>>Don Mikulecky, MCV/VCU, Mikulecky@gems.vcu.edu
>
>>However, if you are not using Rosen's definition of complexity,
>>which one are you using?
>
> My "definition", which is not really precise enough to satisfy me as a
> definition, considers complexity to be the combination of distinction
> (variety of distinct components) and connection (linkages between the
> components). The larger the variety and the larger the connectivity, the
> larger the complexity. For a more detailed discussion, read the following
> quote from my paper
> (http://pespmc1.vub.ac.be/papers/ComplexityGrowth.html):
This is not so far as you might think from Rosen. What he does is to
deal directly with the question of how do we ascertain these attributes?
Then the definition focuses on the number of distinct ways with which
we can interact with the system. (distinct meaning ways which are NOT
derivable from each other)
>
> "Let us go back to the original Latin word complexus, which signifies
> "entwined", "twisted together". This may be interpreted in the following
> way: in order to have a complex you need two or more components, which are
> joined in such a way that it is difficult to separate them. Similarly, the
> Oxford Dictionary defines something as "complex" if it is "made of (usually
> several) closely connected parts". Here we find the basic duality between
> parts which are at the same time distinct and connected. Intuitively then,
> a system would be more complex if more parts could be distinguished, and if
> more connections between them existed.
It is useful to distinguish between "parts" and "functional components" as
both Rosen and Kampis do. The mappings between them are often the key
to the system's functional identity. Components often can not be
reduced or fractionated into parts.
>
> More parts to be represented means more extensive models, which requir
e
> more time to be searched or computed. Since the components of a complex
> cannot be separated without destroying it, the method of analysis or
> decomposition into independent modules cannot be used to develop or
> simplify such models. This implies that complex entities will be difficult
> to model, that eventual models will be difficult to use for prediction or
> control, and that problems will be difficult to solve. This accounts for
> the connotation of difficult, which the word "complex" has received in
> later periods.
This depends so much on what one means by model. Rosen, Casti, and Kampis
see this as the reason why complexity is the study of model making.
>
> The aspects of distinction and connection determine two dimensions
> characterizing complexity. Distinction corresponds to variety, to
> heterogeneity, to the fact that different parts of the complex behave
> differently. Connection corresponds to constraint, to redundancy, to the
> fact that different parts are not independent, but that the knowledge of
> one part allows the determination of features of the other parts.
> Distinction leads in the limit to disorder, chaos or entropy, like in a
> gas, where the position of any gas molecule is completely independent of
> the position of the other molecules. Connection leads to order or
> negentropy, like in a perfect crystal, where the position of a molecule is
> completely determined by the positions of the neighbouring molecules to
> which it is bound. Complexity can only exist if both aspects are present:
> neither perfect disorder (which can be described statistically through the
> law of large numbers), nor perfect order (which can be described by
> traditional deterministic methods) are complex. It thus can be said to be
> situated in between order and disorder, or, using a recently fashionable
> expression, "on the edge of chaos" (Waldrop, 1992)."
Here I see a construction at work, for negentropy in non-linear
nonequilibrium systems has no clear definition if it depends on entropy.
Meixner's paradox demonstrates that unless we have have a COMPLete state
space description for such systems, entropy is not definable uniquely.
(Rheologica acta 7:8, 1968) Further, Rosen and others have clearly
demonstrated that staes are not clearly definable in bifurcating nonlinear
dynamic systems.
>
>> Does it therefore include machines?
>
> A priori, this definition can also be applied to include machines, provided
> they have many, closely connected parts. Unlike Rosen's definition, if I
> have understood it well, this definition is continuous: something is not
> either complex or simple, but can be more or less complex. (although this
> does not entail a linear ordering: A can be more complex than B in one
> respect and less complex than B in another respect).
Ah yes, but look at what you throw away here. The category is based on
a dichotomous set of properties. Machines have a largest model from
which all other models can be derived. Complex systems do not.
Machines have no non-computable aspects, complex systems do.
For a machine an analytical model equals a complex model, for
complex systems they are different. Causalities are separable in
machines, in complex systems they are mixed. How does one spread such
clear, meaningful distinctions onto a scale?
>
>>Which machines are complex and which are not?
>
> The more varied their parts, and the more difficultly their parts can be
> separated, the more complex they are.
Is this a distinction? Is there a criterea for "varied" and for"difficulty"
and for "separated"?
>
>>Are organisms machines?
>>Are they complex?
>
> Depends on your definition of machine. I tend not to make an absolute
> separation between the one category and the other, but obviously see big
> differences between "typical" machines, such as cars or computers, and
> living organisms. In the framework presented in my paper, one essential
> difference is that "typical" machines tend to have relevant organization
> only on one or a few scales. E.g. for a computer, which is one of the most
> complex machines we know, the relevant scales are the one of the external
> parts, keyboard, monitor, disk drive, the scale of the components on the
> motherboard, and finally the microscopic scale of the elements on the chip.
> The more scales a system extends over, the more complex it is.
>
It also depends on the definition of organism. Organisms are closed
under efficient causation, machines are not.
> Organisms on the other hand extend over many more scales, from atoms, to
> monomers, polymers, organelles, cells, tissues, organs, etc. Moreover, the
> connections between the organizations on these different scales are
> typically much more complex for organisms than for machines, which are
> designed in such a way that the internal structure of the components has
> minimal interactions with other components. E.g. if you change one hard
> disk by another, or one processor by another, the computer will in general
> continue to run in the same way. With organisms, changes on the molecular
> level can have effects on the level of the whole body.
>
>
> ________________________________________________________________________
> Dr. Francis Heylighen, Systems Researcher fheyligh@vnet3.vub.ac.be
> PESP, Free University of Brussels, Pleinlaan 2, B-1050 Brussels, Belgium
> Tel +32-2-6292525; Fax +32-2-6292489; http://pespmc1.vub.ac.be/HEYL.html
Thank you for spelling these things out. I am afraid I must conclude
that I am even more strongly convinced that Rosen alone has given us
clear, rigorous definitions and categories. I find that very useful.
Respectfully,
Don Mikulecky
http://views.vcu.edu/complex/mikulecky/mikuleck.htm