The use of mathematical analogies in the interpretation of self-knowledge of the Divine Super-Being

Chekrygin Oleg ORCID: 0009-0007-4393-1445 PhD in Philosophy Independent researcher 24 Serpukhov val str., Moscow, 115419, Russia ochek@bk.ru Other publications by this author     Nadeina Dar'ya ORCID: 0009-0006-6063-8171 Postgraduate student; Institute of Philosophy of St. Petersburg State University; St. Petersburg State University 115682, Russia, Moscow, Orekhovy str., 59 Bogoslovblog@gmail.com Other publications by this author

Mezentsev Ivan Valer'evich ORCID: 0009-0008-8723-5641 PhD in Philosophy Independent researcher 690025, Russia, Primorsky Krai, Vladivostok, Dzhambula str., 7, sq. 1 mezivan@yandex.ru Other publications by this author

Introduction

Despite the rather strict restrictions imposed by the dogma of Christian theology on the knowledge of the essential depth of the Deity ("Basil the Great ^[1] says that the deity is knowable by the tropos of existence, but unknowable by the logos of nature, that is, essence. ^{[2, p. 93]}"), classical philosophy retained in itself the desire to know divinity precisely in the sense of penetrating into the essence of its very nature, while relying on the method of analogy: since everything was created by God in one way or another, what was created cannot but reflect the essence of the divine in itself, being involved in the Creation according to There was no analogy with his own essence, because apart from himself, the deity had nothing from which or by analogy with which he could create the world.

Moreover, man, as an ontological likeness of God, understood in different systems as his image, reflection, or particle, invariably strives to reunite with the deity who gave birth to him. And therefore, the desire for knowledge of God in the sense of knowing the very nature of the divine is a natural reflection of the divine nature of Man himself, the original Adam Kadmon, his godlike Mind ^[3].

The new ontological perspective developed by the authors in the publication ^[4] introduces the concept of Givenness as an analogue of traditional theological Providence, the divine plan of the universe and world existence from the beginning to the end of time. At the same time, Reality itself is, according to the authors, an ontological entity given by a personal deity to being, which arises and develops in time from Reality as the source of its existence in the form of the observable universe.

The return in our time of interest in the metaphysical concepts of the ontology of the Superbeing, to faith in God and His divine presence in the world, indicates that the last word in this area has not yet been said, and philosophy continues to reflect on the main ontological issues, including the opposition of being and non-being, being and non-being, which have been devoted to many works of the greatest minds in the history of mankind ^[5].

However, it is important to understand that any new concepts are preceded by previously accumulated philosophical knowledge, which forms the basis for building new theoretical models. Within the framework of the new ontological perspective developed by the authors, we have attempted to build our concept on the basis of some revision of the Neoplatonic concept based on one of Plato's most notable works, the dialogue Parmenides.

Let us recall the essence of the emergence of the hierarchy of ontological levels in Neoplatonism. The "neo" lies in the fact that Plotinus took from the dialogue "Parmenides" Plato's concept of the Like-minded in the form of a hierarchy of generation of ontological levels from a Single: The Absolute One>Relative unity with the transition from one to many other things.>The relative one is the other many > The absolute other is the complete Nothing, negating both all that exists and the Super–Existent One - and filled it with a peculiar cosmological content: "... identified the Origin of all that exists with the One of the first hypothesis of Plato's dialogue "Parmenides"" ^{[6, p. 657]}. As a result, the following cosmological hierarchy turned out: The first Single Principle generates the Second, the One-Being – Mind, which generates the Third, and many other things – the Soul, which in turn generates the Fourth, Cosmos as the embodiment of the ideas of the Soul into matter from the Fifth, Chorus, Nothing, which denies both being and Super-Being, as well as the One itself. However, the Super-Existent Absolute has no reason to manifest itself in Being, emerging from its Super-non-being: "In an extremely abstract form, the aporia of the transcendent principle is revealed in the 1st hypothesis of Plato's dialogue "Parmenides". It is shown here that if we consider the one in itself, regardless of everything that does not coincide with it, then any definition of existence will have to be denied with respect to such a one. In this case, we will have to say that it does not exist, including as a single one. It is “neither identical to itself or to another, nor distinct from itself or from another.” This means that one cannot say about it “the one is the one”, because it is devoid of any certainty and meaning that would distinguish it from other things and make it something existing alongside them. It also does not differ from anything else, i.e. it does not allow anything else outside of itself. Being such and denying its other, the one cannot be the beginning" [ibid., p. 660].

