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.
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 R.Standish.domain.name.hidden
Australia http://parallel.hpc.unsw.edu.au/rks
International prefix +612, Interstate prefix 02
----------------------------------------------------------------------------
- application/pgp-signature attachment: stored
Received on Fri Jul 15 2005 - 01:18:02 PDT