Where does differentiation collide?

The operation of computing a derivative, that is, the rate at which one quantity changes as another varies: given a function, differentiation returns a new function giving its instantaneous slope at every point, and it is the inverse of integration. Leibniz's 1684 Nova methodus pro maximis et minimis introduced the differential and the notation and rules for this calculus. The referent here is a formal procedure carried out on functions, an operation in pure mathematics, and it has nothing to do with a cell taking on a specialised job, a firm setting its product apart, or a society splitting into distinct institutions.[1]

Unit

An operation on a function that returns its derivative, its instantaneous rate of change

Recovery means

Integration recovers the original function from its derivative, up to an additive constant

Measured by

Carried out by the rules of calculus, or approximated numerically by finite differences of sampled values

The developmental process by which a less specialised cell becomes a more specialised cell type, taking on a distinct structure and job, driven by changes in which genes it switches on: a stem or progenitor cell with broad potency gives rise to committed lineages such as muscle, nerve, or blood. Hemberger, Dean, and Reik's 2009 Epigenetic dynamics of stem cells and cell lineage commitment traced how epigenetic marks channel a cell down one path and narrow its options. The referent is a biological transition inside a living organism, read off from markers of cell identity, and it is unrelated to a calculus operation, a marketing strategy, or the structure of a society.[2]

Unit

A cell's transition from a less specialised to a more specialised type

Recovery means

Reprogramming can reverse commitment and restore potency, but under normal development the change is largely one-way

Measured by

Assessed by lineage-specific gene and protein markers, cell shape, and functional assays of the mature type

The strategy of distinguishing a firm's offering from its rivals so that buyers treat it as distinct and not a perfect substitute, which loosens direct price competition and can support a higher margin: the differences may be real or perceived, in features, quality, branding, or service. Smith's 1956 Product differentiation and market segmentation as alternative marketing strategies, in the Journal of Marketing, set this out as a deliberate strategy alongside its counterpart of segmenting the market. The referent is a competitive move by a firm in a market, judged by demand and pricing power, not a cell's specialisation, a calculus operation, or the internal structure of a society.[3]

Unit

A firm's offering positioned as distinct from competing offerings

Recovery means

Not applicable

Measured by

Gauged by brand and attribute perceptions, any price premium, cross-price elasticity, and market share

The process by which a society develops distinct, specialised parts, separate roles, institutions, and subsystems that each handle their own function, such as law, the economy, or science: as the division of labour deepens, these parts grow more autonomous and more interdependent. Luhmann's 1977 Differentiation of Society described modern society as differentiated into functional subsystems rather than ranked layers, building on Durkheim's earlier account of the division of labour. The referent is a structural feature of whole societies, described by how their parts are organised, and it shares nothing with a calculus operation, a cell's specialisation, or a firm's market positioning beyond the word.[4]

Unit

A society's division into distinct roles, institutions, and subsystems

Recovery means

Not applicable

Measured by

Described by the number and autonomy of specialised institutions and roles, and by indices of the division of labour