I want to correct an error, the "1st idea" in my last reply was
erroneous, since in the set {0,1}^P(T) one will find descriptions that
do not belong to any imaginable thing t in T. Thus, it would not be
possible to use the total set and the whole idea is rather useless.
So, I restrict my arguments to the second idea that I present in
detail:
The task is to justify why Russell and I use the Schmidhuber ensemble
of infinite bitstrings in order to represent the Everything. The
Schmidhuber ensemble can be constructed if we start from the set P of
properties. Ad hoc we assume P to have the cardinality of the natural
numbers. Every imaginable thing t can be described as follows:
We take every property p in P and say whether the thing t has the
property p or not. We express this by assigning a 0 if it has the
property and a 1 if it doesn't. The set of descriptions is thus given
by the infinite bitstrings:
{0,1}^P
If P has the cardinality of the natural numbers than this can be
identified with the Schmidhuber ensemble
{0,1}^IN (IN being the set of the natural numbers).
In a final step I will say why this approach to the Schmidhuber
ensemble is very useful. When we talk about observation, than we
imagine (according to Russell) an observer reading some of the bits
contained in the infinite bitstring. The observer can now restrict the
plurality of worlds he is in: The worlds' descriptions must have the
bit values he has read. But a priori, there is no justification to
think that these remaining worlds are somehow "similar" to each other
(because we did not mention how the descriptions were made. The
English expressions "combat" and "fight" denote similar things though
their spellings are very different. "Light" and "fight" are spelled
similarly though they denote completely different things. Analogous
situations could happen for unfortunate choices of how to describe a
world using bitstrings). If we construct the Schmidhuber ensemble as I
proposed it, then our intuitive expectation that worlds having a
similar description are "similar in kind". If two worlds have the
bitstring "01011" after let's say 3 bits, then they definitely have
(5) properties in common.
I'd be thankful for a comment, Russell.
Youness
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Received on Thu Sep 13 2007 - 19:58:42 PDT