It’s a straw dummy to say that I haven’t updated my priors about insert ridiculous thing here. Those are not the things I described having residual posterior mass on; my “sky wizard” is currently content to play by very different rules. As for the epi-phenomena of how a society embraces religion, or does not, I agree, this does suggest that it would be foolish to base one’s beliefs SOLELY on the “evidence” of the crowd as you grow up.
Also, incidentally, MML/Kolmogorov complexity and Solomonoff are not the same here. The former do not give a posterior on models, they select one model. The later could and would easily put posterior mass on multiple programs that were observationally the same up to the amount of data we have currently observed.
Consider the sequence of numbers: 1,2,3.
MML would (for most Turing machines anyway) select the program: next=old+1.
Solomonoff would have posterior mass on many other sequences (e.g. do a query on http://oeis.org/). It’d put most of it’s mass on that program, but leave nonzero mass on other programs, like one that computes this sequence, say: http://oeis.org/A006530, and if the next numbers reveals the sequence:
1, 2, 3, 2, 5, 3, 7, 2, 3, 5
Then you can bet that’s where a lot of the mass will shift.
… And the really subtle bit, that I don’t want you to miss, is that it doesn’t all shift there, it’s still not a point posterior. There’s still mass on:
That mass won’t go away for a LONG time (that is if the data keeps coming from http://oeis.org/A006530 for at least Googol/2 steps.
And there are many possibilities like this out there. Sure, they have less mass individually, but there ARE many of them. And some don’t even have appreciably less prior mass (under a Solomonoff prior and a “reasonable” Turing machine). Computability is a whole ’nother issue.
Thanks for mentioning belief hysteresis.
It’s a straw dummy to say that I haven’t updated my priors about insert ridiculous thing here. Those are not the things I described having residual posterior mass on; my “sky wizard” is currently content to play by very different rules. As for the epi-phenomena of how a society embraces religion, or does not, I agree, this does suggest that it would be foolish to base one’s beliefs SOLELY on the “evidence” of the crowd as you grow up.
Also, incidentally, MML/Kolmogorov complexity and Solomonoff are not the same here. The former do not give a posterior on models, they select one model. The later could and would easily put posterior mass on multiple programs that were observationally the same up to the amount of data we have currently observed.
Consider the sequence of numbers: 1,2,3. MML would (for most Turing machines anyway) select the program: next=old+1. Solomonoff would have posterior mass on many other sequences (e.g. do a query on http://oeis.org/). It’d put most of it’s mass on that program, but leave nonzero mass on other programs, like one that computes this sequence, say: http://oeis.org/A006530, and if the next numbers reveals the sequence: 1, 2, 3, 2, 5, 3, 7, 2, 3, 5 Then you can bet that’s where a lot of the mass will shift.
… And the really subtle bit, that I don’t want you to miss, is that it doesn’t all shift there, it’s still not a point posterior. There’s still mass on:
Use http://oeis.org/A006530 for the first Googol entries, and then, all zeros.
That mass won’t go away for a LONG time (that is if the data keeps coming from http://oeis.org/A006530 for at least Googol/2 steps.
And there are many possibilities like this out there. Sure, they have less mass individually, but there ARE many of them. And some don’t even have appreciably less prior mass (under a Solomonoff prior and a “reasonable” Turing machine). Computability is a whole ’nother issue.