"The book of the universe is written in mathematical language and its characters are triangles, circles and other geometric figures without whose mediation is humanly impossible to understand a word" (Galileo Galilei).
The existence of a particular relationship between physics and mathematics has universal recognition. Through the history of physics abound explicit testimony in this regard, starting with the famous statement of Galileo : "Philosophy is written in this immense book always open before our eyes (the universe), but it can not be understood unless we learn first to know the language and characters is written. It is written in mathematical language and its characters are triangles, circles and other geometric figures without whose mediation is humanly impossible to understand a word. "Three centuries later, astrophysicist Jeans wrote:" The Great Architect seems to be a mathematician. "Could be collected an anthology of quotations from this style. And every chapter of physics looks good example for such claims.
physics mathematics used successfully . Despite this statement, as it looks far from strict observation, is full of quotes, but summarizing an immediate view of the situation. But leads directly to inquire into the causes of that success. How can it be that mathematics, generally reputed as the study of pure abstractions, "work" in physics, regarded as the science of the concrete for excellence? Attest physicists themselves often naive or a surprise in terms of an awkward confession, that this adjustment presents a problem: "However, it is remarkable that none of the abstract constructions of mathematics performed, taking only to guide the need for logical perfection and generally increasing, there seems to remain useless for the physical. By a singular harmony, the needs of thought, concerned with building an adequate representation of reality, seem to have been foreseen and anticipated by logical analysis and abstract beauty of mathematics "( P. Langevin ). "The idea that mathematics could adapt somehow to the objects of our experience seemed extraordinary and exciting" (W. Heisenberg).
The mathematics is the language of physics . Galileo to the quoted text can be added two quotes: "All laws are drawn from the experience, but to enunciate it requires a special language, ordinary language is too poor, and is also too vague to express relations so delicate so rich and so precise. This is the reason that the physicist can not dispense with mathematics, they provide the only language they can speak "(H. Poincaré ). "The mathematics is, so to speak, the language through which can be raised and resolved a question" (W. Heisenberg). This conception of mathematics as the language of physics can, however, be interpreted in several ways, depending on whether you think that language like that of nature, and that the individual who studies should seek to assimilate, or that he conceived the reverse, as the language of individual , which must translate the facts of nature to make them understandable. The first position seems to be that of Galileo, Einstein also: "According to our experience so far, we have the right to be convinced that nature is the realization of the ideal of mathematical simplicity. Purely mathematical construction enables us to find those concepts, and principles that relate to, that give us key to understanding natural phenomena. "The second view is that of Heisenberg:" The mathematical formulas and do not represent nature, but the knowledge that we possess it. " However, both attitudes, far from being opposed, are but the extremes of a continuum, and what it is to find a balance within a structure that relies on pairs of opposite notions nature -man, experience, theory, concrete-abstract, scientific fact, scientific laws.
To the great mathematician and physicist Roger Penrose , somehow, the mind seems to have "access" the world of ideas he was referring to Plato. Reviewing some of the assertions made in his book "The Emperor's New Mind": To what extent are "real" world of mathematical objects?. From one point of view it seems that there can be nothing real in them. Mathematical objects are just concepts, they are mental idealizations that mathematicians make, often stimulated by the apparent order of certain aspects of the world around us, but mental idealizations anyway. Can be more than mere arbitrary constructions of the human mind? At the same time it seems that there is a profound reality in these mathematical concepts beyond the mental musings of a particular mathematician. Instead, it's like mathematical thinking was being guided to some external truth-a truth that is reality itself and that only partially reveals one of us. To learn more: "Thinking Mathematics", directed Metatemas series. By Jorge Wagensberg Tusquets Editores. Are articles by various authors. The post refers to the article by JM Lévy-Leblond , professor at the University of Nice and great popularizer of mathematics.
On Penrose and mathematical Platonism: See link .
It seems like yesterday, but today a year ago my father died . DEP
