Natural sciences are associated with philosophy, and following different directions of philosophy, undoubtedly, is reflected in the works of scientists of any sciences. Philosophy divides the worldview of people into idealistic and materialistic. Materialists have always been in the minority, therefore, in the key areas of science, preserved from ancient times by scientific schools in the form of scholasticism, the ideas of learned idealists flourish. It is usually believed that scholasticism, that is, a system of logical arguments invented by the authors of various fantastic ideas, in order, in their opinion, to reconcile them with reality, had an impact on science only during the Middle Ages. This is not true. In reality, scholasticism is and will always be in science, because science is, first of all, a school for transmitting the views of predecessors to their successors, and secondly, an area of accumulating real knowledge. In science at all times there have been many different schools of followers of any fantastic ideas, only according to the ideas of their adherents, connected with reality. Insofar as the ideas were fantastic, representatives of different schools saw the unreality of the ideas of their opponents, while not seeing the fantasticness of their own ideas. Therefore, scientists representing different schools, that is, different fantastic ideas, were usually at odds. Jonathan Swift, in a satirical form accessible even to limited people, showed the model of the struggle of scientific schools, as a struggle between pointed and blunt scientists, arguing about how to break an egg correctly, from the blunt or sharp end.
In our time, points and blunt points in physics are represented by relativists and aetherists. This division of the originally unified school arose in the process of transformation of physics into an appendage of mathematics.
The idea of the microcosm as the world of the smallest particles of any of the available substances, preserving their composition and properties, was philosophically clear already in ancient times, but in reality the atomic structure of the world was revealed in the process of creating Mendeleev’s periodic table of elements. An approximate idea of the structure of the atom and the particles of the substance of its constituents were revealed in the works of Thomson, Rutherford, Planck. But, the lack of observations of the interaction of objects of this level of the structure of matter, the great difficulty of understanding the processes occurring at this level of the structure of matter, led to the fact that purely physical experiments began to be more and more evaluated with the help of mathematics, which led to the dominance in physics of mathematicians who positioned themselves as physicists. theorists.
It was arbitrary mathematical theories that had nothing to do with reality that allowed theoretical physicists to build very different, but always only fantastic, models of the world that did not reflect the real world in any way.
The dominance in physics of theorists-mathematicians and state funding of this science, like all other sciences, gave rise to numerous falsifications of the data that were nevertheless obtained in experiments. The falsifications were done to fit data into fictional theories in which theorists were so confident that they had no doubt that experiments were only meant to confirm them. The obvious and proven lack of confirmation of theories by experiments was interpreted as a paradox on the part of nature, and not an incorrectness of the theory.
Since the days of Ancient Greece, two approaches to mathematics have been known. Some believe that mathematics is an independent science, not directly related to any other sciences, others believe that mathematics is part of physics. That is, someone believes that mathematical objects exist in some abstract world, and not in real life, and someone believes that mathematical objects reflect the properties of the real world. These two options, in the formulation of well-known mathematicians, look like this: Mathematical calculations relate to the real world, where they are either true or false, even if they cannot be mathematically proven or disproved. (Kurt Gödel. A well-known mathematician of the beginning of the 20th century.) – Mathematical theories are simply fictional formulas linking the axioms taken into service by this mathematician, and not at all a model of the external world. (Paul Cohen. Famous 20th century mathematician.)
Few scholars understand that Mathematical Analysis is just formal rules for transforming one letter and number symbols into others. All the secrets of mathematics are hidden in the coding by mathematicians of the initial data about physical objects into numbers. This coding may or may not be adequate to nature. And this, in turn, depends on the philosophical position, materialistic or idealistic interpreter. Further transformations of the data about the object encoded in mathematical language do not bring new information about it. All information obtained in transformations is equal to the original one. Mathematics is simply a “chain of tautologies”. If the mathematical expression of the thought about a certain physical reality really corresponds to it, then it turns out to be similar to the expression of the thought about the same physical reality, formulated not by mathematical means.
tvami, that is, expressed in ordinary language. In fact, there are two mathematicians – theoretical, which is only of humanitarian interest and applied, which is part of many sciences. Few people understood mathematics at all times, and the creators of new directions in it were rare mathematical geniuses, such as Pythagoras and Archimedes, such geniuses of modern mathematics include, first of all, I. Newton, J. D’Alembert, J. Lagrange, L. Euler, P. Laplace, J. Fourier, C. Gauss, E. Galois, G. V. Leibniz, L. Euler, P. Ferm, D. Boole, B. Riemann, M. V. Ostrogradskiy G. F. L. Frege, G. Cantor, D. Peano, E. F. F. Cermelo, B. Russell, A. N. Whitehead, A. Poincare, D. Gilbert, P. I. Bernays, A. N. Kolmogorov , G. Perelman.
In the 19th century, mathematicians tried to build a unified system for constructing mathematical theories on the basis of Cantor’s intuitive theory of sets. But contradictions or, in other words, paradoxes were found in it. (For example, Russell’s paradox.) After revealing the contradictions of Cantor’s intuitive set theory, theories of other mathematicians appeared, called the theories of logicism, intuitionism and formalism.
Logicism arose at the end of the 19th century in connection with the construction of mathematical logic. Its founders, G. Frege and B. Russell, hoped to “derive” all mathematics from logic, but failed. D. Hilbert said: “Mathematics, like any other science, cannot be based only on logic; on the contrary, as a precondition for applying logical inferences and activating logical operations, we must already be given something in our representation, namely – certain extra-logical concrete objects that exist visually, as direct experiences before any kind of thinking. ” However, variants of logicism continue to exist.
Intuitionism at the beginning of the 20th century was formulated by L. Brauer and A. Geyting, who tried to give mathematics “real meaning”. However, their concepts and theorems turned out to be more complicated than their classical counterparts, and the hope for the obvious consistency of constructive mathematics was not justified, and intuitionism followed the path of formalism.
Formalism (or the formal direction in mathematics) is the development of the ancient idea of the complete axiomatization of mathematics, in a modernized form set out in the “Hilbert program”. Despite the fact that Hilbert’s program was refuted by Gödel, it actually became the leading one in mathematics of the 20th century. Hilbert was an apologist for the legitimacy of any mathematical theory, for which its consistency was proved, despite the possibility of correlating it with what exists in nature, and it was this point of view that triumphed. Mathematicians with such attitudes simply do not need to pay attention to the real world.
Theoretical physicists, in fact, formalist mathematicians, having displaced physicists from physics, in fact, have replaced physics with mathematics. They, in their theories, kind of turned real particles of the microcosm and objects of the macrocosm into mathematical formulas and signs. The tale of the famous mathematician Lewis Caroll “Alice in Wonderland” can serve as a vivid and understandable even for limited people illustration of how plausibly mathematical theories reflect the real world. No less like a fairy tale, for example, Heisenberg’s statement that there are no trajectories of particle motion in the microcosm, and the particles themselves cannot be localized in accordance with the uncertainty principle. Heisenberg admired the Pythagorean-Platonic “magic” of numbers, which underlies the pseudo-physics created by mathematicians. He wrote: “In modern quantum theory, there can hardly be any doubt that elementary particles, in the final analysis, are mathematical forms, only of a much more complex and abstract nature. Mathematical symmetry, which plays a central role in the regular bodies of Platonic philosophy, forms the core equations. An equation is only a mathematical representation of the whole series of symmetry properties, which, of course, are not as clear as the ideal Platonic solids. “