! The sphere is tangent to every one of the 2n faces, yet takes up almost none of the space inside the cube.
Note that the distance from the middle of any face of the cube to the opposite face is 1, yet the length of a diameter of the cube (corner to opposite corner) is sqrt(n).