4 ms·

But it's only easier to comprehend because it's vaguer. If you wanted to express specific, nontrivial mathematical statements in CA language, it would immediate

by knzhou 7y ago

But it's only easier to comprehend because it's vaguer. If you wanted to express specific, nontrivial mathematical statements in CA language, it would immediately get more complicated. Certainly, a paragraph about Euclid's Elements would be easier to comprehend than a paragraph from the Elements, but that's not a fair comparison...

JackFr 7y ago
But my point is if the CA and the mathematical expression show the same things, then you could say the mathematics are simply a roundabout and confusing way to characterize the CA. As a thought experiment (and a timely tribute) how would you (mathematically) characterize and/or describe an ongoing evolution of an instances of Conway's Game of Life if you didn't have a grid. Or even better, if you didn't have the grid and you could only see things a resolution of neighborhoods of 10-20 cell resolutions? You might be able to come up with some crazy complex math which does it. But if you knew about the grid and the underlying rules it would explain all of the observations perfectly AND more simply. Don't get me wrong -- I don't think Wolfram has done that, nor do I really hold out hope that it could be true. But it's a real compelling, if only it were.