I’m having trouble understanding how you identify ‘life rules’ and ‘gliders’ in arbitrary universes encoded as arbitrary turing machines.
You say:
To accomplish this, fix a way f to bijectively encode histories of V as binary sequences. Allow arbitrary histories: don’t impose Game of Life rules.
where V is the ‘forward light cone’
And then:
Here W(h) is the set of cells h in which satisfies Game of Life rules,
You use W(f^-1 (x) ) to represent the idea of mapping an arbitrary universe history represented as a bit sequence x into your W function which somehow detects the set of cells satisfying game of life rules.
I think I get your idea … but how do you actually imagine this function would work?
Defining what constitutes a ‘thing’ across any universe is … hard. Can your W(..) function recognize cells in a game of life running on my computer? ( once you have established or defined ‘cells’ , recognizing gliders is of course easy)
In other words, how do you ground these symbols so that it works across the multiverse?
Suppose P is a program generating some binary description X of our universe. Suppose h is a program which extracts the cell values of the game of life on your computer from X in a format compatible with f. h is relatively low complexity since apparently the cell values are “naturally” encoded in the physical universe. Therefore the composition of h and P will have a significant contribution to the Solomonoff expectation value and the agent will take it into account (since it lives in our universe and therefore makes decisions logically correlated with X).
I’m having trouble understanding how you identify ‘life rules’ and ‘gliders’ in arbitrary universes encoded as arbitrary turing machines.
You say:
where V is the ‘forward light cone’
And then:
You use W(f^-1 (x) ) to represent the idea of mapping an arbitrary universe history represented as a bit sequence x into your W function which somehow detects the set of cells satisfying game of life rules.
I think I get your idea … but how do you actually imagine this function would work?
Defining what constitutes a ‘thing’ across any universe is … hard. Can your W(..) function recognize cells in a game of life running on my computer? ( once you have established or defined ‘cells’ , recognizing gliders is of course easy)
In other words, how do you ground these symbols so that it works across the multiverse?
Hi Jacob!
Suppose P is a program generating some binary description X of our universe. Suppose h is a program which extracts the cell values of the game of life on your computer from X in a format compatible with f. h is relatively low complexity since apparently the cell values are “naturally” encoded in the physical universe. Therefore the composition of h and P will have a significant contribution to the Solomonoff expectation value and the agent will take it into account (since it lives in our universe and therefore makes decisions logically correlated with X).