A.V. Nesteruk

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6. Irreversibility of Time and the logos of Creation

Irreversibility of Time and Eternity – Irreversibility of Time and Boundary Conditions in the Universe – Penrose’s Model and Its Theological Interpretation – Irreversibility of Time through Irreversibility of Processes – Irreversibility and Two Views of Nature – Prigogine’s Treatment of the Time Paradox – From Irreversibility in Physics to Theological Contingency

Irreversibility of Time and Eternity

This section contains some theological reflections on the problem of irreversibility of time in modern physics. We will discuss only this particular aspect of the phenomenon called “time,” understanding its property to be in a flux leading toward novelty and to the endless unfolding of the reality of the world. This means that we will intentionally avoid discussing the notion of time in the context of the theory of rela­tivity and its geometrical representation by Minkowski space.

Special relativity does not solve the problem of flowing time. In its extreme, geometrized form, it treats time on equal footing with space and treats the whole space-time as eternally existing. The universe that corresponds to this picture is called the deterministic “block-universe,” a “frozen being” in which one has only the rearrangement of events, no true becoming.385 The problem here is similar to that touched on briefly in the previous chapter: how to explain the emergence of macroscopic irreversibility from microscopic reversible dynamics. This is a matter of continuing scientific debate, and only a few scientists have tried to address this issue by revising the foundations of classical physics. One of these scientists is I. Prigogine, and his collaborators in Brussels and Austin, whose approach to the riddle of time’s arrow we will discuss later in this chapter.

It is typical for the block-universe view to assert that the division of time into past, present, and future is an illusory one and that all events in the universe are given at once, but in a Platonic sense. In this case, it is understandable why there is no flow of time and novelty in this universe: its time, according to the terminology referred to in chapter 5, is transcendent time, which somehow incorporates all events that are experienced by human beings as distinсt in time. This makes it possible to suspect that the block-universe is not a model of the real visible and empirical universe but, rather, is an attempt to represent the totality of all possible empirical experience of time through a pattern existing in the intelligible realm. The problem, then, is how to link the intelligible frozen time with the empirical flow of time. It has analogies with what we have discussed in the context of Hawking’s model of the universe with imaginary time in the previous chapter, so the whole issue of the source of time’s irreversibility can have some theological implications.

The debate over the block-universe thus reveals an interesting point in nearly all discussions on the nature of time, namely, some inevitability in the appeal to the Platonic vision of time as an image of timelessness and eternity, in order to justify the empirical time. Indeed, the supporters of the block-universe perceive the eternal reality of Minkowski space-time as an essential ingredient of relativity theory. This manifests an interesting, but predictable from a philosophical point of view, split of the whole being into the empirical and intelligible realms, if one attempts to address the problem of time. We will show below that some sincere attempts of modern physics to solve the riddle of irreversibility of time strictly within a physically realis­tic ontology cannot be sustained. To justify this point, we intentionally reduce the whole spectrum of problems around time to one in particular – to time’s irre­versibility, or, to be more precise, to the problem of the source or foundation of this irreversibility. In other words, we concentrate our quest for the source of irreversibil­ity and the arrow of time, assuming that this source exists somehow. Our aim thus is to understand the nature of the reality of this “source.” The result of this search will lead us to the conclusion that the “source” of the macroscopic irreversibility of time transcends not only the empirical world but also the Platonic world – that is, it orig­inates from the split in the created realm, from the basic diaphora between the sensi­ble and the intelligible. One can anticipate, then, our conclusion that the problem of the irreversibility of time cannot be seriously discussed by physics on its own but requires one to employ philosophy and theology to address this issue adequately.

Indeed, even in the context of the Platonic block-universe, assumed as existing eternally, there is a theological question about the ground of its existence – that is, what is the sufficient reason for its existence? It also can be approached as an issue of the contingency of the block-universe (treated either realistically or Platonically), that is, the nonworldly grounds of its existence. The very structure of the block-uni­verse (with no becoming), if it is considered as an arena of God’s actions in the world, would be very destructive for Christian assertions about salvation history and for Christian eschatology in general. This is why, from a theological point of view, the question of becoming and its ultimate origination in the mystery of the creatio ex nihilo is important in our discussion here. We want to assert once more that we do not discuss time here as a background of God’s economy in the world; rather, we discuss the origin of temporal flow as linked to the Christian concept of creation. It makes our interest here much closer to the problem of time and contingency.

The definition of time, its meaning and logical expression, can be presented in many different ways. On the one hand, it seems psychologically evident to speak about time and to pretend to know what it is, appealing to time not in terms of its underlying essence but rather to empirical events, which are in time and which describe time in terms of things that are themselves not time. Time is usually described in notions that are finite and contingent in all possible senses. The prob­lem, however, if we long to understand the ultimate source of the irreversibility of time, is to justify the definition of time in rubrics of thought that transcend the immediate surface of temporal appearances of things and refer to the realm of the unconditioned and the necessary.

Time can be seen as a fundamental, all-encompassing entity that has to justify everything diverse, concrete, and contingent in the empirical realm by uniting all of them in time. This shows, therefore, that there is something in time that originates not from the empirical world. We can only perceive the empirical world through the mode of temporal experience, so that any hypothetical removal of time in reasoning about experience would mean its negation, that is, the affirmation of its nonbeing. Time, however, is not reduced only to its temporal manifestation in experience, which consists of specific and distinct phenomena that in their diversity do not exhaust the essence of time, leaving its intuitively asserted unity and undivided foundation beyond experience itself.

This tells us in turn that any possible philosophical definition of time as the sum of events contains some negation of the temporality of time, pointing thereby toward the realm that is beyond the empirical expression of temporality itself. In Kantian parlance, we can say that the origin of that temporal time, which we know through the immanent form of sensibility, is itself beyond the world, which is known to us in temporal terms. The Russian philosopher N. Lossky comments on a similar thought: “Time is a condition for the world to fulfill its task for the sake of which it was created.”386 There are two points in this comment where we find that time, under­stood as materialized in the world, has its foundation beyond the world. First, time is understood as a condition for the underlying and forming principle of creation (its logos, which is uncreated itself) to be realized in the world, but this condition (time) is revealed to us only in its immanent form of the temporality of the world and its history. Second, one can argue that by projecting itself into the domain of the cre­ated, the forming principle of creation (logos), which initiates time in order to fulfill the task of creation, does not exhaust itself; it is still beyond this world and is the ground of creation and time. Despite this theological treatment of time, it indicates that one comes to similar insights on the nature and origin of time in modern scien­tific inquiry.

To understand this better in general terms, not yet employing specific scientific theories, it would be useful to rephrase the theological insight into this problem in modern terms. We understand time, which is experienced as a temporal order of events. In other words, our experience is possible only as experience in time. That is why the problem of the foundation and origin of time can be understood in a twofold way. If one adopts the notion of time as a directed and irreversible flow of events, one could try to give justification for its irreversibility in local terms, that is, as some physical cause that coexists logically and physically “simultaneously” with the displayed aspects of irreversibility. In this case, the irreversibility, being an immanent aspect of time, is caused by some deep underlying physical processes and may be explained from within the same level of reality (that is, the same ontology as tempo­rality itself) with no appeal to the idea of the transcendent cause of time. Prigogine and his collaborators follow this methodology in order to tackle the mystery of the irreversibility of time.387

This methodology has two problems. One will be analyzed later in this chapter, where it will be shown that an attempt by Prigogine to find the source of irreversibil­ity of time in some deep level of physical reality leads him, in fact, beyond empirical physical reality into the realm of conceptual spaces with different ontological properties and criteria for their existence.388 This adds to our previous assertions that the source of irreversibility of time has its ground in the nonempirical realm. The theo­logical analysis that we apply to Prigogine’s ideas will help us to reinstate the problem of the irreversibility of time to its proper theological status in the context of the con­cept of creation out of nothing.

