Availing the Physics of Least Action

Amidst the talk about totality of language—its logic, its rhetoric, its aesthetics, its politics—there persists an unapparent action that we do every day. Like Wittgenstein’s language games that we use as commonplace, this kind of action seems not to have a locutionary figure of speech, perhaps because we do it unskeptically. Yet this principle of action seems to have been tacitly or explicitly granted in history: we act upon the belief that our least acts are physically reciprocal. Each of our acts entails a compensating reaction. C. S. Peirce thought that all dualism springs from the feeling of resistance to “Brute Force.” ¹ If I feel the wind blow against me, I have to push back to gain equilibrium. Though an act be singular, its occasion is always at least dual. In physics, least action means, among other things, that natural events use the smallest measure of energy necessary for acting along a path adjusted by the pressures of reciprocating circumstances. The Heraclitean stream of contradictory events is measured by recurrent intervals of troughs and peaks.

This action rule has occasioned the oldest principle in the nature of things—Retribution, the lex talionis, the equation of an eye for an eye. The Golden Rule second guesses this “aesthetic” feeling of equivalent recurrence. “Do unto others as you would have others do unto you,” has been called the leading principle of ethics. Confucius, however, used it anesthetically, “do not to another what you would not like to happen to you,” in order to stress his social laws of government as patrilineal family. ² In his essay “Compensation” Emerson said, “The world likes like a multiplication-table, or a mathematical equation, which, turn it how you will, balances itself.” ³ Jesus said, “with what measure ye mete, it shall be measured to you again” (Matt. 7:1). Measure for measure, this is an aesthetic interpretation which turns upon a reversed dialogue of reciprocal action, in which one looks at recurrent acts from the perspectives of the empathetic first person and of the apathetic third person. It seems that we act socially yet diversely upon our belief in the measures of least reaction. Even if I believe only in the stock market, I act reciprocally so as to be in front of the oscillations of troughs and peaks. I act according to my belief in the inverse equation, “Buy cheap and sell dear.” Least action seems to be our basic code, but it is applied to diverse ends in science and ethics. I take this diversity to be a pluralistic telos of social action. Although some may believe in one reductive law of action and of invariant reaction, other interpretations of least action can admit incompatible reactions as ends. ⁴

Let us admit that over time definitions of “Nature” or “Power” or “Energy” or “Action” have been socially constructed to serve the heuristics of a dominant community of inquirers, a “Whig interpretation of history.” To understand social behavior is in part to interpret the theory of action that governs the narratives of a sect. If we act upon what we believe, then our beliefs will entail a theory of action. Over time, as we shall see, people have justified their ends by the least action of God and Nature enacting their ends by the most economical means. ⁵ Least action has been the code for gauging the diverse ends of science and ethics. In that sense, least action seems to have been the practical hermeneutics of the sciences and humanities. Least action still seems to be the means of social inquiry, but each community tells its story toward different ends. So in granting that the power to act is the economic principle of least action, one is not saying that the ends of action are similarly singular.

That is, in desiring to know and to reenact the nature of things, some tend to say more and more about stuff with fewer and fewer counters, so that all events can be coded by simplest units. Pythagoras’s inverse square law about the sides and hypotenuse of a triangle...