On 11 Oct 2011, at 22:14, Russell Standish wrote:
On Tue, Oct 11, 2011 at 06:03:42PM +0200, Bruno Marchal wrote:
With COMP, and via your UDA, our observed universe is selected from
the set of all infinite strings (which I call descriptions in my
book).
My non observed "future"; or computational extensions, is selected,
making the comp physics explainable in term of statistics on
computations. This leads to general physical laws invariant for all
observers. There is no selection of a particular computations, just
a relative indeterminacy bearing on all computations going through
my state. In particular we cannot use Bayes theorem, for example.
Like Brent, I don't follow you here.
See my answer to Brent. Basically, Bayes is induction. Conditional
probability is usual deductive-type probability.
Computations are not infinite strings, but can have infinite strings
as inputs, and so infinite strings can play a role in the
(re)normalization needed to avoid the infinities of abnormal
histories.
That wasn't my point. The set of computational extensions is infinite,
uncountable cardinality even.
Yes. A point where Schmidhuber disagreed on this list, but I am glad
that we agree on this.
Without the anthropic principle, ISTM that your theory would suffer
the Occam catastrophe fate. How do you avoid that?
Is that equivalent with the white rabbits?
No, it is quite the opposite problem. As Einstein purportedly said
"Everything should be made as simple as possible, but not
simpler". Occam's razor theorem, which comes from Solomonoff and
Levin's considerations of algorithmic information theory would imply
that we don't see anything interesting at all. That is the Occam
catastrophe. Something prevents the world from being too simple. I
think that something is the Anthropic Principle, but I'm interested if
you have an alternative suggestion.
You can give me a link to this. Does the OCCAM catastrophe relies on
Bayes? What would it be with respect of UD*?. I don't use probability
at all in my reasoning, except as a result (first person
indeterminacy) which transforms physics into a probability or
uncertainty or indeterminacy calculus on computations or arithmetical
relations, without using Bayes, nor #-thropic principles.
If you explain this in your book, remind me the pages, or just the
title of your paper (which I have on some of my hard disks). I deduce
(or show how to deduce) the necessary physical laws for all machine-
observer. I don't infer anything from observations at all (which would
be needed to use an anthropic principle and Bayes).
Bruno
http://iridia.ulb.ac.be/~marchal/
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