The solution proposed by the authors in ^[7] to this problem, known as the "aporia of transcendence", involves the descent of ontological levels from higher to lower without any volition on their part. The freedom of a Single Super–Being consists in the fact that it can - and it can only "be or not be", remaining due to its indicated freedom in both possible positions at once: until the act of observing itself, its position remains parallel and dual. "To accept one of the two possible positions of oneself present in parallel in the Super-Being itself is possible only through the discovery of oneself in a reflection from one's negation, which is a double negation: the other is the One itself, which has identified itself, distinguished Itself from its own non-existence, and become to be. There is no volitional act on the part of the One, but only a reflection of one in the other, One in the other, and the other in the One, like a system of two parallel mirrors that create an endless perspective of their own mutual reflections in each other, the very world of many other things that multiplies not because it wants to, but because it can. In fact, this system of mutual reflections of the Super-Existent One and Nothing unnecessarily creates a world of many things" [ibid., p. 168]. If we apply this model of "negation of negation" to lower ontological levels, then each of them will necessarily "automatically" generate the next condescending level of beingness: The Mind, denying its own disappearance, will generate a Soul, the Soul will embody ideas into things so as not to disappear: "And in general, everything that has already reached perfection. — gives birth; and what is always perfect always gives birth, and gives birth to the eternal, but worse than it itself" ^{[8, p. 327]} – and the explanation of the existence of hora as a low-quality matter simply disappears in this model, which leads to the rejection of the need to immerse spiritual ideas in the chaos of primordial matter and frees Neoplatonic ontology from the accusations of primary materialism of both emanationism and creationism.

In the previously published work ^[9] by the authors, along with the justification in the already mentioned work ^[7] of the descent of ontological levels from a Single Super-Being into the being of our world through the self-reflections of each previous higher level of ontology into a lower one (Absolute→God is a person→A world of many things (ideas)→ the existence of the observable universe), our proposed version of the process of a Super-Living God gaining self-knowledge in successive acts of expanding the self-knowledge of the Absolute, who has limited knowledge of himself as a personal God, onto himself as an unknown One was shown and justified. In the First Principle generated by the Super-Existent Absolute through the denial of Self-denial of his divine Super-Existence, God sees himself as Super-Existent, surrounded by a fog of infinite and boundless Super-Existent Absolute, the First Principle, which has not yet been fully recognized. The process of self-knowledge begins, anticipated by Eriugena ^[10]: "The act of creating the universe is at the same time an act of Divine self-knowledge. God recognizes himself in the Son-Logos, i.e., thereby in the act of creating truly existing ideas; in this act, God himself receives his being in accordance with the principle: "The knowledge of what exists is that which (itself) exists" ^{[11, p. 160]}. The deity strives to know himself, and the infinity and unknowability of the Absolute lead to the infinity of the process of his own self-knowledge. "In the initial state of the process of self-knowledge, the Absolute-Being resides within himself, and his surroundings are also his essence, which he has not yet recognized... The Absolute sets the boundaries (of Himself–known - author's note) by appropriating a Name for himself.… The appearance of the name gives rise to the idea of a "mirror-in-itself"... Having defined itself by a name, the Absolute continues to expand into namelessness, appropriating new names for itself as self-perception expands... within new boundaries. God appears as a process, not a stasis, and the worlds (generated, in turn, by the Names of God – author's note) – as the product of a system of mirrors in which God contemplates himself" ^{[9, p. 157]}.

The name or Word of God, belonging to the ontological level of the Soul, or the world of Ideas, contains in a collapsed form the Idea of the whole world in its development, like our observable universe, being what theology calls God's Providence for the world of being, or a Given– a concept introduced by the authors in their previously published work ^[4]. In fact, the Name is a Word at its ontological level, similar in everything to the Super-Existent Absolute: it is impersonal, mindless, lifeless and weak-willed in itself, containing the idea of the development of the whole world in a collapsed form. As Nikolai Kuzansky wrote, "everything is wrapped up in the one God, since everything is in Him; and He unfolds everything, since He is in everything" ^{[12, p. 104]} – and this is quite applicable to Reality at its ontological level of the Soul. It can be said that the Word in this sense is like the Absolute, the First Principle of its world, and its self-awareness as a Given, as the god of its world, by analogy with the Absolute's self-awareness of itself as a Super-existent Personal God, leads the Given to self-knowledge in the existence of the world, unfolding in its ontological time. From the point of view of the authors, expressed in the above-mentioned work ^[4], the ontological time of the world is nothing more than the boundary between the existence of the present and non-existence, into which the past of the world goes and turns every moment. "Reality manifests itself through time in an endless series of momentary flashes of being-non-being, and being and non-being are discrete in their continuous continuity. Time is given only as a moment of realization of the moment of being from the Given: having arrived, time cuts off being from itself, turning the past into non-existence, and sending being into the future of what happened in the past. Figuratively speaking, time cuts out an instantaneous frame of Reality from Eternity and implements it in existence, thereby predetermining the future as a consequence of the past. Then time is M. Heidegger's "last God" in the sense of the ontological level of Super-Being closest to us: it turns Reality into being-non-being by itself, sending the first to the future and the second to the past, which determines the apparent space-time continuity of the observable universe" ^{[4, p. 94]}.

