Moulton Lava

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Sunday, October 30, 2005

Disjunction Dysfunction and the Error Function


The polisphere is flush with characters (pejoratively known as Control Freaks) who are enamored of the wonderfulness of the fabled Heaviside Switch Functions, who, alas, don't grok the mathematical subtleties of their true dynamics.

But there is a huge cognitive leap to get to where Poincare and Lorentz got us when they uncovered the essential elements of Chaos Theory.





The Building Blocks of Chaotic Dramas

There is a story to be told here, but I don't quite see how to tell it. The young heroes of Harry Potter know instinctively that to solve the problems at hand in a functional manner, they are going to have to break every rule in the book. And Dumbledore knows that too. But not the other kids or adults.

No one is a better storyteller than JK Rowling. And yet this point seems to be lost on most people.

A useful mathematical insight into terrorism can be found in the angular crookedness of the elementary function known as the Heaviside Switch Function.

For reasons unbeknownst to me, humans since the days of Adam and Eve have become foolishly enamored of the wonderfulness of such dreadful Heaviside Switch Functions.

Perhaps the Heaviside Switch Function is the only mathematical function that a politician can wrap his nimrodic brain around.

But such functions are graceless. As we learn from the study of Nonlinear Dynamics, they typically yield erratic, chaotic, dysfunctional systems. After all, a tiny perturbation in the vicinity of the switching point yields an abrupt and dramatic switch in the value of the function. This sudden reversal is the key feature of systems which produce chaotic, catastrophic, tragic, and disastrous outcomes.

None of this is a new observation. The story of Adam and Eve and the Apple is perhaps the oldest story in our culture about this ubiquitous problem which exemplifies the functional learning disability which has plagued Homo Schleppians since the dawn of civilization.

There may not exist a prayer of a chance of exploring such issues in political venues which are themselves ensnared in the selfsame perennial error in reasoning.

Here, by way of comparison, is the more enlightened, unsung and obscure alternative, known to mathematicians as the Error Function (shown in blue) ...




Error Function (Blue) vs Heaviside Switch Function (Yellow)


As you can see, the Error Function (shown in blue) is continuous and gracefully transitions from one extreme to the other. That's what makes it more functional than Heaviside's graceless and abrupt Switch Function.

Now, how could one work that distinction into a story that could be understood by ordinary readers who are not all that keen on math?

The storytelling problem begins with the observation that the graceful Error Function cannot be expressed with any precision in any text language. One is obliged to turn to mathematics or graphic art. So for starters, one would be obliged to employ the cartoon expressiveness of the graphic novel.

In business, leadership amounts to offering something (of value) to trade at a tempting price. If the price is right, trade takes place by mutual consent.

The Error Function suggests that leadership in business and trade includes the opportunity to adjust the shape of the price function, so as to produce the most vital and vibrant trade economy.

In short, the Error Function is an Engine of Trade, since it establishes the conditions of free trade along an entire axis of consumption (the axis spanning Saintly Good to Demonic Evil).

By comparison, the Heaviside Switch Function is not an Engine of Trade, but an Engine of Drama. That's because there occurs a dramatic switch when some 'player' crosses the boundary (or is merely adjudged to have crossed the imaginary boundary between Saintly Good Conservation of Resources and Demonic Evil Gluttonous Consumption). A variety of classical pathologies arise in the wake of the Heaviside Switch Function, including disagreements and conflict, violence and oppression, injustice and rebellion, corruption and scandal, alienation and inequality, hopelessness and suffering.

Perhaps the enlightened solution is to traffic in stories which present simplified transaction examples arising from the erratic dysfunctionality of the Heaviside Regulatory Model. After all, JK Rowling made a fortune trafficking in such stories. There is clearly a market for them.

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