**From:** Ben Goertzel (*ben@goertzel.org*)

**Date:** Mon Apr 15 2002 - 11:32:53 MDT

**Next message:**Emil Gilliam: "ARTICLE: Non-Turing computation"**Previous message:**Ben Goertzel: "thoughts & their remembrances"**Next in thread:**Eliezer S. Yudkowsky: "Re: definitions of pattern"**Reply:**Eliezer S. Yudkowsky: "Re: definitions of pattern"**Messages sorted by:**[ date ] [ thread ] [ subject ] [ author ] [ attachment ]

***

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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