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Strictly Speaking

Differential and Difference

DIFFERENTIAL

The word differential was introduced to the world by one of the intellectual giants in human history, although he himself, ironically, was not much bigger than knee high to a grasshopper. He favored tall wigs, not just because he thought of himself (although not politically) as a big whig, but because he, like everyone else, wanted to measure up. But his brilliant neologism, differential, was conceived as a diminutive of the word difference in response to a functional need that never previously existed. Differential was related to difference but distinct from it, introduced in order to better communicate the ability of his revolutionary calculus (a system of mathematical examination of the instantaneous properties of mathematical equations, nearly co-discovered by Wilhelm Leibnitz) to determine the relationships between – and here it comes – infinitesimally small quantities along a nonlinear graphic curve.

A differential along any of three Cartesian coordinates in Euclidean space is a conceptual entity that – by its nature, and unchangeably – is too small to be measured by any scale, however well defined are its measurements. A differential is too finely divided for that. By its nature and definition and intent, differential defines the low end of a scale that reaches upwards toward infinity in bigness.
The introduction of this novel concept of the differential may be one of history's most well concealed puns. Newton, a Unitarian minister, believed that each of God’s creatures had some unique gift to bestow on humankind, whatever shortcomings that creature suffered. Ergo, being tiny himself, Newton may have had an inordinate fondness for probing smallness with the same obsession that he accepted a God so vast and ubiquitous that he was not only eternal but he was ubiquitous. Thinking this way, God was beyond twenty-first century electronic eavesdropping in that His knowledge (it was always a He in Newton’s time) defied the Einsteinian limit of the speed of light limiting the rate of information transfer.

Way ahead of his theoretical time, Newton would have been pleased by what Einstein called spooky action at a distance, stuff now well established experimentally, like quantum entanglement, through which a change in state of one particle induces an entangled partner particle across the universe to change its state at the same instant. Since particles are limited by the speed of light, such changes are not conventionally causal. They do not arise by transmitted information reaching out and touching another particle. In the laboratory, and reproducibly, an excitation of one particle creates an identical response in its quantum-entangled partner in an interval instantaneously. Faster than the speed of light could connect them.

Forget cause and effect. Think simultaneity. A change induced in one particle does not stimulate the other follow; their states are coupled forever instantly. Think of identical twins separated by half a world but united by telekinesis.
Maybe their neurons are quantum-entangled.

Less perplexing is that when Newton invented and articulated differential in use, he slammed the door forever on its confusion with the root word difference from which it was derived. Derivation is a process in differential calculus, so there is a neat unity and connectedness in linguistic process and intent. This is no less than seems appropriate to the kind of genius who comes around once every four hundred years or so.

Here is the consequence of this genius in usage: if a real quantity, however small, can be measured on a numerical scale or by an established method of physical probing rather than calculated by the operation of differentiation on another function, then such a well measured quantity is a difference. If it is too small to be directly measured, existing only as a statement of smallness below the capacity of instrumentation (instruments measure things; machines make things) and inconsequential to the marco world, then it is a differential. In definitions, as would have pleased E.B. White, every word counts. That part of the definition of the word differential than ends all bar room arguments is the requirement, per Newton, that is be infinitesimal, immeasurably small.

Somewhere along the bumpy road of distinction, poor old differential suffered the fate of so many other previously unconfusing and practically defined words: it got highjacked by a pattern of usage where the users were seeking intellectual inflation by using (not utilizing, please) words that made their pronouncements seem less vague or more authoritative. It has become a pattern of extending and decorating simpler, shorter words, then, like rococo architects, infecting them with ornaments until the collapse under the escalating burden of pretension. In its most popular parody, it might – except for the fleeting half-life of popular memory – be deemed Palinism, after Sarah Palin.

This validity of this view was conceded to me by Alfred Kahn, former Cornell economics professor and senior economics adviser to President Jimmy Carter, who admitted, “It helps in getting things done to be perceived as belonging. So in meetings large and small we get trapped playing mister nice guy to avoid an embarrassment to someone who misuses a word, so eventually everyone is misusing the word a word like ‘differential’ order to remain accepted. The first guy to score a point for semantics and insist on true meanings is henpecked to death by a flock of chickens too social to risk being ostracized by insisting on correct definitions.”
For sports commentators – except for Dick Button now and rarely in any case since Howard Cossell exemplars par excellence of comprehensible utterances – to argue heatedly over the differential (contradictorily and erroneously assigned numerical values) between two teams. This simply establishes that poorly informed beliefs and open microphones can form durable bonds.

In a rage to win arguments as convincingly as competing teams win games, commentators have ignored the undebatable semantic fact that measured distinctions between anything, even sports scores and stats, must by the process of being measurable be differences.

In considering what team has the edge “on paper” (where real games are never played), the arguments had better discuss differences, because differentials – being immeasurably small – cannot affect outcomes. Nor does repeated misuse (not misutilization) however vocal and adamantly expressed, alter this situation.
The rebuttal by Dick Vitale will probably be, “I don’t care what it used to mean, baby, this is what it is in sports and who can say that twenty-first century sports is less important than seventeenth century calculus?” To which a long dead Isaac Newton might respond, “The word ‘differential’ was created to represent a mathematically important smallness that no one previously had recognized. Neologisms are often born of fashion and as quickly pass into disfavor. The need for a word as different and distinct as difference and differential means that foreverafter the words need be properly applied in their distinct senses unless the intention it to mistakenly suggest that they are identical in meaning and simply sound different (not differentially). In truth they are as irreconcilably distinct as God and Satan. Only a bedeviler of comprehension and meaning would attempt to confuse them.”

My vote is for Newton, and I’ll give you favorable odds (the likely difference in two irreconcilably different outcomes, as expressed by a ratio expressing the confidence of putative experts in Las Vegas) that if we could reconvene three hundred years from now, and if (and only if) we escape the ongoing collapse of distinct words into one steady, deafening, nonsensible sound, Isaac Newton will still be as broadly recognized and commonly misunderstood as Dick Vitale and his many miked friends will be a collective, long-forgotten puzzlement. And that’s the bald truth.  Read More 
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