Chris ("CJ") Fearnley kindly agreed to post this message here.

From cjf@linux00.LinuxForce.net Fri Apr 28 17:55:41 2006

To: Doron Zeilberger

Subject: Regarding your Diatribe against the so-called infinity

Doron,

I attended your talk "A Diatribe Against the So-Called Infinity" at Swarthmore College and commented that R. Buckminster Fuller was also an "ultrafinitist". Thank you for your engaging presentation in the sun!

I earned my BA in Math from Binghamton University where I studied Combinatorics with Tom Zaslavsky. In addition to my "day job", I am Executive Director of the Synergetics Collaborative (http://synergeticists.org) which is an fledgling educational non-profit dedicated to organizing workshops and symposia to critically examine and further develop Buckminster Fuller's mathematical and scientific legacy which he called "Synergetics". I gave a presentation to the Synergetics Collaborative in 2002 called "The Search for an Algebra or Calculus forSynergetics". However, now that I have seen your Discrete Analysis, I am significantly intrigued that you may very well have discovered the way to put Fuller's Synergetics on a sound mathematical footing. I would like to develop this line of thinking further. I have copied several parties in case an opportunity for further discussion is realized.

As I promised, I will share some quotes (with references) from Buckminster Fuller's magnus opus "Synergetics" vis-a-vis his criticism of the calculus and infinity. I think you will agree that you and he share an angst against the "so-called infinity".

The calculus assumes that a sphere is infinitesimally congruent with a sphere to which it is tangent. The calculus and spherical trigonometry alike assume that the sum of the angles around any point on any sphere's surface is always 360 degrees. Because spheres are not continuous surfaces but are polyhedra defined by the vectorially interconnecting chords of an astronomical number of event foci (points) approximately equidistant from one approximate point... http://www.rwgrayprojects.com/synergetics/s02/p2400.html#224.11 ,

The phenomenon "infinity" of the calculus is inherently finite. Universe is nonsimultaneous but finite, because all experiences begin and end, and being terminal, are finite; ergo, Universe as the sum of finites is finite. http://www.rwgrayprojects.com/synergetics/s05/p3500.html#535.01

My contemporaries and I were taught that in order to design a complete and exact sphere and have no materials left over, we must employ the constant known as pi, which I was also taught was a "transcendentally irrational number," meaning it could never be resolved. I was also informed that a singly existent bubble was a sphere; and I asked, To how many places does nature carry out pi when she makes each successive bubble in the white-cresting surf of each successive wave before nature finds out that pi can never be resolved? ... And at what moment in the making of each separate bubble in Universe does nature decide to terminate her eternally frustrated calculating and instead turn out a fake sphere? I answered myself that I don't think nature is using pi or any of the other irrational fraction constants of physics. Chemistry demonstrates that nature always associates or disassociates in whole rational increments.... http://www.rwgrayprojects.com/synergetics/s09/p86060.html#986.088

MathIsFun

We are on a spaceship; a beautiful one. It took billions of years to develop. We're not going to get another. Now, how do we make this spaceship work?

-- Buckminster Fuller

CJ Fearnley | Explorer in Universe cjf@CJFearnley.com | Design Science Revolutionary http://www.CJFearnley.com | "Dare to be Naive" -- Bucky Fuller

back