The second problem is that if Prigogine’s attempt were successful and the arrow of time were to be explained, this could bring his supporters to claim that there is no need for any nonwordly agency in order to describe irreversibility and in a sense the description of temporal flux would be monistic, needing no justification for either its “beginning” or its “end,” because the irreversibility destroys any ontological significance of the unknown past and indefinite future. This would imply that any speculation on the nature of the initial conditions in the universe would be fundamentally untestable. The claims of the block-universe proponents would then also be extremely unsound, for the idea of a global space-time with deterministic dynamical laws would be irretrievably undermined. It is understandable that in such a universe the permanent emergence of novelty would make it difficult to advocate the stability and intelligibility of the patterns in the universe, which represent the outcomes of the laws that drive the irreversibility. The only ultimately stable feature would be the very law of irreversibility. The problem, then, is about the origin of this law. If one believes in evolving cosmology, does it mean that these laws come into existence together with the universe? In this case, their contingent status follows from the contingency rooted in the initial conditions of the universe, which, as discussed in chapter 5, have grounds in their otherness, that is, in the realm of the God-Creator. This implies that an attempt to explain the irreversibility of time by postulating some underlying irre­versible laws whose outcomes lead to the observed irreversibility – that is, to make it a part of a new law – still does not succeed in explaining away the contingency of irreversible phenomena, for these irreversible laws need to be justified, which indi­cates that they are contingent on their own.

It is also important to remind the reader that, in its essence, the approach to the irreversibility of time in physics is usually associated with the irreversibility of processes. In other words, one asserts the irreversibility of time not in terms of time itself, which is a difficult and ill-defined concept, but in terms of some physical processes whose behavior manifests the irreversibility of time. Philosophically and theologically, this approach is justifiable, for time was created together with the world, which means that it is difficult to separate a “pure” time from its manifesta­tions in the processes. This was anticipated early, by the Jewish philosopher Philo of Alexandria, who developed a biblical exegesis through its synthesis with Hellenistic philosophy. In his account of the creation, he asserted that time cannot be separated from what is observed as change in time: “Before the world time had no existence, but was created either simultaneously with it, or after it; for since time is the interval of the motion of the heavens, there could not have been any such thing as motion before there was anything which could be moved.”389

Time discloses thus a special kind of “reality,” which is immanent to the world but which does not exist before or without the world. One can even strengthen the last proposition by saying that time, understood as temporal change in physical bodies, does not exist beyond the world, where the bodies’ motions are exhibited. The view that time and the world have foundation in their common otherness led historically, as articulated before, to the replacement of the Hellenistic idea of the demiurgic cre­ation of the world in space and in time by the Christian concept of creatio ex nihilo. The fundamental change in comprehension of time that accompanied this shift can be commented on as follows.

Since creation out of nothing is not a temporal act in the same sense that we understand temporality in the created world, the creation of the world is not in time; however, it is through the creation that time is held – that is, it is being brought into existence. By following the logic of the created temporal world, we could articulate the “act of crearion” in terms that are opposite to time; for example, one could affirm that creation is timeless and that time is brought into existence out of timelessness. But, unfortunately, the term timelessness suffers from a deficiency of being produced within the logic of the created world. Indeed, it is introduced into the philosophical lexicon by means of a simple negation of time as temporality and represents a special and rather narrow understanding of eternity, which can be treated in an opposite way as transcendent time – that is, the overall time of all times, which was discussed along with Neoplatonism in chapter 5. But even the transcendent time (eternity as a changeless state of affairs) manifests the mode of the creation, namely, the invisible in creation, the world of angelic forms and Platonic ideas. The Greek language denotes eternity as aeon, and different aeons measure the spans of existence of different intel­ligible worlds.

It is because of this that when one asserts that the temporality of the visible creation has its ground in eternity, understood as the opposite to time, one should be very careful, for eternity itself can be an attribute of the created realm and will need further justification in terms of its nonworldly foundation. This reveals the whole scale of the difference between the uncreated realm of the Divine and the created world, leading to the necessity of introducing the third and, according to G. Mantzaridis, the loftiest concept of the aidion as the “everlasting,” which is “older than all time and eternity in its being.”390 Maximus the Confessor, in some of his texts, elucidates this concept by referring to Scripture, which is saying “that there is some­thing which transcends the age. Scripture has indicated that this thing exists but it has not specified what it is, as the following text shows: ‘The Lord rules the age, and above the age, and for ever’ (Exod. 15:18. LXX). There is therefore something above the age, namely the inviolate kingdom of God.”391

It is difficult to articulate further the meaning of the aidion in discursive mode except by defining it in purely apophatic terms, which start from negating the time of the visible world. What is interesting, however, is that the Patristic writers, such as Gregory the Theologian (Nazianzus), also anticipated that the understanding of time itself is problematic by definition, for if it is a part of visible creation and falls under the temporal categories itself, how is it possible to define time in categories that assume that they are already temporal? Gregory put this query in the following form: “Is Time in Time, or not? If it is, what is the Time it is in? What is the difference between them? How does one contain the other? If Time is not in Time, how acute your wits are to get us non-temporal Time.”392

The rationale of this quotation is that any attempt to speculate about the foundations of time requires one to abandon language that is inherently temporal, including all simple modes of its expression in terms of timelessness or eternity, in favor of a silent affirmation that God, being the ground of the world and time, is beyond both time and eternity. This observation is important in the methodology of philosophi­cal and theological analysis of scientific concepts of time, and of temporal irre­versibility in particular, for any affirmation that time has its foundation in timelessness or eternity is not sufficient in order to be qualified as a theological assertion. This is because, to find the indication of the ultimate ground of time, one should pose both time and eternity in their relation to aidion as transcending both of them and being peculiar to the timeless being of the uncreated God. In accordance with the line of reasoning developed in chapters 4 and 5, this implies that the Platonism in arguments for the foundation of time must be reinstated in its Christian version when both empirical time of macroscopic processes and timeless mathematical spaces that mirror these processes through their constitutive difference (diaphora) will be referred to the common ground of their unity, that is, to the logos of their creation.

The problem of time thus can be seen from a theological perspective as a problem of the relationship of time, either empirical or conceptual, to the everlasting (aidion). Still, it is interesting to ask which particular «form” of empirical time (that is, its past, present, or future), the question of its relationship to creation from the everlasting realm of God, it is more appropriate to address, for the human perception of time is always inclined to seek its foundations through the limiting forms of temporal series, which are directed either to the past or to the future. This question cannot be answered on scientific grounds only, for, as will be demonstrated in this section, the appeal to the source of time as existing in the cosmological past (Penrose’s model, discussed later in this chapter), as well as the invocation of the source of temporal flow as existing in the underlying level of reality at “present” (Prigogine’s theory, also discussed later in this chapter), leads scientific reason inevitably beyond the empiri­cal realm of time, transcending into timeless conceptual realities and making the “historical dimension” of the problem of the origin of temporal flow unimportant.393

If, however, one asks the same question in theological terms – that is, from within the perspective of the cosmic history of human beings, the asymmetry between the past and the future (the future that is expressed in eschatological terms as the goal to which human beings as well as the universe are steadily progressing) – then it would be reasonable to argue that the unfolding of the cosmic history goes on toward the future, which comes into the present from the perspective of the ulti­mate purpose of the world. But the direct analogy between physical time and escha­tological time, coming from the kingdom of God, is not simply a working tool in tackling the problem of time from within the scientific context, for the “reality” of the kingdom and the ontology of the coming from the future have a different status in comparison with what is argued in science. This means that the role of the future in the sustenance of time, as its creation from the kingdom, can be articulated only through an appeal to ecclesial and liturgical experience. Can, then, the scientific models of becoming serve as discursive prototypes of the experience of God from his kingdom?394

Since the act of creation cannot be conceived as a temporal act, it constitutes an “everlasting” act, which, metaphorically speaking, is contemporaneous with all times, for example, with all temporal spans of the evolution of the universe.395 But the evo­lution of the visible universe has a beginning, in the time of the created world. The temporality of the visible universe thus represents an aspect of aidion that projects the act of creation into its temporal appearance in the visible creation. The creation, however, is initiated from the atemporal and noneternal realm, which means that there is something in it that cannot be projected into the created realm through any form of temporality. It is exactly this remnant that is intuitively sought by science when it attempts to provide the theory of the origin of time. We have seen in chapter 5 that in order to establish the link between the visible universe in its temporal mode of existence and the source of its existence and the source of temporality, scientific means alone have been insufficient. This is because the basic diastema in creation can be grasped only through the detection of the presence of the logoi of creation in sci­entific theories. These logoi point toward the logos of the entire creation, which holds all things together, including irreversible time, with respect to God.

