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James Brody
March 15th, 2005, 07:48 PM
"Show me the money!" Cuba Gooding Jr. in "Jerry McGuire"
"Show me the numbers!" Jim Brody
"Show me the crayons!" Howard Bloom

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Pythagoras (500-580 BC) traveled a lot, lived a long time, and eventually set up his club on a dot in the Mediterranean where he bullied his students while he studied numbers and, especially, the power of triads. (Two thousand years later, Stu Kauffman and Bowen Family Therapists do the same thing!) Howard Bloom (2000) recognizes Pythagoreans as wanderers who believe odd things but become scientists and the ultimate insiders. Stevens and Price (2000) call us schizophrenic. Baron-Cohen speculates we have Asperger's Syndrome, perhaps an outcome of too much uterine testosterone.

Bloom's caricature is perhaps the kindest...
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Several years ago, I compared the proportions of a sports car with those of a cat: body hung below its suspension rather than sitting on top, independent suspension at all four corners, maximum power from the rear for straight-line acceleration, and greater braking effectiveness on the front end! Both cat and car have more forward gears than backward ones, both have a shock system, and both blow smelly gases from the rear.

The car and cat reflect convergence: similar outcomes from different origins attributed to similar evolutionary forces and the Suzuki motorcycle in my garage joins their club. When Max rambles across my floor, his head and front paws lead but his back sometimes keeps on going in its original direction and I think of patterns that unfold when the bike and I move at low speed. (We also resemble women shopping within a single aisle of a grocery store: their head often rotates first and their shoulders follow, hips pivot later. Watch them sometime!)

Furthermore, for Max, the bike, and most people we find receptors, signals, and decisions mostly on the front end, followed by a thorax that is lower than the head but higher and wider than the stuff that comes next. Traction from the rear still works best in straight lines: accelerate and mass shifts backward, brake and it moves forward. Expect to see big back tires but big front brakes. And for both cat and bike, swerving usually works better than braking. Finally, if a fast-moving biker brakes when cornering or, if he, even when going straight, applies too much rear brake in comparison with the front, then he becomes an organ donor.

I've never seen a cat that dumb...

As for showing the numbers: linear equations and arithmetic work best in the orderly half of the phase transition wherein we make our home. We take the order that we find around us and arrange it further to suit our self, creating still more order for our children, who by imprinting and genes, will share some of our preferences and refine them. Biologists sometimes produce numbers that apply to runners or to fliers and relate body proportions to metabolic rate. Within environments that humans construct, engineers line us up with homes and automobiles by means of numbers. (And engineers also obey the numbers from accountants, those mothers of resource availability.)

Numbers become more difficult, however, when we explore nonlinear boundaries on the chaotic side of our phase transition. Thus, Richard Feynmann sold his ideas and won his Nobel with drawings. Ed Lorenz gave us three simple equations that never produce the same results but whose three dimensions can be portrayed as two and resemble a butterfly.

Most complex of all, the Suzuki, Max, or ladies in the Acme consist of modules, each module an emergent cluster with its own set of numbers that resembles the sets of numbers that are associated with other modules. Each set of numbers has local influence within its own module but the composite of different modules, the mosaic, is another hox-like assembly that grew from selection, duplication, compartmentalization, variation, and selection again. (Get to know Raff, 1996!)

A pretty girl can, therefore, be seen as loosely stacked (sic!) equations. Wasps and women are segmented and, as Alfred Wallace knew, each segment follows a somewhat distinct evolutionary path. On the one hand, we have met numbers that describe emergent networks in regard to connectivity, path length, and resistance to jamming and we can recognize numbers are part of our evolutionary environment. On the other hand, we may never find one equation that describes all of the Intruder, a woman in the Acme, or Max.

Bloom is right, we will make pictures for a very long time.

JimB

*Thanks to Howard for his encouragement...

REFERENCES

Bloom, H. (2000) Global Brain: The Evolution of Mass Mind from the Big Bang to the 21st Century. NY: Wiley.
Brody, J. (2005) ADHD: Inhibition, Emergent Networks, and Maternal Investment. In Michelle Larimer (Ed.) Attention Deficit Hyperactivity Disorder (ADHD) Research. Hauppage, NY: Nova Science Biomedical Series. 41 pp.
Gleick, James (1992) Genius: The Life and Science of Richard Feynman. NY: Vintage.
Kauffman, S. (1995) At Home in the Universe: The Search for the Laws of Self Organization and Complexity. NY: Oxford.
Kauffman, S. (2000) Investigations. NY: Oxford.
Lorenz, E. (1993/2001) The Essence of Chaos. Seattle, WA:University of Washington Press.
Raff, Rudolf (1996) The Shape of Life. Chicago, IL: University of Chicago Press.
Stevens, A., & Price, J. (2000) Evolutionary Psychiatry: A New Beginning (2nd Ed.). NY: Routledge.

Copyright 2005, James Brody, all rights reserved

Fred H.
March 16th, 2005, 06:12 PM
A Pythagorean? One who perceives objective and transcendent truth and beauty in things like Pythagoras’s a^2 + b^2 = c^2? Freighting JimB—open yourself to such things and before long you may be contemplating the possibility of objective goodness. What’s next? Meaning, purpose, direction, perhaps even, god forbid, deism?

Are atheists allowed to believe in an objective transcendent Platonic mathematical world?