From: Ben Goertzel (ben@goertzel.org)
Date: Mon Apr 15 2002 - 11:32:53 MDT
***
My definition of pattern differs in that it is based around
tractability
rather than simplicity. If A is a pattern in B, then the question is
not
whether A is simpler than B, but rather whether A is, on average, less
expensive to compute.
***
Actually, my definition of pattern allows for a variety of definitions of
"simplicity".
The most straightforward mathematical definition is "brevity of program
size", but as I state explicitly, another valuable definition is "brevity of
runtime". The algorithmic info. theory literature contains discussion of
both measures, and of averages between the two measures, etc. Of course,
both space and time are important in pragmatically assessing "simplicity."
***
So under my definition, Y is a pattern in X, if Y produces a useful
approximation of X, and Y is more tractable than X - that is, less
expensive
computationally.
***
I think that the perspective you outline here can be seen as special case of
the general framework I've defined.
In fact, I state elsewhere in my (past and present) writings on this that,
in practice, the similarity and simplicity measures involved in the
definition of pattern must be considered as relative to a given system of
knowledge K. In the case of an AI system assessing patterns, this system of
knowledge K is simply its own knowledge base.
So, your definition is my definition with:
-- simplicity defined as some sort of average of space and time cost
-- similarity defined relative to the knowledge base K defined by the system
in question
-- ben g
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