1. Purpose and methods, as well as scientific novelty of the research

In this work, the authors aim to define and show the realization of Reality in the existence of the world as a process of self-knowledge of Reality through being, by analogy with the "process theism" of self-knowledge of the Absolute, the First Principle in the Super-Existence of a personal God.

The research continues the development of the new ontological perspective developed by the authors in their publications and represents a significant scientific novelty in the proposed innovations in understanding the nature of being, cosmogony and cosmology of the world, the ontology of the Superbeing and the nature of ontic and ontological time.

The authors mainly rely on the method of analogies, including mathematical analogies, the use of which is justified by the fact that any ideas found in Creation have foundations and are already contained in a collapsed form in the Super-Essential Absolute as the First Principle of everything. Moreover, the very "mechanisms" of process development at all levels of ontology, from the highest Absolute-in-itself to the lowest level of being in the world, should be repeated in a single "model" according to the principle of "reflection", noted by the Neoplatonists: "The One, being the most perfect being, necessarily extends its activities to the other, creating as a Plotinus compared the material world to a mirror image" ^{[6, p. 669]}. At the same time, the very "mechanism" of such "top-down reflections" should obviously also be unified, identical, and equally effective at all levels of metaphysical ontology. Such, from our point of view, is the reflection model shown by us in the already mentioned works, based on the principle of "negation of negation", which allows us to uniformly describe the process of theism at all levels of ontology. This is also a significant scientific novelty for a number of general philosophical disciplines.

2. The applicability of the analogy with imaginary numbers in theology

In this article, the authors want to propose a new model for revealing the ontology of the divine through mathematical analogies. The history of the use of mathematical and geometric analogies in the interpretation of divine existence is found more than once in the history of philosophy. The development of ideas about mathematics as a divine given can be traced back to the Pythagoreans, who deified numbers: "Many modern philosophers and historians of mathematics claim in their works that Pythagoreanism was the first philosophical theory of mathematics. One cannot disagree with this point of view, since the sources that have come down to us claim that it was the Pythagoreans, who called themselves after their teacher Pythagoras, who discovered in mathematics an expression of the deep essence of the world, something connected with the true and unchangeable nature of things. The main thesis of Pythagoreanism is that "everything is a number", it is "number that owns ... things" ^{[13, p. 47]}.

Plato and the Platonists, in turn, deepened and expanded their argumentation, which also had a significant impact on the entire development of mathematics. "According to Plato's description, when true being is reflected in matter, a multitude of triangles, equilateral and rectangular isosceles, arise, which are then arranged into five types of regular polyhedra; each of the five types corresponds to one of the primary elements: tetrahedron — fire, octahedron — air, icosahedron — water, cube — earth, and dodecahedron — element of the sky. (subsequently, the fifth element, quinta essentia, was called “ether” and was considered a particularly subtle living fire, which consists of the celestial sphere and all celestial bodies). The matter in which these geometric shapes and bodies exist is called “space” by Plato, but it is not thought of as a real empty space, but rather as a mathematical continuum. Its main characteristic is “boundlessness” (τὸ ἄπειρον), not in the sense of infinite extent, but in the sense of absolute uncertainty and infinite divisibility. Such matter acts primarily as the principle of multiplicity, opposing a single being. Plato is not concerned with the obvious difficulty: how to explain the transition from purely mathematical constructions to bodies with mass and elasticity" ^{[14, p. 510]}. An example in this regard is Nikolai Kuzansky, who wrote the following statement: "Entering the path paved by the ancients, let us say with them that if we can approach the divine only through symbols, then it is most convenient to use mathematical signs because of their enduring reliability" ^[12].

