>>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):
>
Not as far as you seem to think from Rosen. The issue of difference is
that the above statement leaves out how we actually make that determination.
Rosen puts it into something which seems more operational to me. He
saus that the way we KNOW how much variety and connectivity may be
there is by INTERACTING with the system. Thus he measures complexity
in terms of the number of independent ways we can interact with it
(independent meaning one not derivable fron the 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.
>
> 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 certainly connotes irreducibility or non fractionizability
>
> 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)."
Negentropy in nonlinear non-equilibrium systems must be a construct.
Entropy is not capable of being defined for these systems unless
there is a COMPLETE state space description available (Meixner's paradox
Rheologica Acta 7, 8, 1968).
>
>> 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).
Here's where Rosen's definition and analysis pay off! Machines have a
"largest model" from which all others can be derived, complex systems
do not. Machines contain no non-computable components, complex systems do.
For machines, analytical models equal synthetic models, for complex systems
they do not. Each of these properties is useful and rigorously definable.
I think you loose something by forsaking this.
>
>>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.
That is a distinction?
>
>>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.
>
Yes it depends on the definition of machine AND on the definition of organism.
Again a clean distinction is possible. Organisms are closed under
efficient cause, 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
Thanks for clarifying these distinctions. As a result I am even more
strongly convinced that Rosen has done what no one else has so far. He
makes clean, rigorous definitions and categories. I find this very useful!
Respectfully,
Don Mikulecky
http://views.vcu.edu/complex/mikulecky/mikuleck.htm