On 14 Sep., 02:27, Brent Meeker <[EMAIL PROTECTED]> wrote:
> 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
The approach constructing the Everything ensemble using "properties"
as fundamental building blocks has its difficulties. We need a set of
distinct and independent properties (such that having property p and
having property q is no contradiction if p and q are different)
because otherwise we wouldn't get the whole Schmidhuber ensemble which
ensures zero information content. Hence, the way I proposed is still
vague---It's only a postulate that such a set of properties exists.
Though, I think it gives an idea of how we imagine the Schmidhuber
I'll give an example: Let's study the ensemble of all possible images
your monitor can display. It is then possible to describe the images
pixel by pixel, every pixel being mapped to a color value. This would
be a description using perfectly independent properties (since every
combination of colors gives a possible image). "Relations" are not
part of this description, they are seen by observers who assign a
meaning to what they see. For example they see a person on the image
holding a pencil. Similarly, we imagine the Schmidhuber ensemble.
Descriptions are built up of elementary and independent properties
(corresponding to the pixels on your monitor).
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