S. Krajevsky, speaking about the theology of Kuzants, writes: "Mathematical models in theology can be viewed as the result of using logic to construct complex metaphors.… Mathematical models representing religious issues can be considered as extreme examples of logical-type theological metaphors" ^[15].

A well-known systematizer of Christian theology from the era of the Ecumenical Councils, St. Peter the Great. John of Damascus: "Mathematics is the knowledge of that which is disembodied in itself, but is contemplated in the body" ^{[16, p. 52]}. Despite the fact that, of course, mathematics from the time of John of Damascus is very far from its modern counterpart, using this example of the theologian's work, fundamental to the history of Christian Orthodoxy, we see that mathematics is somehow embedded in his "Accurate Presentation of the Orthodox Faith."

Despite the criticism of Aristotle, who first posed the problem of infinity ("You can always come up with a larger number: after all, the number of times a quantity can be divided in half is infinite. Consequently, the infinite is potentially never relevant; the number of parts that can be taken always exceeds any assigned number" ^[17]), Platonism in modified forms still exists as mathematical realism. The clarity of natural counting one by one was so obvious, so indisputable, that for thousands of years mankind did not even think seriously about its formal justification, following Plato, considering him a direct epiphany, a revelation from above. It was only at the very end of the 19th century that the Italian mathematician Peano announced the five axioms and four rules of arithmetic formulated by him in the language of mathematical logic ^[18], which made it possible to develop and derive from them, as the foundations, almost the entire bulk of modern mathematical knowledge. In this case, it must be recognized that it was platonic ideas that lay at the foundation of formal Peano arithmetic: the nineteenth century marked the peak of the development of mathematical Platonism. "Platonists don't create mathematical objects—they discover them."

Natural numbers were followed first by fractional (rational) numbers, which had clear analogies with parts of whole things, then zero as the absence of anything, negative as a disadvantage, and finally irrational, which first manifested themselves in the quadrature of a circle — all this has been known since ancient times, and the question of the infinity of the numerical series posed as as already mentioned, there is also Aristotle.

The so-called imaginary and complex numbers are very difficult to interpret directly, which are an attempt to explain the paradoxes that arose during the formal application of the procedure for extracting the square root from a negative number, which seems impossible in the logic of the aforementioned Peano arithmetic. Imaginary quantities were first mentioned in Cardano's work "The Great Art or on Algebraic Rules" (1545) as part of a formal solution to the problem of calculating two numbers whose sum is 10 and the product is 40. He obtained a quadratic equation for this problem, the roots of which contain the square root of -15. In a comment to the decision, he wrote that "these most complex quantities are useless, although very clever," and "arithmetic considerations are becoming more and more elusive, reaching a limit as subtle as it is useless" ^{[19, p. 138]}, that is, he considered them a useless arithmetic paradox. Only in the XVIII century . Euler introduced the generally accepted notation i (square root of -1) for an imaginary unit, and Gauss introduced the concept of a complex number in 1881.

Leibniz wrote about the "imaginary unit" in 1702: "The Spirit of God has found the subtlest outlet in this miracle of analysis, a freak from the world of ideas, a dual entity located between being and non-being, which we call the imaginary root of the negative unit" [ibid., pp. 138-139]. Based on this definition, in which the phenomenon of complex numbers to humanity is attributed to the very Spirit of God, the authors decided to offer their own view on the applicability of imaginary and complex numbers to describe the nature of the divine, the world of Nothingness, and ontological Super-Existence. We would like to emphasize that our application of analogies from the field of mathematics of complex numbers to the divine Superbeing is mainly metaphorical in order to make it more clear in the description of the model proposed by the authors of the descent of the Superbeing of Reality into the being of our world.

In the light of all the above, the attempt in our discussion to apply mathematical analogies to the knowledge of the divine seems to the authors to be not without perspective, since mathematics, like everything that exists in nature, cannot be deprived of the divinity of its origin for the same reason that divinity is reflected in all manifested existence.

3. Visualization of the philosophical and theological use of imaginary numbers on a coordinate plane

Let us turn to the Platonic ontology of absolute divinity, which is understood as a Single Super-Being. According to the logic of the hypotheses of the dialogue "Parmenides", the predicates of absoluteness, unity-uniqueness and super freedom are attributed to the Super-Being. Christian dogmatics has introduced this Platonic logic into its doctrinal developments, despite the assertion, already mentioned in the introduction, of the fundamental unknowability of the divine essence, its superiority in relation to all the principles of the created world and thought.

