Let’s try to reconstruct the likely course of this process.

Let’s try to reconstruct the likely course of this process.

The completed universalism of myth absorbed the entire content of the spiritual sphere of human existence, leaving nothing in question. The myth held together and sanctified all forms of human activity. Due to the fact that all the economic and social activities of people received their highest explanation and highest sanction in the myth, it served as a kind of memory matrix on which knowledge useful for a person and human society was fixed. In particular, all technological innovations had to receive a mythological interpretation, had to be projected onto the plane of the mythological model of the world, becoming parts of its highest unity.

Of course, the mythologizing of technology has gradually diminished over time; becoming more complex, it gradually developed relatively independent ways of consolidating knowledge, the mythological coloring of which was rather a tribute to tradition. However, even if it separates itself from the myth, technology does not contradict it and does not conflict with it. Technological thinking turns out to be compatible with mythological thinking. This may seem strange at first: after all, technology demonstrates the effectiveness of its decisions, the myth only explains the essence of everything that happens, while appealing to higher, extra-experienced forces. However – and this is a fundamental aspect – both types of thinking are equally universal: just as there are no wrongly set tasks for technology, there are no unexplained questions for a myth. That is why technology is always able to find its justification in the myth (and many modern myths prove this superbly), while the myth is capable of assimilating any advances in technology. Consequently, technological progress, even moving away from its mythological basis, does not destroy it.

The universalism of technology and myth gives rise to many deeply similar features between them. Both types of thinking do not feel the need to think about their own nature, do not seek to look “from above” at the knowledge they generate. A technology for which all tasks are in principle similar to each other is interested only in obtaining the desired results; the myth, explaining everything, does not need its own justification and explanation. It was only important for the ancient master to know that a certain thing would come out from under his hands. The modern engineer will probably need information about the causes and the specific course of the technological process. But both of them, while performing their functions, may not think about the principles and boundaries of the technological activity itself. Likewise, a consciousness locked in a mythological worldview will not seek to go beyond the explanations contained in the myth. This is the essence of the myth that “from within” it is always seen as something absolute and final. To understand the impossibility of absolute explanations, it is necessary to go beyond the framework of not only a specific sum of mythological images (they just might still remain), but a mythological attitude to the world.

The example of Greek philosophy in this respect is very indicative: its mythological coloring persisted even when the basic structures of a fundamentally non-mythological worldview had already been found and assimilated. Another example illustrating the opposite situation may be the success of the film “Memories of the Future”, which has recently been shown on our screens, which offers a completely mythological, despite its ultra-modern decoration, scheme of the origin of the monuments of ancient earthly civilizations that have come down to us.

Now we need to dwell on one important feature of mythological thinking. The myth could not fail to reflect in itself the idea of ​​the interdependence of the phenomena of the surrounding world, which entered the consciousness of people very early. The realization that the course of events is not arbitrary, but obeys some kind of regularity, the consolidation of this understanding in the cultural memory of mankind was probably one of the most important acquisitions of its early history. This consolidation took place on the basis of mythological perception. Moreover, it can be assumed that the very formation of the myth took place in parallel with the process of such consolidation, being, as it were, its expression and design. Therefore, for a myth, the question of the origins of phenomena turns out to be natural and necessary: ​​comprehensive explanations should be limited to some last, universal and unified for all existing sources of its being.

Fragment of a leather scroll containing a list of simple ratios between fractions. Found near the funeral temple of Ramses II in Thebes. Dates back to about 1700 BC. (British Museum.) Image: “Nature”

Of course, the origins themselves varied in different mythologies: if Greek culture found an explanation for the emergence of the world as a transition from the kingdom of blind chance, Chaos, to the Cosmos, an ordered world ruled by the will of the Olympian gods, then for Chinese mythology the idea of ​​divine dictate was alien, and the formation of the world it I saw it as a struggle between two principles, disturbing and restoring the highest harmony of being. Thus, if the “Chinese version” originally expressed, using modern terminology, the idea of ​​a dynamic balance of alternative tendencies, the idea of ​​homeostasis, then the “Greek version” set the idea of ​​control carried out by an external source.

