2012/10/22 Russell Standish <li...@hpcoders.com.au> > 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. >
Thanks. I'll read your paper. From all the mathematical consideraitions. IMHO the kolmogorov-solomonof research is the closest one to solving the conundrum of the discovery of the macroscopical laws by computing living beings in a mathematical universe (which may have a underlying computational nature, but I think that this is a limitation that is not justified). > > 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 > > >> > > >> > ---------------------------------------------------------------------------- > > >> > > >> -- > > >> You received this message because you are subscribed to the Google > Groups > > >> "Everything List" group. > > >> To post to this group, send email to everything-list@googlegroups.com > . > > >> To unsubscribe from this group, send email to > > >> everything-list+unsubscr...@googlegroups.com. > > >> For more options, visit this group at > > >> http://groups.google.com/group/everything-list?hl=en. > > >> > > >> > > > > > > > > > -- > > > Alberto. > > > > > > > > > > > -- > > Alberto. > > > > -- > > You received this message because you are subscribed to the Google > Groups "Everything List" group. > > To post to this group, send email to everything-list@googlegroups.com. > > To unsubscribe from this group, send email to > everything-list+unsubscr...@googlegroups.com. > > For more options, visit this group at > http://groups.google.com/group/everything-list?hl=en. > > > > -- > > > ---------------------------------------------------------------------------- > 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 > > ---------------------------------------------------------------------------- > > -- > You received this message because you are subscribed to the Google Groups > "Everything List" group. > To post to this group, send email to everything-list@googlegroups.com. > To unsubscribe from this group, send email to > everything-list+unsubscr...@googlegroups.com. > For more options, visit this group at > http://groups.google.com/group/everything-list?hl=en. > > -- Alberto. -- You received this message because you are subscribed to the Google Groups "Everything List" group. 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