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Wow, the list is hopping today!
Hi Glen,
I can't speak for anyone else, but in my view honest questions are
never "too pedestrian". (I have a question of my own.... What does
"RTFM" mean? I can come up with a number of possibilities that
fit the initials, but there's no way to know which, if any, are the words you
mean!)
You have put your finger on one of the most important aspects of my
father's work, in asking what makes Von Neumann's idea
for "self-reproducing automata" different from an organism. The reason I
say it's one of the most important is because of what it means, for science. The
difference doesn't sound all that earth-shattering... until you follow the lines
of logic to what the natural consequences are, particularly for science.
My paraphrase of my father's argument goes like this: Von Neumann
described a complex system as a system that has "more" of something, which
he called complexity, than a non-complex system. He described a
complexity threshold that a system could (theoretically) cross, which
was the demarcation point between complex systems and non-complex systems. In
this worldview, complexity is equivalent to a high level of
detail and/or intricacy, which we can achieve in a non-complex
system by adding more detail and intricacy to it. This definition of
complexity differs markedly from the Rosennean one. If Von Neumann's
definition were true (meaning, if it commuted with reality), then life is
computable, all systems really are just like machines, and we will be
able to create a self-reproducing machine which would be a living
organism. Von Neumann's idea of a self-reproducing machine was a
theoretical idea, based on a particular conceptualization of what complexity
might be, and it's never been officially tested (unless we consider the past
several decades of science trying like hell to achieve it "a
test").
Robert Rosen said that this definition cannot be the case:
complexity cannot be the same as "complicatedness" because if it were,
we wouldn't have the problems we are having in science when dealing with complex
systems-- where we can compute planetary trajectories on a galactic scale, and
have our computations commute when predictions are compared with behavior of the
actual system-- and yet we cannot account for the systemic behaviors of a
single-celled organism. If Von Neumann were correct, there would be no such
thing as a system being "more than the sum"... etc. Size would matter, in a
sense. So, RR followed the problem: If complexity is some
property or quality which is innately different from complicatedness, then what
is it? His answer ended up being that complexity was
an organizational issue. The relations, as specified/created/maintained by
the system organization, are the source of the added value in a complex
system. The nature of the relations is key, therefore the way some system is
organized is what determines complexity or non-complexity (simplicity) of that
system.
In this definition, complexity is something which is true of
the system organization from the outset. In other words, it isn't something
which can be achieved by adding detail to the existing organization of
a non-complex system. No one knows how complex systems
spontaneously self-organize in this universe, but, however it happens, complex
systems are that way from inception. Therefore, it is not a matter of
arithmetic. The only way to make a simple system into
a complex system, in the Rosennean sense, is to reorganize it. Thus,
complex systems are innately different from simple systems, and cannot be
productively analyzed by reductive means the way simple systems can. All
the "added value" disappears as soon as the system is fractionated and we are
left with "the sum of the parts". There is no way to figure out what's missing
and add it back in. Do you see?
My father often used mathematical arguments
to illustrate things like this; for example, pointing out that it is not
possible to reach infinity by addition. In order for some system to be
infinite, it has to include a circularity or what he described as
an "impredicativity," in its organization. If you try to straighten the
circularity out into linear form, you lose the system. My way of describing
this concept is to say that, in a complex system, time itself is
incorporated-- as an ingredient-- into the system's organization. With a
system like this, there is no such thing as a "state", even in a theoretical
sense. (Frankly, it seems to me that there is no such thing as a "state" in this
universe, period. It is a condition devoid of time which can only be
approximated experimentally and only exists in human theoretical models.) The
models based on notions of state, then, are inapplicable to complex systems
except in very limited ways. And this is what the difference between Von
Neumann and Robert Rosen leads to. Nothing at the foundations of science can
remain the same.
There are several "tests" or conditions by which complex
organization will reveal itself. One is reduction to syntax: If you can
do that to a system and not lose the system in the process, it's a simple
system. In order for a system to be computable, it must be reduced to syntax, so
we can extrapolate from that: complex systems are not computable. Fractionation
is another test: if you can take the system apart and not lose information
(which means you can also put it back together again, using
the information learned purely from studying the parts), then
it's a simple system. If fractionation destroys the system, irrevocably, then...
it was complex.
By this measure, atoms are complex systems. Can you see what the
consequences of that realization are?
Judith
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