and

Fractals

What is the length
of the
periphery?

How long is our coastline?
Well that depends?

No it doesn't.

Yes, it does.

No.

Yes.

No, no.

Yes, yes.

Length is whatever it is. It does not depend! Depending is irrelevant!

No. The question of relevance is ... uh ... actually, relevant. How long is the coast of New Jersey? I don't know a real answer, so say - for discussion - 300 miles. But, somebody asks, Measured how?.

"Well?"

"The USUAL way."

"Which is what?"

Ahh. See? That's the point. One person is saying miles as measured from aerial photos - with a ruler. Another is saying George Washington, surveyer he was, measured it when his troops traversed the state chasing the British (or running from them). A sailing hobbyist offers triangulation - by landmarks along the inland waterway. We learn that the most used measurement is from the department of roads & highways - used to set out the exit number names on the parkway.

Follow the coast, a highway, a meandering foot path that seeks out river narrows (Patton did that) - the ancient routes, before bridges. What about a bug that follows the tide edge? What about a microbe sized higher intelligence which follows every itsy bitsy pebble contour? The length can go from some number like 300 miles to as high as approaching infinity.

Geez.

LENGTH is actually MORE a measure of RELEVANCE (length for what intended use) than it is of distance!!

We must ask the relevance or length has no meaning at all. How far by boat, on foot, by bird, by main roads, by atomic contour... As you look closer, things change. And yet - somehow - there are formulas that can be used to generate very close answers to the question of distance when given the scope of our relevant measure.

How?

Well, nature seems to organize all this seemingly random stuff in a fractal kind of way. AS YOU GO SMALLER, THINGS CHANGE, BUT STILL LOOK SIMILAR WHEN MAGNIFIED. Start at the very smallest bit of a fern leaf. Go bigger. The next structure looks much like that smallest part - overall. The very next level higher again looks similar as well. The information to generate that big complex shape made up of smaller shapes is a simple rule that repeats. Each repetition is a wee bit different as random tiny interactions vary it such that no two repetitions are exactly the same - but they sure are similar.

Complicated stuff is USUALLY made up of similar looking much smaller stuff repeated many times with lots of small random variations.

Now take a math geek and have them make pictures from tiny simple shapes that assemble into bigger shapes and you get computer nature scene generators - mountains with lakes and trees and ferns and all sorts of stuff. Why does it LOOK like nature? Because that is precisely HOW nature is actually making all that stuff. The complexity of nature comes from simple rules repeated over and over at successive scales with variation from trace chance events making nothing exactly like anything else.

Including us. We do >> NOT << have every nook and cranny of our person gene determined. Processes which endlessly repeat and interact - LOW LEVEL - tiny processes - repetatively interact to generate us in all our complexity. Our huge super complexity of brain neuron structure could not even be approximated drectly by the scope of our genes. But the rules to be applied in repetition are what gets encoded in a cascade of building from which this very insight emerges.

Fractals are shapes used to build larger similar looking shapes. The fancy term is self-same structure. It turns out that just about all the important stuff has self same structure. This includes things you might not suspect (that's why we have geeks, to apappreciate it for us). Economic trends and population shifts follow similar mathematics. Physics has been taken over by this new chaos math which is the first math able to handle the specifics and generalities of reality.

Indeed, chaos math has taken over all the major fields of science - physics, biology, ecology, chemistry and even statistics of economics. The last hold out has been literature. Editors demand singlular heros in linear plot constructs. This is exactly what new science in virtually every field has discarded. The Pool was written as a self similar structure whose development is based on a chaos math model.

A Mandelbrot set (which produces a graphic looking similar to that on the left) was used to set up the chapters and content distribution. The Mandelbrot set is a graphic representation of a nonlinear equation which can both run amok by flying off to eternity the way the number pi does or it can behave in a stable repeating way. At the juncture of the stable realm and the horizon where things fly away to never return to a prior value we see a strange universe on the edge. That is a universe of ever repeating similar and amazing forms of which no two are alike and yet no two are dissimilar.

Typically - no, wrong - by editor & publisher demand, with nearly no exceptions - a popular story told in novel form has got to be a linear story, overall, the development of which is the linear answer to a "what if" question - all of which ends in 250 published pages. You can forget about getting published if you don't follow that rule.

The Pool was written to very different specs just to see if it could be done - for the fun of it. As with chaos math, it is not linear and has many repeating qualities and aspects which repeat at different scales, but never quite the same. Small random events or circumstnces affect flow and outcome. There are "strange attractors". Strange attractors are forces that tend to bring what seems as an errant flight back to a base condition but never as it was exactly. Within different developments there arise similarities of smaller social domains. The flight of a moth about a light is a good idea. The path always has a similarity but never gets to the actual attracter center nor ever exactly repeats what it did before.

Interestingly, we can watch a moth, or waves on the ocean, or fire - which are examples of motion with strange attractors - for hours. They mesmerize. But try working in a place where some demo tape keeps replaying the same discussion, or shows the same visual exacly over and over. You go nuts. We like infinities.

