FWIW, Penrose describes it: "a space that can be thought of as 'curved' in various ways, but where /locally/ (i.e. in a small enough neighbourhood of any of its points), it looks like a piece of ordinary Euclidean space." -- The Road to Reality
On 03/01/2017 12:26 PM, Steven A Smith wrote: > Robert C - > > I did a tiny bit of research, as I have also been curious, but found no > specific > etymology beyond the "obvious" many-foldedness origins from early anglo-saxon. > > 1 dimensional manifolds are nearly trivial and 3+ dimensional manifolds are > nearly incomprehensible intuitively, leaving only the 2 dimensional manifold > as > an interesting, intuitive example. In practice, the "hydrological manifold" > which is roughly used to channel one to many (or less common, many to one) > fluid > flows, has from it's form/function. These would seem to be the first > *examples* > of geometric spaces with locally euclidean properties but significant > global/topological complexity. 2-dimensional surfaces with continuous > deformations away from euclidean. From a form-function duality, the need for > "smooth flow" of fluid through volumes bounded by continuous (and smooth) > surfaces, convolved with an obvious method of fabrication (distorting and > folding ductile surfaces such as metal or clay until the surfaces > self-intersect) seems to reference "many folds" or "manifold". > > This is merely speculation that has developed over decades with very little > input. > > The range of more "interesting" 2D manifolds is obscure to me... donuts and > "knots" (like gerbil habitrails or loop-de-loop roller coaster envelopes?) > are > the only obvious ones for me, with a Klein bottle being the lowest order > "exotic" example? In my research I tripped over a recursive "Matrushka-Klein > example": > > > which I haven't taken the time to properly sort thorugh in my head to know if > it > is topologically (as well as geometrically) different than a regular Klein? > And > are there even-odd species? I don't think they have Chirality? Puzzling! > >> OK, why are mathematical manifolds called that? It seems such a weird and >> out >> of place term. I've tried to find out without success. >> >> Robert C -- ☣ glen ============================================================ FRIAM Applied Complexity Group listserv Meets Fridays 9a-11:30 at cafe at St. John's College to unsubscribe http://redfish.com/mailman/listinfo/friam_redfish.com FRIAM-COMIC http://friam-comic.blogspot.com/ by Dr. Strangelove