On Fri, Jan 11, 2019 at 06:14:14PM -0800, Mason Green wrote:
> Solomonoff’s method of induction seems like a good fit for a mechanist view 
> of things. For instance, it could be used to assign a relative probability to 
> the universe being generated by a universal dovetailer: 2^(-K) * m, where K 
> is the Kolmogorov complexity of the universal dovetailer and m is the measure 
> the dovetailer assigns to universes like ours.
> This formula implies that a (more complex) non-universal dovetailer might be 
> preferable _if_ it assigned a much higher measure to universes like ours. 
> Such a dovetailer might, for instance, output only (or mostly) habitable 
> worlds, instead of outputting mostly uninhabitable worlds as the standard UD 
> does, and the higher resulting measure would offset the increased Kolmogorov 
> complexity.

It doesn't work like that. Let's say that the mᵢ is the measure of
our universe by program i, and Kᵢ the Kolmogorov complexity of that
program, with respect to some fixed reference universal machine U.

Then for any universal dovetailer u, m_u will be >= ∑ⱼ 2^{-Kⱼ} mⱼ, so
there will be at most only be a short constant difference Kᵤ in
complexity between the universe implemented on universal dovetailer
and the one implemented on the non-universal dovetailer. Once you sum
over all programs, m=∑ⱼ2^{-Kⱼ}mⱼ, converges to a value that is basic 2
to the power of the complexity of our universe. The sum will be
dominated by contributions from universal dovetailers, as these are
such short programs.

> If we live in a highly “atypical” universe, that might also affect how we 
> should do Solomonoff induction. For instance if we knew that we lived in a 
> universe with much less suffering than an “average” inhabited universe, that 
> could imply we were generated by a dovetailer that doesn’t like suffering. If 
> the opposite is true and we live in a “mean world”, that means we might be 
> generated by a sadistic dovetailer, etc.

One could say this about any property, such as the density of black
holes present, or flatness of the universe. It is the stuff of
anthropic reasoning. However, computing the measure of even those
formulae expressed above in known to be highly intractible, so what
tends to happen is a bunch of heuristics are assumed about the
measure, which may well make the whole argument devoid of meaning...


Dr Russell Standish                    Phone 0425 253119 (mobile)
Principal, High Performance Coders
Visiting Senior Research Fellow        hpco...@hpcoders.com.au
Economics, Kingston University         http://www.hpcoders.com.au

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