On Sun, Oct 21, 2012 at 10:03:48PM +0200, Alberto G. Corona  wrote:
> This does not implies a reality created by an UD algorithm. It may be a
> mathematical universe, that is a superset of the computable universes. The
> measure problem in the UD algorith translates to the problem of the
> effectivity of the Occam Razor, or the problem of the apparent simplicity
> of the phisical laws, or, in other words, their low kolmogorov complexity,
> that solomonov translates in his theory of inductive inference.
> 

I don't know. Around here, that problem is called the "White Rabbit
problem", and IMHO is solved by Solomonoff's theory of inductive
inference (with appropriate modern nuances). Not everbody agrees,
however.

The UD measure problem (as I understand it), is a computational
question of what the measure actually is. Whatever it is, it will
satisfy the properties of Solomonoff's universal prior, so will solve
the WR problem. However, it is conjectured that the UD measure will
differ in some measurable way from a universal prior obtained by
postulating a uniform measure over the set of all infinite length
binary strings treated as binary expansions of real numbers (see my
paper Why Occams Razor for as an example work doing exactly that). If
measurable, we have a means of selecting between different ensemble
everything theories by experiment.

It is still very much an open problem.


> 2012/10/21 Alberto G. Corona <agocor...@gmail.com>
> 
> > Ok
> >
> > I don愒 remember the reason why Solomonof reduces the probability of the
> > programs according with the length in is theory of inductive inference. I
> > read it time ago. Solomonoff describes in his paper about inductive
> > inference a more clear and direct solution for the measure problem. but I
> > though that it was somehow ad hoc.
> >
> > I tough time ago about the Solomonof  solution to the induction problem,
> > and I though  as such: living beings have to find, by evolution, at least
> > partial and approximate inductive solutions in order to survive in their
> > environment. This imposes a restriction on the laws of a local universe
> > with life: It demand a low kolmogorov complexity for the *macroscopical* 
> > laws. Otherwise these laws would not be discoverable, there would be no
> > induction possible, so the living beings could not anticipate outcomes and
> > they woul not survive.
> >
> > Solomonoff is a living being in a local universe, so shorther programs are
> > more probable and add more weight for induction.
> >
> > I惴 just thinking aloud. I will look again to the solomonof inductive
> > inference. I was a great moment when I read it the first time.
> >
> >
> > 2012/10/20 Russell Standish <li...@hpcoders.com.au>
> >
> >> On Sat, Oct 20, 2012 at 09:16:54PM +0200, Alberto G. Corona  wrote:
> >> > This is not a consequence of the shannon optimum coding , in which the
> >> > coding size of a symbol is inversely proportional  to the logaritm of
> >> the
> >> > frequency of the symbol?.
> >>
> >> Not quite. Traditional shannon entropy uses probability of a symbol,
> >> whereas algorithmic complexity uses the probability of the whole
> >> sequence. Only if the symbols are independently distributed are the
> >> two the same. Usually, in most messages, the symbols are not id.
> >>
> >> >
> >> > What is exactly the comp measure problem?
> >>
> >> A UD generates and executes all programs, many of which are
> >> equivalent. So some programs are represented more than others. The
> >> COMP measure is a function over all programs that captures this
> >> variation in program respresentation.
> >>
> >> Why should this be unique, independent of UD, or the universal Turing
> >> machine it runs on? Because the UD executes every other UD, as well as
> >> itself, the measure will be a limit over contributions from all UDs.
> >>
> >> Cheers
> >> --
> >>
> >>
> >> ----------------------------------------------------------------------------
> >> Prof Russell Standish                  Phone 0425 253119 (mobile)
> >> Principal, High Performance Coders
> >> Visiting Professor of Mathematics      hpco...@hpcoders.com.au
> >> University of New South Wales          http://www.hpcoders.com.au
> >>
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> >
> >
> > --
> > Alberto.
> >
> 
> 
> 
> -- 
> Alberto.
> 
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Prof Russell Standish                  Phone 0425 253119 (mobile)
Principal, High Performance Coders
Visiting Professor of Mathematics      hpco...@hpcoders.com.au
University of New South Wales          http://www.hpcoders.com.au
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