“The answer is, we can view the physical universe as a program that runs S as a subroutine, or more generally, view it as a mathematical object which has S embedded within it.” A big computation with embedded discrete copies of S seems to me like a different concept from doing logical updates on a big graph with causal and logical nodes, some of which may correlate to you even if they are not exact copies of you.
The sentence you quoted was just trying to explain how “physical consequences” might be interpreted as “logical consequences” and therefore dealt with within the UDT framework (which doesn’t natively have a concept of “physical consequences”). It wasn’t meant to suggest that UDT only works if there are discrete copies of S in the universe.
In that same post I also wrote, “A more general class of consequences might be called logical consequences. Consider a program P’ that doesn’t call S, but a different subroutine S’ that’s logically equivalent to S. In other words, S’ always produces the same output as S when given the same input. Due to the logical relationship between S and S’, your choice of output for S must also affect the subsequent execution of P’. Another example of a logical relationship is an S’ which always returns the first bit of the output of S when given the same input, or one that returns the same output as S on some subset of inputs.”
I guess I didn’t explicitly write about parts of the universe that are “correlate to you” as opposed to having more exact logical relationships with you, but given how UDT is supposed to work, it was meant to just handle them naturally. At least I don’t see why it wouldn’t do so as well as TDT (assuming it had access to your “general-logical-consequence algorithm” which I’m guessing is the same thing as my “math intuition module”).
FWIW, as far as I can remember I’ve always understood this the same way as Wei and cousin_it. (cousin_it was talking about the later logic-based work rather than Wei’s original post, but that part of the idea is common between the two systems.) If the universe is a Game of Life automaton initialized with some simple configuration which, when run with unlimited resources and for a very long time, eventually by evolution and natural selection produces a structure that is logically equivalent to the agent’s source code, that’s sufficient for falling under the purview of the logic-based versions of UDT, and Wei’s informal (underspecified) probabilistic version would not even require equivalence. There’s nothing Cartesian about UDT.
“The answer is, we can view the physical universe as a program that runs S as a subroutine, or more generally, view it as a mathematical object which has S embedded within it.” A big computation with embedded discrete copies of S seems to me like a different concept from doing logical updates on a big graph with causal and logical nodes, some of which may correlate to you even if they are not exact copies of you.
The sentence you quoted was just trying to explain how “physical consequences” might be interpreted as “logical consequences” and therefore dealt with within the UDT framework (which doesn’t natively have a concept of “physical consequences”). It wasn’t meant to suggest that UDT only works if there are discrete copies of S in the universe.
In that same post I also wrote, “A more general class of consequences might be called logical consequences. Consider a program P’ that doesn’t call S, but a different subroutine S’ that’s logically equivalent to S. In other words, S’ always produces the same output as S when given the same input. Due to the logical relationship between S and S’, your choice of output for S must also affect the subsequent execution of P’. Another example of a logical relationship is an S’ which always returns the first bit of the output of S when given the same input, or one that returns the same output as S on some subset of inputs.”
I guess I didn’t explicitly write about parts of the universe that are “correlate to you” as opposed to having more exact logical relationships with you, but given how UDT is supposed to work, it was meant to just handle them naturally. At least I don’t see why it wouldn’t do so as well as TDT (assuming it had access to your “general-logical-consequence algorithm” which I’m guessing is the same thing as my “math intuition module”).
FWIW, as far as I can remember I’ve always understood this the same way as Wei and cousin_it. (cousin_it was talking about the later logic-based work rather than Wei’s original post, but that part of the idea is common between the two systems.) If the universe is a Game of Life automaton initialized with some simple configuration which, when run with unlimited resources and for a very long time, eventually by evolution and natural selection produces a structure that is logically equivalent to the agent’s source code, that’s sufficient for falling under the purview of the logic-based versions of UDT, and Wei’s informal (underspecified) probabilistic version would not even require equivalence. There’s nothing Cartesian about UDT.