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History of Science

The main causes of the emergence of science and the motivations for its development were human curiosity and the need for solutions to concrete problems. It is possible to identify three directions in the history of the development of science: philosophical, mathematical and experimental.

According to F. Rosenberger (F. Rosenberger, History of Physics in antiquity and the Middle Ages. Part 1, ONTI, Moscow, 1934, Leningrad, p. 8 and 10): "Ancient science was primarily a philosophical science. The most striking figure of ancient science is Aristotle... By limiting the circle of his universe, Aristotle was able to move in that circle completely confidently and categorically. His system clearly demonstrated his conviction that it already contained everything necessary for the resolution of theoretical issues... The categories of 'matter,' 'form' and 'movement' in Aristotle's doctrine of nature immediately exclude any possibility of a quantitative mathematical treatment... it should be emphasized that Aristotle achieved ​​the unity of his worldview and, in particular, of his physics, using tools extreme anthropomorphism tools and the most naive teleology. However, it is precisely these distinct manifestations of Aristotle's reluctance to break with the tradition of his naive sense-based worldview that should have made his speculations successful."

"Aristotelian physics also typically tended towards purely qualitative thinking. All the numerous attempts in the late Middle Ages to use Aristotelianism as a basis for quantitative theories of nature were completely fruitless". 


The religious approach was superseded by the philosophical approach, which was refined at the expense of the success of Aristotle's philosophy. In the religious approach to science, it had been postulated that the structure of the world was reported to humanity by God, through the prophets (Daniel, Elijah, Isaiah, Mohammed, Moses, etc.), and described in the Bible. Any doubts and even clarifications offered by people interested in science were considered heresy and were rejected, and the authors of these heresies were persecuted for dissent. The role of prophets in the philosophical approach was performed by Aristotle and Descartes. In works on the history of science, declarations (experimentally unconfirmed assertions) are described as genius prophecies which deservedly left a mark in science.

A widely known statment attributed to a number of authers describes the primary idea of the next direction in the development of science: "There is as much science in science as there is mathematics in science." This idea began 3000 years ago, at the time of Pythagoras, who proclaimed -"mathematics is the gate to science." Isaac Newton is the symbol of that era. Four Newtonian laws, as well as the axioms of Euclid, enable us to derive a vast number of other patterns.

We agree with Rosenberger: "...the strength of mathematical physics is the logical completeness and necessity of its conclusions. Adopting certain initial provisions, the mathematical physicist operates using mathematical means. All his conclusions eventually represent an expanded expression of the content of these provisions. However, mathematical reasoning is as unable to create physics as is philosophical speculation. The reasons for this lie in specific features attributable to mathematical reasoning. Like philosophical physics, it must borrow its material from outside, from observations that have already been made. In other words, the same trait of passivity in regard to material is typical for mathematical physics that is peculiar to philosophical physics, which supposes certain limits to its development. Moreover, by asking only the question "how big?" mathematical physics essentially does nothing to uncover the qualitative mechanism of the investigated phenomena and is limited only by their quantitative description."

According to Rosenberger, the strength of the next direction, experimental physics, "should be a constant enrichment of science with new material. The activity of the mind questioning nature is concentrated expressly in the experiment. However, to correctly ask a question of nature, it is necessary to start from some common presuppositions and criteria. In order to judge the accuracy of hypotheses based on these criteria correctly, it is necessary to use mathematical constructions to carry out constant quantitative validation of the results, which are in turn experimentally tested. In other words, without the apparatuses of philosophical and mathematical physics, experimental physics is blind. To a great degree, experimental physics can be reduced to a technique of scientific work, and the question is where to use this technique. Philosophical and mathematical physics plays a decisive role in answering this question".  


Rosenberger summarizes his views on the relationship of three kinds of physical knowledge: "Human nature in general is characterized by a tendency to try to explain in one single effort everything that is mysterious in nature, not content with methods that move forward by slow, deliberate and strictly checked steps. Moreover, the farther people are from their essential goals, the more natural it is for them to see the experimental way as hopeless and to look for help in pure speculation. However, beware of unfair treatment of the merits of philosophy and mathematics to physics and excessive re-evaluation of the experimental method. Unfortunately, there have been instances of this re-evaluation in the past as well. The art of conducting experiments is completely incapable of advancing science alone. Speculation that looks beyond the current state of experience will always indicate the way of and dictate a plan for further observation. On the other hand, science dealing with the phenomena of nature will always be dependent on mathematics when investigating phenomena quantitatively".

According to Rosenberger and most of the famous philosophers, both ancient and modern, experimenters are the people who are good at conducting delicate experiments but are not able to work with their heads. The phrase "practice without theory is blind" has become a trite slogan. The belief that tasks are given to experimenters by mathematicians has become fully natural to mathematicians and philosophers and has even taken root among many experimenters. Of course, all three approaches existed in science simultaneously. However, there were periods when mathematicians and philosophers defined fashion in science. A comparison of these periods with periods of science and the works of well-known scientists-experimenters in this period leads to the conclusion that the real qualitative development of science is determined by a very small number of scientists-experimenters working in this period.

