From: elias@fitz.TC.Cornell.EDU (Doug Elias)
Subject: Re: Can a part be greater than the whole?
Organization: Software and Consulting Support Group, Cornell Theory Center,
	C.U.
Distribution: alt
Date: Mon, 23 Nov 1992 14:45:45 GMT


My apologies (to alt.info-theory) for copying the original article in
its entirety, but i'm including sci.systems in this particular thread
and wanted that readership to see the whole thing:

>  From: tolman%asylum.cs.utah.edu@cs.utah.edu (Kenneth Tolman)
>  Subject: Can a part be greater than the whole?
>  Date: 20 Nov 92 15:15:21 MST
>  Message-ID: <1992Nov20.151522.26315@hellgate.utah.edu>
>  Organization: University of Utah, CompSci Dept
>  Distribution: alt
>  
>  Can a part be greater than the whole?
>  
>  Specifically, can a part have more information than the whole?
>  
>  At first glance, it appears not.  For instance, if you were to consider
>  the information content of half of a computer versus the whole, or part
>  of an organism rather than the whole it seems that the part must be less
>  than or equal in informational value.
>  
>  but consider this, the whole is a sequence like this: 
>  1111111111111111111111111111111111111111111111111111
>  and the part is:
>  10110110010110101010010111100111110101101011110001000
>  
>  Here, the part seems to have a higher informaition content than the whole.
>  
>  So it appears we must also consider the method by which we extract or 
>  define the part from the whole.  
>  
>  Therefore, would it be correct to say that the part itself does NOT have
>  more information than the whole, but the method by which we define the part
>  is that which contains the information?  This seems pretty weak.  It appears
>  that a part MAY have more information than the whole.
>  
>  

From the aspect of "systems of subsystems of subsystems of...", it
could be argued that a "whole", or a system at a given level in the
hierarchy, can only be judged to be as complex as the view presented
at the level of its constituents, or subsystems one-level-down in 
the hierarchy.

As far as the system itself is concerned, the complexity of these
component-entities is essentially just that which can be seen from
outside of them, say, the number of inputs/outputs attached, and the
total number of states observed over those.  But a particular
subsystem,  viewed as a system in its own right, may have much more
internal complexity than might be immediately apparent from the level
of the system of which it  is a part, in the form of internal
variables, and interconnections, and a subsystemic structure of its 
own that is not visible at the level of the higher-level system. 

The argument would then run that it would then make sense to claim
that, from the point of view of analyzing each "system" from its own
position in the hierarchy, the "subsystem" may actually be more
complex than the "system", simply because, for the purposes which
brought about the definition of the systems in the first place, the
internal structure of the subsystem is of a higher degree than that of
the system of which it is a part, and this internal structure is not a 
necessary consideration of the higher-level system.

Your car is an excellent case-in-point: from the point of view of
getting you to and from work, the car can be considered to be a not-
terribly complicated collection of black-boxes, all attached together
in such a way that the overall system is capable of performing its
function: you need to consider power, steering, braking, certain
electrical functions, driver comfort, and maybe a few other things
that are relevant to getting from point-A to point-B.  As long as
things run smoothly, you probably don't spend much (if any) time
dwelling on the intricacies of the carburetor or computer-controlled
ignition system...but if things start to go wrong, each of the
possibly-relevant black-boxes has to be opened and evaluated, at which
point the complexity of the overall system, in terms of the purpose of
"fixing it", becomes much greater than when it was simply viewed as a
means of transportation.  

Bottom-line: in order to address the question of systems-complexity,
you also need to consider the purpose for which the system was defined
on the object-under-observation in the first place -- the reason
you're looking at it controls how complex you see it.

doug
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