About the Creation of Numbers Randomness and Creativity in Mathematics
Francoise Chaitin-ChatelinProfesseur de Mathematiques Universite Toulouse I Scientific Adviser for the Qualitative Computing Group at CERFACS
Wednesday, February 13st, 15.00 p.m., CERFACS Conference Room
Abstract :
It is classical to describe the construction of Numbers by a chain of increasing complexity which starts with the integers N and climaxes at the complex plane C. In this conventional view, the continuous emerges from the discrete. The dual viewpoint, that is the creation of the discrete from the continuous, which is so central is Scientific Computing and Numerical Analysis, is seldom considered in the domain of Arithmetic. In this talk, we shall review some of the facts (from Physics to Computing) which indicate that it might be usefull to look at integer numbers as being the result of repeated multiplicative processes on multidimensional real numbers. Then we shall play the game of the creation of numbers by multiplication in a 4D space of reals. This will shed new light on some dual pairs which are ubiquitous in Scientific Computing such as randomness/creativity, order/chaos and discrete/continuous. Nota bene: Even though the subject is Mathematics and Computation, the talk will be almost free of mathematical formulae. It will be illustrated with graphical displays realized in collaboration with Elisabeth Traviesas.
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