It seems that question about two cultures raises some interest. Many years ago (probably about 30 years) I attempted to do something on that, but it didn't come. About two years ago I attempted to revitalize the idea and made some sketch. I did'n finish it and most probably will not finish it ever. Here it is.

BEAUTY AND SCIENTIFIC TRUTH

Boris Zakharov

Abstract. The article analyzes the origin of the process of evaluation of the truthfulness of the theory of the natural sciences. The practice or experimental evaluation cannot satisfy fundamental science. This dissatisfaction originates from: 1) eternal incompleteness of human practice; 2) impossibility of experimental evaluation in some natural sciences; and 3) significantly faster advancing of the science theory compare with it practical application. Author believes that the internal reason for research inquiry and falsification of scientific theory lies in the realm of the scientific aesthetic and the beauty is a fundamental criterion of the truthfulness of the scientific theory.

Key words: beauty, truth, harmony, organization.

            The truthfulness of scientific knowledge is a crucial question for the philosophy of science. It is not a surprise that this question was interesting for all generations of scientists from ancient time till present days. This question becomes especially important during the turning points of the scientific development. Very often one hears that the practice is a criterion of the truthfulness of our knowledge. However, there are a set of considerations that put this point of view in a doubt. On one hand, it depends on the incompleteness of our knowledge and our practice. On the other hand, it is connected with anticipation of a faster growth of the theoretical knowledge in comparison with the practical usage. Thirdly, there is a very particular scientific aesthetic, which dictates scientists the direction of the study and the most preferable way of the presenting results of the study. Finally, the statement that the practice is a criterion of the truthfulness of the scientific theory contains a tautology. According this view, the scientific knowledge is growing through the practice and may be falsified (or verified) also only through its practical application. This “vicious circle” cannot generate positive knowledge, because it does not give us a chance of testing the truthfulness of the scientific theory. To break out this circle, the positive scientific knowledge has to: 1) have the origin other than practice; or 2) be tested by other means then practice.

            Human practice is and always will be incomplete. It cannot embrace the whole totality of Universe, and, because of that, our knowledge cannot attain the whole truth. Moreover, this incompleteness presupposes that forever unfinished knowledge may give rise to many (at least one alternative) different scientific theories. The fundamental science is characterized by a rapid anticipation of the development of the theory compare with its experimental proof and practical application. In some scientific disciplines, such as astrophysics, for example, the most general and fundamental theories cannot be proved experimentally at all. Nevertheless, these theories are accepted by the scientific society and they have their supporters and developers.

            Thus, the practical criterion of scientific truth if it is not false, at least has serious restrictions in an application. Tarski made a conclusion, presented in a logical theorem: The universal criterion of the scientific truth does not exist (Traski, 1933; 1944; 1969). However, as was noted by Popper, the absence of the criterion of the truth does not convert the idea of truth into nonsense, like the absence of the criterion of the health does not make the health a senseless idea (Popper, 1963). Beside other limits, the usage of practical criterion of the scientific truth demonstrates a very negative tendency by reduces scientific study to exclusively empirical collecting of data without aspiration toward theoretical thought. The idea of the principal ability of the mankind to understand the world contains an inevitable recognition of its organization. Only organized world can be studied. Kant put it in statement: The world is not chaos, but it is cosmos (Kant, 1838). This presupposes that the law of harmony is really embedded in a diversity of real material objects and they may play a role of an explicit principle of the scientific enquiry.

            The idea of beauty, as other universal concepts, is not arbitrary. It reflects some fundamental principles of the organization of the world. The law of harmony discovered by Pythagoras, the color contrast, etc. are reflection of some eternal true relations of the real world. The intuition of this lawful organization and the feeling of the “internal beauty” creates a comfort or discomfort that scientist takes into consideration, when one deals with this or that scientific theory. That is why we can hear such words as: “this is a very beautiful (elegant, gracious, etc.) idea”, or “this theory looks awkward”.  

