The Grammarphobia Blog

An algebraic occasion

Q: I hear people who should know better use the term “unknown quantity” when “unknown entity” is what they are really getting at. It is the quality of whatever is referred to that is unknown, not the quantity.

A: The expression “unknown quantity” originated in the terminology of algebra in the 17th century. A simple algebraic equation has an “unknown quantity” (often referred to as “x”) plus several known quantities. Solving the equation gives you the value of “x.” For example, in the equation x – 2 = 3 + 4, the unknown quantity (x) equals 9.

The Oxford English Dictionary gives two early citations for this usage: “The degree of Composition in the unknown Quantity of the Æquation” (1676). And “The Root of an Equation, is the Value of the unknown Quantity in the Equation” (1728). So an “unknown quantity,” in this case, is the object in a mathematical operation.

But “unknown quantity” has long been used figuratively as well. The essayist Walter Bagehot wrote in the Fortnightly Review in 1865: “The first election of Mr. Lincoln … was government by an unknown quantity.” The expression likens an unfamiliar or mysterious person or situation (say, a “wild card” or a “loose cannon”) to that part of an equation that remains hidden – the yet-to-be-solved “unknown quantity.”

All things considered, I’d say this is a fair use of metaphor.

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