It is clear that such mediations on the nature and origin of time cannot be the task of positive science; that is why scientific experience is destined to accept dispassionately the time of the material world, which manifests itself through the change of sensible things. Despite this acceptance, however, it is amazing to witness how scien­tific knowledge, being part of the human cognitive faculties, incessantly leads to the production of multiple theories of time. Nevertheless, time, this fascinating feature of all existence in the world around us, inevitably escapes from our scientific under­standing into a spiritual world of ideas, becoming again the subject of rather wide contemplative experience, but this time it is the contemplation of meditating scien­tists, not that of devoted believers.

This shows that there is something about time that will always escape from any attempt of human science to look at it under a microscope. Meditating about the irreversibility of physical time, scientists silently lift their thoughts beyond the phys­ical world, transferring the problem from the sphere of physics to the sphere of ideas. The proper way to treat the problem here, however, is to apply to it the methods of philosophy and theology.

By saying that physics understands time through material process, we implicitly accuse physics of a reductionism that might diminish the meaning of the proposed research.We are not afraid of that, however, because this reduction is used only as a starting point for our discussion. We are convinced in advance that any truth about time that we may discover will inevitably urge us to modify our reductionism and that, in consequence, the subject of time will hence be reinstated to its proper place in the sphere of human ideas based on the wholeness of experience. Nevertheless, being respectful to science and its attempts to obtain a glance into the unfathomable depths of a reality that underlies the everyday world of our senses, we consider two particular accounts of irreversibility. We shall see that, irrespective of its search for some ultimate truth about time, this truth turns out to be a metaphysical, and even a theological, truth.

In what follows, we analyze two accounts on the irreversibility of time: the first provided by the theory of Penrose, who argues that the source of this irreversibility lies in special initial conditions of the universe, and the second by the program of Prigogine, who, on the contrary, sought the source of irreversibility from the per­spective of new local dynamics, which represents the extension of classical physics.

Irreversibility of Time and Boundary Conditions in the Universe

The issue of design in modern cosmology is closely connected with the fundamental question on the nature of the observed postcollision correlations between “particles” in the universe, which, in our human comprehension, appear as a kind of order or design. The nature of such correlations relates to the present-day value of entropy in the universe, for it is entropy that indicates quantitatively the extent to which the uni­verse is in a state of order/disorder. It is known that this entropy (S) is measured as the number of baryons in the observed universe and that its numerical value is estimated to be S = s * 1080, where the specific entropy s* = 108 is the number of photons per baryon. s* is a fundamental physical parameter that is critical for the existence of stable physical systems: a hypothetical variation of s* by two orders of ten will break the condition for gravitational stability of the stars and galaxies and existence of life in the universe.396 The thermodynamic understanding of entropy is based on the second law of thermodynamics, which teaches us that the world is in such a state of change that its entropy is constantly growing. This implies that the value of the present-day S is a result of irreversible evolution in the universe from initial state with the entropy less then S, thus suggesting that there is the universal irreversibility of processes in the universe. The specificity of the universe’s present state, which exhibits some order and correlation of its parts, is connected with special initial conditions, rather than with any possible intrinsic mechanism that drives the flow of time and gives direction to the evolution of the universe to its present designlike state.

Two outstanding attempts to solve the riddle of temporal flow in modern physics exist. The first trend, developed by Prigogine’s scientific school, tried to introduce irreversibility at the “local” level, that is, to claim that irreversibility is inherent in some underlying physical laws, which are to be discovered.397 An alternative approach to the nature of the present state of the universe, as a state with a relatively low entropy and hence a high level of postcollision correlations, dates back to an idea of Penrose’s – that the present special state of the universe, which is associated with a kind of design and irreversible flow of time, has its origin in boundary conditions in the remote past of the universe.

The dichotomy that we observe in these two approaches to explaining the entropy and a specific arrow of time in the universe, which is observed by us locally (“here” and “now”), reflects a general difficulty in distinguishing whether this arrow of time is caused by local factors or by the boundary conditions in the distant past or future. Because the universe is unique, it is difficult to distinguish between laws of nature and boundary conditions governing solutions to those laws (any proposal in this regard is untestable scientifically).398

In this section, we discuss an attempt to catch the source of the irreversibility of time (leading to the existence of complex systems with a high degree of postcollisional correlations, that is, exhibiting some designlike properties) by appealing to the starting point of its evolution. This approach was developed by Penrose and is based on his firm belief that “if the important local laws are all time-symmetrical, then the place to look for the origin of statistical asymmetry is in the boundary conditions.”399

Classical dynamics teaches us that boundary conditions can be posed either in the past or in the future. But, as our macroscopic experience shows, imposing boundary conditions in the future presupposes an infinitely precise arranging of the velocity distribution of particles composing the system, so that one would need an infinite amount of information to obtain the present state of the system. Such boundary conditions are separated from what is physically possible by an “entropy barrier.”400

We accept that lack of information about a system may correspond to a nonzero entropy state and that imposing boundary conditions in the past or future may reduce the entropy to a minimum. The imposition of future low-entropy boundary conditions in this way overcomes the “entropy barrier,” which has been shown to be a consequence of the second law of thermodynamics. This means that such a system will evolve in the direction of entropy decrease, which goes against the current view of thermodynamics. To eliminate this apparent contradiction with the second law, we might instead think of the future low-entropy conditions as “time-reversed past conditions”.

The relatively small entropy of the present state of our universe, which is evidenced by the existence of stable structures, must stem from the low-entropy conditions at its initial state. The irreversible evolution of the universe toward states with high entropy must hence have its origin in low-entropy conditions at the initial singularity. These are the cause of time’s arrow as indicated by the irreversible processes; notice that “time’s arrow” is just a shorthand term for the marked tendency of the majority of the observed processes. According to Penrose: “The entropy concept… refers to classes of states… not individual states.”401

This shows that the definition of entropy depends on what kind of changes we observe and what methods of description we choose. The very idea of irreversibility, which is associated with the growth of entropy, is relevant not to separate objects following well-known dynamical laws but to aspects of the collective behavior of these objects that is normally observed.

In Prigogine’s model of time, the growth of entropy in the universe is driven by the flow of correlations among particles, and the arrow of time, which is related to this mechanism of aging of a system, is associated with a flow of correlation toward complex states involving more and more particles.402 One must, however, answer a fundamental question: what is the ultimate reason for this flow of correlations to even start? According to Penrose’s view, the answer is that the origin of this flow, and of the arrow of time, is hidden in the low-entropy initial conditions for the evolution of the universe.

In itself, the expansion of the universe does not explain time’s arrow. Already in 1979, Penrose had pointed out that there is no direct link between the expansion of the universe, the growth of entropy, and the arrow of time. It is easy to understand that, in the approach connecting increase of entropy with a flow of correlations, there is no object in equilibrium in the universe and that the increase of entropy continues forever independently of the universal evolution, whether it be due to expansion or to contraction. This eliminates the idea of a thermal death of the universe, which is inevitable if evolution is considered only in terms of binary correlations.

Classical physics considered entropy to be an attribute of matter attached to such ingredients as radiation and particles. It was assumed ad hoc in classical cosmology that the state of matter near the big bang is approximately in thermodynamic equi­librium with a maximum of entropy (despite the fact that all physical parameters are effectively infinite at the singularity and that any hypothesis on the physical state there is pure speculation). However, it is evident that the state of affairs the universe displays at present is such an ordered state that the entropy of the universe, as a measure of its disorder, is not high enough to prevent the emergence of states showing precise macroscopic after-collision correlations (great disorder in the universe could not support the stable systems, such as clusters of galaxies, galaxies, and star sys­tems). These correlations, observed in a variety of structures, are evidence that a state preceding the present one must show an entropy that is much less if the second law of thermodynamics is true and applicable to the whole universe. This contradicts the hypothesis of maximum entropy at the big bang.

To overcome this paradox, Penrose pointed out that one should take into account the gravitational degrees of freedom of the universe, that is, to consider the state of the universe not only in terms of its matter content (its particles and fields) but also in terms of its geometry linked in general relativity to the gravitational field.403 He proposed to introduce a new entropy-like property of the gravitational field, later called gravitational entropy (GE). Evaluating the possible amount of entropy that can be produced in the universe during the whole period of its evolution from the big bang to the big crunch, he discovered that there is a tremendous lack of entropy in the baryon universe we observe now, namely, 1088 as compared to the possible value of 10123. The reason for this was thought to be found in the low GE condition at the big bang, which suppressed the “disorder” at the very beginning of the evolution of the universe, making this state extremely ordered but leading then to a strong irreversibility in the evolution of the universe, as a change directed toward disorder and a high degree of postcollisional correlations. The second law of thermodynamics, then, can be treated itself as the display of the evolution of the universe from an extraordinary ordered state to a much more probable state with a high degree of disorder.