There is no actual math in The Pool, but those who are inclined can find it hidden in the structure along with the use of elements from which it is generated.

For those of you not in tune with the revolution in science brought on by chaos mathematics, here is a wee bit of the what and why.

Newton described the overall interaction between two bodies. But he was, himself, troubled by the magic it relied on - immediate effect at immense distances. He had no answer and dealt with that by opting to not deal with it. He knew he lacked the data and tools. Einstein patched Newton by establishing that it was not magic in that the interactions were NOT immediate, but took time. Gravity had to reach from one object to the other (at the speed of light).

However, a serious problem forseen by Pascal, even before this, was that given a good idea of what two bodies do to affect each other, we did not have the means to compute what might happen if THREE were involved.

Why? Our mathematics is a complex of computational tools built layer upon layer with one overriding property - avoiding nonlinear multiple interactions. All that calculus, all those laboratory rules and equations were CONTRIVED in complexity to allow LINEAR calculation.

What's linear?

Rulers. Arithmetic. 2+2=4 and easily deduced is 4+2=6. Same increment same expansion. But when relationships are geometric, we can compute them if there is one interaction involving two factors or bodies. But NONE of the math works if there are THREE BODIES which have nonlinear interrelationships. We are calculation blind and therefore clueless. Why? Because when that happens the math becomes crazily perturbed by the very smallest deviations, things so small that we have no hope of measuring them.

It turns out that the expression: S__t happens is a very cogent summation of three body processes. Biologists never signed on to the methods of physics and were seen as the dummies of science. We didn't have those nice wall sized equations. Why? Were we too stupid?

No.

Wall sized or otherwise, the equations simply didn't work. You can beat all the theory you wanted, but put to the test in the field (which isn't the lab), failure. The field did not allow for the constraints on all those other variables as was the practice in physics.

Comes along Lorenz, Mandelbrot, and Feigenbaum and everything becomes clear. We know now why we are so utterly messed up. The math that includes the very insignificant and breathes life into that all time barrier to measurement, turbulance, now makes sense. It also tells us how things can head toward organization and control - life - in an entropy driven system. Eddys. Flow produces turbulance and turbulance has eddys, islands of stability and organization driven by the passing flow.

Lorenz found for us, the reality that even though chaos driven events never ever exactly repeat, they do hover around states and return toward conditions which though never attained are never rejected and persist as ever influencing - like moths to flame  never in the fire but ever flitting around it.

In The Pool, the mileau or stream is English speaking WASPish America with dominantly European English culture.

The ultimate confounding problem of calculation is taken on - three body interactions. They are three main characters, one of Italian descent, one Afro American, and one Irish. Each lives in his own universe, though the three have strong similarities.

There are strange attractors that glue each main body in its own domain. Some are obvious, and others strangely invisible but whose mark is the behavior of that which is seen.

The Pool asks us to make a judgement about ourselves and our ability to do wrong by siding with convenient powers and forgetting basics. To help that along, The Pool assigns a very nice people to play the heavy. The idea is relativity, what is reasonable to them is horrid from another vantage. Thus the Irish -English as a metaphor for self interest driven by self logic rather than by humanity. That we have a similar problem in our lives ought not escape the discriminating reader.

Chaos. Chance. Luck? Is luck merely coincidence? Random clustering of favorable outcomes? Can we depend on luck? Or, must we read the signs of what is really out there and make our fortune happen? But what signs?

Do plans really work? Or is planning the formula for rigidity - linearity - doomed in the nonlinear world of minute interaction and chaotic outcome? Maybe the best plan is no plan but flexibility and predisposition or willingness to move on no notice at all? Are heros those who just react - and react well?

The big issue in The Pool is the new description, a practical definition, of EVIL. It isn't by any phiosophic means defined, but biologically, by behavior. That which grows without regard to the host, is evil. Cancer. It is recognized by formlessness, it goes as far as it can go and goes anywhere it can. Thus it takes its shape from that which contains it.

As water takes the shape of the glass which holds it, evil assumes the contours of whatever inhibits it. Thus at the boundary of evil may be another evil in a balance which contains both. Life may well exist in that fragile zone of impasse between greater forces. This is our fractal world of infinite dimension in constrained space. The inherent good of balance of power requires no inherent philosophy, no liberal or conservative predisposition. Any power that defies restraint by the people IS evil. Period. It does not matter what it claims to be, what it says, or even what it does. Sooner or later unrestrained power poisons.

In The Pool there are parallel worlds of symmetry. So we have three books with repeated themes delivered by differing methods but with strong interconnection and strong self similarity. There are puzzles to solve along the way. ALL the facts needed to solve those puzzles are right out in the open. Nothing is held back. The problem of what are true signs becomes lived by the reader.

The Pool...  McGuiness...  Wormly...

Enjoy.