Q: When I encountered “orthogonal” years ago in geometry class, it meant perpendicular. In recent years, I hear it used in everyday English to mean “irrelevant.” How did this happen?
A: Yes, the old mathematical meaning of “orthogonal” has evolved over the years, but the sense you describe as “everyday” is not all that common, and certainly not heard every day.
The English adjective comes from Middle French, where orthogonal meant “having a right angle,” but the term ultimately comes ancient Greek, where ὀρθογώνιος (orthogonios) was “right-angled.”
The word first appeared in English in a 16th-century mathematical treatise, according to the Oxford English Dictionary. At the time, it also meant “right-angled.”
The earliest OED citation is from A Geometrical Practise, Named Pantometria, begun by the mathematician Leonard Digges sometime before his death about 1559 and finished in 1571 by his son, Thomas, also a mathematician:
“Of straight lined angles there are three kindes, the Orthogonall, the Obtuse and the Acute Angle.” The word “pantometria” (or “pantometry”) in the title of the treatise is an old term for “metrology,” the scientific study of measurement.
In the late 1600s, the OED says, “orthogonal” took on a somewhat wider sense of “relating to or involving right angles; at right angles (to something else).”
In the 19th and 20th centuries, it developed several other mathematical senses that aren’t relevant here. But one sense that appeared in the early 20th century—“statistically independent”—may be pertinent.
We think this sense could have led to a more general, but relatively uncommon meaning that we’ve found in only two standard dictionaries.
American Heritage online defines it as “very different or unrelated; sharply divergent.” The dictionary has this example: “Radical Islamists are ultimately seeking to create something orthogonal to our model of democracy” (from an article by the American national security expert Richard A. Clarke in The New York Times, Feb. 6, 2005).
Dictionary.com defines it as “having no bearing on the matter at hand; independent of or irrelevant to another thing or each other,” and has this example: “It’s an interesting question, but orthogonal to our exploration of the right to privacy.”
The OED, an etymological dictionary, doesn’t include this newer sense. As far as we can tell, it first appeared in the late 20th century.
Here’s an example that we’ve found from a lecture by the ethnobotanist Terence McKenna on Oct. 20, 1990, at the Carnegie Art Museum in Oxnard, CA:
“Art is this endeavor to leave the animal domain behind, to create another dimension, orthogonal to the concerns of ordinary history.”
And here’s a later example from Why People Believe Weird Things (2002), by the American science writer and historian Michael Shermer: “For the most part intelligence is orthogonal to and independent of belief.”
We especially like this discussion of “orthogonal” at the US Supreme Court on Jan. 11, 2010. Richard Friedman, a University of Michigan law professor, used the term in arguing for the plaintiffs in Briscoe v. Virginia:
Friedman: “I think that issue is entirely orthogonal to the issue here because the Commonwealth is acknowledging …”
Chief Justice John Roberts: “I’m sorry. Entirely what?”
Friedman, “Orthogonal. Right angle. Unrelated. Irrelevant.”
Roberts: “Oh.”
Justice Antonin Scalia: “What was that adjective? I liked that.”
Friedman: “Orthogonal.”
Roberts: “Orthogonal.”
Friedman: “Right, right.”
Scalia: “Orthogonal, ooh.”
Justice Anthony Kennedy: “I knew this case presented us a problem.”
Friedman: “I should have … I probably should have said …”
Scalia: “I think we should use that in the opinion.”
Friedman: “I thought … I thought I had seen it before.”
Roberts: “Or the dissent.”
(We cobbled this account together from reports in The Washington Post, the ABA Journal, The Volokh Conspiracy, and The BLT: The Blog of Legal Times.)
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