How to define complexity?
What a newborn baby perceives is a change amidst a huge mess. Fortunately
it is equipped with instincts and prior (or a priori) knowledge called
here wisdom of the body (WOB) with which it simplifies this mess to
meet its needs. For the baby this mess is extremely complex, it is
the hallmark of complexity. Yet since the baby lacks a mind which it
will develop later on, “complexity” (the concept) is meaningless to
it or better not relevant. After all it has the necessary tools to
make this mess meaningful.
Some babies grow to become physicists whose main concern is how to
harness this change in order to build machines. In order to proceed
they adopt the following concepts: The whole is the sum of its parts,
every change has a unique cause. The context in which change occurs,
is random and negligible. Or better one may always define a context
in which the cause and effect relationship will hold. They are assisted
by a special language, mathematics, with which these concepts may be
studied rationally.
When physics confronted life (Descartes) and regarded it as a special
kind of machine, which has a soul. The latter you need for religious
purposes and since soul is not a scientific entity (not even a context)
it can be ignored. Yet already Aristotle claimed that this soul controls
the machine (organism) and therefore ought to be regarded as its context.
For the next centuries complexity was hardly an issue. Since the whole
equals the sum of its parts, you may always reverse engineer it and
discover its structure. Then came two sobering discoveries:
1. Godel’s incompleteness theorems revealed that even mathematics is
incapable of encompassing any complexity. “any theory capable of expressing
elementary arithmetic cannot be both consistent and complete”.
http://www.answers.com/topic/g-del-s-incompleteness-theorems
In order to make a system “complete” you need additional statements
from outside the system which I regard as the context of this particular
system.
2. A three body system whose parts obey Newton’s laws yet the system
as a whole may become chaotic.
I regard a system as complex when the whole is more than the sum of its parts and it cannot be understood by dissecting it into its elements. The parts interact and it appears as if the whole controls them. Yet it lacks any central control.
A complex system may be quite small, like my two CA
system called proliferon.
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