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From: briand@infmx.UUCP (brian donat)
Newsgroups: comp.ai
Subject: Re: PROBABLE COMPLEXITY QUOTIENT
Summary: Relative Definitions
Keywords: A step towards quantification of chaos?
Message-ID: <1600@infmx.UUCP>
Date: 22 Jun 89 18:02:10 GMT
References: <1591@infmx.UUCP> <361@calmasd.Prime.COM>
Organization: Informix Software Inc., Menlo Park, CA.
Lines: 160

> Walter Peterson >> Brian Donat

>> Please feel free to hack away at the following:

>OK. 

Very simply put.

Having read your response through once, I thought I'd point that out.


>> Given that the Human Brain is complex, complex to the point that we regard
>> it now in the terminology of chaos theory...

>Complexity alone is not a sufficient condition for chaos.  The
>necessary and sufficient condition for chaotic behavior is that the
>system be a non-linear dynamic system.  

I have some misgivings that a lot of people really do not know (fully)
what Chaos Theory implies.   You for example, are certainly correct in
saying that complexity alone is not a sufficient condition for chaos.

However, what is complexity?    The german word for simple is 'einfach'
which literally means 'onefold'.    Is a twofold system more complex than
a onefold system?  How complex is a 'manifold' system? 

Complexity is a relative measure.


Now this 'non-linear dynamic' thing is more revealing.    However, chaos
theory sees 'order from chaos' and therefore there is implied a necessary
requirement that linear systems also be inlcuded as part of a study of 
chaos.   The textbook definition is misleading.

So what is linearity?    

This sounds to me like 'order', something regular and repeating, something 
with a proportional rate of change or an 'x' for 'y' correspondance, so to 
speak.   

That chaotic systems speak of dynamic systems, this is true.   But what
really is a 'static' system?   It can be argued that a static system is
really dynamic, but balanced.   Therefore this definition is also misleading,
for 'chaos theory' must consider static systems in this light.  Chaos Theory
is however, more concerned with the study of such systems when they are 
exposed to 'change', such that 'prediction' of systematic outcomes are 
possible or especially, in some systems, noted to be 'not possible' because
the relative degree of complexity is too great for observational recording
of the variables involved.

Consider a standing wave in a river, or less complex, a centrifuge as used
in bio-chem.    We can predict or extrapolate (either way) the dynamics
involved with the centrifuge based on the forces involved (gravity and inertia)
and the characteristics of the objects within the system.   The centrifuge
results in a linear system.      This is 'control'.

Therefore, chaos theory is inevitably bound up with concepts of Information
and Control theory.

Consider now, a skin cell (not just any skin cell, but a subcutaneous cell,
say on the palm of your hand.   What makes this cell different from others
is not its DNA compliment, but its actual protein makeup.   Cell metabolism
is ordered; it has linear components; it is 'controlled' by a host of 
complex variables.   While a cell is 'subcutaneous', it has no need to 
produce the 'hard' proteins which make up surface skin.  However, such 
cells, when exposed will.  Why?   Remember that the DNA compliment is the
same.  RNA?     Within a skin cell there are several levels of control.
We'll describe most of these as molecular, but all respond to both external
and internal influences and the results of their motion, is the dynamic
expression of another level of control at the cellular level.

Most people make another mistake when relating to chaos theory.  They 
jump off the boat to talk turkey in terms of quantum mechanics.   Chaos
is concerned with relative complexities and the varying levels of 'order'
or control which are seen occuring within the system.   Prediction is
easy when addressing an ordered system simply because of the 'control'
seen at that level.   However, small changes below the level of expressed
control are said to have large global effects such that prediction is
not so easy.

What is global?   Global is the surface context of a level of control.
It's what we note to be the system itself.  If there were not control, 
we wouldn't be able to talk about anything global.


>> [Has anyone ...]
>> 	2.   done any mathematical calculations to estimate a probable   
>> 		complexity figure characteristic for the human brain?
>> 
>> 		Is there such an animal as a probable complexity figure?
>> 		Complexity quotient? 


>The term dosn't sound familiar. What do you mean by it ?

What I was after here was a prompter to the community out there to take
a look at the current efforts in AI and see if they were applying something
to their definition of artificial intelligence such that they do not
measure their success merely on the successful imitation of certain 
human communication concepts, but to the extent that their intelligent
system is also subject to the same lack of prediction that the real McCoy
is.   

In a separate response to someone else's article, I pointed out that a
truely intelligent system 'defines its own problems'.   To me this is
something which may well be spontaneous and is not a hardwired iteration
through a series of decision processes which give solutions to a 
pre-defined problem.   To achieve this level of intelligence in a machine,
one would have to model the machine on concepts which allow the machine
the sponteneity to define its own problems (The illusion of freedom).   

Preliminary to this is the problem of getting the machine to maintain
it's own health.

However, to measure success in the development of such a machine and, to
assist in addressing the theoretical constraints, I propose that some
quantitative measure be derived for the complexity (relative of course)
required to achieve 'apparent spontaneity' or an equivalent degree of 
spontaneity as seen in 'non-artifically intelligent' systems.

It is my belief that these concepts must be know before the AI community
progresses further even with simpler systems.  

If I can call something threefold or three times more complex, that is
in itself a relative measure.   However, with what we are working with
here, it is too simple.   A complexity quotient is however, a relative
measure of the complexity of the system such that global outcomes
are less predictable given minor changes below the global level, thus
giving the allusion of spontaneity in decisions, and allows that
global actions are at least partially predictable, at the global level
because of the control which exists at that level.  Let's not forget
that intermediate levels of control exist also.

A complexity quotient is thus a milestone by which AI scientists may
measure their success in achieving this particular aspect of 'intelligence'.


>> What 'non-living' synthetic model could match the complexity quotient of
>> all these variations and still reflect the order of control necessary to 
>> play trivial games such as passing a Turing Machine Test? 

>I don't really think that the Turing Test, if properly performed, is
>all that trivial a task for a machine.

Please consider my use of the word trivial to be also a relative usage.

Certainly, the effort required to get a machine to behave in a manner
which allows passing the Turing Test is no trivial thing.

However, a machine that will achieve the true sponateous character of 
intelligence is by far more displaced from the notion of trivial.


-- brian

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| Brian L. Donat		Informix Software, Inc.  Menlo Park, CA        |
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