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How could a Game of Life grid possibly have more state or require more storage than the ruleset for generating it! Gasp! It can't have more state. The initial
by T-hawk 14y ago
How could a Game of Life grid possibly have more state or require more storage than the ruleset for generating it! Gasp!
It can't have more state. The initial conditions have just as much state as any later generation. The initial state is {off, off, off, off, off, off, ... }. That's just as many bits as any later stage.
What you really mean is that the initial state is easily compressible. (Run-length encoding can express an entire empty grid in two numbers as length, value.) And that's pretty much what Kurzweil means, actually the Game of Life is a great analogy here. The genome is a compressed data set, which doesn't express or exhibit anything useful in itself, but can be decompressed using external inputs of organic matter and energy to procedurally generate the neurons that will form the intelligence.
- kd0amg 14y agoIt can't have more state. The initial conditions have just as much state as any later generation. The initial state is {off, off, off, off, off, off, ... }. That's just as many bits as any later stage. That encoding is only viable if you restrict the game to a finite grid.
- dbaupp 14y agoWhile true, the infinite case is of no interest here: a brain is finite. (Many infinite grids require an infinite amount of information to store, and clearly many of our assumptions break down there.)
- dbaupp 14y agoThe initial conditions in the game of life isn't normally all-off, because then every generation would be all-off. In any case, the amount of information in the game of life is merely (initial state, number of iterations) which is certainly finite for a finite board.