To express the condition of the order in geometrical terms, it was noticed that the growth of GE corresponds to a clustering of matter that is accompanied by an increase in the degree of anisotropy of the gravitational field, which is itself described by the Weyl curvature (WC). This led Penrose to propose a scenario for the development of the universe in which the evolution begins from a state resembling, in a way, the low GE entropy corresponding to weak gravitational anisotropy and evolves to a high GE state marked by strong gravitational anisotropy, presupposing that WC can be somehow correlated with a quantitative measure of GE. A more precise statement of this idea is his well-known Weyl curvature hypothesis (WCH): “The Weyl curvature tends to zero at all past singularities, as the singular­ity is approached from future directions.”404

The physical implications of the WCH for the present state of the universe can be expressed as follows: we regard the character of the actual state of the universe, assuming that it began with a big bang and WC = 0, as being more and more of the “precise correlation” type and less and less of the “low-entropy” type as time progresses. This is consistent with Prigogine’s ideas that the complexity of the universe is due to a steady flow of correlations among particles, which can explain a very spe­cial state of the present universe. The WCH acquires the features of a special initial condition in the universe, being a local condition, which cannot itself be derived from the retrospective macroscopic dynamics. It is because of this that the WCH is a priori asymmetric with respect to time, for it is not a part of the temporal series of causations that follow the state with WCH. Similarly to Hawking, Penrose believes that this special initial condition is itself subject to some underlying physical law that is asymmetric in terms of time. According to Penrose: “There are in fact… laws which only become important near space-time singularities, these being asymmetric in time and such as to force the Weyl curvature to vanish at any initial singular point.”405 This assumes that there must be some laws, “local in time,” that are responsible for macroscopic irreversibility; but, in contradistinction to the ideas of Prigogine, these laws are important only at the singularity, that is, in the remote past. As a result, according to Penrose, “the problem of time’s arrow can be taken out of the realm of statistical physics and returned to that of determining what are the pre­cise physical laws.”406 In other words, instead of attempting to explain the statistical tendencies in the macroscopic world by using “nondynamic” theory here and now, Penrose proposes to treat all statistical behavior as the remote result of the local and “precise” law, which is only true at the cosmological singularity. Put further in a dif­ferent way: the observable irreversibility of time, according to Penrose, can be explained not in terms of temporal series themselves, which are displayed because of this irreversibility, but in terms of some yet unknown but theoretically possible local and unique physical law, which is itself not a part of a temporal series.

These laws would have a fundamental importance since they predetermine the entire thermodynamical evolution of the universe and the outcome of this irreversible change, which we contemplate through flow of time and by observing com­plex structures in nature. From a methodological point of view, such an approach presupposes the search for hidden (unknown) “laws” existing at the singularity, which we can guess at only by observing their macroscopic effects in the present-day universe and which we associate with a kind of design and with the entropy 1088. This means that what is assumed as a hidden physical law at the cosmological singularity in its outcome serves as the explanation of the observable arrow of time and evolving complexity in the present-day universe.

We observe here an interesting shift of the problem of the arrow of time and its particular manifestation through the order and harmony in the present-day uni­verse toward that in the remote past, that is, to the moment of origin of the universe. This means that the issue of thermodynamic irreversibility and its entropic characteristic acquires the colors of the special, original “creation” of the universe. This way of thought is reminiscent of the Kantian treatment of the physico-theological (teleological) argument for God, based in fact on the ideas of design – namely, his demonstration that the design argument, in order to become a theistic argument, assumes its foundation in the cosmological argument, in the idea of totality of the world in space and in time. This is exactly the way of Penrose’s logic when the prob­lem of “special entropy at present” is treated as one of a special temporal origination of the universe.

Penrose’s Model and Its Theological Interpretation

To illustrate that WCH implies such atypical conditions in the early universe, Penrose appeals to the idea of a “phase space” of different initial conditions for all possible universes.407 Taking the figure 10123 as a maximum potential entropy for a universe of our type, he estimates the phase-space volume corresponding to its possible initial conditions to be V = 1010(123). But our actual physical universe corresponds to a phase space volume of size V = 1010(88). This shows that the initial conditions of the universe we live in constitute an infinitesimal part of V, namely: W/V = 10–10(123); that is, the precision with which the big bang must be set up is nearly infinite.

In different, probabilistic language, the a priori probability for our universe W with a pattern of irreversibility we observe at present approximates to zero. This is because V remains “almost infinite” relative to W. Consequently, the amount of information necessary to select our physical universe, as a particular region in a space V, will likewise be “almost infinite.”

Since there is no natural foundation for this kind of event, Penrose introduces the idea of a god powerful enough to “create” all kinds of worlds: only an omniscient cre­ator may possess the knowledge of that infinite amount of information necessary to pinpoint that tiny part of phase space that describes the initial conditions of our own universe.

The function of this creator is only to launch the universe, not to govern it. According to Penrose, it is governed by the time-symmetrical laws of physics. The universe W, where S = 1088, which we associate with the presence of a particular kind of irreversibility, appears only because of the very special type of “creation” that is formulated geometrically as the condition WC = 0.

In the rest of this section, we discuss this idea from a philosophical and theologi­cal perspective following the lines of methodology we used while discussing Hawking’s model of creation out of nothing in chapter 5. The philosophical and the­ological treatment of Penrose’s approach to the source of irreversibility of time will, however, be closer to the genuine philosophy of Penrose himself, for he, in comparison with Hawking’s positivistic views, is explicitly Platonist with regard to mathematical physics. According to Penrose, the physical world “emerges out of the (‘timeless’) world of mathematics.”408 He considers the Platonic world of absolutes as the world of mathematical truth, existing prior to and independently with respect to the physical world. He illustrates his position using a diagram similar to the one shown in figure 6.1, which will be important for our interpretation of his model of special initial conditions.

Figure 6.1

First let us realize that Penrose introduced the world W as a concept of the visible universe we live in that contains a specific arrow of time and indicates the pattern of design associated with the entropy S. The task of the theory is to explain the origin of the universe W as having special initial conditions. Since what we observe in the uni­verse W is by assumption contained in the initial state of this universe, it is impossible to provide its further explanation in terms of the state of affairs within the universe itself. In other words, we cannot explain the specificity of W in terms of its various elements. It is because of this intrinsic contingency of the universe W and the number S = 1088 that the metaphysical understanding jumps from the manifold of the universe in its varied content and unlimited extent to the assumption that the universe is built with some determinate purpose; that is, it is designed. From observ­ing the order that science uncovers in the universe (such as, in modern parlance, large-scale structure, cosmic coincidences, and fine-tuning), one comes next to the conclusion that this order and beauty do belong to the universe contingently, because it is hardly to be believed that the diverse things in the universe could cooperate themselves in order to fulfill the formation of the order to which we attribute pur­pose and design.409 At this point, the physical reason appeals to some wise cause, which could be the cause of the world.410

Penrose’s intention is to remove the contingency of the state of affairs in the universe, as it is now, back to the remote past, where, according to him, there was a “law” that made the contingency, which is observed by us here and now, to be a necessary contingency. In other words, the universe that we observe now as a contingent was not such in the past, because there was an original necessary law that caused the further development of the universe. This law, however, does not belong to the empiri­cal series of causations; that is, it transcends the universe W itself. Indeed, it was necessary for Penrose to introduce two more supernatural ingredients to his expla­nation, namely, the multitude of the universes with different initial conditions V and the “Creator.” The V plays a role of the substratum, which is necessary for the “Creator” to be able to choose our universe W. The “Creator” therefore is not a cre­ator at all: it is an architect of the world (a demiurgic god) who is constructing the world W from the material given in V, but who is not the creator of the world out of nothing, for V is not “nothing”, but rather the potentiality of all possible states of affairs – that is, in philosophical terms, the maximal symmetrical state of undifferentiated being.

