Youness Ayaita wrote:
> 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
In order to observe something about the world it will be necessary to observe relations, not just things with properties. If you allow countably many n-place relations, how will you encode them and how will you express that things like "George owes an explanation of counting to Bob." Do you assume that every thing has enough distinct properties to make it unique?
Brent Meeker
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Received on Thu Sep 13 2007 - 20:28:01 PDT