On Fri, Jan 13, 2006 at 11:12:15AM -0500, Benjamin Udell wrote:
> [Russell]> The particular Plenitude I assume (ensemble of all bitstrings) is
> actually a completely uninteresting place to have a view of (it has
> precisely zero informational complexity).
> Is this kind of Plenitude (ensemble of all bitstrings) more or less
Tegmark's Level IV of all mathematical structures? (I.e., if it's
different, does the difference involve a restriction to discrete or
finitistic structures or some such? 

It does correspond to Tegmark's level 4, but Tegmark's proposal "All
mathematical structures" is rather vague. I have interpreted his
proposal as "all finite axiomatic systems". This is in fact a subset
of my ensemble (well basically Schmidhuber's ensemble) of all
descriptions (since an FAS is a description), yet one can also
describe the entire ensemble of descriptions by a finite method (the
"dovetailer"), hence one can find the ensemble of all descriptions
contained within Tegmark's.

Note, however that the relationships going both ways do _not_ imply
equivalence between the two ensembles. This is described in my paper
"Why Occam's Razor", as well as talked about on the everything list.

> IV. possibility waves (variational principles)
> III. probabilities for various outcomes 
> II. information, news, outcomes, events, interactions, phenomena
> I. evidence of causes/dependencies (dependencies, e.g., emission --> open 
> slit --> hit)

I'm somewhat sceptical of your associations here, but it is possibly
because I don't understand what you're getting at. You may need to
develop this some more.

*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
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A/Prof Russell Standish                  Phone 8308 3119 (mobile)
Mathematics                                    0425 253119 (")
UNSW SYDNEY 2052                         [EMAIL PROTECTED]             
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