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These are all reasonably good beginnings in that they don't do what
most "complexity" theories I've seen are doing: these don't try to use the "old
rules" to explain complexity. That's the aspect that is Rosennean about these
alternate definitions. That doesn't mean they're sufficient; far from it.
The problem with all of these alternate "definitions" is that
none of them explain why complexity has been shut out of the scientific
mainstream, and therefore they don't show how the old rules (meaning
reductionism and mechanism) make an organization-based paradigm a radical change
of perspective from the current particle-based one. In fact, none of these
definitions puts a finger on the fact that complexity forces a change of
paradigm; because none of them follows the logic of what they are saying to
find out what it's leading to.
Why is it that, historically, organization has never been
considered an important feature in any given system
for scientific analysis? Science never allowed organization to be defined
as a basis for causal ramification in generating the behaviors and qualities of
any given system. All of the alternate definitions of complexity that I found on
the net and posted here refer to the causal impact of organization and yet
do not follow the implications of what they are saying. The reason complexity
falls outside the mainstream is precisely because the reductionist,
particle-based paradigm cannot see complexity.
The reason my father's work was so controversial was because he DID
follow those lines of logic and he saw the implications. He described the
implications and wrote about them. He discussed what the ramifications were. The
implications blow the reductionist particle-based paradigm right out of the
water. Therefore, any definition of complexity that tries to use the old
paradigm to explain complexity itself is not worth anybody's time; those people
are fooling themselves. They are talking about "complicatedness".
In contrast, Gallagher, Appenzeller, Auyang, and
Reitsma.... all seem to be on the right track but they haven't
realized what the implications are. That's what I mean when I said they are all
reinventing the wheel, meaning that my father's work already did that. That's
why I'm looking for contact info on all of them. I figure, either they will be
interested in it or they won't. But it could help them skip the hard work of
reinventing science from the paradigm up, like my father was forced to
do.
Judith
----- Original Message -----
Sent: Sunday, August 01, 2004 11:53
PM
Subject: Re: [ROSEN] Some pretty good
alternate definitions of complexity
Judith,
Why do you
consider these reasonably good definitions? I am surprised that you would
consider Auyang's to be so. To me, neither the (syntactic) information measure
nor the computational measure address anything to do with Rosennean
complexity.
Regards,
Tim
I did find some reasonably good definitions on the net while I
was being outraged over the Mikulecky mischaracterization of my father's
definition/s:
Richard Gallagher and Tim Appenzeller have written several
things together, most of which I can't access because one needs to be a
subscriber of Science magazine apparently... But I found the following, by
them:
?Complex System?: one whose properties are
not fully explained by an understanding of its component parts.
and
at http://www.usyd.edu.au/su/hps/newevents/Auyang1.html
I found Sunny Y. Auyang's work, from which I excerpted:
4. Formal Definitions of Complexity and the Combinatorial
Explosion
There is no precise definition of complexity and degree of
complexity in the natural sciences. I use "complex" and "complexity"
intuitively to describe self-organized systems that have many components and
many characteristic aspects, exhibit many structures in various scales,
undergo many processes in various rates, and have the capabilities to change
abruptly and adapt to external environments. Nevertheless, there are two
definitions of complexity in the information and computation sciences that
can help us to appreciate nonreductive strategy for studying complex
systems.
The idea of complexity can be quantified in terms of
information, understood as the specification of one case among a set of
possibilities. The basic unit of information is the bit. One bit of
information specifies the choice between two equally probable alternatives,
for instance whether a pixel is black or white. Now consider binary
sequences in which each digit has only two possibilities, 0 or 1. A sequence
with n digits carries n bits of information. The information-content
complexity of a specific sequence is measured in terms of the length in bits
of the smallest program capable of specifying it completely to a computer.
If the program can say of a n-digit sequence, "1, n times" or
"0011, n/4 times," then the bits it requires
are much less than n if n is large. Such sequences with
regular patterns have low complexity, for their information contents can be
compressed into the short programs that specify them. Maximum complexity
occurs in sequences that are random or without patterns whatsoever. To
specify a random sequence, the computer program must repeat the sequence, so
that it requires the same amount of information as the sequence itself
carries. The impossibility to squeeze the information content of a sequence
into a more compact form manifests the sequence's high complexity.
The information content complexity belongs to the definite
description of a specific system, thus it is not useful in science because
science is usually not so much interested in specific systems than in
classes of system that satisfy certain general criteria. It often happens
that totally random systems, which have highest information content
complexity, exhibit other types of regularity than can be characterized
rather simply if we are willing to adopt some other criteria of
classification, e.g., use the law of large numbers. We have the probability
calculus for such systems, and usually systems susceptible to the calculus
are regarded as not that complex. Here we have the first instance of the
theme of this talk; the flexibility to choose different criteria is
paramount in scientific research.
The second definition of complexity describes not systems
but problems. Suppose we have formulated a problem in a way that can be
solved by algorithms or step-by-step procedures executable by computers, and
now want to find the most efficient algorithm to solve it. We classify
problems according to their "size"; if a problem has n parameters, then the
size of the problem is proportional to n. We classify algorithms
according to their computation time which, given a computer, translates into
the number of steps an algorithm requires to find the worse-case solution to
a problem with a particular size. The computation-time complexity of a
problem is expressed by how the computation time of its most efficient
algorithm varies with its size. Two rough degrees of complexity are
distinguished: tractable and intractable. A problem is tractable if it has
polynomial-time algorithms, whose computation times vary as the problem size
raised to some power, for instance n2 for a size-n
problem. It is intractable if it has only exponential- time algorithms,
whose computation times vary exponentially with the problem size, for
instance 2n. Exponential-time problems are deemed
intractable because for sizable n, the amount of computation time
they require exceeds any practical limit.
And then, of course, there's Femke
Reitsma, the writer of the masters thesis which had the
offending mis-characterizations of my father's work. Aside from the fact
that Femke didn't do the proper homework-- by going to original sources for
quotes rather than relying on second-hand interpretation-- I thought the
musings on complexity contained in what I read were going in the
right direction. By "right", naturally I mean the same direction that my
father had already gone in! (I'm sure that comes as no surprise to anybody?)
The definition of a complex system here was "a whole that cannot be fully
delineated through an analysis of its component parts".
It is encouraging to see so many unrelated voices
saying that reductionism cannot help us understand complexity, but each of
these voices is talking about a mere piece of the larger framework that my
father already developed. It's a shame to have so many people re-inventing
the wheel when their time could be better spent using it to travel where my
father never got to.
Judith
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