This difference will turn out to be essential for our subsequent consideration; for now, we just note that the tradition of searching for governing origins was preserved in early Greek philosophy, which, gradually moving away from the myth, still could not help but retain some of its features due to the continuity.

The first line of search for the beginning is associated in ancient philosophy, as is known, with the Milesian school. For the first time, the Miletans abandon the idea of ​​the divine nature of the first principles, trying to explain the origin of the world by natural reasons comprehended by reason. It is hardly necessary to prove the enormous significance of this leap in human thought: after all, the liberation of consciousness from mythological structures is the most important condition on the path of its evolution. However, among the Milesians, such liberation occurs at the level of superficial constructions: the internal structure of the explanatory scheme they created retained the essential features of the mythological paradigm.

Rejecting sacredness to the primitives, the Milesians accept the principle of deduction of the perceived world from a single universal source, which stands above any explanation, which is defining for Greek mythology. For Thales, such a source is water, for Anaximenes – air, for Anaximander george orwell face crime – an infinite imperceptible substance (apeiron).

Thus, the Milesians reduplicate in their philosophical system the universalism of myth, its focus on creating universal models of being that do not need substantiation. This circumstance necessarily entailed the figurative, metaphorical character of their explanations. Replacing the deity with a single substance, Milesian philosophy, as it were, changed the starting point, but retained the main features of the coordinate system itself: there is no longer the external content of the myth, but an invariant scheme of the methodological approach to explaining the world is traced. The radical shift that marks the transition to a different paradigm has not yet occurred2.

This shift is associated with the activities of another school, much more extensive and long-term – the union of the Pythagoreans. The achievements of the great mathematicians of antiquity (Theodore, Theetetus and Eudoxus) are well known; however, the foundations of a new approach to mathematical objects originated much earlier, somewhere at the turn of the 6th and 5th centuries. BC, and it was they who gave the first germ of truly scientific thinking.

The greatest achievement of the Pythagoreans consisted in inventing new principles of operating with the “material” of their activity, principles that changed this material itself and gave it an independent existence unattainable in the “technological” approach. For the first time, the Pythagoreans began to consciously strive not to demonstrate the empirical adequacy of their constructions, but to prove them, and in a way that does not cause any doubts or objections. It is the logical, more precisely logical-deductive style of thinking, consisting in the most accurate determination of the initial hypotheses and in the extraction of logical consequences from them, according to well-defined ways of reasoning, that is indicative for modern science. It is all the more striking that, in its main features, this style was formed among the Pythagoreans by the middle of the 5th century. BC.!

The mathematicians who worked a century later used the deductive method as a completely traditional way of obtaining mathematical knowledge. The great Euclid gave it an axiomatic form, but even here he developed the ideas found by the Pythagoreans (according to some sources, the axiomatic approach was already contained in the treatise of Hippocrates from Chios, written in the middle of the 5th century BC). A certain system of theoretical thinking, theoretical mastering of abstract objects “subordinate” to mathematics has been formed. Further, this system could develop under the influence of the logic of the problems that arose here.

Ancient Babylonian cuneiform text. The plot shown contains 16 problems with solutions related to the calculation of dams, shafts, wells. The task provided with a drawing relates to the calculation of a circular shaft. (British Museum) Image from sonic-arts.org

Of course, ancient mathematics was not yet a science describing the real world (it arose on the basis of the negation of any empirical orientation), but it already contained such principles of thinking, which later became the core of the scientific-theoretical attitude to reality. What was the impetus for the emergence of the deductive method? It is not easy to answer this question: the first mathematical texts have been lost, and later it appears in a complete form. But if history is powerless, logic should help. Let’s try to reconstruct the likely course of this process.