Let us recall that the above-mentioned concept of Reality introduced by the authors in its super-existence is the Word of God, the Name God appropriated to Himself in the process of self-knowledge of the divine Absolute. At this stage, Reality is a faceless entity containing a whole world of divine reflections in a collapsed form, the development of which should occur in parallel with the process of unfolding Reality in its self-knowledge, similar to the process of infinite self-knowledge of the Super-Existent Absolute in the Super-Existence of a personal God. And in this context of representations of Reality as a self-realized living God, the Word of one's own world, it seems promising to use the concept of numerical "imaginary", so highly appreciated by Leibniz as a direct gift of the Holy Spirit, in relation to the ontological level of Reality, as Ideas from the world of the Neoplatonic Soul, unobservable from our world.

To illustrate our proposed idea of Reality and the Existence of the world given by it in their relations, we will need, first of all, the point zero on the coordinate plane. From it, we will draw coordinate rays: to the right, horizontally, will be the axis of existence of the observable Universe, developing in time — in fact, with some further reservations, this is the axis of the current time of Existence; up, perpendicular to the axis of existence, will be the axis of imaginary numbers i, 2i, 3i ... Also, from point zero, we will draw a ray down from the arrangement of the imaginary numbers is i, –2i, –3i... and this ray goes down from point zero to negative infinity, and the upper one goes from the same zero to positive infinity. Similarly, the horizontal ray from point zero goes to infinity to the right, but we will not draw the ray to the left, and thus the left half of the coordinate plane will be unused.

Now let's start with more detailed explanations of this visual geometry. To do this, let us first clarify the concepts we introduce that describe the divine process. The personal God generated in the process of self-knowledge of the Absolute, in turn, generates a Name-Word for fixing the achieved level of self-knowledge. The word contains in a collapsed form the idea of the whole world as a reflection of the Personality of God at this stage of self-knowledge of the Absolute. In its expanded form, the Word appears as Providence, that is, the idea of the world fully unfolded in Eternity from the beginning to the end of time. The axis is pointing upwards, which is the whole Word, from zero to infinity, in an expanded form, that is, a Craft. And Reality is an analogue of personal God on its ontological level in relation to a Providence unknown to it, the knowledge of which is Given as self-knowledge of the Absolute in personal God, and the imaginary numbers on the positive part of the vertical axis correspond to the levels of development of Reality as self-knowledge of the Word. That is, the Word-Name provided by the Personality of God, assigned to the future world, is mastered by the Given in the process of self-knowledge as the unfolding of the Providence wrapped up in the Name in the movement of the Given along the axis of Providence from bottom to top from zero to infinity. These imaginary numbers, as levels of self-knowledge of the Word in Reality, as it is clear from the presented scheme, are infinitely many, and, moreover, uncountable. The ontological levels of Nothingness and super-existence are located down from zero along the axis, each of which is symmetrical through the point zero to the corresponding level of the Super-Being. The already mentioned axis of existence goes from zero to the right, but the real numbers on it do not mean a quantitative increase in things, but a numbering of the states of the observable Universe in successive moments of its development. That is, in fact, the horizontal axis is, in the ontological sense, the axis of the Universe's existence, containing successive states of its development, instantaneous "snapshots" of its states, each of which can be directly correlated with the moment of the current time of the observable Universe. The point zero will correspond to the beginning of time, that is, existence as such, an empty multitude containing nothing in place of the cosmos that has not yet been born, which corresponds to the theological idea of the beginning of the creation of the world.

Now let's turn to the vertical axes of our coordinate half-plane. The upper half-axis of positive imaginary numbers corresponds to those states of Reality that are reflected on the horizontal axis in the form of the corresponding states of the observable Universe, manifested in being from Reality. The process of mastering a Given self in self-knowledge begins at the same point "zero", corresponding to the "empty" set of being as such, from which the self-realization of the presence of a Given in being begins. By analogy with how God comes to life in his Super-Existence from the lifeless Absolute in his act of self-knowledge, comparing himself with his own non-existence, so the Reality reflected from his stay in timeless Eternity in the form of Providence into his own non-existence and back, comes to life as an ontological entity, and reveals himself in the existence of the future Universe. The revived Reality at the point of its birth from Eternity generates existence as an empty set corresponding to the point zero on the horizontal axis of the real numbers. Further, one can imagine that Reality, moving upward from zero along the +i axis, realizes self–knowledge by comparing itself with its own non-existence, symmetrically located on the negative-i axis through the act of negating negation (any non-non-essence = the essence itself), and thus turns out to be manifested in being by that part of Providence which is mastered by the self-aware Datum to a level corresponding to the point of ascent from zero to the positive imaginary number mastered by the Datum on the +i axis. Then Reality, the whole from zero to "imaginary" infinity, appears as an integral super—existent Idea of the world generated by the Supreme Mind, capable of generating the existence of the observable Universe in its development over time through self—knowledge. In this case, the points on our positive half of the coordinate half—plane will have two coordinates, imaginary and real, in the form (+iy; +x), where +iy is the level of self—knowledge of a Given, and +x is the state of development of the observable Universe corresponding to this level. As we can see, the development of the Universe takes place in time from moment to moment of self-knowledge, which means a certain sequence in the self-knowledge of Reality in the form of a process that also has a certain semblance of time as an ordered sequence of transitions from state to state.

