I feel like this didn’t really go anywhere? In the discussion section he says that this should provide reason to not expect easy theorems or answers, but I don’t feel like that was really derived from the results of the experiments?
What’s the point if you aren’t even going to try to prove a theorem? Or, heck, even really test a hypothesis?
This is all pretty interesting. I think seeing every possible strategy compete with every other one makes for useful conversation, and his summary makes some sense to me, which is depending on ruleset, getting access to a pocket of what Stephen calls computational irreducibility generally can gain you the upper hand across a wide range of strategies is an interesting CS / Combinatorics result.
Probably most interesting is just throwing down a bunch of strategies that are provably better than tit for tat in rule constrained environments, and showing that some more complicated form of tit for tat doesn’t win as you get more space than your opponents - better is to manipulate simpler opponents into predictable behavior.
Anwyay, this particular Wolfram essay was devoid of name dropping, and full of interesting (if occasionally hard to parse) dense infographics, I enjoyed it and learned something.
A fascinating intellect at play. Whether the exercise has practical purpose or result, that's the nature of experiment and exploration - you don't know what insights may be discovered until you perform the experiment. He pursues a hunch, a question, persistently and comprehensively, mapping out the terrain systematically by running programs and visualizing the results. You can see in his train of thought that he has an intuitive sense for recognizing higher-order patterns.
I love that he's using his own programming language and environment for exploring mathematical spaces, and his articles are written as computational notebooks. The diagrams and graphs are actual running code, as fundamental and natural part of his writing and thinking process.
His work is rich, multifaceted, intellectually interesting and often novel. And fun! Not only entertaining for the reader, but there's a joy of a brilliant mind at play, which is a valuable motivating aspect of doing philosophy, science, art.
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[ 0.20 ms ] story [ 17.8 ms ] threadWhat’s the point if you aren’t even going to try to prove a theorem? Or, heck, even really test a hypothesis?
Probably most interesting is just throwing down a bunch of strategies that are provably better than tit for tat in rule constrained environments, and showing that some more complicated form of tit for tat doesn’t win as you get more space than your opponents - better is to manipulate simpler opponents into predictable behavior.
Anwyay, this particular Wolfram essay was devoid of name dropping, and full of interesting (if occasionally hard to parse) dense infographics, I enjoyed it and learned something.
I love that he's using his own programming language and environment for exploring mathematical spaces, and his articles are written as computational notebooks. The diagrams and graphs are actual running code, as fundamental and natural part of his writing and thinking process.
His work is rich, multifaceted, intellectually interesting and often novel. And fun! Not only entertaining for the reader, but there's a joy of a brilliant mind at play, which is a valuable motivating aspect of doing philosophy, science, art.