Merveilleux entretien avec M. P. Cartier. Beaucoup de choses à méditer. A commencer par cette remarque si simple sur l'utilisation et l'utilité des matrices. Je ne m'en étais pas encore rendu compte, moi qui calcule constamment de Jacobiens (associés à des singularités lagrangiennes) et qui, après traitement informatique, produisent des dessins de surfaces singulières (caustiques) d'une beauté fascinante... Encore merci M. Cartier

Merci pour cette vidéo. Un plaisir d'entendre Pierre Carier.

C'est vraiment tres impressionnant a écouter. Cette modestie face a des concepts qui demandent tant de travail à comprendre meme pour ces grands professionnels.

Passionnant, et passionné, CQFD. Celui qui sourit a entrevu la lumière et l'entretien soigneusement. Même si je ne fais plus de mathématiques depuis des lustres, je reste accroché à ce conteur inspiré.

Absolument génial !

Quand on voit JP Serre et P.Cartier, on se dit que les maths conservent bien l’esprit et le corps.

Merci Pierre Cartier , un si bon conteur .

Sans les catégories, il n'y aurait plus de logos dans le monde mathématique.

The overall structure of our top-down Platonic universe, where monads are quanta by Roger B. Clough (10/26/14) Abstract Here we briefly describe the universe as being simultaneously mental (as monads or quanta) and physical (as bodies or particles of matter). These particles or bodies also have a range of what Leibniz calls perfection, and they indirectly interact such that a more perfect body makes a less perfect body more perfect, the more perfect evolving toward the supreme perfection of the One. The mental sphere (Mind) contains not only monads in the form of quanta but a pre-established harmony (PEH) as well as forces (which are ideas), which can act on them, of which there are two kinds: a) physical forces, which act on mass (as linear momentum) and on spin (angular momentum) and b) electrical forces, which act on the charge of a particle. Mind also contains the powers of creation, reasoning, experiencing, and perception , and control. Mind controls matter just as mind controls the brain. Introduction and discussion The platonic universe consists of two halves of a single entity which we might call the Absolute : comprising the One and the Many, or Self (subject) and Other (object) , as in Fichte. The structure is completely cybernetic, by which we mean that all causation is mental and top-down.. The purely mental or subjective One or singular ruling creator and governor, is a purely mental subject (first person singular) . The Many, its monadic objects, consist of a network of an infinity of mental monads, all alive and conscious to various extents, as well as the physical bodies in spacetime described by them. These bodies. while we call them physical, are actually phenomenal. They move in spacetime only according to the pre-established harmony (PEH), The PEH is not entirely deterministic. Higher order living entities move in various degrees purposefully, by what Aristotle called "final causation". Life is a property of all of the universe of particles, where by life we mean autonomous intelligence, freely able to make its own selections at least according to the PEH. This intelligence is that of Mind, and since Mind causes all and creates all, it is Mind out of which the Big Bang exploded. Time and space are phenomenal, not actual entities, but instead are simply the four dimensions of spacetime , x, y, z and t. These are mathematical or phenomenal variables, not real entities. At the same time, spacetime and the objects in it appear as real when experienced, either by perception or measurement. Thus Leibniz does not consider the everyday world as an illusion, you can still stub your toe in it and perform experiments. Leibniz thus calls this phenomenal world "well-founded". Closing We close by summarizing Plato-Leibniz's conception of the universe, which Bertrand Russell dismissed in passing as a fairy tale-- a vain remark, since Russell never proposed an alternate working model. Plato's universe is cybernetic (top-down), which makes it largely analytic, except for the fact that in the case of life, Aristotle's final causation (purposeful action ) is invoked. In contrast, Panpsychism seems, to this author at least, to be mob rule. There is also Whitehead's metaphysics, but I prefer the computer-like rationality of Plato-Leibniz. So, to summarize Plato-Leibniz's universe: 1. The universe is governed on the large scale mentally and necessarily (if we are to avoid conflict) by a single monarch (the One). This creates all, perceives all, and causes all action mentally, not physically, through Plato's cybernetic, top-down administration. 2. Here space and time only exist as spacetime, which is an artifact (like a map) created locally by the presence of mass in particles or bodies. Spacetime is not a reality, it is simply the mathematical path as curved by the mass. 3. On the small scale, the rules of Leibniz's Monadology come into effect. The universe is made up completely of physical matter in the form of distinct and completely independent bodies moving in spacetime according to the PEH , which is the practical form of the One's control. 4. Each particle or physical body has two simultaneous versions: in spacetime the body is a conventional physical body but it also has a mental mirror version in mental space called a monad. Monads are simply the quantum or mental forms of the particles. 5. Thus we have the One, which controls the Many (the particles or physical bodies with corresponding simultaneous mental monads 6. The particles are behaviorally characterized through through three indexes of force- spin, charge and mass. Charge is a single pole of electromagnetic force. 7. Mass and spin are mechanical , with mass corresponding to linear momentum and spin corresponding to angular momentum of the particle about an axis. Thus each particle is moved either by charge or by momentum. 8. This PEH is simply a top-down cybernetic (mathematical) structure based at the lowest level largely on Einstein's relativity theories, as well as other deterministic theories such as electromagnetic theory, and the broader, nonlocal (entangled) and less deterministic theories of statistical mechanics and thermodynamics. Physics has yet to recognize the nonlocal character of thermodynamics, especially evident in its conservation laws. -- Dr. Roger B Clough NIST (retired, 2000). See my Leibniz site: rclough@verizon.academia.edu/RogerClough For personal messages use rclough@verizon.net