Roger Penrose (Colchester, August 8th 1931 -) is a physicist and British Mathématicien .

He teaches the Mathématiques with the Birkbeck College of London where he works out the theory describing the collapse of stars on themselves (“  Death off stars  ”), between 1964 and 1973, where it meets celebrates it physicist Stephen Hawking. They work then with a theory of the origin of the universe, Penrose contributing there its mathematical share to the general Theory of relativity applied to the Cosmologie and the study of the black holes.

In 1974, it publishes an article where it presents its first nonperiodic pavings: the pavings of Penrose ( Pentaplexity , Bulletin off the Institute for Mathematics and its Applications, 10,266-271, 1974). One owes him some impossible objects, the such Escalier of Penrose and the Triangle of Penrose.

Career

Graduate with mention in mathematics of the University College of London, Penrose redécouvre in 1955 - whereas it was always student - a generalization of the concept of matrix opposite (known also under the opposite term of of Moore-Penrose, or matrix pseudoinverse).

Penrose obtains its Ph.D. with Cambridge (College St John) in 1958, with a thesis on the tensorial methods in algebraic geometry under the direction of an algebrist and famous geometrician: John A. Todd. In 1965, in Cambridge, Penrose proves that gravitational singularities (as those in the center of the holes black) can be formed starting from the gravitational massive star collapse at the end of the lifetime. (Ferguson, 1991:66).

In 1967, Penrose invents the Théorie of the twisteurs which projects objects of the Espace of Minkowski in a complex space having a metric signature (2,2). In 1969, he conjectures the assumption of the cosmic Censure. This one affirms that the universe protects us from the violations of causality inherent in the gravitational singularities, by systematically masking them behind a horizon of the events. This assumption constitutes the weak principle of cosmic censure . Penrose will formulate in 1979 a called stronger version strong principle of cosmic censure . These assumptions (without forgetting the Conjecture BKL, and the non-linear problems of stability) constitute one of the current problems most important of the General relativity.

Penrose is known for its discovery into 1974 of the pavings of Penrose, which consist of 2 forms having the property to cover completely a plan in manner not-periodical. In 1984, similar arrangements were observed in the provision of the atoms of the quasicristaux.

In 1971, Penrose did others notable discoveries: the Réseaux of spin which were to later form the geometry of the space time in the theory of the quantum Gravitation to loops. It also popularized the use of diagrams representing the causal relations in space time: the diagrams of Penrose.

Honors

Roger Penrose received many honors rewarding his contributions to mathematics and physics.

Standpoint and ideas of Penrose

Penrose made always proof, in its various work and works, of a great originality of spirit and took positions discussed on physical and epistemological problems important.

Platonism and mathematical ontology of the laws of Physics

Penrose defends, in its principal works, a Platonic vision Mathematics and joined, on the bottom, the similar positions of Roland Omnès or Alain Connes. It expresses without ambiguity its point of view, for example in " the spirit, the computer and laws of physics " :

I imagine that each time the spirit perceives a mathematical idea, it contacts the Platonic world of the ideas When us " voyons" a mathematical idea, our conscience penetrates in this world of the ideas and contacts him directly.

In the same order of idea, Penrose expresses its belief in the heuristic power of mathematics to guide us on the way of the physical theories describing the world adequately. In particular, it proposes coherence, the beauty of the structures, and the mathematical fruitfulness of the complex numbers, to make of it an ontological base of the physical theories, and in particular of the Théorie of the twisteurs of which it is in the beginning.

Conscience and Physics

Consequently of its platonism, Penrose wonders about connections between the human conscience and the laws of physics, in two principal works the spirit, the computer and the laws of physics and the shades of the spirit.

It first of all tries to show that the computers (founded on the principle of the machines of Turing and the formal systems) are basically in the incapacity to model the intelligence and the conscience. Indeed, the computers are deterministic systems, having all the limitations of the formal systems, for example the insolvency of the Problème of the stop or the Théorème of incomplétude of Gödel. According to him, the spirit of an authentic mathematician is able to overcome these limitations, because it with the capacity to be extracted with the need for the formal system in which it reasons, whatever this one.

The comprehension even of the demonstration of the Theorem of incomplétude of Gödel, calling upon the Argument of the diagonal of Cantor, is according to him an illustration of this capacity. Because, just as to include/understand the Argument of the diagonal of Cantor requires " visualiser" a number which does not belong to the list infinite of the numbers of Cantor, to include/understand the demonstration of the theorem of Gödel also requires " visualiser" a truth (which one is " intimement" convinced that it is about a truth), which does not form part of the infinite list of the truths established by the formal system of Gödel used for its demonstration. This " visualization" require " extraire" formal system used by Gödel. This " extraction" could certainly be formalized in a computer, but not for all the possible formal systems. Whereas a mathematician in is able a priori, according to Penrose, in all the conceivable formal systems.

This demonstration caused the controversy and the criticism, to which Penrose attempted to answer point by point in the shades of the spirit. Despite everything, this point of view remains enough insulated in the scientific community.

Even if he refuses the possibility of an intelligence or a conscience for a Machine of Turing (and thus for a traditional computer), Penrose does not exclude the possibility of an artificial intelligence, which would be founded on quantum processes. Because according to him, they are quantum processes and in particular the process of Réduction of the package of wave (which cannot be modelled by a formal system, because - inter alia - basically indeterminist) which comes into play the phenomenon of the conscience.

To develop this last point, it develops its sights on the Problème of quantum measurement, and it proposes biological solutions making it possible phenomena of quantum superposition to take seat in the brain.

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