From the point of view of the relation to the Super-Being as an Absolute, any processes of development in it seem forbidden because of its absolute self-sufficiency and immutability. It would seem impossible for any semblance of time to flow as a measure of process in the Absolute, which remains in unchanging timeless goodness. However, we admit the super-existence of a personal God as a self-realized Absolute and the endless process of self-knowledge in him; similarly, we admit the existence of some intermediate subject, an Idea, between the Supermind we mentioned (the personal God who gave birth to him) and the idea-created existence of the world in the form of an observable Universe. This position is quite consistent with the theological view of the begetting Father, the begotten Son, the Word, and the world created by this Word of the Father from Nothing or from himself in various interpretations of religious philosophy. That is, it is not the Absolute itself that knows itself and through this creates the existing world, but through the mediation: at the first stage — of the Personality God generated by the Absolute, and at the second - through the Word—Son generated by this God-Father in his Super-Existence, or the Idea designated by us as Providence. In our model, it is conditionally located entirely along the imaginary axis of our coordinate half-plane and is in the process of self-knowledge as a Given, leading to the process of creation of existence in time from zero (time has gone, having begun to be) to infinity of the time of existence of the observable Universe.

4. The problem of time and the theological use of imaginary numbers

Then what is time for a super-essential Given? To answer this question, it is necessary to review the achievements in the field of studying time as a phenomenon in our universe and its properties. Since time immemorial, time has been presented to mankind as one of the two fundamental properties inherent in existence, along with space. Einstein combined them into a space-time continuum; he also proved the relativity of the subjective flow of time for the observer, which laid the foundation for the development of the philosophy of time in postmodernism, which divided time (Heidegger) the ontological "external" time and the ontic time of the subject who creates it in himself. In M. Heidegger's philosophy, "Ontic" refers to the order of being, in contrast to "ontological" as referring to the order of being: "Heidegger calls cognition of being ontic cognition, and what makes it possible is ontological cognition (pre—understanding of being)" ^[20]. Academician Kozyrev considered time to be the only material source of energy in the universe ("time burns up in the stars" ^[21]) and even conducted evidence-based experiments, but his theory has not yet received experimental confirmation during its scientific verification. Bartini considered time to be three-dimensional and on this basis was able to obtain the values of fundamental physical constants analytically ^[22]. It is also assumed that time is discrete, and even the value of the time quantum, the chronon, has been calculated. A specific chronon model was proposed by Piero Caldirola in 1980. In his work, one chronon corresponds to 7 × 10-2⁴ seconds ^[23], but, unfortunately, it is still impossible to confirm this experimentally due to the indefiniteness of the very nature of time as an object of experimental research.

In intuitive perception, time is represented as a continuous, uniform flow from the past to the future. However, considering time as a single act of ontological generation, as a transcendent gift of being-non-being by a Given, we get a different picture. Existence turns out to be the future, non–existence is the past, and time is a moment of transition, an instantaneous transformation in which the old world is destroyed, passing into oblivion, and a new one arises, striving for existence only to, in turn, give way to the next. This is confirmed, for example, by Plato's arguments in Parmenides and Plotinus' thesis about the eternal creation of the eternal ("That which is always perfect always gives birth, and gives birth to the eternal...").

Let us turn to A. F. Losev's explanation of the second hypothesis of the dialogue "Parmenides", namely, to the concept of border introduced by him: "But even when one differs from the other, it means that it has a border with him, which equally belongs to himself and the other. Consequently, in the concept of borders, one and the other coincide" ^{[24, p. 500]}. The very concept of a boundary as an independent entity, embedded between two others, raises the question: what is this boundary between being and non-being in its essence? Due to the fact that, according to general concepts, being from non-being is separated by the moment of transition from life to death, from being to non-being, a short, infinitesimal instant, it remains to assume that the boundary of being-non-being is time as a given.

