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