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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

#41

Post by romwell »

zamadatix wrote: post #33
esquivalience wrote: post #32

Earlier quoted context omitted.

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…

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 they change their mind and decide that only 0.0000001% will make them happy, they simply tack on a few more rounds.

The key here is that the probability that you can cheat for arbitrarily long is exactly zero — for the same reason that Zeno's paradox is resolvable (and limit of 1, 1/2, 1/4, 1/8, 1/16, ... is exactly zero, and not just a very small number).

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

#42

Post by MCSP »

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…

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 responses to this:

1. The probability can be made incredibly small, like smaller than the the chance, say, your computer got hit by a gamma ray burst that would flip bits from 0 to 1 (I really have no idea if this actually happens but people have said it to me).

2. It turns out it is mathematically impossible to get the zero knowledge property if you want true proofs (i.e., no probability of being wrong). So, there's a trade off: if you want zero knowledge, you have to accept some (small) failure probability

P.S. Adding an easter egg for coloring the larger graph is on the todo list :)

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

#43

Post by gowld »

MCSP wrote: post #16
AndrewOMartin wrote: post #4

Can you add to the FAQ at the end an answer to the question "How do I know you're not just showing me two random colors?"? It's possible this is already addressed and I missed it.

Thanks for the feedback! As hcs suggests, this is part of the physical post-it assumption. I'll think about ways to make it more clear -- adding an FAQ is a good idea :)

All that's missing is more info in the answer to this question:

> Question: How do you do this in the digital world, without post-it notes?

Answer:

"When I give you a map labelled with numbers for each region, the numbers are the "post-it notes", "covering" the list of factors (which encodes a color). You can't see the primes factors inside them, because, even though generating an multiplying large primes is easy for computers, factoring numbers is much, much harder.)"

I think if, when the player checks "reply the demo, with numbers", you move the game down to where the prime number discussion is, it's easier to understand.

Also, note that the digital versionis better than the physical version. In the physical version, you can't stop me from removing extra notes. (A better example might be to put each color in a locked box, each with a different lock/key.) In the digital version, the factor lists are the "keys".

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

#44

Post by romwell »

chromy wrote: post #6

The Republic of Ireland (the west most region on the first page) isn't part of the United Kingdom. The term for the group of regions shown is 'the British Isles'. See https://qntm.org/uk While it seems like a trivial distinction the whole thing is somewhat fraught ( https://en.wikipedia.org/wiki/The_Troubles ).

It's about as "trivial" a distinction as considering Crimea (or the entirety of Ukraine, for that matter) a part of Russia.

Many, many people have died for this triviality.

"Somewhat fraught" is a very interesting choice of words, but then again, so is "The Troubles" (when the subject matter is decades of bombings and killings).

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

#45

Post by gowld »

soneca wrote: post #25

Great job! I enjoyed going through the steps. The final though seemed like a huge leap for me, who don’t know anything about those math mysteries (which I assume is your target audience). First I was curious to learn how is the fast way to understand that 1, 2, or 4 colors suffice. And why finding out such a way for 3 is so hard. The zero-knowledge proof demonstration felt like “changing the subject”. Probably I miss…

ZKP is the subject. The maps part is a helper lemma.

It would help to clarify that in the beginning. The game is a bit of a shaggy dog tail. It would be good to give an outline and progress bar at the start (without spoilers)

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

#47

Post by gowld »

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

Safest to just remove Ireland from the map. It's not needed for the demo.

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

#48

Post by messe »

russellbeattie wrote: post #31
messe wrote: post #22

Earlier quoted context omitted.

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.

And it's use in English only comes from the mid 16th and 17th centuries, right around the time that much of Ireland was being colonized by the British.

Frankly, I find the term offensive, and think it should be discouraged in much the same way people have shifted away from "the Ukraine" to simply Ukraine.

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

#49

Post by darajava »

MCSP wrote: post #13
chromy wrote: post #6

The Republic of Ireland (the west most region on the first page) isn't part of the United Kingdom. The term for the group of regions shown is 'the British Isles'. See https://qntm.org/uk While it seems like a trivial distinction the whole thing is somewhat fraught ( https://en.wikipedia.org/wiki/The_Troubles ).

Whoops! Switched to "British Isles" -- update should be percolating now

I prefer the term “Atlantic Archipelago”. The “British Isles” encompassing a non-british sovereign state is contentious. Other good terms are “Britain and Ireland” or the “British-Irish isles”

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

#50

Post by returningfory2 »

russellbeattie wrote: post #31
messe wrote: post #22

Earlier quoted context omitted.

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.

Sure, but more recent history should have a higher weight. It is reasonable that our names for things reflect recent history and current affairs more than ancient history.

Two thousand years ago Britain and Ireland were ethnically and linguistically pretty similar (I believe). Since then they have diverged in many ways - most significantly during the Reformation period when people in Britain largely left Catholicism, but people in Ireland remained Catholic. Changes like this and the legacy of colonialism this have ultimately resulted in Ireland having distinctly non-British identity. It is reasonable that our naming for things reflect this current state of affairs.

As always, it useful to consider other examples to clarify the point. For example, by the same argument, should we deprecate the phrase "Latin America"? After all, Latin Europeans only arrived in the Americas 500 years ago and the continent has had people for 10 thousand years before that. Are people who include a European adjective in the name of this cultural area "fighting against ten millenia of history"?

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