Sunday, January 23, 2005

Shooting for the Middle: Amdahl and Zeno

Is there some sort of law that guarantees mediocrity; where natural selection chooses the best within guidelines rather than the best of species? Consider for a moment the law of diminishing returns. Within such a mindset, there might exist a demonstration of a diseconomy of scale, where the extra "effort" of producing and selecting only the "best and brightest" is not offset by the gain.

There is an analogy to such a diseconomy in computer science: Amdahl's Law (another resource here). Interestingly, according to Amdahl's law, the increased effort does not have a linear relationship to gain, but rather a sort of inverse geometric or even Fibonaccian one. That is, the effort to increase gain rises more quickly than the gain itself and, thus, we see diminishing returns.

An early exploration of this idea is Zeno's Paradox of Dichotomy (recently used as the basis for an experimental film by Robert Arnold). Essentially, in this paradox, one never reaches the end-point because of the infinite number of midpoints. I am presenting (possibly) a bit of an oversimplification, but one gets the point. However, if one takes, for example, Zeno's illustration of the tortoise and Achilles as a metaphor for natural selection, then one sees another way in which increased effort does not scale to increased gain. Essentially, the situation is fixed: we may "evolve" further, but we never quite catch the tortoise.

Of course, I am applying a literary structure to scientific theoretical models - a reversal of the typical modern relationship. This is a useful exercise for pondering, but not much else. As opposed to Amdahl's law, I cannot quantify or define; I cannot assert a Grand Theory relationship among Zeno, Amdahl, and Darwin. However, I can reflect upon the persistence of what we call mediocrity and wonder if, instead, mediocre is really best, if a bell/Gaussian curve is better than disruption.

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