From sullivan0212@gmail.com Wed Mar 17 23:08:36 2010 Date: Wed, 17 Mar 2010 23:08:31 -0400 From: dennis sullivan To: John Morgan Cc: Tony Subject: Re: Mandelbrot set john, you wrote:  I got your message from yesterday evening. You made scientific arguments for the inclusion of the M. set; I agree with all of those. My issue with it is rather practical and aesthetic.  I don't see how we could render enough of its structure by carving in stone so that we would get a representation that indicates its nature. It seems to be preferable to have a color picture of it on the wall somewhere. I am responding: yes that was the point made at the meeting which seemed ok until i thought about it...the mandelbrot set is already iconic and bob brooks original computation (at stonybrook) and mandelbrots early one are rough but would be recognized immediately even by waiters in greenwich village as happened to me one day while scribbling on a pad..."is that the mandelbrot set?" the waiter asked...   the iconic mandelbrot set is a remarkable mathematical-physical object !  to me it represents the present and the future. dennis -- John W. Morgan Director, Simons Center for Geometry and Physics Stony Brook University Stony Brook, NY 11794-3636 631-632-8298 From jim@euclidcap.com Thu Mar 18 16:39:41 2010 Date: Thu, 18 Mar 2010 16:39:35 -0400 From: Jim Simons To: Tony Phillips Subject: Re: current status of formularium I neglected to check the list and now see that Gauss Bonnet is in. More importantly, I believe Bott periodicity for U skips by 2 and not by 1. Jim On 3/18/2010 4:03 PM, Tony Phillips wrote: > Please check http://www.math.sunysb.edu/~tony/scgp/formulas2.pdf > > 1. please check new statement of Aharonov-Bohm #55 > > 2. the left-hand sides of Atiyah-Singer #24 and > Riemann-Roch Hirzebruch #57 are inelegantly similar > (decoratively speaking). > > 3. the supergravity expression #65 and the Chern-Simons > action #27 are definitions. We could just use the right-hand side. > > 4. I'd like to put in another plug for the Jones polynomial > of the trefoil and also for Witten's equation relating it to an infinite- > dimensional integral. Uses #27 then. > > 5. I'll work up some graphics for Feynman and for Aharonov-Bohm > and take a stab at the Mandelbrot set. > > Tony > From sullivan0212@gmail.com Thu Mar 18 18:09:12 2010 Date: Thu, 18 Mar 2010 18:09:06 -0400 From: dennis sullivan To: Tony Phillips Subject: Re: current status of formularium and GIGOT tony thanks for trying mandelbrot don't forget gigot ce soir 630 to 700 i am already drinking the  just opened  to air chateau ca....2005 dennis On Thu, Mar 18, 2010 at 4:03 PM, Tony Phillips wrote: Please check http://www.math.sunysb.edu/~tony/scgp/formulas2.pdf 1. please check new statement of Aharonov-Bohm #55 2. the left-hand sides of Atiyah-Singer #24 and Riemann-Roch Hirzebruch #57 are inelegantly similar (decoratively speaking). 3. the supergravity expression #65 and the Chern-Simons action #27 are definitions. We could just use the right-hand side. 4. I'd like to put in another plug for the Jones polynomial of the trefoil and also for Witten's equation relating it to an infinite- dimensional integral. Uses #27 then. 5. I'll work up some graphics for Feynman and for Aharonov-Bohm and take a stab at the Mandelbrot set. Tony From sullivan0212@gmail.com Wed Jul 21 06:06:28 2010 Date: Wed, 21 Jul 2010 05:06:26 -0500 From: dennis sullivan To: Tony Phillips Subject: proof of figure using supplementary angles color the faces of the octahedron    (obtained by gluing two pyramids together) black and white so that two faces with a common edge get different colors. now glue a tertahedron onto each black face.... the resulting object has four flat faces.each one is a large equilateral triangle made out of four of the original equilateral triangles. so this new figure is actually a tertahedron of side length twice that of the original sized tetrahedra... this is half of your figure   the other half of  your figure would be obtained by adding tetrahedra to the white faces of the octahedron. From sullivan0212@gmail.com Thu Jul 22 00:38:17 2010 Date: Wed, 21 Jul 2010 23:38:14 -0500 From: dennis sullivan To: Tony Phillips Subject: Re: proof of figure using supplementary angles righti was just formally verifying your figure exits as suggested...with intersection the octahedron... is this obvious a priori? On Wed, Jul 21, 2010 at 8:45 AM, Tony Phillips wrote: I would say: take 2 tetrahedra and intersect them as shown. On Wed, 21 Jul 2010, dennis sullivan wrote: color the faces of the octahedron (obtained by gluing two pyramids together) black and white so that two faces with a common edge get different colors. now glue a tertahedron onto each black face.... the resulting object has four flat faces.each one is a large equilateral triangle made out of four of the original equilateral triangles. so this new figure is actually a tertahedron of side length twice that of the original sized tetrahedra... this is half of your figure the other half of  your figure would be obtained by adding tetrahedra to the white faces of the octahedron. From sullivan0212@gmail.com Thu Jul 22 00:42:40 2010 Date: Wed, 21 Jul 2010 23:42:36 -0500 From: dennis sullivan To: Tony Phillips Subject: you are right the picture proves itself