Q: As a mathematician (PhD), I’d like to take issue with the WNYC caller who said Leonard Lopate misused the word “equation” on the air. It’s true that in mathematics, an equation is an equality between two expressions involving at least one object that is unknown and must be found. The ideal situation occurs when only one object can actually be determined—the solution of the equation. However, an equation can have no solution, or many, even infinitely many solutions. On the other hand, “equation” has a quite different meaning in standard English, and I can attest that Leonard’s metaphorical use of the word was quite correct.

A: Thank you for setting the record straight. For readers of the blog who didn’t hear Pat’s appearance last month on the Leonard Lopate Show, here’s the story.

A caller to the show said Leonard used the word “equation” incorrectly. The caller insisted that it should be used in a non-mathematical sense only when referring to situations involving two equal things.

But as Leonard and Pat noted on the show, the term is commonly used in a broad, metaphorical sense as well as the more literal one.

*The American Heritage Dictionary of the English Language* (5th ed.) has as one of its definitions “a complex of variable elements or factors.” *Merriam-Webster’s Collegiate Dictionary* (11th ed.) has “a complex of variable factors.”

Some dictionaries allow even broader meanings. But first, a little history.

The noun “equation” came into English in the late 1300s from the Latin *æquationem*. The Latin noun was derived from the verb *æquare* (to make equal), which in turn came from the adjective *æquus* (equal).

As it happens, “equation” was used by astrologists long before mathematicians adopted the word.

In Middle English, according to the *Oxford English Dictionary*, its original meaning was “equal partition,” a reference to the astrological division of the heavens.

For example, “equations of houses” meant “the method of dividing the sphere equally into ‘houses’ for astrological purposes.”

Nearly 200 years later, in 1570, the mathematical sense of “equation”—that is, a “statement of equality”—was introduced.

And one of the senses of this definition, the *OED* says, is “a formula affirming the equivalence of two quantitative expressions, which are for this purpose connected by the sign =.”

A century later, more general uses of the word came along.

In astronomy, for example, “equation” meant “the action of adding to or subtracting from any result of observation or calculation such a quantity as will compensate for a known cause of irregularity or error.”

This is where the terms “personal equation” and “human equation” came from.

“Personal equation” was a phrase introduced by 19th-century astronomers, the *OED* says, and originally meant the correction required to account for inaccuracy on the part of the observer.

A variation on this theme, “human equation,” came along in the mid-20th century. Here are a couple of *OED* citations:

“The Oakland Bridge suffers from such a simple, unpredictable human equation as the preference of truck drivers to loaf on a ferry” (from a 1938 issue of Reader’s Digest).

“We must throw out the human equation as much as we can in our search to find an explanation for seeming aberrancies” (from Fredson T. Bowers’s book *Bibliography and Textual Criticism*, 1964).

Current standard dictionaries, as we said, have endorsed even wider metaphorical uses of “equation.”

The *Collins English Dictionary* includes these definitions: “a situation, esp one regarded as having a number of conflicting elements (‘what you want doesn’t come into the equation’)”; and “a situation or problem in which a number of factors need to be considered.”

The *Macmillan Dictionary*, in both the British and American editions, says “the equation” can mean “all the different aspects that you have to consider in a situation (‘In a choice between the use of rail and car, the question of cost will come into the equation’).”

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