From: jeroenm@cwi.nl (Jeroen van Maanen)
Newsgroups: comp.ai.philosophy
Subject: Re: The Complexity Required for intelligence
Keywords: complexity AI
Date: 15 Dec 92 09:01:33 GMT

wagner@hp800.lasalle.edu (Jon Wagner) writes:


>Here are come thoughts about the complexity of systems and AI.

>Assume that a system can be modeled by a Turing machine, and define
>the complexity of the system as 

>	C(s) = some function 

There exists such a function C. C(s) is known as the Kolmogorov
Complexity of s. For an introduction see `Inductive Reasoning and
Kolmogorov Complexity' in the april '92 issue of the Journal of
Computer and System Sciences.

>Some special minimum values of C:

>	C(self-awareness)	the least value of C such that self-awareness
>				is possible.

Self-awareness is not a system that can be modelled by a Turing
machine, but a property that could be assigned to a system. I doubt
very much that the complexity of the simplest self-aware system is a
computable number. You would first have to specify (in mathematical
terms) which systems are aware of themselves. Furthermore I suspect
that it is necessary to take the environment into account to determine
whether a system is (self-)aware or not.

>	C(humans-brain)		the complexity of a human brain

Do you mean the average human brain here, or the minimal brain we call
human? Actually, it won't be easy to estimate the complexity of a
brain. Nerve cells appear to be much more complex than the simple
linear threshold units they use in Neural Nets.

>	C(replication)		complexity required for the system to be
>				able to create another system with
>				greater or equal complexity

I think that the complexity of replication can be quite low. Consider
a virus (a normal or a software virus) it can be quite simple. Note
that a sufficiently rich environment (living body resp. harddisk) is
of vital importance here too.

>Some points to discuss:

>	1) C(self-awareness) <= C(humans-brain)

I never saw a self-aware disconnected human brain :-). I could however
be made to believe this.

>	2) Is C(humans-brain) >= C(replication)?  Does this have any
>		implications on whether we will ever create an intelligent 
>		system?

I think so (trivially), see above. But I doubt that _this_ will have
any consequences.

>	3) If C(humans-brain) < C(replication), then
>		if C(human-society) >= C(replication)?

C(humans-brain) < C(replication)? I don't think so. My first guess
would be: C(human-society) < C(human-brain < C(DNA). I think, however,
that the compexity of human society is growing faster than the
complexity of human brains (evolutionary). Actually this is a problem
with this C function. To use it you have to assume that for instance
society is a fixed computable function, which it probably isn't. So
you have to approximate the system with a computable function that is
at least able to describe its behaviour up until _now_. (So next year
you would probably have to use a different -- more complex --
approximating function).

--Jeroen van Maanen

>Jon Wagner                                              wagner@hp800.lasalle.edu--------------------------------------------------------------------------------
>The answer to the Ultimate Question, of Life, the Universe, and Everything is
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