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# Article: Edward Weston and Boy's Surface Manifold

1. ## 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.

Weston :

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.[31] 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,"[32] and when she showed it to Rene d'Harnoncourt he said he felt "weak at the knees."[33] 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.[38]

Here is the wikipedia cut below.

Here is the moving one at wikipedia with an 3d moving image.

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.[1]
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.

MANIFOLD:
http://en.wikipedia.org/wiki/Manifold
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.

2. "Trimmed" by request.

It is more likely that Weston, like Henry Moore, was influenced by the human form, rather than Boy's Surface.

RR

3. No , they all used scientific findings at their art , it takes time to understand that AFTER reading hundredS of books on physics , mathematics and art.

You can trim your post also.

4. Did Weston read math and physics papers? He doesn't seem like he was the manifold type.

5. The book "EW 100: Centennial essays in honor of Edward Weston" has an article by Mike Weaver. His seems a simpler explanation of Weston's intrigue with form.

6. Many years ago I had the great pleasure of being in Henry Moore's home and studios. Fortunately for me he was in Paris at the time and my wife and I got to spend a couple of hours with one of his sculptors. He showed us how the monumental metal sculptures were made as well as taking us into Moore's study where he kept the stones, bones and other found objects from which he got his inspiration. He was keenly aware of form as I suspect Weston was. I have also seen many vintage Weston prints and don't think either artist was really concerned with mathematics or physics. They more likely were extremely talented artists who greatly appreciated and saw beauty in the forms most people pass by every day without noticing.

http://www.jeffreyglasser.com/

7. Originally Posted by Mustafa Umut Sarac
No , they all used scientific findings at their art , it takes time to understand that AFTER reading hundredS of books on physics , mathematics and art.

You can trim your post also.
Hi Umut,

While I could imagine you are right about some photographers (say Andreas Feininger or Ralph Morse or Wynn Bullock - a few science-minded photographers I can think of)... I believe it is more likely that the Boy's Surface Manifold is reflected in Nature (as in fractals and other mathematic constructs)...

And it's just a coincidence that Weston studied Bell Peppers... It's the peppers who developed their surfaces perfectly to meet the model, by their nature.

8. When I was a mathematician, I was a 3-manifold topologist. That stuff is fun, it contains visual inspirations aplenty, but it would astonish me if Weston were keeping up with leading technical discoveries in projective geometry (published in German, no less). Boy's surface isn't a particularly well-known construction even in that world---it's a neat curiosity, but there's not much you can do with it once you've noticed that it exists.

IIRC, Man Ray did take some explicit inspiration from geometers.

-NT

9. The mathematical constructions show no beginning point
Dont you believe in big bang ?

10. John,

I believe these manifolds can change from one shape to other. Perelman proofed the Poincare conjecture and it was about proof of evolution of todays universe shape from big bang or one point. And he showed us the heat loss on surface and the surfaces reaction to this detail loss.
I read many things but I cant do nothing on mathematics.

What do you say to above.

Take care,
Umut

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