Thanks for taking me on that journey!
Show HN: I made a puzzle game that gently introduces my favorite math mysteries
141–150 of 177 posts
Re: Show HN: I made a puzzle game that gently introduces my favorite math mysteries
#142Nice!
I knew the 4-colour theorem but the zero knowledge proof illustration was great. I didn't get it initially but the FAQ cleared it up and I felt like I learned something as it wasn't obvious on the first look.
Re: Show HN: I made a puzzle game that gently introduces my favorite math mysteries
#143I showed this to my two kids, and we all three enjoyed it. The zero knowledge proof portion didnt really click for me, but we liked the four color map theorem stuff. This led me to download some maps for my kids to attempt coloring on paper, and also got me wondering about how this holds or doesn't on non-euclidian spaces. Turns out the maximum is four colors on a sphere, but 7 colors on a torus! More details here: h…
The best analogy of zk-proofs I've heard is to suppose you have found Waldo in "Where's Waldo," and want to prove that you have done this without revealing the location. You could take a piece of paper (much larger than the picture/book), and cut out a waldo-shaped hole it and position the paper such that he is shown in the hole. Then, when you show it to the challenger, they know that you have found him without you…
I think that conveys what a zero knowledge proof achieves but it doesn't really correspond to any real zero knowledge proof algorithms. You can't do that over the phone, which is kind of the whole point.
Re: Show HN: I made a puzzle game that gently introduces my favorite math mysteries
#144[spoiler alert] I knew that 4 colours sufficed for any arbitrary map from back in the day when I learned this, but still I found it VERY rewarding by attempting to draw a map that needed 5 colors, and how intuitive this demo was for getting a "feel" for a thing that I knew only theoretically! Like I needed an impossible geometry to fit, either an area that stretched to a zero-width path (which would becomes a point,…
It was really enjoyable to try. I got an optimal 4-color map on the first try, so I was over confident. My approach was something like: put a bunch of the 4-color maps next to a long Chile-like thing. When that didn't work I added borders until my device couldn't render it any longer. Very very fun.
Re: Show HN: I made a puzzle game that gently introduces my favorite math mysteries
#145I showed this to my two kids, and we all three enjoyed it. The zero knowledge proof portion didnt really click for me, but we liked the four color map theorem stuff. This led me to download some maps for my kids to attempt coloring on paper, and also got me wondering about how this holds or doesn't on non-euclidian spaces. Turns out the maximum is four colors on a sphere, but 7 colors on a torus! More details here: h…
Four colours also isn't enough for some real-world country maps. Countries with enclaves (like Alaska, Kaliningrad or Sint-Maarten, though only the last actually makes 4- colouring impossible) change the topology: you can think of what shape the earth would have if there was also a tunnel connecting Alaska and New York.
Torus, of course, but how does that relate to enclaves, which are planar ?
Re: Show HN: I made a puzzle game that gently introduces my favorite math mysteries
#146Can 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 :)
Thanks for the response, this and the rest of the comments here helped it finally click for me. I'm "recreationally" familiar with ZKPs, and always found the example of "video recording of alibaba" the most disappointing explanation, and the "I'm not color blind" demonstration the easiest to understand.
This demo was fun, and cool, and short (a undervalued virtue!). Awesome work. Thanks.
Re: Show HN: I made a puzzle game that gently introduces my favorite math mysteries
#147Just FYI the “map of the UK” includes the Republic of Ireland, which is very much not part of the UK. There’s not a 100% great term for the collective unit of land. Generally people go with “UK & Ireland” if they’re trying to be sensitive.
These kind of things are also why four colours are actually _not_ always enough, in the real world. Countries can have exclaves :)
Re: Show HN: I made a puzzle game that gently introduces my favorite math mysteries
#148Earlier quoted context omitted.
Four colours also isn't enough for some real-world country maps. Countries with enclaves (like Alaska, Kaliningrad or Sint-Maarten, though only the last actually makes 4- colouring impossible) change the topology: you can think of what shape the earth would have if there was also a tunnel connecting Alaska and New York.
Torus, of course, but how does that relate to enclaves, which are planar ?
You might want to colour the exclave the same colour as the rest of its country, even though no connection can exist between them on the plane.
Re: Show HN: I made a puzzle game that gently introduces my favorite math mysteries
#149So, there was this one question "Can every map be colored with just 4 colors?"...
And there I sit, knowing that every map of CONTIGUOUS territories can be colored with 4 colors - but on real world maps, there are enclaves - little islands that belong to a country that they have not connection to. And if those shall have the same color as their parent country, then 4 colors is not enough...
So I pick the answer "NO".
> you are wrong!!!!! every map can be colored with 4 colors! it has been proven!!!!!
Re: Show HN: I made a puzzle game that gently introduces my favorite math mysteries
#150I showed this to my two kids, and we all three enjoyed it. The zero knowledge proof portion didnt really click for me, but we liked the four color map theorem stuff. This led me to download some maps for my kids to attempt coloring on paper, and also got me wondering about how this holds or doesn't on non-euclidian spaces. Turns out the maximum is four colors on a sphere, but 7 colors on a torus! More details here: h…
same that was extremely fun but im not sure i'm going to grasp the zk proof thing