Edward Weston and Boy's Surface Manifold
That mathematical , physical concept from 1901 and I think source of imagination of Weston's peppers.
Manifolds are the main research area of string and super string theory also. I believe like all ages artists , he impressed from the developments of science at his time.
At this same time he met Canadian painter Henrietta Shore, He asked to look at her work and was intrigued by her large paintings of sea shells. He borrowed several shells from her, thinking he might find some inspiration for a new still life series. Over the next few weeks he explored many different kinds of shell and background combinations - in his log of photographs taken for 1927 he listed fourteen negatives of shells. One of these, simply called Nautilus, 1927" (sometimes called Shell, 1927), became one of his most famous images. Modotti called the image "mystical and erotic," and when she showed it to Rene d'Harnoncourt he said he felt "weak at the knees." Weston is known to have made at least twenty-eight prints of this image, more than he had made of any other shell image
In 1930 Weston began taking close-ups of vegetables and fruits. He made a variety of photographs of cabbage, kale, onions, bananas, and finally, his most iconic image, peppers. In August of that year Noskowiak brought him several green peppers, and over a four-day period he shot at least thirty different negatives. Of these, Pepper No. 30, is among the all-time masterpieces of photography.
Here is the wikipedia cut below.
Here is the moving one at wikipedia with an 3d moving image.
Please have a look to that link :http://en.wikipedia.org/wiki/Boy's_surface
In geometry, Boy's surface is an immersion of the real projective plane in 3-dimensional space found by Werner Boy in 1901 (he discovered it on assignment from David Hilbert to prove that the projective plane could not be immersed in 3-space). Unlike the Roman surface and the cross-cap, it has no singularities (i.e., pinch-points), but it does self-intersect.
Boy's surface is discussed (and illustrated) in Jean-Pierre Petit's Le Topologicon.
Boy's surface was first parametrized explicitly by Bernard Morin in 1978. See below for another parametrization, discovered by Rob Kusner and Robert Bryant.
Boy's surface is one of the two possible immersions of the real projective plane which have only a single triple point.
In mathematics, a manifold is a topological space that near each point resembles Euclidean space. More precisely, each point of an n-dimensional manifold has a neighbourhood that is homeomorphic to the Euclidean space of dimension n. Lines and circles, but not figure eights, are one-dimensional manifolds. Two-dimensional manifolds are also called surfaces. Examples include the plane, the sphere, and the torus, which can all be realized in three dimensions, but also the Klein bottle and real projective plane which cannot.
The surface of the Earth requires (at least) two charts to include every point.
Although near each point, a manifold resembles Euclidean space, globally a manifold might not. For example, the surface of the sphere is not a Euclidean space, but in a region it can be charted by means of geographic maps: map projections of the region into the Euclidean plane. When a region appears in two neighbouring maps (in the context of manifolds they are called charts), the two representations do not coincide exactly and a transformation is needed to pass from one to the other, called a transition map.
The concept of a manifold is central to many parts of geometry and modern mathematical physics because it allows more complicated structures to be described and understood in terms of the relatively well-understood properties of Euclidean space. Manifolds naturally arise as solution sets of systems of equations and as graphs of functions. Manifolds may have additional features. One important class of manifolds is the class of differentiable manifolds. This differentiable structure allows calculus to be done on manifolds. A Riemannian metric on a manifold allows distances and angles to be measured. Symplectic manifolds serve as the phase spaces in the Hamiltonian formalism of classical mechanics, while four-dimensional Lorentzian manifolds model spacetime in general relativity.
Last edited by Mustafa Umut Sarac; 10-11-2013 at 06:44 AM. Click to view previous post history.
No, it's not. The Poincare' conjecture has no cosmological content, it just says that the only 3-manifold with a certain technical property is a sphere. (That's the 3-dimensional sphere, which you can't visualize easily because it takes 4 dimensions to embed it.)
Originally Posted by Mustafa Umut Sarac
Perelman's *proof* of the conjecture uses this concept called Ricci flow, which is kind of about a structure in the manifold that allows the concept of "distance" to change over time. The quantum-gravity people and other mathematical physicists do some things with Ricci flow, but Perelman just used it as a tool to show "this hypothetical object can't exist, because when you apply a Ricci flow to it it would do something impossible". It's a rather elegant approach to the problem but it doesn't say anything about the "real" universe (whatever that means).
My thesis advisor, after retiring from academia, took up sculpture in a serious way (http://www.sieradskistudios.com/). His work isn't explicitly mathematical, but I can see where it reflects a lot of time spent visualizing low-dimensional topology. It's an interesting question---how can one bring that sort of inspiration into the photographic world?
Man Ray's answer seems largely to have been to construct mathematically-inspired objects and photograph them, which is fair enough but seems more about "mathematical sculpture, followed by photography". I'm not sure how to bring geometric content directly into the photographic process, but it's an interesting concept.
San Diego, CA, USA
The lady of the house has to be a pretty swell sort of person to put up with the annoyance of a photographer.
-The Little Technical Library, _Developing, Printing, And Enlarging_