Inflection Upon Reflection

Got into a discussion today about the use of the term inflection with another individual who appreciates the finer nuances of words. We were discussing a written description of a program that has encountered sufficient obstacles to undermine its ongoing success. As the document stated, it has "reached an inflection point." I contended that this is an obscure term for conveying the idea that the program has reached a point where change must happen and this usage seems pretentious. I suggested that a more straightforward way to say it would be turning point. My colleague countered that inflection is a particularly apt term that conveys a more deft nuance that turning point doesn't capture. After delving into the matter, I think you could decide either of us is right, depending on how you're familiar with the term.

My understanding of the term inflection comes from the context of language. I am, after all, a former English lit grad student. Inflection is a word I think of as associated with speech, more specifically intonation, how someone inflects, or modulates, his voice to convey meaning. For example, by the inflection of his voice, you can tell whether a person is making a statement or asking a question. Or you can tell whether a teen is using "dude!" to mean "way to go!" or "no way!" The term is also a grammatical device, the variation of a word -- generally the ending -- to signify a particular tense, mood, gender, etc. Given this context, I'd say it's not entirely surprising that I would stumble over its usage upon first read of this document.

Had my background been more science and mathematics oriented, however, perhaps I would have encountered the phrase inflection point or point of inflection previously. In geometry, inflection point refers to the particular point on a line that is changing from convex to concave (or vice versa) at which this change takes place. It's the stationary point right as the change occurs. The Wikipedia page on the topic (assuming it's generally accurate) offers a useful example for us non-math majors: "If one imagines driving a vehicle along a winding road, inflection is the point at which the steering-wheel is momentarily 'straight' when being turned from left to right or vice versa."

At its roots, the word inflect means "to bend inwards, to curve or bend into an angle," according to the Oxford English Dictionary. The OED's first definition of inflection is the literal meaning of "the condition of being bent or curved" and then the figurative meaning of "a mental or moral bending or turning." The use of inflection to refer to the modulation of written or spoken language derives from the figurative use of the term's sense of alteration, change.

So are inflection point and turning point direct synonyms in the context of the document we started with, or do they convey different meanings? My colleague made the case that inflection point conveys a sense of a less radical or less dramatic change, which is appropriate to the program being described, whereas turning point can convey a sense of a sharper or quicker rate of change, a right-angle or 180-degree change. (Grant you, I'm paraphrasing here.) From a scientific mindset, thinking of that steering wheel at that static point before veering into the next curve, I can see how that makes sense. Moreover, in that mathematical sense, the term means being on the cusp of change, and that is another point I think the document's authors wished to convey.

However, as a layperson who found the term's usage in the document akin to a stumbling block that tripped up my reading, I'm still not convinced that it works here. Nor am I convinced that turning point isn't a reasonable substitute. After all, turns can be gradual as well as sharp; and bends can be sharp as well as gradual.

The bottom line of what this document is trying to convey is that this program is at a point where change must happen. Curve, inflection, and turn all figuratively convey the idea of change and therefore, I think, all could substitute for one another in most readers' minds. Given that of these choices, inflection is the least familiar, I personally think turning point would better achieve the ultimate goal of communicating the essential idea to the greatest number of potential audience members.

But you may side with my colleague and my mind is still open to inflection.