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The unreasonable effectiveness of mathematics (I)


In 1959, in his "Richard Courant Lecture in Mathematical Sciences" at New York University, Eugene Wigner made this expression famous.

He noted that mathematical concepts unexpectedly offer a very accurate description of a phenomenon. Wigner said that since we do not know why mathematics is unexpectedly useful, we are not able to say with certainty whether a theory, which we consider to be true, is uniquely appropriate to the phenomenon or not.

For Wigner, and for all of us others, the usefulness of mathematics can be a great mystery and have no rational explanation.

The mathematician of the individual's game of life (MJVI) has, with this fascinating question, an opportunity to test his minimalist strategy (“Seeing Believe I, II, III”, Earlier Columns) of the logical impossibility of creation, verifying whether it is possible. imagine a way around the controversy surrounding Wigner's phrase.

The plan is simple. To examine some thoughts and visions about the famous expression and to show that they are imbued with the ancient and ingrained belief that “there are things” and they populate the “natural world” which, in turn, is also a “thing,” all of which are observed by “Thinking thing” or “rex cogitans” as Descartes proposed. As, by the axiom of the impossibility of creation, "things do not exist", because they would have to be "created", and this process would be a return ad infinitumThen the MJVI instantly glimpses the reasons for the controversy as it becomes clear that these are but disputes over the power to possess the true description of the "things of the world."

Pythagoras bequeathed us the idea that "number is the language of the universe," Galileo proposed the idea that "the laws of nature are written in mathematical language," and Newton, Einstein, and many others magnified them magnificently. Wigner joined the chorus and noted that only a few mathematical concepts are used in the formulation of the laws of nature and are not chosen arbitrarily.

Nature, Laws of Nature, Universe, and number are irrefutable evidence that self-consciousness, even after thousands of years of experience, remains convinced that the beings of its imagination have "unquestionable automatic existence."

It should be remembered at this point that for the MJVI Being is not confused with Existing, and that the greatest unfathomable mystery is a plausible impulse that vibrates the "NOTHING" allowing the Being to appear to manifest.

To the self-conscious convinced of the existence of the natural world, one element of the great mystery of mathematical effectiveness is the fact that the physicist finds a mathematical concept, which best describes a phenomenon, and finds that the mathematician had already developed it independently.

For example, complex numbers and functions and their role in the formulation of complex Hilbert space, so essential in quantum mechanics.

The MJVI notes here that while Newton found his teacher Isaac Barrow's calculus and the Cartesian plane curves prepared by Fermat and Descartes, on the other hand he put motion in the points (x, y) and endowed them with fluxions, or infinitesimal movables, eventually finding that every reasonable curve in some sense had instantaneous velocity and thus opened a huge avenue for mathematical exploration which was called “Differential and Integral Calculus” which, in turn, He served Laplace to describe the sky of stars and planets in his Celestial Mechanics, encouraging himself to declare that Napoleon did not need the hypothesis of a "creator."

For the MJVI, the importance that mathematics and physics have for each other is indisputable. Therefore, the physicist finds the mathematical concept ready as the mathematician evolves and draws inspiration from the physical imagination, and sees some of its difficult problems solved by theoretical physicists. Mathematicians awarded Edward Witten his top medal (Fields medal) for his astonishing physical imaginations solving difficult problems, almost impossible until then, from the exclusively mathematical point of view, of algebraic geometry, the eye girl of a large number of important mathematicians. .

These are not objects of the natural world determining mathematical objects, nor the other way around. Rather, for MJVI, imaginations are inspired by each other, remembering the behavior of those cylindrical cell grains in documentaries on electron microscopes, beating against each other, as if to merge into a larger structure. .

For MJVI, living matter follows a Pleasure Principle seeking to structure itself into larger and more complex information systems, especially the most pleasurable ones. Physical and mathematical imaginations fulfill their archetypal tradition, which, in turn, goes back to the greater mystery of the instability of "NADA" slipping into appearances of Being. Thus, for the MJVI, there are no surprises of the effectiveness of "mathematical things over physical things." . There is only the continuity of the greater mystery, and of the lesser mysteries, as the evolution of living matter motivated by the pleasure of the transformation of energy into imagination and the pursuit of the fulfillment of the greatest of desires, precisely that of existing.

Wigner argued that mathematical concepts are not accidentally useful but are necessary because they constitute the correct language of nature. However, he also pointed out that false theories, such as Bohr's first atom model, Ptolemy's epicycles, and free electron theory, as well as some held to be true (for example, quantum electrodynamics) yield surprisingly accurate results.

In the MJVI's view, if there were a way to distinguish between false and true theories that would be preserved forever, then there would be "created" here a "real-world thing." So there is no surprise, though not a trivial imagination, with the impossibility of distinguishing between true and false theories.

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