What’s an inflection point?

Because they seem to be everywhere.

Inflect, a transitive verb, is from the Latin inflectere, to bend. The Oxford English Dictionary gives its earliest meaning (early 1400s): “to bend inwards; to bend into a curve or angle; hence, simply, to bend, to curve.” By the late 1500s, the word had taken on figurative senses: “to bend, incline, dispose.” By the late 1600s, the word had acquired a meaning in grammar: “to vary the termination (of a word) in order to express different grammatical relations.” By the early 1700s, the word had found a place in optics: “to bend in or deflect (rays of light) in passing the edge of an opaque body or through a narrow aperture; to diffract.” By the early 1800s, the word was used with reference to the voice and to music: “to modulate (the voice); spec. in Music, to flatten or sharpen (a note) by a chromatic semitone.”

All of which (thanks, OED ) is getting us closer to inflection point. For that we need the noun inflection, which, like inflect, takes on figurative, grammatical, optical, and musical meanings. But since the early 1700s, inflection has also meant something in geometry:

Change of curvature from convex to concave at a particular point on a curve; the point at which this takes place is called a point of inflection (or shortly an inflection).

That’s as much of the OED definition as is relevant here. A more readable definition, from Merriam-Webster: “a point on a curve that separates an arc concave upward from one concave downward and vice versa.”

The OED entry for inflection — apparently in need of updating — doesn’t account for the non-mathematical meaning of inflection point. For that we need M-W: “a moment when significant change occurs or may occur : turning point.”

So that’s an inflection point. I like the way a turning in space has turned into a turning in time. A curious difference between mathematical and non-mathematical inflection points: the one marks a fact; the other marks a fact or a possibility.

Google’s Ngram Viewer shows a marked rise in the use of inflection point beginning in 1948. A symptom of Cold War tension? In American English, the Ngram Viewer shows 1963 as the term’s peak year. In British English, it’s 1989. Perhaps Vietnam and Margaret Thatcher had something to do with that.

Is inflection point overused? I think that in many instances, crossroads or moment of decision might better apply. When I read this sort of nonsense — “There has been a strategic inflection point that we’ve all gone through as society” — I begin to think that the term has lost a clear meaning. We may be approaching an inflection point in the use of inflection point. We may even be at a crossroads. But I doubt it.