Re: "manifold" in mathematics
Posted by
Roger Critchlow-2 on
URL: http://friam.383.s1.nabble.com/manifold-in-mathematics-tp3385914p3386710.html
A manifold is something that can't be a function because it is multi-valued where a function must be single-valued.
A circle, the set of points which satisfy the equation x^2 + y^2 = r^2, is a manifold of points because there are two values of y that satisfy the equation for each value of x, -r < x < r. If we restricted ourselves to y >= 0 (or to y <= 0) then we would get a set of points which is a function of x.
-- rec --
On Tue, Aug 4, 2009 at 11:12 AM, Nicholas Thompson
<[hidden email]> wrote:
I wonder if anybody has any comment to make on the following passage from EB holt? (Remember, I am the guy who tends to ask questions of PEOPLE when he should look them up, so feel free to ignore me here.)
Holt (1914) writes: "If one is walking in the woods, and remarks that "All this is Epping Forest," one may mean that this entire manifold of some square miles is the forest; or else, that every twig and leaf which one sees, in short, every least fragment of the whole is Epping Forest. The former meaning is the true one; the latter meaning is absolutely false. Everyone admits that while a circle is a manifold of points, a single point is not a circle; while a house is a manifold of bricks, boards and nails and any single brick is not a house. "
I am interested in this concept of "manifold" . Can anybody make the metaphor come alive for me? Is it like a shroud?
Nick
Nicholas S. Thompson
Emeritus Professor of Psychology and Ethology,
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