            The beauty has many definitions, most of which stem from ancient times. Other definitions appear recently. The definition of beauty that is ascribed to Plato and Pythagoras who identify the beauty as a strong coordinated harmony of all parts united by the whole entity (Xenophon, 1994). The other way to define this concept is of Socrates and Aristotle lineage: “Everything is good and beautiful in relation to that for which it best fit” (Xenophon, 1994). The philosophy of enlightenment continues this tradition. Diderot wrote that the perception of relation is a foundation of beauty (Diderot, 1995). One ramification of the definition of the beauty that originated from the Plato’s tradition states that beauty is a reflection of the eternal divine entity, which emerges through the material world. The fundamental characteristics of the divine entity are unity, absoluteness, internal harmony presented in proportion and accordance, clearance and simplicity (Plotinus, 2003).

            A great diversity of publications on beauty gives many other definitions. For us, the most important that most of them in one or another form contain some common characteristics of the beauty, such as:

1. Truth
2. Harmony
3. Unity
4. Proportions
5. Simplicity
6. Purposefulness
7. Value

The aim of science is a study of the relations between phenomena.  Heisenberg formulated it in this way: “…understanding never is something else but the realization of the existence of connections, i.e. uniting properties…” (Heisenberg, 1971). Only “beautiful” and “harmonious” theoretical constructs can motivate scientists on a new study. The feeling of the beauty of the world is the driving force of scientific study, inspiring thinkers of the past as well as scientists of the present time.

The feeling of the beauty of the world and the truthfulness of the theory that explains its organization is the internal measure with which we evaluate every theory or hypothesis. Only “beautiful” and “harmonious” theoretical generalizations are able to stimulate a new study. The feeling of the beauty of the world is a driving force of research that inspires the thinkers of the old time and modern scientists. If we are stay on the position of the principal understandability of the world, than we have to agree about the lawful organization of this world. The world is organized systematically and this presupposes that the principles of the harmony are embedded in the total diversity of natural entities (Lubischew, 1977).

Harmony, wholeness and accordance are ideas, which essentially can be expressed in the formal language of the mathematics. Mathematics describes phenomena in their relations through ratio and magnitude. Thus, mathematical description reflects harmony of the world; and that is why the Mathematical Aesthetic plays such important role in this science. Rephrasing the Latin proverb, we can say: “Initium scentia est admiratio”.

Our understanding of beautiful is contemporary. It is in a continuous process of development. Thus, the criterion of the truthfulness of the scientific knowledge is also in a constant evolutionary process. This development of the concept of beauty represents relativity of our knowledge and its inheritance. Thus, the feeling of beauty of the world and harmony of the theory that explains its construction is that internal measure according to which every hypothesis or theory is evaluated as truthful. The falsification of the scientific theory, from this point of view, consists of the search of the disharmony among its parts and the whole, and violation of the wholeness of the theory.

            This criterion is much broader than the criterion of the practice and opens new opportunities for the thinking mind. One can evaluate the most abstract and difficult for experimental examination theories. As far as the understanding of beauty has a transitional character and is in a constant process of development, our understanding of the truth changes in time too. In this development of the idea of beauty consists relative to our knowledge and its heritage through the history of humanity. It is necessary to note that usage of this criterion of the truth changes the fundamental direction of scientific inquiry. On the other hand, specialists on Aesthetics knew that despite the relative, transient nature of the idea of harmony, there always remains something unchangeable in its core. This suggests that criterion of harmony is not arbitrary. The science shifts its interests from the field of the creation of practically significant theories toward the search of the harmony of the world. It is that harmony which inspired the great thinkers such as Copernicus, Kepler, Newton, Einstein and others. In this case the meaning of the scientific inquiry is similar to the understanding of the world through the art. The difference between the art and science is only in the methods of inquiry. Arts study the world through individual, subjective intuition and are very personal; whereas, science tries to formalize man’s intuition and create objective picture of the world. Thus, different tools are developed. Art develops toward deeper unrolling of intuition. Science develops toward drawing most universal concepts. But both are doing that by means of symbolic description of the world.