Friday, April 18, 2008

Man As An Exponential Power

In 1920 as he was writing Manhood of Humanity, Korzybski believed that the growth of knowledge in the sciences and technology exemplified time-binding progress. Could he represent this mathematically? If time-binding was cumulative, the result of time-binding in any generation would be proportional to the amount of knowledge already present. This would have to involve an exponential or geometrical function. By early May, he was playing with this kind of progression—Y= 2x—on a piece of scrap stationary that he had already used to draft some letters. On the stationary he also doodled some branching lines whose geometric growth followed the equation. It was a diagram of what 25 years later would become widely known as a “chain reaction”—the secret of the atomic bomb. (1) Starting with x=1, then 2, then 3, etc., he had written the successive values of Y: 2, then 4, 8, 16, 32, 64, 128, 256, 512, 1024, etc. The series showed an accelerating rate of growth since each number was proportional to the quantity already present––i.e., it came from multiplying its predecessor by the value of the exponent x. Underneath this set of numbers, Alfred had written the arithmetical or linear sequence of Y=2X: 2, 4, 6, 8, 10, 12,14,16,18, 20, etc. Relative to the geometric sequence, this sequence grew at a constant, slow rate because each number came from adding—not multiplying—2 to its predecessor.

For Korzybski, it seemed that he had gotten to the core of the distinguishing characteristic of humanity: “…a man is some exponential function where the exponent or power is Time.” (2) But what was the specific function? As an examination of both the draft and final versions of the book shows, “Power” was an important term for Korzybski—not only in its limited sense as a mathematical exponent. For him, time-binding involved ‘power’ in both the physical science and the social-cultural senses. The accumulated achievements of past generations provided the present generation with increasing means of power for doing productive work. Starting from the notion of power in physics and extending this into the social-cultural realm led Alfred to what he considered “the natural law for the human class of life.” (3)

In the physics formula for power, P=W/T. P stands for power, W stands for work (defined in term of energy—force times distance) and T stands for time. The formula defines power as the rate at which work (energy) is expended. Multiplying both sides by T gives the formula W=TP, Work equals Time x Power. It seemed to Alfred that if ‘Man’ was a part of the natural universe, human social-cultural life could be understood by extending the framework of such physical terms.

Wealth could be viewed, for example, in terms of work, i.e., as the accumulated work or products of work of previous generations. He made P equal to progress (the accumulated time-bound work inherited from the dead at any point in time). T times P gave it the same kind of unit as W. To account for the growth from one time-binding generation to the next, he brought in a factor R which represented the ratio of progress having the exponent of time—i.e. RT. The time exponent T could be represented most simply by an integer showing the number of generations. VoilĂ —he had a formula for time-binding—W=TPRT—with Wealth equaling human progress as an exponential function of time.

In the published book, Korzybski dropped T as a factor, and ended up with the basic formula, PRT:
The typical term of the progression is PRT where PR denotes the ending progress made in the generation with which we agree to start our reckoning. R denotes the ratio of increase, and T denotes the number of generations after the chosen ‘start.’ The quantity PRT of progress made in the Tth generation contains T as an exponent, and so the quantity, varying as T passes, is called an exponential function of time.(4)
Korzybski theorized that the growth of knowledge in the physical sciences and technology approaches exemplary time-binding. Its relatively high rate of growth seemed to show a rapidly-rising exponential character—its curve growing steeper with each generation of scientists as more and more knowledge accumulated. For the most part, our social/behavioral knowledge—law, politics, economics, morals, human relationships, etc.—did not appear to represent successful time-binding. These areas of knowledge, what Korzybski called the semi-sciences, seemed to grow at a much slower rate, as if in an arithmetical straight line, in comparison with the more rapidly rising geometrical growth curve of science.

1. Doodle from draft of letters to Charles Armour and the Blackstone Hotel manager, N.d. (probably early May 1920), Alfred Korzybski Digital Archives (IGSDA).
2. The Manhood of Humanity and its Universal Language, Unpublished First Draft of Manhood of Humanity , p. 34. IGSDA.
3. Manhood of Humanity (1921), pp. xii-xiii.
4. Ibid., pp. 110-111.

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