Re: Solomonoff induction and mechanism
> On 16 Jan 2019, at 05:05, Russell Standish 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 StandishPhone 0425 253119 (mobile)
> Principal, High Performance Coders
> Visiting Senior Research Fellowhpco...@hpcoders.com.au
> Economics, Kingston University http://www.hpcoders.com.au
>
>
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Re: Solomonoff induction and mechanism
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 StandishPhone 0425 253119 (mobile)
Principal, High Performance Coders
Visiting Senior Research Fellowhpco...@hpcoders.com.au
Economics, Kingston University http://www.hpcoders.com.au
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Re: Solomonoff induction and mechanism
> On 12 Jan 2019, at 03:14, 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. That works for the individual mind, and with some luck for the first person plural physics, but you have to drive them from the universal dovetailing (if not you will reintroduce some identity thesis hardly compatible with computationalism (even with oracles). > 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. That leads to technical difficulties, although a subpart of this might explains the “thermodynamical part of physics”, relying on the laws of big numbers. But to make all this works, I am not sure it possible with taking into account the “mental” abilities of the universal-observers. > > 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, ? What do you mean by “suffering” in an 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. If such a malevolent or benevolent program exists, it has to be explained by the sum on all universal dovetailing, that any single universal dovetailer produces. The initial one does not matter, and I use the sigma_1 arithmetic sentences (equivalent to their own provability at the G* level) to start with (or sometimes the combinators, which are more handy but much less known). Bruno > > -- > You received this message because you are subscribed to the Google Groups > "Everything List" group. > To unsubscribe from this group and stop receiving emails from it, send an > email to everything-list+unsubscr...@googlegroups.com. > To post to this group, send email to everything-list@googlegroups.com. > Visit this group at https://groups.google.com/group/everything-list. > For more options, visit https://groups.google.com/d/optout. -- You received this message because you are subscribed to the Google Groups "Everything List" group. To unsubscribe from this group and stop receiving emails from it, send an email to everything-list+unsubscr...@googlegroups.com. To post to this group, send email to everything-list@googlegroups.com. Visit this group at https://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/d/optout.
Re: Solomonoff induction and mechanism
On 1/12/2019 3:12 AM, Philip Thrift wrote: On Friday, January 11, 2019 at 8:14:14 PM UTC-6, 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. 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. Generating universes without any emotion (taken widely) possible is sort of like "Invasion of the Body Snatchers". A universe without emotion is logically consistent; but it's the same as a universe without life, which is highly unlikely. Brent -- You received this message because you are subscribed to the Google Groups "Everything List" group. To unsubscribe from this group and stop receiving emails from it, send an email to everything-list+unsubscr...@googlegroups.com. To post to this group, send email to everything-list@googlegroups.com. Visit this group at https://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/d/optout.
Re: Solomonoff induction and mechanism
On Friday, January 11, 2019 at 8:14:14 PM UTC-6, 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. > > 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. Generating universes without any emotion (taken widely) possible is sort of like "Invasion of the Body Snatchers". - pt -- You received this message because you are subscribed to the Google Groups "Everything List" group. To unsubscribe from this group and stop receiving emails from it, send an email to everything-list+unsubscr...@googlegroups.com. To post to this group, send email to everything-list@googlegroups.com. Visit this group at https://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/d/optout.
Solomonoff induction and mechanism
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. 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. -- You received this message because you are subscribed to the Google Groups "Everything List" group. To unsubscribe from this group and stop receiving emails from it, send an email to everything-list+unsubscr...@googlegroups.com. To post to this group, send email to everything-list@googlegroups.com. Visit this group at https://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/d/optout.
