We know neural networks cannot solve the halting problem. But isn’t the question whether they can learn the transition table for game of life? Since each cell depends only on neighbors, this is as easy as memorizing how each 3x3 tile transitions.

The original question, maybe. Mine is basically the halting problem, I think.

The other difference is I don't take it seriously.

Wolfram looked at this recently on his blog.

https://writings.stephenwolfram.com/2024/05/why-does-biologi...

He says it's possible for smaller games (fewer rules) but unlikely for larger ones.. IMHO anything Turing complete would have this problem.