On Mon, Jun 19, 2006 at 11:12:52AM +0200, Bruno Marchal wrote: > > ?
I'm not sure which bit you were having trouble with. A description is an infinite length bitstring. It is therefore equivalent to a point in the unit interval [0,1] (modulo a little bit of funny stuff on a set of measure zero). The uniform measure on the unit interval is equivalent to the Levin-Solomonoff distribution, or universal prior, were sets of descriptions are partitioned by a UTM. Information (or complexity) is simply the negative logarithm of the set's measure: I = -log mu(S) Clearly, the set of all descriptions is equivalent to the unit interval, and has I=0. This is the zero information object. Subsets of the unit interval have smaller measure than 1, so the equivalent sets of descriptions have larger information content. A finite string can be thought of as a set of descriptions that share the same finite prefix, and so have I <= length of string. > > > > I think he > > is wrong too, and agree with you, however I'm not so sure his > > arguments are this easy to dismiss. > > > > Which argument in particular? > The speed prior argument (advanced in his "Algorithmic Theories of Everything") paper. > > > > > > It is related again to the ancient > > debate on ASSA vs RSSA - Schmidhuber's argument works if you assume > > just one computation is selected as your universe, which is rather > > contrary to functionalism (and COMP). > > Remember Schmidhuber assumes comp. > I'm not so sure. At heart, I suspect he is a computationalist, however what he assumes in his papers is that the universe (that we see) is a single specific computation selected from the dovetailer algorithm. With COMP (and with functionalism too) we assume that consciousness supervenes on all consistent computations, which leads to your famous first person indeterminism result. Schmidhuber's assumption directly implies determinism (we are living inside one particular computation only). I do not see Schmidhuber's argument as inconsistent, but it does seem to contradict COMP, so Schmidhuber may have inconsistent faiths if he insists both on this argument and COMP. I'm thinking out loud here, so I welcome comments and corrections, of course. > > Bruno > > http://iridia.ulb.ac.be/~marchal/ > > > -- *PS: A number of people ask me about the attachment to my email, which is of type "application/pgp-signature". Don't worry, it is not a virus. It is an electronic signature, that may be used to verify this email came from me if you have PGP or GPG installed. Otherwise, you may safely ignore this attachment. ---------------------------------------------------------------------------- A/Prof Russell Standish Phone 8308 3119 (mobile) Mathematics 0425 253119 (") UNSW SYDNEY 2052 [EMAIL PROTECTED] Australia http://parallel.hpc.unsw.edu.au/rks International prefix +612, Interstate prefix 02 ---------------------------------------------------------------------------- --~--~---------~--~----~------------~-------~--~----~ 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 [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list -~----------~----~----~----~------~----~------~--~---