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:
“Histories are more full of examples of the fidelity of dogs than of friends.”
—Alexander Pope (1688–1744)
“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)
“An accurate charting of the American woman’s progress through history might look more like a corkscrew tilted slightly to one side, its loops inching closer to the line of freedom with the passage of time—but like a mathematical curve approaching infinity, never touching its goal. . . . Each time, the spiral turns her back just short of the finish line.”
—Susan Faludi (20th century)
“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)