Where does inflection collide?

In geometry and calculus, a point of inflection is a point on a smooth curve where its curvature changes sign, so the curve stops bending one way and starts bending the other. Newton's The method of fluxions and infinite series (written in 1671, published in English in 1736) gave a general procedure for locating such points from the rate of change of a curve's slope, and later calculus treatments identified them with a change in the sign of the second derivative. The referent here is a purely geometric feature of a curve, found by differentiation, and it has nothing to do with a change in the form of a word or a turning point in a company's fortunes.[1]

Unit

A single point on a curve where concavity reverses

Recovery means

Not applicable

Measured by

Located analytically where the second derivative changes sign, or numerically from a curve's tabulated values

In grammar and morphology, inflection is the modification of a word's form to mark grammatical information such as tense, number, case, or person, as when walk becomes walked or child becomes children. Grammarians described this in antiquity: the Greek grammatical tradition, for example the Techne grammatike attributed to Dionysius Thrax (about 100 BCE), classified words by how they change their endings, and Matthews's 1974 Morphology gave the modern theoretical account of how inflected forms are built. The referent is a change in the shape of a word within a language, and it is unrelated to a geometric turning point on a curve or a turning point in a market.[2]

Unit

One inflected form of a word, marking a grammatical category

Recovery means

Not applicable

Measured by

Described by paradigms of forms and by rules or features that map a base to its inflected variants

In business strategy, a strategic inflection point is a moment when the fundamentals of a business change, so that the way a company competed before no longer works and it must adopt a new approach or decline. Andrew Grove introduced the term in his 1996 book Only the Paranoid Survive, drawing an analogy to the mathematical point where a curve changes direction, and he and Robert Burgelman developed the idea further in later work on how firms manage such transitions. The referent is a turning point in the conditions facing an organization, judged in hindsight or anticipated by managers, and it is not a geometric property of a curve or a change in the grammatical form of a word.[3]

Unit

One transition in an industry or firm after which the old strategy fails

Recovery means

Not applicable

Measured by

Identified qualitatively from shifts in competitive forces, technology, or demand, usually recognised in hindsight