Russell Standish writes:
> On Wed, Jul 13, 2005 at 04:20:27PM -0700, "Hal Finney" wrote:
> >=20
> > Right, that is one of the big selling points of the Tegmark and
> > Schmidhuber concept, that the Big Bang apparently can be described in
> > very low-information terms. Tegmark even has a paper arguing that it
> > took "zero information" to describe it (but frankly I am getting pretty
> > turned off on the "zero information" concept since several people here
> > use it to describe completely different things, and if it really took
> > zero information then there couldn't be more than one thing described,
> > could it?).
> >=20
>
> Tegmark does not say his model has "zero information" (at least not in
> the classic 1998 paper). His words were (pg 25 of my copy):
>
> "In this sense, our "ultimate ensemble" of all mathematical structures
> has virtually no algorithmic complexity at all."
>
> Note, this is not zero, but simply small (at least compared with the
> observed complexity of our frog perspective).

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Thanks for the correction. I was actually thinking of a different Tegmark
paper, http://space.mit.edu/home/tegmark/nihilo.html, but I see on closer
reading that he also says there that the algorithmic information content
of our universe is "close to zero" but does not actually say it is zero.
> There is only one zero information object, and that is the set of all
> descriptions (all infinite length bitstrings).=20
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