> On 16 Jan 2019, at 05:05, Russell Standish <li...@hpcoders.com.au> wrote:
> 
> 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…



The measure is on the first person experiences, which needs the “theaetetus' 
solution" of the “knower” problem. It works, because incompleteness refutes 
Socrate’s refutation, and it also, provides, thanks to incompleteness again, 
the distinction between private non communicable knowledge, and sharable 
beliefs, or even the locally sharable first person *plural* relative measure on 
the physical predictions. Physics still needs an identity thesis to make its 
prediction, and that one is only locally correct, but globally, and 
fundamentally, inoperative.

Bruno



> 
> 
> -- 
> 
> ----------------------------------------------------------------------------
> 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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