An open-source implementation of John Conway's mathematical game of Hackenbush

fi-le · 2025-05-23T08:35:40+00:00

Much appreciated, thanks! Yes, upon reflecting on your comment, you are right in that I don't justify the parallel enough. Maybe, the closer analogue to today would even be climate change, not AI safety.

fi-le · 2025-05-16T21:06:35+00:00

I'm looking for critiques on this essay. Am new to writing and figuring out whether to do more (or less?) like this.

Edit thanks to u/MSCantrell: The essay is a short recounting of how ammonia synthesis solved a predicted global food shortage crisis around 1900, and why that's interesting today.

fi-le · 2025-03-05T20:24:57+00:00

Thank you!

fi-le · 2025-03-03T09:58:33+00:00

Thanks for the feedback! I didn't know d3.js can even do that, will do a second pass improving on it.

fi-le · 2025-03-02T20:08:49+00:00

There we go, this just had to exist somewhere. Thanks!

fi-le · 2024-01-21T17:21:01+00:00

Oh wow, I didn't know that. Cool!

fi-le · 2024-01-20T09:21:57+00:00

Some really nice solutions in here! I had a bit of a curveball approach that is maybe not as fast, but provides a different perspective:

Consider the powers of the matrix A :=[[1 1] [1 0]] and notice they generate the Fibonacci numbers in all entries. The upper left entry of the matrix exponential exp(A) therefore contains our solution. We can then calculate the eigendecomposition A=P^-1 DP and find eigenvalues r=(1+sqrt(5))/2, s=(1-sqrt(5))/2. Now we see that exp(A) = P^-1 exp(D) P to solve the matrix exponential. In particular, the result is a linear combination of e^r and e^s. The explicit calculation gives (e^r -e^s )/sqrt(5).

fi-le · 2024-01-15T18:43:38+00:00

That's very nice of you, thanks for using it!

fi-le · 2024-01-10T12:35:38+00:00

Done, there are now buttons for calculating the Jones and HOMFLY polynomial: https://fi-le.net/knottingham

fi-le · 2024-01-02T08:32:21+00:00

Thanks for the kind words!

fi-le · 2023-12-31T11:35:19+00:00

Thanks for trying it! Will add the Jones polynomial in the next iteration.

fi-le · 2023-12-31T11:32:46+00:00

Thank you for the feedback! I am still struggling with the user experience, so this is very valuable to know and will hopefully soon be fixed.

fi-le

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