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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

#111

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…

OP: Although I'm not really in the target audience for this demo (I already knew all the punchlines), it does occur to me that it might be helpful to readers like the parent-commenter — and even perhaps thought-provoking to us know-it-alls — if you provided a mode at the end of the demo where the graph was in fact not three-colorable , and the computer actually would lie about its being three-colorable. So it would g…

For me it was less about the idea of how likely you'd quickly it converges to you almost certainly outing them vs misunderstanding the idea that a zero knowledge proof is about, more or less, the "limit" of the validation behavior to an arbitrary point choosable by the tester not necessarily an actual guarantee you can finitely reach the conclusion.

Prior to this I'd only seen "proof" in math where it has meant you can absolutely guarantee there to bo no counterexample not just that it seems impossibly unlikely there could be a counterexample. E.g. the Tarry-Escott problem where we have proof there is no sets exists with n=4 and m=5 even though we haven't ever found numerical values of sets matching that description or Merten's conjecture where the smallest counterexample is estimated to be so large (~10 billion digits) we've not even been able to find the first counterexample value despite knowing it exists due to a proof. On the other side of things we have things like the Goldbach conjecture or Riemann Hypothesis where we've poured our hearts, brains, and souls into trying to find a counterexample or proof and don't claim to have either yet.

Adjusting to that definition of "proof" for the context it all makes a lot more sense now.

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

#112
post #42

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…

Very glad you enjoyed it! For the ZK example, the math behind it is this: if there are m bordering regions and I am lying, you have a 1/m chance of catching me each time. Thus after k repetitions the chance you haven't caught me is (1-1/m)^k \approx e^{-k/m} which is extremely small for k sufficiently larger than m. Now, you may rightfully say: hey that's still not a "proof," you could still be lying! There are two r…

Thanks for the explanation, it seems the definition was slightly different than I assumed it to be previously and that was my missing link to it all making sense. Thanks also for the demonstration to share this info!

Looking forward to the easter egg :)

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

#113
post #41

Earlier quoted context omitted.

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…

It's the same thing as limits in spirit. It's not that the chances of lying are small, it's that they can be made arbitrarily small. Let's say my standards of "proof" are that there's only 0.1% chance that you're cheating. We play that game several times, and I'm satisfied. Next comes someone else whose standard is 0.001% chance of cheating. They simply play the game a few more times, and they're satisfied too. If th…

Great description in that "proof" in this context is more referring to the limiting behavior and being able to get to your desired level of arbitrary happiness than necessarily providing a traditional "proof" about it being a certainty within a finite amount of estimation. Thanks.

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

#114
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.

zero knowledge corroboration isn't the same thing as a zero knowledge proof. If the provided evidence isn't enough, then you keep iterating until it's proven.

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

#119

Earlier quoted context omitted.

That's the idea at the end about presenting the "sticky notes" as products of primes. Assuming you can't factor the primes yourself, you can be given the whole grid of those products and then interactively ask for the factors or a pair of them. The requestor can't give an alternative factorization (ie. make up a color on the spot) since each number can only be factored one possible way and its easy to verify.

I really liked this part that shows all the numbers up front, and none of them change during the reveal step. I think it would present better if introduced as "To show that there's no cheating going on behind the scenes, we will..."

Yeah I agree it could be presented clearer. Maybe make the analogy of multiplying the factors together and "covering with a post it" more explicit
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