Where does composition collide?

Function composition is the operation of applying one function to the result of another: if g turns an input into an output and f then acts on that output, their composition, written (f ∘ g)(x) = f(g(x)), is the single function that does both in order. Eilenberg and Mac Lane's 1945 General theory of natural equivalences placed this chaining at the centre of mathematics by treating the arrows between objects, called morphisms, as things that compose and do so associatively, meaning the grouping of a chain does not change the result. The referent is a rule for combining two operations into one, governed by order and associativity, not a piece of music, the makeup of a material, or the craft of writing.[1]

Unit

A single composite operation built by feeding one function's output into the next

Recovery means

An invertible function has an inverse that undoes it, so composing the two returns the identity that leaves every input unchanged

Measured by

Checked by whether the output of one function matches the input the next accepts, and studied through the algebraic laws the composition obeys

Chemical composition is the identity of the components that make up a material and the proportions in which they are present: an alloy, a mineral, or a rock is described by which elements or compounds it contains and how much of each. Clarke and Washington's 1924 The composition of the Earth's crust is a landmark tally of exactly this, reporting the average proportions of the elements in the crust. The referent is the static makeup of a substance, given as percentages of its parts, not an operation on functions, a piece of music, or the act of writing.[2]

Unit

The constituent elements or compounds in a material, with the share of each by weight or by count of particles

Recovery means

Not applicable

Measured by

Determined by chemical analysis, from classical wet assays to spectroscopy and mass spectrometry, and reported as the percentage of each constituent

In writing studies and education, composition is the practice and teaching of producing written texts: the composing of an essay, a report, or a story, and the field that studies how writers plan, draft, and revise. Flower and Hayes's 1981 A cognitive process theory of writing, in the journal College Composition and Communication, modelled composing as a set of thinking processes rather than a straight march from a first word to a last. The referent is a human craft of making meaning in prose, taught and assessed as a skill, not a mathematical operation, a musical work, or the elemental makeup of a material.[3]

Unit

A single act of producing a written text, and the taught practice of doing so

Recovery means

Not applicable

Measured by

Studied through drafts, revisions, and think-aloud records of writers at work, and assessed by rubrics applied to a finished text