We observe here an analogy with the Kantian criticism of the physico-theological argument for the existence of God. The problem of the physico-theological argu­ment is that one cannot achieve an understanding of the wise cause of the universe W on purely empirical grounds; one needs to appeal to the cosmological argument, that is, to invoke the concept of the world as a totality of the series of alterations. But the concept of the world in this sense does not deviate from the series of appearances, which regresses in accordance with the empirical laws of causality, and therefore it assumes that the world itself is a member of this series. There is no chance, however, to find any first beginning or any highest member (as a primary or ultimate cause) in the series of the world W, for which a concluding term of the series will be in fact the world V.

Science always tries to discover the ultimate source of temporal series in nature by making some regress toward the fundamental but hidden physical law or to the very first beginning of this series somewhere in the remote past. The inevitable consequence of this search for the believed existence of the absolute cause of the irreversibility and order in the universe is a departure from the field of empirical realities and the temporal series in the world W and an appeal to theoretical mod­els, or constructs, such as V: this is the logic of the transition W → V as it is invoked in the thinking of Penrose.

The striking thing, however, is that the constructs of such underlying reality as V, which is supposed to be the first beginning and the highest term in the series of rea­soning based on the laws of empirical causation, are far away, by their epistemologi­cal nature, from the empirical domain of being; they turn out to be in the world of conceptual realities, or in the world of ideas, which itself does not bear any predicates of temporality. This is why the very cause of temporal flow and irreversibility does not belong to the temporal series. In other words, this ultimate cause of the empiri­cal appearances of irreversibility is not actually the cause of empirical series in a strict sense of empirical causation, because it does not belong to the empirical world. It means that we witness a typical transcendental jump in theoretical thinking from the series of empirical analysis to the series and causation of intelligible nature, that is, to a kind of regress in a conceptual space, where the highest term or the very first “beginning” is revealed not by the methods of empirical advance but by purely logi­cal formulations of the absolute necessity of such a being, which is responsible for the temporal series in the world. One must admit that Penrose’s mathematical model (WCH) gives an actual example of such a regress within conceptual realities.

The logic of an inverse transition V → W, which describes the actualization of our world W out of V, is then understood from our W perspective as a causation in the conceptual space, whereas for “the Creator,” for whom the manifold of the world V, and the world W as a part of V, are given in their actuality, the transition V → W means a transition between two ontologically homogeneous objects V and W. This implies that a divine entity that actualizes the world W out of V is seen by us also as a construct from the conceptual space.

We observe here a kind of mental inversion from causation in the temporal series (W → V) to causation in the purely intelligible series (V → W), the completeness of which is based on the existence of an absolutely necessary cause (the creator). This jump in reflection is based on an inability to build the empirical content of the concept of the unconditioned condition (V + creator) in the series of empirical causes. According to Kant, the special features of the world W, involved in irreversible flux, cannot bring us through the empirical analysis to the existence of such a necessary cause that would not be contingent itself. For Kant, this is why one can state that there is not an absolutely necessary cause or being.

This means, in Kantian parlance, that the idea of the ensemble of possible initial conditions V and the idea of Penrose’s creator have no ontological reference in the empirical realm. They both exist in the sphere of thought as logical forms that func­tion instead only for the purpose of the logical justification of W as a contingent and temporal state of affairs with some pattern of design. Some physicists, however, inspired by the idea of many worlds that appears in different parts of physics, believe that V has the same physical ontology as W and that this is why the causation that brings W into existence out of V is sought as a physical law.411 The same takes place in Penrose’s argument when the WCH is formulated metaphysically, that is, as a law imposed by the creator by means of pinning out a “point” in a set of all possible uni­verses.

The clash between the realistic treatment of V and the creator, drawn from Penrose’s argument, and the negative result on the same treatment, following from the Kantian analysis, leads us to the only justifiable formula for dealing with the sit­uation, namely, to treat Penrose’s statement about the transition V → W as an antinomy, which is similar to the fourth Kantian antinomy on an absolutely neces­sary being:

Thesis: There belongs to the world the ensemble of all possible universes V with different initial conditions whose existence is absolutely necessary for our universe W with low initial entropy to exist as a part of V; this is a causal condition for the arrow of time in W (there is causal connection between V and W).

Antithesis: There nowhere exists the ensemble of universes V in the world as the cause of our universe W with low initial entropy and the cause for the arrow of time in W; there is no connection between V and W: they belong to different ontological realms (intelligible and empirical correspondingly).412

In analogy to what we said in the context of a similar antinomy in Hawking’s model, Kant would use this antinomy for a negative conclusion about empirical evi­dence for the existence of V, playing the role of a cause of the universe W with the arrow of time. He would argue that the V and the creator both belong to the intelli­gible realm and do not have an independent ontological being apart from the thought that brought the ideas of V and the creator into being. From the perspective of Penrose’s philosophical position (that is, his Platonism), this will not constitute any trouble, for the world V can be easily treated in Platonic terms as an element of the intelligible realm existing independently from W. The meaning of the transition V → W can then be interpreted in terms of the diagram in figure 6.1 as the tran­sition from the intelligible realm to the sensible realm. This kind of transition we have met before in the context of Hawking’s model. To accomplish the theological treatment of this idea, we should add one particular detail to the whole picture, namely, to affirm that the world of Platonic ideas, containing V as well as the visible universe W, constitutes the created world in its differentiation; that is, both are part of the created realm. In this case, the transition between V and W – caused, accord­ing to Penrose, by a demiurgic deity – as the “explanation” of the emergence of the visible universe W out of the intelligible ensemble of the universes with different ini­tial conditions means, in a theological context, the differentiation between the intel­ligible and the sensible in the created domain. In other words, the split between V and W that is presented in Penrose’s model as the setting up of the initial conditions in W can be treated through Patristic eyes as the difference (diaphora) between the intelligible and the sensible as the constitutive element of creation of both V and W out of nothing. This treatment can be illustrated with the help of the diagram shown in figure 6.2 (which, in a sense, is a reinterpretation of figure 6.1 through the eyes of Christian Platonism):

Figure 6.2

Finally, this view explains to us what was really indicated in Penrose’s model. Definitely it has nothing to do with the creatio ex nigilo taken in its pure affirmative form, for the world V (out of which the sensible realm W emerged) preexisted before the actualization of W. The “creator” also belonged to the same realm as V, and its work was simply mastering the W from the material given in the V. Both V and the “creator” belong to the intelligible series of causation, as demonstrated earlier.

The Orthodox theological view, which we now employ, is that the V is an object from the intelligible domain, whereas the W, in its appearance to us, can be consid­ered a part of sensible creation. What, then, does the transition V → W mean? It shows not the creation of W out of V but, rather, the differentiation between the intel­ligible potentially existing worlds V and the sensible world W. Indeed, both V and W exhibit the fundamental diaphora in creation. An effort to explain the observable irreversibility of time in W, as an attempt to find the foundation of the whole world W in the nonbeing of W, led us to the scientific model of diaphora in the created world. The specificity of the big bang, articulated by Penrose, points in fact to the specificity of the constitution of the creatio ex nihilo, but not to its ontological mechanism. We contemplate these special constitutive elements of the creatio ex nihilo through the model of this difference between V and W. The difference between the worlds W and V is the indication of the presence, or absence, of a particular irre­versibility of time and the observed order in the universe. This means that the fact of the irreversibility of time in W with its specific entropic features can be treated as a constitutive element of the creatio ex nihilo, because it provides the characteristic of its difference from other intelligible worlds V, where there is no irreversible flow of time, or time’s arrow.

The antinomy formulated above in the context of Penrose’s model can now be rephrased as an affirmative proposition on the constitution of creation:

God, creating the world out of nothing, sets up the difference between V (plurality of conceptual universes with different initial conditions) as the domain of intelligible creation, and our universe W (with low initial entropy and hence irreversibility of time and presence of complex structures) as the realm of sencible creation.

From this point of view, the WCH of Penrose can be treated as an attempt to describe this diaphora between V and W, as it is seen from within W, that is, in physico-geometrical terms. The presence of the diaphora in the created being, detected in the Penrose model, reveals thus the common logos of both W and V, that is, that both of them are created (they have nonbeing as the ground for their being).413 From here, one can conclude that the logos of the irreversibility of time (and the complexity and design following from it) is the principle that there is nonbeing of temporal flow, which is the ground for its being. This was exactly demonstrated in the model of Penrose, and it is why we can conclude that Penrose’s model, treated through the eyes of Patristic theology, points toward the logos of creation.