It is not so important that the Pythagorean school arose several decades later than the Milesian one. Much more essential is the underlying basis of this emergence. First of all, it should be noted that the Pythagoreans more clearly trace the continuity between their philosophical concepts and traditional mythologemes. But the choice of mythologemes is already different. Pythagoras brought from the East not only arithmetic and geometric knowledge – he got acquainted there with very ancient mythological traditions associated, as noted earlier, with the sacralization of numbers. It should be noted that Greek culture was well prepared to accept such innovations. The cult of Dionysus, widespread by this time, also (although not so clearly) contained elements of such sacralization. Pythagoras took the next step: borrowed from the ancient myth, the tradition of searching for the governing principles was projected by him onto the Eastern priestly wisdom. This is how the main element of his teaching arose: the beginning of the world is number. The world order is created by numerical harmony and is governed by it. The number is sacred, the number is the highest power of the universe. In understanding the relationship between numbers – the highest knowledge and the highest good.

One should not rush from the height of the 20th century to ridicule the naivety of the Pythagorean teaching. Think about the consequences of the perspective he saw. The leap of thought of Pythagoras, as it were, tore the numbers away from the sinful Earth, from their instrumental use, lifted them up the mountain heights, cleansed of everything base, perishable, and transient. Numbers for him are no longer tools of economic practice, not the length of ropes and not the weight of sacks of grain, but eternal and unchanging essences, the existence of which does not depend on people’s attempts to use them for their own purposes. Thus, for the first time, the Pythagoreans comprehend numbers and geometric figures as an abstraction: the number five is no longer five horses or five sacks, but simply five as an independent entity, whose existence lies above direct experience, although it can be projected onto it.

An ancient Babylonian cuneiform text containing a list of right-angled triangles with rational sides (Plympton Library, Columbia University). Image from the site www.uni-graz.at

The assignment of the role of the universal principle to the number gave an impetus to the emergence of the installation to study the set of numbers as a new integrity – after all, it is its internal structure, its structure that encodes the order of the universe. Consequently, comprehending the structure of this integrity, comprehending the relationship of numbers, a person can come closer to understanding the foundations of being. This idea gave rise to the Pythagoreans focus on the study of the number series as an abstract system, a study that obviously could not be done “in Babylonian”, that is, through the accumulation of experimental techniques and deriving from them some useful recipes in practice.

Let us now ponder over the consequences of what happened. The Pythagoreans saw in front of them a series of numbers striking in their correctness and completeness, going into infinity, they saw a variety of ideal geometric figures free from any earthly embodiment, they found the highest meaning of existence in comprehending the structure of the world of mathematical abstractions. This was the Truth to be seen. But how could you be sure that this is the Truth? Henceforth, it could not be weighed or felt, it had to be convinced of its existence in other ways, and the experience of technological thinking was powerless here. The experience of mythological explanation was also powerless. The truth of the myth is the truth of indisputable traditions, the truth of what is known initially, is clear to all initiates and cannot be questioned. In the world of numbers and figures, there was neither clarity nor predetermined certainty – the way to them was yet to be discovered.

Square with diagonals. Ancient Babylonian cuneiform text. (From the collection of Yale University.) Image from www.math.ubc.ca

Let us now dwell on one important circumstance. The Pythagoreans formed an alliance – a collection of people who had to communicate with each other, develop collective judgments and make sure of their truth (and the existence of such a truth was originally assumed!) in what justifications, besides their own confidence – it should have become the shared truth of the community. What one was convinced of had to be made certain for many. The world of numbers and figures was, according to the initial setting, intelligible by everyone. The authority of the Teacher could indicate the way to such comprehension, but it was not able to replace the work of the mind required to penetrate into its structure. Something else had to replace experience and faith and establish itself as the main organizing principle of the emerging system of knowledge.

And this new thing has come. It did not come from Olympus, still inhabited by aging gods, but from the noisy city squares. VII-VI centuries. BC BC – the era of a great turning point in the life of Greek society, the era of liberation from the power of tribal leaders, the growth of self-governing cities, the intensive development of navigation, trade, crafts, the era of the emergence of the form of government, which was called democracy. The democratic system is the greatest achievement of ancient civilization, the degree of participation of the broad masses of the free population in the decision of state affairs, unprecedented and impossible in the conditions of eastern monarchies.

  • April 18, 2020
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