solonomonoff induction, time penalty, the universal program, and deism

posted on 2022-06-18

if you subscribe to the standard solomonoff induction, with its uncomputable universal distribution, then the answer to "where are we in it?" is often "in the universal program"; if it's not, then it's somewhere "below" the universal program — maybe in rule 30 (or maybe rule 30 likely implements its own universal program, and serves as a minimum?)

this makes the universal distribution limited in usability: where are we? oh, this one program that contains everything. to remedy problems like this, people come up with UDASSA, with the "world and claw" assumption — this roughly means that you have to describe not just a program that contains us, but also a program that locates us within the computation. so, sure, we're somewhere in the universal program, but now you have to find where, and this is where the bits of interestingness come back.

an alternative is to penalize computations that run too long; levin search uses exponential time, but if exponentials put you off, my time step proposal uses linear time.

so now, the question remains: where (which also now includes when) are we in the prior? in the spirit of that question, let me get into a tangent.

i was thinking the other day about what a fully rationality-equipped argument for atheism looks like. the basic structure is something like: {computation seems fundamental + simplicity seems to work} → solomonoff induction → the prior dislikes god. the rough idea is that a personified god is a needlessly rich computation to describe, to get to our world.

while this remains true for human-like deities like the abrahamic gods, it makes an interesting argument for deism emerge: what occurs earlier in the prior? the raw code for our universe, or the code for an intelligent program which in turns designs our universe? it is hard to reason about this, but if the bootstraping code for an intelligent and stuff-caring intelligence is simple, then there's a reasonable argument to be made for some form of deism. notably: if the program of the cosmos turns out to be the bootstrap for a universe in which an intelligence appears that itself spawns our universe, i think that that mildly counts as deism.

the "world and claw" or "locating time step" approaches to locating us within the computation make this perhaps even more plausible: what's more likely to compute us first, a naive computation of everything everywhere, or a lazy computation focused on a set of places that includes us — for example, because we're interesting, notably this century.

depending on which universal prior you choose (the standard uncomputable universal distribution with the "world and claw", levin search with log time step, the universal program with linear time step, or some other universal prior), i think you can make reasonable arguments for our existence being the product of a caring entity. examining whether our laws of physics are more likely to be designed or emerged, as well as considering how interesting we think we are, might help.

posted on 2022-06-18