We see that the problem of the irreversibility of time – that is, an attempt to explain the source of irreversibility of time through the special boundary conditions in the universe – leads inevitably to the result that it can be posed only in the context of the theological concept of creatio ex nihilo. This makes it possible to argue that it is in the problem of the irreversibility of time that we witness the presence of funda­mental contingency, as the openness of physics to further explanation, coming from philosophy and theology. In this, the phenomenon of time manifests itself as rela­tional upon atemporal reality and the nonintelligible (in human terms) reality of the uncreated God.

Irreversibility of Time through Irreversibility of Processes

In this section, we analyze a different attempt to explain the irreversibility of time, not in terms of geometrical boundary conditions in the universe but as the phe­nomenon that is driven by some underlying physical law that acts universally everywhere and which is revealed through the behavior of large complex systems. In this approach, which has been developed by Prigogine and his collaborators, empirical time, seen as irreversible temporal flow, is not a primary ontological entity in itself. Instead, it is determined by the processes in physical systems, which are involved in irreversible change because of special deep-level physical laws, so that the deep reason of time is in not the macroscopic world but the underlying (quantum) realm.

Prigogine expresses explicitly his view that the irreversible flow of time is something that can be connected only with a special kind of connection among particles in a complex system: “The arrow of time expresses a relation among the objects – be it among particles or fields. Time is not in the objects, but results from the dynamics; … irreversibility is not related to particles but to relations among particles.”414

The rationale of this statement is straightforward: there is no time as a kind of physical or ontological entity apart and beyond the links and relations among the components of the physical world that are revealed through interactions and collec­tive dynamics. In other words, there is no time and time’s arrow as it is in itself. The arrow of time thus is not a mysterious metaphysical entity; rather, it is an epiphenomenon of the internal dynamics of physical systems, including the whole universe. This is why, if one wants to explain the nature of irreversibility of time, one should explain, according to Prigogine, why certain processes turn out to be irreversible.

To state this another way, Prigogine seems to assume that the nature of the irreversibility of time in this approach is hidden in some underlying physical factors that may be responsible for physical irreversibility in general. Unfortunately, this approach to the riddle of time in no way brings us closer to solving the riddle of time’s irreversibility, because macroscopic flowing time escaped from the scene from the very beginning. Nevertheless, a heroic attempt to solve the mystery of the arrow of time in such an approach exposes further that the problem of the irreversibility of time is a philosophical (or even a theological) problem and can be tackled only by means of a proper discipline.

Let us trace some important stages in Prigogine’s program of tackling the prob­lem of time. The major motivation is the existence of the “time paradox” in classical physics, recalled briefly here. According to the commonly accepted view of classical dynamics, represented by either Newton’s mechanics or Einstein’s relativity, it does not provide in its mathematical expression any adequate means of tracing qualitative transformations in a physical system that could be associated with irreversibility or historical change. Simply speaking, classical mechanics (and actually all physics based on it) is time reversible.

This is because the dynamics of processes in classical mechanics is described by the solutions of ordinary differential equations, which by themselves do not contain any indication of the direction of time or history in the system they describe. In fact, the solutions of these equations are not unique if the set of the boundary conditions is not specified. The relation between the possible solution and the actual dynamics in the physical system can be established only if a particular trajectory is picked up out of many solutions by specifying, for example, its initial point. In fact, the condi­tion that specifies a particular trajectory can be chosen at any point of this trajectory, which makes no difference between “initial” or “final” conditions or any other con­ditions in the middle. This implies that if one associates the points on this trajectory with a kind of “time” (it can be any parameter that provides a correspondence between the points of trajectory and the set of real numbers; the length measured along this trajectory from its initial point could be a good example), then all “moments” of this time in this dynamics are equivalent in the sense that they are all linked deterministically according to the dynamical law encoded in the differential equations. This means that there is effectively no distinction among “moments” corresponding to different points of trajectory; all of them are uniform and indistinguishable, so that one can affirm that there is no time as irreversible flow of novelty in this system. The complete symmetry between all points of a given trajectory means that “past,” “present,” and “future” in reversible dynamics simply do not exist. This allows us to guess that time, from the point of view of these simple processes, also does not exist. One concludes, then, that the ideal reversible processes, which are described by classical dynamics, do not contain time and cannot be used in order to study time. One can even speak about the timelessness of these special processes, for there are no temporal distinctions in their nature.

The time paradox appears, then, as an obvious contradiction between the time-reversible laws of classical mechanics and the outcomes of these laws in the macro­scopic world, which exhibit irreversible patterns of behavior in complex systems, and the creation of novelty in chemical, biological, geological, and other physical phenomena.

Let us formulate the essence of the time paradox in some technical terms. We start with classical dynamics (that is, Newton dynamics and Maxwell-Lorentz theory). From a formal point of view, the dynamics of a free single particle is described by a trajectory in so-called phase space. The phase space corresponding to a single particle constitutes an abstract space of all its possible motions and, for a one-dimensional motion, is presented by a plane with two dimensions: one corresponds to the coordinate of the particle, the other to its momentum. A trajectory that corresponds to some particular motion is represented by a curve (one-dimensional manifold) with two boundary points, which are usually called the initial and final points of the particles evolution. As pointed out earlier, in the reversible dynamics both of these points are dynamically equivalent as well as equivalent to all other points on this tra­jectory. The “time,” appearing in this description as a parameter marking the points on trajectory from its initial point to the final point, can be easily reversed in the opposite direction so that the dynamics remains, although the logical order becomes reversed. Such reversible dynamics does not feature evolution in a proper sense of this word, because there is no real change in the system and no novelty emerges.

If we generalize this result, we can affirm that if for some physical system the “tra­jectory” presentation of its dynamics is possible, then the system is time reversible and does indicate the arrow of time.

One might hope that, by considering ensembles of free (noninteracting) particles, we would be able to introduce irreversibility into its dynamics. This is not the case, however, for we can easily replace a single trajectory by a “tube of trajectories” in phase space described by density function ρ. In analogy with our previous result, we can generalize as follows: if for some physical system of many particles the “tube of trajectories” presentation of its dynamics is possible, then the system is time reversible and does not indicate the arrow of time.

If we turn now to a quantum description of dynamics of a single particle – based on the Schrödinger equation for a wave function Ψ, where the location of a particle in space is determined only probabilistically in terms of |Ψ(x)|2 – the dynamics of probabilities is deterministic itself, for it follows, in a way, the same deterministic Schrödinger equation. This means that if we consider the motion of a single particle with a constant energy E, the solution of the Schrödinger equation is an oscillating function of time, leading to a trivial result that there is no change at all in the proba­bilities of locations of the particle, which implies that there is effectively no evolution in the system and, in fact, no time, for there is no distinction between past, present, and future. The same result (in analogy with nonquantum mechanics) holds for an ensemble of noninteracting particles.

We see thus that the reversibility present in dynamical equations of classical and quantum mechanics – or, in different terms, the symmetry of dynamical laws of physics with respect to the inversion of time – leads in fact to the conclusion that physics, based on these laws, does not allow any description of “history” as the emergence of novelty, which is irreversible in the sense that the events of history, being brought into being, cannot be undone or eliminated by “antievents.” In this, historicity contrasts with determinism, which is present in the laws of dynamics.415 Prigogine affirms that a change present in the classical description of trajectories is, in fact, a denial of becoming, for “time” is a mere parameter, which is not affected by the process it describes. This is a manifestation of determinism, which in its ideal denies contingency as well as empirically observed irreversible processes; the growth of complexity in physical, chemical, and biological systems; the emergence of life and the arrow of time. The contrast between the determinis­tic and time-reversible dynamics, which (according to classical physics) drives the world, and the evidence of irreversible processes and systems – which cannot be precisely described by these laws cannot be understood from within the complete set of given conditions and requires some extra-factors not described by dynam­ics – constitutes, according to Prigogine, the “paradox of time.” On the one hand, there is no time in the underlying deterministic description of the physical world; on the other hand, there is empirical irreversibility of time observed in complex systems. This paradox, Prigogine argues, must be resolved, for otherwise it leads to dualism in physics.