The interpretation of time as a dynamic boundary of being and non-being, firstly, gives it an ontological status. Secondly, it presupposes the successive generation of being-non-being from the transcendent eternity of Providence, where all changes in existence are predetermined. Reality, therefore, contains the potential of all events, preceding each act of the emergence of being-non-being. Therefore, being is the future, non–being is the past, and time, as the boundary, is their point of contact.

The boundary of being and non-being is thus presented as a divine act of creation, the instantaneous giving of being to all things with the simultaneous disappearance of the previous state. However, the Reality itself, which manifests itself in time, remains in unchangeable Eternity in the form of the eternal Name-the Word - given by God to the world. We can talk about the manifestation of Reality in the existence of the world in the form of an infinite sequence of instantaneous acts of being-non-being, where being and non-being are discrete in their continuity. Time acts as an instantaneous realization of a moment from Eternity, in which the Given resides: it separates being from itself, transferring the past into non-existence and directing being into the future, determined by the past. Time, as it were, "snatches" an instantaneous frame from Eternity and embodies it in existence, predetermining the future as a consequence of the past. In this sense, time acts as Heidegger's "last God" ^[25] ("The Last God is a unique figure in Heidegger's philosophy. He appears through Ereignis, passes by people, leaving them only a nod, a hint (Wink). He is neither the being nor the creator of being, but he manifests himself at the moment when being as Seyn comes true in the one-time event. Heidegger writes: "In the being of the hint (Wink), Seyn-being itself comes to its maturity. Maturity is the willingness to become a fruit and be given. There is a last one in this, which is essentially (wesentliche), an expected, non-accidental End from the Beginning. This reveals the deepest finiteness of Seyn-being: in the nod of the last God“ [p. 410]. And further: "The last God is not the end, but another Beginning of the immeasurable possibilities of our destiny (Geschichte)." [p. 410]" ^{[26, p. 107]}), the ontological level of the transcendent closest to us: it transforms Reality into being-non-being, forming the visible space-time continuity of the Universe.

5. Discreteness of the ontological time of the universe as a reflection of the process of self-knowledge of Reality

If we look at the ontological time of the Universe as a reflection in the being of the ontic (subjective) "time" of the development of the process of self-knowledge of the subject of a Given, then, firstly, the irreversibility of time in our Universe becomes self-evident, and secondly, its discreteness: time, as a unidirectional stream that we perceive continuously flowing at a constant speed from the past to the future. the future does not exist, but represents, as already mentioned above, a series and a set of static "snapshots" of the states of the universe, reflecting each successive level of self-knowledge of Reality, reflected in being.

Self-knowledge of Reality, in our opinion, should occur step by step, that is, in the form of a discrete, rather than continuous, process. This should be due to the fact that each next step on the path of self-knowledge from the zero of one's own awareness is to define oneself in one's self-awareness and fix one's state as static, accomplished: here I am, completely visible and unchangeable inside myself, and around me, too, but not yet recognized by myself. This step, no matter how small, cannot correspond to continuity and must be performed discretely, occupying a certain area in the Given, defined by It for self-knowledge. Thus, the Given, having defined itself in the act of self-knowledge, comes to self-limitation in self-designation, that is, it appropriates a name for itself (by analogy with the Names of God in the self-knowledge of the Absolute), separating its self-awareness from its own infinity. This name, conventionally, is a number on an imaginary axis that defines the boundary between the named and the unnamed (here it is appropriate to recall the deification of numbers by the Pythagoreans). The name-number gives rise to the idea of a mirror-in-itself, in which Reality can see and examine itself, and this is Its reflection in existence, a "snapshot" of the state of the self-recognized domain of Reality reflected in existence in the form of the corresponding static state of the observable Universe. Further, this process of self-knowledge in the self-limitation of given names—numbers spontaneously develops infinitely: having realized itself in the name, the Given continues to expand into namelessness, appropriating names-numbers to itself as the self-contemplation of itself in the mirrors of names expands as ideas of private self-knowledge, first of a Given, self-limiting, and then going beyond its own boundaries into itself unlimited - and again getting to know herself within new boundaries-names.

