On Thu, Jul 14, 2005 at 07:15:02PM -0700, "Hal Finney" wrote: > > Do you really think there is such a thing as a "zero information object"? > If so, why do you have to say what it is? :-) > > Is this just an informal concept or is there some formalization of it? > > Surely Chaitin's algorithmic information theory would not work; inputting > a zero length program into a typical UTM would not produce the set of > all infinite length bitstrings; in fact, I don't see how a TM could even > create such an output from any program. > > Hal Finney

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Well I should point out I use a slightly different definition of information, which is the logarithm of the measure of the set of all bitstrings having a given meaning. Associating meaning with the output of a prefix Turing machine, this notion information is equivalent to KCS complexity, up to an additive constant (dependent on only the machine, not the message). With such a definition of information (which is more general than KCS complexity, but equivalent up to an additive constant when the latter is defined), only the set of all bitstrings has zero information. Cheers -- *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 ----------------------------------------------------------------------------

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