Complexity Threshold (Was: The moral questions)
>Uwe Zdun writes:The book that "At Home in the Universe" is based on ("The Origins of Order")
>>>This seems to be pretty much the same argument as complexity theory as
>>>applied to biology (see Stuart Kaufmann's "At home in the universe"). The
>>>basic argument here is that molecular systems "spring" into life in an
>>>autocatalytic process. There is a critical threshold of complexity in
> Jeff Replied:
>I haven't yet read this book. Does Kaufmann provide any lower limits for
>the complexity threshold? This is where I feel we should be focusing more
>simulation time. Can we, with either a physical system or a simulation,
>duplicate this complexity threshold in a meaningful way?
actually gives an answer to this. It has to do with the way that networks
of control genes (not structural genes) must be structured. To come
straight to the point, it is when the number of controlling relationships
between genes are between greater than the number of genes.
When the relationships between genes exceed twice the number of
genes that there is an actual loss of coordinated complexity, since
the control relationships tend towards non-convergent chaotic patterns.
Kauffman compares such systems to "gas", and identifies them
as being in the "chaotic regime" of systems.
When the number of relationships are less than the number of genes,
the system tends to have isolated transitions that peter out quickly.
Kauffman compares such systems to "solid", and identifies them
as being in the "frozen regime" of systems.
The space in the middle is where "complex" systems (Kauffman's term)
emerge. Systems having significant "frozen" portions between portions that
"percolate" seem to be the most adapted to change because they are stable
but also explore variation, making "adaptive walks to the edge of chaos."
Sounds like a good software development house, right? ;-)
The discussion of autocatalysis has to do with systems that
transform "food" molecules into the components that make it up,
thus ensuring a configuration that doesn't just fall apart or
come to a standstill. He is talking about organic molecules
like carbohydrates, amino acids, and nucleic acids, of course.
I'm not sure what the exact analog would be for digital systems.
He postulates that living systems arose from "hypercritical"
systems (rapidly permuting polymer combinations)
that cooled down into "hypocritical" systems (slowly permuting
polymer combinations). What I have read about "synergistic"
systems is that they go through a period of "noise" where
they are basically moving through very high dimensional state
spaces until they find an attractor, and then they stabilize.
This sounds like certain kinds of neural networks to me.
The complexity threshold necessary to do complex
things seems to require a degree of self-referential
structure, and then some kind of promotion and inhibition
system. I've heard about fuzzy logic systems that use
this kind of technique.