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 < nickthomp...@earthlink.net> 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, > Clark University (nthomp...@clarku.edu) > http://home.earthlink.net/~nickthompson/naturaldesigns/<http://home.earthlink.net/%7Enickthompson/naturaldesigns/> > > > > > > ============================================================ > FRIAM Applied Complexity Group listserv > Meets Fridays 9a-11:30 at cafe at St. John's College > lectures, archives, unsubscribe, maps at http://www.friam.org >
============================================================ FRIAM Applied Complexity Group listserv Meets Fridays 9a-11:30 at cafe at St. John's College lectures, archives, unsubscribe, maps at http://www.friam.org