Irreversibility and Two Views of Nature

Past attempts to resolve the time paradox were based on the common belief that its origin comes from the specificity of the scientific description of the world. In fact, there were two views of nature: one held that the deep, fundamental level of physical reality was described by classical physics and that knowledge about this world is a perfect knowledge; the other was derived from everyday experience and from those parts of experimental physics that demonstrated explicitly the existence of irre­versible processes in nature. Scientists tried to explain the irreversibility and irreducibility of its description to deterministic time-symmetric dynamics by referring to the lack of knowledge of microscopic motions of particles involved in macro­scopic irreversible processes. If we could know all parameters of microscopic motions with an infinite precision, we might achieve a “perfect knowledge,” which would explain away the observable macroscopic irreversibility.

What is striking, however, is that nobody expressed any doubt about the perfectness and exactitude of the underlying reality (or ontology, denoted here as UR), in which the deterministic and time-symmetric physics were supposed to reign and which were supposed to be responsible for the macroscopic (empirical) level of real­ity (ER), where time irreversibility is undeniable. Nobody could assume that the realm of deterministic and time-reversible physics was a special case of a much more complex state of affairs in the UR, which could be complex and irreversible. Thus the separation of the deterministic and time-symmetric processes in UR and the irre­versible processes in ER led to a strange dualism in views about nature.

Historically, however, this was a contradictory dualism, for it was a tendency to explain irreversible phenomena in terms of deterministic dynamics (for example, the attempt by Boltzmann to explain the growth of entropy from dynamical equations). Such attempts manifested the belief that there must be a single level of reality that explains everything. But it was not realized in the past that processes in UR and ER manifested two different types of behavior in physical systems that cannot be ultimately reduced to each other. In other words, an attempt to provide a physically con­sistent explanation of the transition

UR → ER (fig. 6.1)

by removing thereby rhe dualism in views of nature did not succeed, because it was an epistemological attempt to reconcile the descriptions of two ontologically differ­ent realms, which cannot be described in the same conceptual terms. To succeed with such a unification, one should change the whole physical paradigm so as to be able to justify the transition (fig. 6.1) on the ontological level.

The historical development of classical physics demonstrated that it was unable to solve the mystery of irreversibility and time’s arrow, which were observed in the empirical realm (macroscopic world). Classical physics had to recognize that its conceptual basis was not sufficient to tacle the problem of the arrow of time and to accept the arrow as a fundamental ingredient of reality, without further explanation in terms of classical dynamics.

Despite all this, a strong subconscious belief existed that there must be a physical explanation of the origin of the arrow of time. This belief in the ultimate character of the arrow of time and, at the same time, an inability to explain it in a logically con­sistent way gave rise to an epistemological situation in classical physics that can be described as an antinomy about the origin of the arrow of time:

Thesis: The world is governed by some unknown fundamental physical law, which is the necessary cause for the existence of the arrow of time in the visible universe.

Antithesis: No special but unknown physical law that is a necessary cause for the arrow of time in the visible universe exists in this universe.

Formally, the thesis represents the point of view of a dogmatically optimistic physicist, believing in the existence of the physical cause of the arrow of time, while the antithesis represents the point of view of an empirical physicist who observes the arrow of time but is unable to explain it. Together, the two conflicting views indicate that the arrow of time manifests itself as a brute fact that cannot be explained by positive science and needs for its clarification an intervention from philosophy and theology.

According to our previous experience of dealing with antinomies, we should assert that their presence expresses the fact that classical physics approached closely the borderline between the two distinct realms of being with which it was dealing, with no successful attempt to reconcile them. Namely, there was the world of ideal motions, in which time was not present at all; this was first the world of classical mechanics, by its constitution an intelligible state of affairs, which was described by using abstract mathematical space and nonobservable trajectories in phase space. On the other hand, there was the evident presence of the arrow of time in the empirical realm. The reconciliation of these two realms was problematic by definition, for how could one find the foundation of the arrow of time, which is revealed through the empirical temporal series of causations, by appealing as a cause of it to the laws, which have no indication at all of the presence of temporality, for they represent the “dynamics” in intelligible series, rather than temporal. The trick with using the atemporal physical laws as a limiting term of temporal causations in the empirical realm did not work, for the laws of classical dynamics were considered as acting here and now, rather than from the remote past or future of a temporal series. This makes the problem of time’s arrow in classical dynamics different from the problem of time’s arrow in the context of the cosmological initial conditions, which was discussed in previous sections.

For Penrose, the time-symmetry of the local physical laws was an indication to look for the source of irreversibility in special boundary conditions, avoiding thereby the time paradox in Prigogine’s sense. Whereas, for the latter, the challenge of mod­ern physics is to resolve this paradox without appealing to the remote boundary con­ditions but, rather, trying to extend the local dynamics enough that it would provide a mechanism of an internal irreversibility here and now. In this case, the transition (fig. 6.1) could be explained on the ontological (physical) level by removing the antinomy of classical physics. It is possible to predict in advance, however, that such an attempt would run into severe difficulties with treating the mechanisms that “take place” in UR as physically real. In other words, the hope to change an ontology of UR, in order to level it with the ontology of ER, is philosophically suspicious, for it leads ultimately to a monistic view of reality. Indeed, if the paradox of time’s arrow were to be solved in physical terms, the element of contingency in time, which is present because of the insufficiency of classical mechanics to remove it, as well as expressed epistemologically in the antinomy, would be replaced by an ultimate necessity pres­ent in the world, removing the historical change and making it a part of blind and dispassionate universal dynamics.

Prigogine’s Treatment of the Time Paradox

According to Prigogine, the key element for resolving the paradox of time must be new dynamics, that is, new laws that could explain the emergence of irreversibility at the fundamental level of reality (in UR). This dynamics must be irreversible by defi­nition and must feature two important properties: to contain “interactions” and to be “nonintegrable.”

The view that interactions may be responsible for the observed macroscopic irreversibility dates back to the work of L. Boltzmann, who established the general fact that the evolution of a large system with collisions/interactions among its particles leads to disorder because of these interactions. For Boltzmann, the increase of disor­der, which can be described formally by the function entropy, can be used to indicate the directed evolution in the system, whereas entropy can be viewed as encoding the growth of time.

One can reassert that macroscopic evolution was associated with the interaction of particles, or the different parts of a large system. We remember, however, that clas­sical physics was always trying to remove an element of irreversibility in its theory, so that its first attempt to keep reversible dynamics in its formalism resulted in an attempt to remove all ingredients in the theory that could lead to irreversibility – the interactions among particles, for example. If this were to be possible – that is, if the interacting particles could be described effectively as noninteracting – then they would follow reversible dynamics, and irreversibility would be excluded. The systems where such a transform is possible are called integrable. To establish the dynamics of such a system means to integrate the differential equations that describe it; if it is possible, then it is proved that the system is time reversible. It follows then that the property of a system of particles to be integrable is equivalent to this system being reversible and to its having no internal time.

As is now recognized, the class of integrable systems in nature is quite narrow, so that the reversible processes represent a special case in physics, whereas the majority of realistic systems exhibit such complicated interactions that the integration of the equations and the deterministic description of their motion are impossible. The for­mal distinction between integrable and nonintegrable dynamical systems was intro­duced by H. Poincaré.416 In integrable systems, the potential energy of interaction between parts or particles can be excluded from the expression of the full energy of a system through a suitable transformation of the so-called canonical variables. The system for which this kind of transformation is possible is equivalent to a system of noninteracting particles with reversible dynamics and is called integrable. All sys­tems in which this transformation is impossible are called nonintegrable.

In his famous theorem of 1892, Poincaré proved that, in general, this transformation is impossible. He described a special class of systems, which later were called Large Poincaré Systems (LPS), in which the interactions between the parts of a system could not be excluded due to a special type of behavior (called “resonances”) between their degrees of freedom. If there are “enough” resonances, the system is not integrable. As shown later by A. Kolmogorov, V. Arnold, and J. Moser, the evolution of those degrees of freedom that are involved in resonances cannot be described in terms of trajectories.417 In other words, these trajectories become random and unpredictable, so that the determinism that is usually associated with the trajectory description is lost, and, as a result, the symmetry between past, present, and future is lost in these systems; that is, they manifest irreversible behavior and contain some internal time.

