probability

Hey John Starret,

Since you're a math guy, perhaps you
could fill us all in on the sound statistical
explanation to account for the ubiquity of
irreducibly complex systems in microbiology
and biochemistry.

- Jeff

--- In metatuning@y..., "X. J. Scott" <xjscott@e...> wrote:
> Hey John Starret,
>
> Since you're a math guy, perhaps you
> could fill us all in on the sound statistical
> explanation to account for the ubiquity of
> irreducibly complex systems in microbiology
> and biochemistry.
>
> - Jeff

First, let me guess that you are of the opinion that an organizing
intelligence is necessary for such complex systems to arise. If I am
wrong, please note that it is just an innocent attempt to gauge where
you are coming from. Please feel free to correct me and fill in the
details. Also, I hope you will indulge my little preface below so that
my mathematical explanation that follows will be put in a proper
perspective.

So, let me tell you where I am coming from. I am an experimental
physicist by practice and a mathematician by profession, but I am not
in the atheist camp. If I were to describe my "religion", I would use
Zen Buddhist, Taoist or Hindu terminology and images. That is as
specific as I can get without wasting too much bandwidth. From that
standpoint, when I think of organizing principles in the universe, I
imagine the universe as a sort of universal mind, with "individual"
intelligences sharing in the perception of the whole. The Upanishads
would describe the whole as the dance of Maya.

Thus, when I describe things using mathematics or physics, I am not
ascribing cause, as cause is effectively beyond words, but rather I am
using the language of mathematics to make models of reality. The cool
part is, that when the "right" model is constructed, it acts just like
the real world. Mathematical descriptions of the physical world have
allowed us to build electronic devices, space ships, skyscrapers,
bridges, particle accelerators, and all the other trappings of modern
society, all because the universe is understandable in the simplest
sense, and experiment is repeatable. An engineer knows when he
manipulates the vectors and tensors that describe the forces in a
bridge, for instance, that the answers he gets will be very close to
what would be actually measured. Thus, we can trust the mathematics
and the physics, when we are dealing with well understood phenomena.

Whew. On to your question.
Statistically, complex systems show up in the numbers they do because
they are common. That is a tautology, but it is the best I can do
because statistics are not the appropriate tool to use here. Much
spatiotemporal pattern formation, including chemical species
concentration, leopard spots, and the like are "governed" by some form
of amplitude equation such as the Ginzburg-Landau. Many systems are
self-organizing, in that given a set of initial conditions, over time
they form discernable patterns. No "organizing intelligence" need be
postulated, because the organization is a property of the universe,
and to a very close approximation in well studied and modeled systems,
the pattern formation, or self organization, proceeds as the equations
describe. There is no need to assert the existence or non existence of
"God" or what have you, because that is not what science is about.
Science is about making models with predictive and descriptive power,
and by golly, it is better than anything else we have. It is the right
tool for the job.

So, I can model and describe the appearance of pattern and complexity
with mathematics (the science of complexity is in its infancy, so
don't expect too much of it yet!). That doesn't explain their
ubiquity. Let me do you one better. I assert that the entire universe
is self organizing, pattern forming, life producing, evolving and a
source of unending mystery, delight, horror and perplexity. In other
words, all is Brahman, all is God, and you are it.

John Starrett