Examples of Mathematical Metaphors
Conceptual metaphors described in WMCF, in addition to the Basic Metaphor of Infinity, include:
- Arithmetic is motion along a path, object collection/construction;
- Change is motion;
- Sets are containers, objects;
- Continuity is gapless;
- Mathematical systems have an "essence," namely their axiomatic algebraic structure;
- Functions are sets of ordered pairs, curves in the Cartesian plane;
- Geometric figures are objects in space;
- Logical independence is geometric orthogonality;
- Numbers are sets, object collections, physical segments, points on a line;
- Recurrence is circular.
Mathematical reasoning requires variables ranging over some universe of discourse, so that we can reason about generalities rather than merely about particulars. WMCF argues that reasoning with such variables implicitly relies on what it terms the Fundamental Metonymy of Algebra.
Read more about this topic: Where Mathematics Comes From
Famous quotes containing the words examples of, examples, mathematical and/or metaphors:
“There are many examples of women that have excelled in learning, and even in war, but this is no reason we should bring ‘em all up to Latin and Greek or else military discipline, instead of needle-work and housewifry.”
—Bernard Mandeville (1670–1733)
“It is hardly to be believed how spiritual reflections when mixed with a little physics can hold people’s attention and give them a livelier idea of God than do the often ill-applied examples of his wrath.”
—G.C. (Georg Christoph)
“All science requires mathematics. The knowledge of mathematical things is almost innate in us.... This is the easiest of sciences, a fact which is obvious in that no one’s brain rejects it; for laymen and people who are utterly illiterate know how to count and reckon.”
—Roger Bacon (c. 1214–c. 1294)
“Life, as the most ancient of all metaphors insists, is a journey; and the travel book, in its deceptive simulation of the journey’s fits and starts, rehearses life’s own fragmentation. More even than the novel, it embraces the contingency of things.”
—Jonathan Raban (b. 1942)