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

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.


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A/Prof Russell Standish                  Phone 8308 3119 (mobile)
Mathematics                                    0425 253119 (")
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