>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):
"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 require
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.
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)."
> 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).
>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.
>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.
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