Milestone works in physics like the experimental works of Galileo, Newton and Faraday and discoveries of new phenomena, regularities and rules, look for answers to the following question and, therefore, the clarification of the cause-effect relationship - the determination of the physical nature of phenomena. A mathematical approach, as opposed to the previous approach, assumes the composition of a mathematical equation that describes the experimental data. The result is usually reached by a solution of the inverse problem. Although we searched thruogh physics taxtbooks and scientific publications, we did not find a single case where the matimatical approac to  solving scientific problema was not also a solution to the inverse problem, or in other words, was not a fittig (may be reader will tell us otherwise). Frequently, in the process of inverse solution the most basic and simple rules are violated: qualitative assumptions are adopted that have no independent experimental evidence. In the equations compiled on this pseudoscientific basis, coefficients are entered which have numerical values ​​ determined on the basis of experimental data.

In the 20th century, physics has developed under the slogan "the best way to create a new theory is to guess at equations, paying no attention to physical models or physical explanations" (R. Feynman, Nobel Lecture, 1965). Many laws of K. Maxwell, Drak, Schrodinger, Born, Planck, Louis de Broglie, Einstein and other scientists are described as postulates without mechanisms, and without a clarification of the cause-effect relationships. A striking example of the mathematical approach is the Heisenberg uncertainty principle, which establishes the complete absence of cause-effect relationships (at least in the microcosm). What is most striking is that this principle was recognized by the scientific community of the representative and well-known Copenhagen Congress by vote and not in the course of scholarly dispute. The apotheosis of the generally accepted conception is quantum mechanics and general and special relativity theory (GRT and SRT).

We have already discussed the current arrangement of accents in science in more detail with the example of quantum mechanics and quantum chemistry (see Gankin V.Y., Gankin Y.V. "How Chemical Bonds Form and Chemical Reactions Proceed"). In this article, we want to emphasize that the mathematical approach in execution, as it has been applied in physics and chemistry till the XXI century, has not only contributed to the development of science but also, at times, effectively inhibited its development. This approach removed from the agenda the main driving forces of science, looking instead for the answer to more "why" questions.

Questions and hypotheses about the physical meaning of phenomena led to the confirmation and development of a variety of dead-end paths, which distracted scientists. For example, within the framework of the theory of relativity, cause-and-effect relationships and the mechanism of phenomena ceased to be invariant, i.e. independent of the coordinates and dimension of space. Chance turned from unclear (inconceivable) regularity into the basis of the uncertainty principle of quantum mechanics. A scholarly dispute based on the question "Does God play dice?" lasted 40 years, between the Aristotles of the 20th century, Einstein and Bohr. Einstein believed that "chance is the misunderstood principle." Bohr claimed that the uncertainty principle is the ultimate truth. The bases for this statement were the results of the Copenhagen conference - the first and so far, thank God, only case of the resolution of scientific questions by vote.

The mathematical and philosophical approaches were competitors in the process of slowing down the development of science.

In the late 1980s, at the start of our activity, we agreed with the abovementioned statements. Our respect and admiration of each of the three approaches in science and of the scientists who personify them was close to the religious and proportional to the degree of our misunderstanding of their works. Primarily, it concerned mathematical physics and physical chemistry. Over 30 years of work, we proved that all three directions did not complement each other but, as a rule, were in contradiction with each other, like the swan, crawfish and pike in the well-known fable by Krylov, and each approach exaggerated its significance and incorrectly evaluated the two other directions.

"The ancient Greeks, whose scientific thought anticipated many future discoveries, turned their attention to the nature of the universe and the structure of its constituent materials. Greek scholars, or "philosophers" (lovers of wisdom), were not interested in ways of procuring particular substances or methods of their application. They were interested primarily in the essence of substances and processes. They searched for an answer to the question "why?" In other words, the ancient Greeks first began to practice what is now called chemical theory" A. Azimov.


We were going to solve our chemical problems by asking the question "why?" to ascertain the mechanisms and cause-effect relations between phenomena. The concrete illustration of this conclusion is the model of the  hydrogen molecule that appears on the website of the Institute of Theoretical Chemistry. The correspondence of the calculated and experimentally determined values ​​of the energy and bond length of the hydrogen molecule leads to a number of consequences related to physics and physical chemistry. One of these consequences, deriving from our theory of chemical bonding and chemical structure, is the explanation of the lack of radiation of a single electron moving with acceleration and of the theory of electromagnetic nature of the mass.

In all known cases of the mathematical approach, the model forming the basis of the approach was lagging behind the achievement of the natural sciences. Maxwell's equations were based on a mechanical model, which included rotating gear wheels. All electrical laws (Faraday's, Ohm's, Ampere's, etc.) are based on the assumption that the electrons in metals are free and not connected with nuclei. At the same time, after the experiments of Rutherford, it got out that, in order to tear off an electron from an atom, it is necessary to expend energy more than 4 eV, and the electric current emerging in case of voltages less than 0.001 eV. It is interesting that physics textbooks began to question the existence of free electrons during the period of euphoria towards quantum mechanics. However, until now, guides on physics and chemistry state that one of the main achievements of quantum mechanics is the explanation of the electrons are free in metals. In 2000, we showed in our work "How Chemical Bonds Form and Chemical Reactions Proceed" that the quantum-mechanical explanation turned out to be incorrect.

According to I. Misjuchenko ("The last mystery of God"), in the mathematical approach, the values of coefficients are determined based on the experiment. The number of coefficients in the equations is always greater than the number of equations. This means that the experimental data must be fitted to the theoretical calculations.

"Physical laws should have mathematical beauty" is the inscription on the board of Moscow University, left by Dirac in the autumn of 1955. This scientific view of the world is not new; it dates back to ancient times, to the Pythagorean school, and after painful search it was rejected as untenable.

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