To: Denise Marika <denisemarika@rcn.com>
Dear Denise:
Over the last year, I have been writing another paper on tactile mathematics, which has gotten me a step closer, I think to Corporeal Mathematics -- or a Corporeal experience of Mathematics. <http://emsh.calarts.edu/~mathart/MA_dickson.html>
I have had an experience recently, which has reinforced my more vague notion of the inverse -- Mathematics of the Corpus, or body, itself.
In 1998 George Francis and John Sullivan created a computer-generated animated film called "Optiverse". <http://new.math.uiuc.edu/optiverse> It is on the sphere 'eversion' or the operation of turning a sphere inside-out without cutting it. <http://www.math.uiuc.edu/~jms/Papers/isama/color/opt2.htm>
Bernard Morin is a mathematician, born in 1931, blind from an early age, former Fellow at the Institute for Advanced Study at Princeton University, who now lives in Paris. In 1980, Morin invented one kind of sphere eversion. The "half-way" model of the Optiverse sphere eversion is actually called the Morin surface.
The "Optiverse" applied a "physically-based" computer simulation to Morin's eversion. The simulator applied a constraint to the metamorphosis which minimized the surface bending energy. It modified Morin's eversion.
Professor Morin was interested in the innovations which were done in the "Optiverse" simulation, but could not understand them, because he could not see them.
On Friday, September 22, in Maubeuge, northern France, I presented a talk on Tactile Mathematics to an International Colloquium on Art and Mathematics.
On Monday, September 18, John Sullivan and I presented Bernard Morin with four physical models, from "freeze-frames" of the computer-generated "Optiverse" movie. <http://new.math.uiuc.edu/optiverse/images.html> The stereolithographs -- each approximately eight-inches on a side -- were manufactured at 3D Systems, Santa Clarita, California.
We spent the better part of a day with Bernard Morin in his apartment in Paris. I want to share with you my impressions of this meeting. Please send me your response.
Professor Morin speaks excellent English and at almost 70 years old, he has a marvelous joi-de-vivre. He got a big kick out of exploring the four models. He spoke animatedly, he hooted as he explored them.
And then, he made a connection that I had considered the remote, uncharted territory of physical mathematics. He 'eroticised' the surfaces. He spoke of "These marvelous buttocks!" as he described them.
I had sliced all the surfaces open in CAD to expose the interiors, so that they could be explored tactilly. As he did so, Morin described "The Obstetrical position" for this internal examination. He said, "You know, the way the doctor examines a woman." He said this without hesitation. Indeed, he said it with relish and gusto.
He has used other body-centered references to the surfaces, such as the "gastrula" -- which refers to the phase of embryonic development in which the blastula -- or sphere of cells -- hollows itself to form the internal stomach-shape.
And, after examining the sculptures from the computer simulation, Morin wants to re-design the "Gastrula" phase of the Eversion, itself to "skew" the "jaws". He used a facial grimace to illustrate what he means by this.
So, I must posit the proposal that there is a necessary connection between mathematics and the body, which physical, tactical mathematics necessarily triggers.
Now, is this a male-centered tendency? I know of the "male gaze" -- the male tendency to visually possess. This tendency is extrapolated in three dimensional computer modeling -- the digital scan of a woman's body is a cerebral possession of a new sort. There is a desire to mentally possess the shapes of the female form.
Bernard Morin spoke of these, indirectly, as well -- he referred to Bernoulli's Limniscate to describe the shape of a woman's breasts. However, he spoke of the need for a specialized "saddle-shape" to complete the shape between the breasts in three dimensions. Morin has not completed his mental, mathematical model of the female form.
Morin spoke of the elegant mathematics employed in brassiere design.
Is the tendency to speak openly in this way a typically French-male tendency, which takes my Puritanical American sensibilities by surprise? Or is it the personality of Bernard Morin the educator and communicator on mathematics -- who takes for his illustrative examples references to the body, which anyone can understand? ("Everybody's got one." -- John Lennon, "I am the Walrus").
Is this link between mathematics and the body a product of blindness? Certainly the tendency toward tactile sensation is a product of blind culture. At a CSUN Conference on Technology for the Disabled two years ago, I met a sighted woman from the WGBH, Boston group developing Accessible CD-ROM programs. She was escorting a blind man. I showed her the Braille-Annotated Hyperbolic Paraboloid <http://emsh.calarts.edu/~mathart/Annotated_HyperPara.html> and some other mathematical surfaces I was carrying. <http://emsh.calarts.edu/~mathart/portfolio/SPD_Costa_portfolio.html>
She was all over the objects, touching and feeling them. I was saying to myself, "Yow! This is the most tactilly-oriented woman I have ever met!" There was sensuality there.
I know that there is a path from 3-D digitizing of the body to a generalized mathematical description of the shape of the body. I haven't actually traversed this path and created this description, but I believe that this description can be 'layered': General terms to describe the generic shapes, with tunable parameters to describe the specific variations which make a person physically unique. The archaic Greek Kouros figure is the generic form without the tuned parameters. The classical Greek figure is the finely tuned, completed mental model.
What purpose would such a mathematical representation serve? It is the complete conceptualization, the complete mental model of the physical human form. It is the complete worship of the human body in the integration of the physical and the mental.
"The five or six centuries following the fall of Rome (in the 5th century CE) is often referred to as the Dark Ages of Europe. Leadership in world of mathematics during this period passed to the Arabs and the Hindus." <http://www.mnsfld.edu/~rwalker/geometry.html> "The establishment of Tantra as a religion in India goes back to about 800 AD when the great sacred erotic temples were built." <http://www.tantra.org/> By my reckoning, mathematics and Tantra were invented by the Hindus within same time span of 200 years or so. I think this is significant.
I think this link -- this connection between mathematics and the body -- hits at the heart of what art is. What is your opinion on this?
Thank you in advance for your answer.
Sincerely,