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I'm going to take the time to type in a couple
pages (424-425) of discussion from my father's book, "Anticipatory
Systems, Philosophical, Mathematical, and Methodological Foundations" because
most of our recent discussions have stemmed from issues summed up here, by the
man, himself.
Robert Rosen wrote:
"The totality of mathematical structures of the type we have defined
above forms a category. In this category the class of general dynamical systems
constitutes a very small subcategory. We are suggesting that the former provides
a suitable framework for the mathematical imaging of complex systems, while the
latter, by definition, can only image simple systems or mechanisms. If these
considerations are valid (and I believe they are), then the entire epistemology
of our approach to natural systems is radically altered, and it is the basic
notions of information which provide the natural ingredients for
this.
There is, however, a profound relationship between the category of
general dynamical (i.e. Newtonian) systems, and the larger category in which it
is embedded. This can only be indicated here, but it is important indeed.
Namely, there is a precise sense in which an informational hierarchy can be
approximated, locally and temporarily, by a general dynamical system. With this
notion of approximation, there is an associated notion of limit, and hence of
topology. Using these ideas, it can in fact be shown that what we can call the
category of complex systems is the completion, or limiting set, of the category
of simple (i.e. dynamical) systems.
The fact that complex systems can be approximated (albeit locally and
temporarily) by simple ones is a crucial one. It explains precisely why the
Newtonian paradigm has been so successful, and why, to this day, it represents
the only effective procedure for dealing with system behavior. But in general,
we can also see that it can supply only approximations, and in the universe of
complex systems, it amounts to replacing a complex system with a simple
subsystem. Some of the profound consequences of doing this are considered in
detail in Section 5, above.
This relationship between complex systems and simple ones is, by its
very nature, without a reductionistic counterpart. Indeed, what we presently
understand as "physics" is seen in this light as the science of simple
systems. The relation between physics and biology is thus not at all the
relation of general to particular; in fact, quite the contrary. It is not
biology, but physics, which is too special. We can see from this perspective
that biology and physics (i.e. contemporary physics) grow as two divergent
branches from a theory of complex systems which as yet can be
glimpsed only very imperfectly.
The category of simple systems is, however, still the only thing we
know how to work with. But to study complex systems by means of approximating
simple systems puts us in the position of early cartographers, who were
attempting to map a sphere while armed only with pieces of planes. Locally, and
temporarily, they could do very well, but globally, the effects of the topology
of the sphere become progressively important. So it is with complexity; over
short times and only a few informational levels, we can always make do with a
simple (i.e. dynamical) picture. Otherwise, we cannot; we must continually
replace our approximating dynamics by others as the old ones fail. Hence another
characteristic feature of complex systems: they appear to possess a multitude of
partial dynamical descriptions, which cannot be combined into one single
complete description. Indeed, in earlier work we took this as the defining
feature of complexity.
We shall add one brief word about the status of causality in complex
systems, and about the practical problem of determining the functions which
specify their informational levels. As we have already noted, complex systems do
not possess anything like a state set which is fixed once and for all. And in
fact, in complex systems, the categories of causality become intertwined in a
way which is not possible within the Newtonian paradigm. Intuitively, this
follows from the independence of the infinite array of informational layers
which constitutes the mathematical image of a complex system. The variation of
any particular magnitude with such a system will typically manifest itself
independently in many of these layers, and thus reflect itself partly as
material cause, partly as efficient cause, and even partly as formal cause, in
the resultant variation of other magnitudes. We feel that it is, at least in
large part, this involvement of magnitudes simultaneously in each of the causal
categories which make biological systems so refractory to the Newtonian
paradigm.
Also, this intertwining of the categories of causation in complex
systems makes the interpretation of experimental results of the form
[improvising my father's mathematical notation
here...] "If &A, then &B" extremely difficult to interpret
directly. If we are correct in what we have said so far, such an observational
result is far too coarse as it stands to have any clear-cut meaning. In order to
be meaningful, an experimental proposition of this form must isolate the effect
of a variation "&A" on a single informational level, keeping the
others clamped. As might be appreciated from what has been said so far, this
will in general not be an easy thing to do. In other words, the experimental
study of complex systems cannot be pursued with the same tools and ideas as are
appropriate for simple systems.
Our final conceptual remark is also in order. As we pointed out above,
the Newtonian paradigm has no room for the category of final causation. This
category is closely tied up with the notion of anticipation, and in its turn,
with the ability of systems to possess internal predictive models of themselves
and their environments, which can be utilized for the control of present
actions. We have argued at great length above that anticipatory control is
indeed a distinguishing feature of the organic world, and developed some of the
unique features of such anticipatory systems. In the present discussion, we have
in effect shown that, in order for a system to be anticipatory, it must be
complex. Thus, our entire treatment of anticipatory systems becomes a corollary
of complexity. In other words, complex systems can admit the category of final
causation in a perfectly rigorous, scientifically acceptable way. Perhaps this
alone is sufficient recompense for abandoning the comforting confines of the
Newtonian paradigm, which has served us so well over the centuries. It will
continue to serve us well, provided that we recognize its restrictions and
limitations as well as its strengths."
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