The existence of a particular relation between the physicist and the mathematics enjoy a public acknowledgement. Across the history of the physics the explicit testimonies abound in this sense, beginning for the famous affirmation of Galilean: "The philosophy is written in this immense book always opened before our eyes (the Universe), but it is not possible to comprise it if one does not learn to know firstly the language and the characters in which it is written. It is written in mathematical language and his characters are triangles, circles and other geometric figures without whose mediation is a neither humanly impossible comprehension nor a word.” Three centuries later, the astrophysicist Jeans wrote: "The Big Architect seems to be mathematical.” There might be compiled a real anthology of appointments of this style. And any chapter of the physics seems good like example for such affirmations.
The physics uses successfully the mathematics. Nevertheless this statement, far from being as it feigns a strict observation, is loaded with budgets, although he sums up an immediate vision of the situation. But he leads to wondering straight for the causes of this success. How can it be that the mathematics reputed in general like study of pure abstractions, "work" in physical, considered like the science of the concrete thing excellent? The proper physicists give faith often, with an ingenuous surprise or in terms of an uncomfortable confession, of which this adequacy raises a problem:“ Nevertheless, it is notable that none of the abstract constructions that the mathematics realizes, taking exclusively as a guide his need for logical perfection and for increasing generality, seems that it has to remain without utility for the physicist. For a singular harmony, the needs for the thought, worried for constructing a suitable representation of the reality, seem to have been foreseen and anticipated by the logical analysis and the abstract esthetics of the mathematician” (P. Langevin). “The idea of that the mathematics could adapt, somehow, to the objects of our experience seemed extraordinary and exciting to me” (W. Heisenberg).
The mathematics constitute the language of the physics. Of Galilean two appointments can be added to him to the said text: "All the laws are extracted from the experience, but to enunciate them one is necessary a special language; the ordinary language is too poor, and it is also too vague, to express so delicate, so rich and so precise relations. This is the reason for which the physicist cannot do without the mathematics; these provide to him the only language in which he can speak” (H. Poincaré). “The mathematics constitute, for saying it this way, the language by means of which it can appear and a question be solved” (W. Heisenberg). This conception of the mathematics as language of the physics can, nevertheless, be interpreted of several ways, according to which the above mentioned language should be thought like that of the nature, and which the individual who studies it will have to strengthen for assimilating; or that conceives him on the contrary, how the language of the individual, to which the facts of the nature will have to be translated so that they turn out to be understandable. The first position seems to be of Galilean, also it is that of Einstein: "In accordance with our experience until now, we have right to be sure that the nature is the achievement of the ideal of the mathematical simplicity. The construction purely mathematical allows us to find these concepts, and the beginning that relate them, that give us the key to understand the natural phenomena.” The second point of view is that of Heisenberg:“ The mathematical formulae already do not represent the nature, but the knowledge that of her we possess”. Nevertheless, both attitudes, far from being opposed, are not but the extreme points of a continuous bogey, and of what it is a question it is of scientists - laws find a breakeven inside a structure that supports on the pairs of opposite notions nature - man, experience - theory, concrete - abstract, done scientific.
For the big physicist - mathematician Roger Penrose, in certain form, the mind seems to have “access“ to the world of the ideas to which Platón was referring. Revising some of the affirmations that does in his book “The new mind of the emperor”: Until point are "real" the objects of the world of the mathematician?. From a certain point of view it seems that there can be nothing real in them. The mathematical objects are only concepts; there are mental idealizations that there do the mathematicians often stimulated by the apparent order of certain aspects of the world that surrounds us, but mental idealizations in any case. Can there be anything more than mere arbitrary constructions of the human mind? At the same time it seems that some deep reality exists in these mathematical concepts that goes beyond the mental lucubrations of a particular mathematician. Instead of it, it is as if the mathematical thought was being guided towards some exterior truth — a truth that it has reality as itself and that only we are revealed partially to some of us. To be able: "To think more the mathematics”, of the series Metabe afraid directed. For Jorge Wagensberg de Tusquets Editores. There are articles of several authors. The post alludes to the article of J.M Lévy-Leblond, teacher of the University of Nice and big popularizer of the mathematics.
On Penrose and the mathematical Platonism: To see linkage.
It seems that it was yesterday, but today it has been one year since my father died. D.E.P.
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