At the same time, the intervals of continuity between the steps of self-knowledge represent the area of one-step self-knowledge of a Given, the amount of knowledge in one such step, which corresponds to the length of the segment of the next cognition on the vertical positive semi-axis of imaginary numbers. On the actual axis of reflection of Reality into Being, this "thickness" will correspond to the length of the time quantum, the chronon mentioned above, between the states of the observable Universe "before" and "after" a single act of self-knowledge of Reality. In fact, this chronon is a segment of timelessness, the Universe's stay in stasis, in a frozen state, during which the Self-knowledge of the next step up is mastered, the expansion of the self-awareness of the Given by one more step. During this timelessness, the Given recalculates the state of the Universe corresponding to the mastered step of the Given and the development of the Universe in a time equal to a chronon, as if it did not stop, and all the processes of the Universe would be continuous over time. If we assume that the "frames" of existence are arranged sequentially on the axis of existence at a distance equal to the time interval of the conventional chronon, then we will get a graph of the linear dependence of the flow of time in the observable Universe along the x axis on the step-by-step process of developing self-knowledge along the +iy axis in the form of separate points located on a ray of a directly proportional function y (ontic time of Reality) = t (ontological time of Being). The continuity of Reality will reflect only discrete points of the steps of Its self-knowledge on the axis of being, and time on the x-axis will be discrete with a step equal to a quantum of time.

If you pass this sequential set of frames through a time projector at a constant speed equal to or greater than one "frame" per chronon, you will get a movie for the viewer who is watching it. The only viewer of this film about Himself is the Personal God, the Supreme Mind, who observes the development of his Idea, his Word generated by Him, in the observable Universe. The only thing that is impossible in this model is the reversibility of time because it is impossible for self—knowledge of a Given to abandon what It knows: therefore, in the observable Universe, real ontological time is irreversible.

To this we need to add one more consideration about the beginning of time: where does genesis begin and when exactly time starts from the point "zero". Apparently, this is due to the generation of the Word by the Higher Mind, which, having been born from the Father, begins its Super-Existence with self-awareness, first of all accepting from the Father the inherited freedom to be, not to be, to be oneself or another self, and being as an opportunity. The opportunity for oneself, through immersion in one's own non-existence and comparison with it, to manifest oneself in being, realizing oneself to be: I am. With the Word's awareness of freedom and, as its private manifestation, the possibility of being, which is being as such, the Word becomes a Given and begins its journey of self-knowledge and being from the ground up of being, from which and in which the ontological time of the Universe is launched.

Conclusion

Thus, based on the model proposed by the authors, it can be concluded that the Super-existent Supreme Mind, a personal God, generated in self-awareness by the Absolute-the First Principle into His own Super-Existence, in turn generates in him a creative Word, which is His Name, Idea or Datum, representing the existence of the world provided by God as a possible reflection of Himself in a collapsed state.. The word triggers the process of creating the world by itself through self-knowledge of its Own Reality, manifested in the unfolding of Reality into being generated by the Reality of the Universe. Self—knowledge of Reality occurs step by step as a reflection of the mastered reality through comparison with one's own cognized non-existence - into being; each subsequent step of self-knowledge creates a new static picture of the existence of the world. The sequence of steps of self—knowledge of Reality creates a kind of sequence of "ontic time" of the process of self—knowledge of Reality, which is displayed as an illusion of continuity of the ontological time of the Universe; the observer - both external to being and internal from the world - perceives the process of changing individual static pictures of the world as an ontological temporal continuity of the development of the Universe in time. However, the reality of ontological time is a discrete succession of static "frames" of the state of the Universe; ontological time is discrete, being divided into quanta of abrupt changes in the static states of the Universe; the continuity of the passage of time is an illusion of the observer. The ontological time of the universe is irreversible because of the irreversibility of the process of development of a Given in its self-knowledge. Reality, in its self-development, creates a system of mirrors of being as reflections of God in the being of the universe. Such a view of Reality as a Son begotten by the Father, who creates the world in the process of self-knowledge, creates an idea of the world as successive acts of manifestation in existence of a self-knowing Deity, who creates this world by himself and out of himself; nothing else in existence exists except for the steps of God manifesting himself in it, the Universe is God himself, manifested in being, and its development is the process of his self-knowledge.

It remains only to emphasize once again the exclusively metaphorical nature of our appeal to imaginary numbers in order to make it more clear that Reality resides in the eternal Super-Existence of God, which is transcendent to the world of being, which is inaccessible to those on the "axis of time" of being in its transcendental "imaginary", manifesting itself in being only as a "nod to the last God", time, as the boundaries between the existence of the present and the past that has passed into oblivion.