Article: A mad day’s work: 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
Wikipedia: Algebraic geometry, representation theory, mathematical physics, and category theory.
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.
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 email@example.com
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