Pierre Cartier, IHÉS, 35 Route de Chartres, F-91440 Bures-sur-Yvette

Formerly, ENS-DMA, 45 rue d’Ulm, 75230 Paris Cedex 05, France

Please note: The photo of Pierre Cartier is by Marie-Claude Vergne, 2016.

**Article**: *A mad day’s work* (PDF): From Grothendieck to Connes and Kontsevich

________ The evolution of concepts of space and symmetry CiteSeerX – BibTeX**ArXiv**: A New Perspective On Functional Integration

________ **Note**: Cartier divisors and Cartier duality**Homepage**. Springer Overview: https://link.springer.com/content/pdf/10.1007/s00283-016-9673-y.pdf**ResearchGate****Wikipedia**: Algebraic geometry, representation theory, mathematical physics, and category theory.

Second email: 26 April 2022 at 11:10 AM

Dear Prof. Dr. Pierre Cartier:

I realize that I dropped the ball. It takes many notes and touch points on your key insights before the walls show an opening and a way to walk through it, open it up, and shake hands.

It would have been nice to do so.

My note to you four years ago is here (this page): On following the work of Pierre Cartier https://81018.com/2018/10/04/cartier/

I wish you the very best and send my thanks for all your work,

Bruce

PS We have to go back to PI (π) to really access simplicity. Here the finite-infinite relation is defined and the first moment is given to us in the form of an infinitesimal sphere defined by base units like Planck’s or Stoney’s…. http://81018.com -BEC

First email: 4 October 2018

My dear Prof. Dr. Pierre Cartier:

To pull the curtains back on that “dream” you perceived (perhaps in 1999), “a ghost dimly visible in the fog,” the light of day might be found within Max Planck’s simple definitions of light whereby light is always defined as Planck Length divided by Planck Time.

That is part of his standard formula for Planck Time given in most textbooks and within sites like Wikipedia.

If our intent is to have a simple application of Euler’s multiple series of the same type, we could apply the most simple base-2 application and define 202 notations from Planck Time to the Age of the Universe (*at this moment*). Such a chart of numbers is here: https://81018.com/chart/

Within that spectrum there are no less than 64 notations that are well below our thresholds of measurement. Seemingly finitist points on the continuum, these numbers are small, but hardly insignificant.

64 doublings. All the space and time we need to stay out of the weeds of Euler’s multiple series of the same type (the Euler–Zagier numbers) where the summation extends over all integers and the product of two such numbers is linear, not exponential. That misses the point.

Silly? ….because it is so simple? Thank you.

Most sincerely,

Bruce

***************

Bruce E. Camber

http://81018.com

Austin, Texas

P.S. Other references:

1. Cécile DeWitt-Morette was at the Center for Relativity and Department of Physics of

the University of Texas at Austin and published with Cartier in the Journal of Mathematical Physics ( 36, 2137-2340 – 1995)

2. Maxim Kontsevich: Integral, Homological mirror symmetry, Quantization formula

3. Alain Connes

4. Khristo. Boyadzhiev Department of Mathematics, Ohio Northern University, Ada, OH 45810, USA. EVALUATION OF EULER-ZAGIER SUMS k-boyadzhiev@onu.edu

5. The Quantum World: Philosophical Debates on Quantum Physics, eds. Bernard d’Espagnat, Hervé Zwirn, 2017

**Living in a contradictory world: categories vs. sets?**, Pierre Cartier, Oberwolfach Report, February 2009

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