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…
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.