making the UD and UDASSA less broken: identifying time steps

posted on 2022-03-21

the universal distribution ("UD") and its applicability to anthropics apparently suffers from some issues.

one is uncomputability. i think a speed penalty seems reasonable; but as a more general solution, i think it is unreasonable to "wait for the machine to halt". instead, let us see turing machines as running forever, with getting stuck on a repeating state as a special case. then, the space of all computations on a given universal turing machine ("UTM") is a set of pairs (input program, time step); or more simply, if we use a universal complete program, it is just a time step: every computation will be ran at some point.

this model feels quite natural to me, and seems like an easy way to rank priors: weigh the result of hypotheses by the inverse of the time step at which the universal complete program runs into them.

this also helps with UDASSA: if you use a deterministic model of computation where every computation step only does a finite amount of stuff (like turing machines or SKI calculus, but unlike wolfram-style graph rewriting) then you don't need a "claw" program to locate you within the world described by the world program; you are simply located at the set of time steps which happen to be updating the part of world that is you. this gives us a natural "locator" for persons within the space of all computation; it flattens together time, space, timelines (when a computation splits a world into multiple states all of which it then continues computing), and possible computation machines all into one neat linear sequence of steps.

posted on 2022-03-21