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Show HN: I made a puzzle game that gently introduces my favorite math mysteries

rahulilango.com

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Re: Show HN: I made a puzzle game that gently introduces my favorite math mysteries

#31

Post by russellbeattie »

messe wrote: post #22
MCSP wrote: post #14

Earlier quoted context omitted.

Thanks for pointing this out! Switched to "British Isles" -- update should be percolating now

The British Isles is also a somewhat controversial term with colonial implications, and it's not used by the government of Ireland[1]. "Britain and Ireland" would be a safer bet, as the map doesn't include any other islands. https://en.wikipedia.org/wiki/Names_of_the_British_Isles

Diving into Wikipedia, apparently variations of the name "Britain" have been in use since 30BC, and referred to the big island, with the smaller islands grouped with it, e.g. British Isles.

The Irish may not like it, but they're fighting against two millenia of history.

Re: Show HN: I made a puzzle game that gently introduces my favorite math mysteries

#32

Post by esquivalience »

zamadatix wrote: post #29

Loved the interactions and flow overall but I'm a bit lost on the zero knowledge proof example. I'm familiar with the concept but I don't follow how the example is one. E.g. "By repeating the process enough times, the probability that you never catch me becomes smaller than, say, getting struck by lightning" doesn't seem to show it's a proof? If I pick a hundred numbers it'll look like I just proved some black box fu…

I think the answer is that each time you reveal the colours, you observe that they are within the set of three colours illustrated at the beginning of the proof. Whichever you reveal, you never find a fourth colour.

This confused me at first.

Re: Show HN: I made a puzzle game that gently introduces my favorite math mysteries

#33

Post by zamadatix »

esquivalience wrote: post #32
zamadatix wrote: post #29

Loved the interactions and flow overall but I'm a bit lost on the zero knowledge proof example. I'm familiar with the concept but I don't follow how the example is one. E.g. "By repeating the process enough times, the probability that you never catch me becomes smaller than, say, getting struck by lightning" doesn't seem to show it's a proof? If I pick a hundred numbers it'll look like I just proved some black box fu…

I think the answer is that each time you reveal the colours, you observe that they are within the set of three colours illustrated at the beginning of the proof. Whichever you reveal, you never find a fourth colour. This confused me at first.

For anyone confused by this response I had edited my comment after reading https://news.ycombinator.com/item?id=40740557 but before equivalence had hit reply and now their reply is left hanging. Sorry esquivalience! To summarize the linked answer on trusting the second dot isn't just randomly assigned: keep the context as physical post-its. Barring something like a matter bending psychic you'd be able to tell the dot under the second post-it was swapped as you made your pick.

That still leaves how to rely on chance of picks for a proof though.

Re: Show HN: I made a puzzle game that gently introduces my favorite math mysteries

#34

Post by gergo_barany »

baruchel wrote: post #3

Hi, my two cents; you claim "Although mathematicians believe their proof is correct, it is too complex to verify without computer assistance", but I'm not sure "believe" is the correct verb since the proof has been formally verified (see for instance https://github.com/coq-community/fourcolor for a formal verification in Coq). I understand that you want to emphasize the fact that no human can understand the proof wit…

That Coq proof is not "without computer assistance". No Coq proof is, as Coq is literally an "assistant" that runs on a computer.

And those many jobXtoY.v and taskXtoY.v files sure look like they also do the same as the Appel and Haken proof, namely enumerate lots and lots of cases that are then machine-checked. So I don't think the computerized Coq proof is really qualitatively different from other computerized proofs that enumerate so many cases that a manual check would be impractical.

Re: Show HN: I made a puzzle game that gently introduces my favorite math mysteries

#36

Post by hcs »

MCSP wrote: post #17
hcs wrote: post #7

Earlier quoted context omitted.

You do need to prove that you have assigned the colors before the choice of what to reveal is made, I think. Physically this is guaranteed by the presence of the colors under the post-its (barring dynamic e-paper or something). I'm not sure how it works with the example of the primes, I lost the link to the later pages of the game so I can't read over it again, but I think it's guaranteed because there's just one num…

You're exactly right. The definition via primes ensures there is only one color consistent with each number (formally, this is called a perfectly binding commitment scheme). Also, here's the link if you want to go back: rahulilango.com/coloring/zk

Thanks! And this is a great exercise, thanks for sharing it.

Re: Show HN: I made a puzzle game that gently introduces my favorite math mysteries

#37

Post by hcs »

joshlk wrote: post #11

That was fun. On another note, I dislike how “Zero-Knowledge Proofs” are called proofs. It’s not a proof. You iteratively increase your belief that the result is true, like in experimentation, but that’s not a proof.

It might help to think of the sense of "proof" that's synonymous with "trial", rather than a specific formal math sense of proving a theorem from axioms by formal transformations.

Re: Show HN: I made a puzzle game that gently introduces my favorite math mysteries

#38

Post by valenterry »

MCSP wrote: post #15
baruchel wrote: post #3

Hi, my two cents; you claim "Although mathematicians believe their proof is correct, it is too complex to verify without computer assistance", but I'm not sure "believe" is the correct verb since the proof has been formally verified (see for instance https://github.com/coq-community/fourcolor for a formal verification in Coq). I understand that you want to emphasize the fact that no human can understand the proof wit…

Good point! I'll try to think about a better way to phrase this (happy to hear suggestions)

Nah, actually I agree with you. What counts as believe and what as fact is rather abitrary. Is 2+2=4 a fact? Is global warming a fact? What about man-made global warming? Ask 100 people whether something is a fact or a believe.

To top that up, it's fact that there have been "proves" that were wrong (or maybe that's just my believe? :^]) even for a long time.

Hence, I think we can say that there are 4 options for a theorem:

1) Some mathematician believes the theorem is correct (but can't prove it)

2) Some mathematician believes the theorem is incorrect (but can't prove it)

3) Some mathematician believes the proof of a theorem is correct

4) Some mathematician believes the proof of a theorem is incorrect

Proving that a proof is correct is kind of meaningless. At that point it's all believe anyways.

Re: Show HN: I made a puzzle game that gently introduces my favorite math mysteries

#40

Post by SilasX »

Uh, when you draw the map that requires three colors, I couldn't figure out how to submit it to at least be told it's not good enough. Or if it automatically accepts for a 3-min [1], then it was too hard to make sure that the boundary reached the edge of the screen. (I thought I successfully drew five regions around a point.)

[1] sorry, 3-chromatic or whatever

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