Dear LO,
"Stephen Wolfram, the originator and marketer of the package "MATHEMATICA"
[Bahder, 1995] has determined that cellular automata rules fall into one
of four universality classes:
i. Single point attractor (ball in cup analogy)
ii. Periodic attractors (oscillators)
iii. "Strange" attractors (chaos)
iv. Coherent structures that propagated, grew, split apart, recombined, etc.
Chris Langton was able to develop a parameter called the lambda parameter
defined as follows:
lambda = probability any cell would be alive in the next generation
He found that as lambda is increased the system progressed through
Wolfram's classes as follows:
i & ii ---> iv ----> iii,
which suggests the progression:
order ---> "complexity" ---> chaos
Leap ------)>
The Master, in discussing music with the Lu Grand Preceptor, said, The art
of music, or the part of it that may be understood, is that when it first
begins, it is tentative, but as it continues along, it settles down, it
brightens up, it opens out, and so it comes to an end. (LY3:23.) c0342
Commentary - This is music minus the part that only musicians know
(interval theory and instrumental technique, which by the rule of 3:15
would infringe the province of the expert), namely, a listener's ear
impression of the progress of a piece of court orchestra music. The
passage can be better understood after a year of lead drum playing in a
Japanese gagaku ensemble, gagaku being the nearest extant analogue of
classical Chinese music; next best is exposure to recordings. These pieces
are at first unfocused rhythmically and melodically, but as they proceed
they become more metrically defined, colouristically rich, and
thematically intense. There is also a brief ending phase, called Iwan
when, after the culmination of the gradual climax (typically 5 to 7
minutes) the elements again dissolve. Ravel's tour-de-force crescendo
Bolero, though twice as long has similar constructional features
"None of these reasons for the existence of the house seems unreasonable
as a causal factor. In particular, it is not strange to list the purpose
for the house, final cause, as one of the factors. In science, however,
this would be a foreign, if not repulsive, notion. The Newtonian paradigm
is very special with respect to this way of looking at causality. It is
worth looking at this in some detail.
What Newtonian mechanics did epistemologically was to set up laws of
motion which caused a very important mathematical structure to exist. In
particular, Newton's second law introduces a set of key concepts. In its
simplest form it is
f = ma,
where f stands for some external factor, called a force, which alters the
motion of some body, a is the second derivative of the position of the
body with respect to time (the acceleration) and the two are proportional
with the proportionality constant, m, being defined as the mass of the
body. What is accomplished in this one law is rather striking! The
alternative would not be nearly as useful. Normally, the external force,
f, is a function of position so that the calculus yields the law the
status of a special type of differential equation, an equation of motion.
Through use of the process of integration the equation of motion, which is
really a local description of the body's motion, can be turned into a
trajectory, an equation expressing the bodies position as a function of
time in a global sense. Without the second law, a recursive set of higher
derivatives of position with respect to time would be required to get even
a very local description of the motion. The second law introduces a
technique for solving this problem. It also does something very
interesting in terms of the Aristotelian causalities associated with
motion. It may seem surprising that Newton's formalism lends itself to
being analyzed in terms of this notion of causality at all! In fact, the
causes fit in a very systematic way. The Newtonian Paradigm allows the
following identifications:
Material Cause: Initial conditions and state
Efficient Cause: equations of motion for the states
Formal Cause: Integration of equations of motion to get trajectories
Final Cause: absent
The causalities are separable, consistent with the reductionist approach.
There is no possibility for final cause to be involved!
Complex systems involve final cause and the causes are mixed in ways that
render them not reducible. In living systems, in particular, the
appearance of final cause is often acknowledged when our guard is down,
only to be placed in the evolutionary theory when we wish to tidy up our
philosophical act. Rosen has written extensively about this, and points
out that the property of anticipation is seen often in living and other
complex systems [ Rosen, 1985]. Some common examples in physiology and
biochemistry are the so-called "cephalic phase" of gastric secretion and
the forward activation of a key enzyme in the glycolytic pathway to
prepare the enzyme for a rush of substrate at some later time [Mikulecky
and Thellier, 1994; Stryer, 1994; Prideaux, 1996].
One consequence of Rosen's definition of complexity is a recognition that
systems which are simulable are simple systems. Complex systems contain
something which is not simulable and is context dependent and semantic in
character. In the case of cell signaling systems, this needs careful
interpretation. As in the case of artificial neural networks, these cell
signalling systems are most visibly demonstrating a myriad of mechanistic
behaviors which are clearly apparent to us and which have lead to many
computer simulations. The validity of these simulations as simulations is
not at issue in this discussion. What is at issue is the idea that the
simulations capture any more than the mere mechanistic shadow of the
complex living system. The essence of living systems is their complexity
and their causal structure. Living systems are complex in Rosen's sense
and necessarily contain non-computable components. This, I will speculate,
is where it will be most fruitful for us to look in order to progress. We
construct, train, and interpret the behavior of the artificial neural
network. The cellular network we seek to understand was neither
constructed by us nor is readily interpretable by us. These networks are
rich with properties which I would call "cognitive" (they have a kind of
memory, they learn, etc.). How this cellular network becomes what it is
and what its nature is seems almost totally unknown beyond certain
mechanistic simplifications and a large body of detail which results. The
forest seems totally obscured by the trees. " Donald C. Mikulecky
" One must disintegrate gladly, for God's holy undoing of us to take
place."
All complexologists...do you not, ever get the intuition that you are
being led and leading others up some 'garden path'
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