This leads to the important conclusion that classical determinism, which is assumed to be an inevitable consequence of reversible dynamics, is no longer a uni­versal concept and can now be attributed only to very special physical systems.418

It is not difficult to realize that the observed irreversible processes are the unavoidable result of the evolution of large complex systems (LPS) in the universe. In fact, the very evolution of the visible universe indicates that the universe itself is an example of LPS.

Coming back to Prigogine’s intention to build the new dynamics, we can now formulate more precisely what it means in theoretical terms. We have already mentioned that time-reversible dynamical systems can always be described in terms of trajectories in phase space. It is because of this that the idea of irreversible dynamics on the fundamental level of description is associated with a change such that the tra­jectory representation in this dynamics will no longer be valid.

What are the philosophical implications of this program? First, when one says that the time-reversible behavior of physical systems in the macroscopic world makes it possible to think of this system as following some trajectory in a phase space, one implies that phase space itself is a more fundamental aspect of physical reality than the variety of observable phenomena, and that the macroscopic properties of the system are somehow predetermined by its development in the underlying phase space. But the phase space is not an element of physical reality understood as object in macroscopic space-time. This way of thinking corresponds to the assumption that there is a physical causation from phase space S ϵ UR to observed irre­versibility in space-time in ER that is, that the transition UR → ER is believed to be physical. However, phase space S is an abstract mathematical concept that is believed to have some physical meaning, but its ontological status is unclear.

We are here confronted with an interesting epistemological paradox. We observe time-reversible phenomena on the macroscopic level, describing them in terms of factual appearances. Our understanding then summarizes the multitude of disconnected facts under its own categories to produce some unifying conceptual totality that explains this variety. A striking feature of this description is that it uses mathe­matical constructs that have no direct correlation with anything in physical reality. To explain the observed physical phenomena, one appeals to elements that belong not to the world of physical reality but to the world of ideas. In this approach, the responsibility for the time-reversible character of some processes is ascribed not to the world of physical phenomena (to ER) but to some kind of conceptual “underly­ing reality” (to UR), namely, to mathematical phase space S (whose ontological sta­tus is quite vague).

From this point of view, Prigogine’s program of building irreversible dynamics in phase space that would eliminate trajectories and, as result, lead to macroscopic irreversibility has the following philosophical interpretation: to introduce irreversibility into the description of macroscopic processes, one should attempt to recover irre­versible dynamics not from the physical world of phenomena (from ER) but from a nonclassical mechanism that operates in the mathematical phase space, which is beyond the empirical realm. If this mechanism, which leads to the destruction of tra­jectories in phase space, were found, one would be able to claim that it can be used as a base for the new dynamics and is responsible for macroscopic irreversibility. The major philosophical assumption of Prigogine’s program, which makes it possible to use such an interpretation, is that there is a physical causal link between the mecha­nism in phase space and the processes in the empirical realm, that is, that there is some physics behind the transition S → ER.

An amazing and nontrivial feature of this program is that, in order to invent a mechanism that can eliminate trajectories from phase space S, one has to make a fur­ther appeal to the another underlying reality, so to speak, on the next order, which is in a deeper level than S and which in some sense sustains and explains S. One can name this “reality” provisionally a Hilbert space H. The meaning of H can be illustrated if one presents a trajectory, describing the transition from one state to another in S, as a superposition of all possible trajectories, or histories, in H that can cause this particular transition in S. It is important to remember that these “histories” do not belong to the phase space S, because they describe all potential, but not actual, ways by which the system can evolve from one state to another and which are described by a given trajectory in S. This trajectory is presented mathematically as a continuous sum (integral) of all logically possible histories of the system in H in which the inte­gration goes over some parameter k, which corresponds to a given history.

The achievement of Prigogine’s group was to demonstrate that for LPS systems, where the so-called resonances between the degrees of freedom take place, the amplitude of the transition between two histories in Hilbert space H becomes a “Fokker-Planck operator” that leads to diffusion in momentum space H and, as a result, to the destruction of trajectories in S. This in turn gives rise to macroscopic irreversibility, which is expressed in terms of the flow of correlations among particles. This flow makes it possible to introduce a mechanism of “aging” in many particle systems, that is, to introduce a natural “arrow of time.”419

Since the interactions among particles may be understood as a flow of correla­tions from two particles to three particles and from three particles to four particles and so on, the increase of entropy as a measure of irreversibility in LPS will be an unending process due to the tremendous amount of particles in the universe. Since the irreversible processes turn out to be inevitable ingredients of physical reality, it is understood accordingly that they are responsible for all constructive processes in the universe, such as the creation of its large-scale structure of galaxies, stars, planets, human bodies, and so on. These stable structures manifest the effect of long-range coherence, which is possible only because of interactions and instabilities.420 The top position (in terms of complexity) in the evolving systems belongs to anthropic species. It is because of this that one can affirm along the lines of the so-called anthropic principle that the irreversibility of the universe and the arrow of time constitute the necessary conditions for human beings to come into existence.421

From Irreversibility in Physics to Theological Contingency

Let us reflect on the results outlined above. The structure of Prigogine’s search for the ultimate source of macroscopic irreversibility can be summarized as a double transition among three types of reality:

Hilbert space → phase space → macroscopic world

This formula demonstrates thar in order to explain evolution in the macroscopic empirical world ER, physicists persistently construct the models of its underlying mechanisms using mathematical constructions that are freely created by human rea­son and that by their constitution do not belong to the physical world ER. Classical physics introduced the idea of phase space S, which for a very long time was identified with the first level of underlying reality. A further synthesis in quantum physics forced a physicist to introduce the idea of the Hilbert space H, which functions as the underlying reality of the second level. The conceptual trajectory description of the dynamics in S received its new interpretation as a sum of all logically possible histories in H. By its logical status, the reality that is associated with H is on a deeper level than that of S, so that the new dynamics of Prigogine in H in a sense justifies the dynamics of trajectories in S. In the same way we say that S underlies ER, we can affirm that H underlies S as well as ER. But both S and H are only two peaks of the evolution of our physical theories, in which we have been steadily forced backward, from abstraction to abstraction, always explaining the coarse and solid of empirical reality by means of the fine and ethereal of the intelligible realm.

If there is the set of histories in H such that it can be integrated and hence can lead to the trajectory in S, then the double transition in the last formula could describe the dynamics of the reversible evolution in a physical system. The presence of irre­versibility in the macroscopic world from this perspective can be treated in the framework of classical physics as a puzzle of the transition from the underlying realm UR, with time-symmetric dynamic laws, to the group of irreversible phenomena in ER, which we can denote as ERirr. The problem, then, of classical physics was to explain the irreversibility in ER through the hidden nature of the relationship

URrev → ERirr ϵ ER (fig. 6.2)

If we look carefully at the formula (fig. 6.2), we identify immediately some asymmetry between URrev and ER. The realm URrev corresponds to time-reversible physical laws, whereas ER contains both reversible and irreversible phenomena. As Prigogine showed, one can easily explain the mechanism of the transition URrev → ERrev ϵ ER, that is, to claim that there are some reversible laws in URrev that are responsible for the reversible processes in ERrev. It is clear, however, that the class of the underlying structures, such as phase space S and Hilbert space H, is very special. In other words, the subclass of the reversible phenomena (ERrev) is logically and probably physically connected with a special subset of the underlying realm URrev.

If we now take into account the results of Prigogine’s group, which were explained briefly above, we should admit that it is possible to explain the irreversible phenom­ena in ER only if the structure of the UR is radically changed, that is, if the phase space does not contain trajectories (which effectively means that S itself no longer exists as a space of trajectories). The most interesting result of Prigogine and Petrosky was to show that the mechanism of the destruction of trajectories, which was initially assumed to be in Hilbert space H, destroys the structure of this space, so that neither S nor H can be used as a conceptual ground for explaining the irreversible phenom­ena in ER; that is, they cannot provide logical or physical causation with ERirr.422 This implies that the scheme (fig. 6.2) whose explanation was a final dream of classical physics cannot be used for interpretation of irreversible phenomena.

This implies that to explain the existence of ERirr by appealing to some underlying structures, the structures must definitely be different from S and H; if we denote them as URirr, then the explanation of phenomena in ERirr would mean providing a physics of the transition

URirr → ERirr ϵ ER

We rearticulate the meaning of this formula because, in order to explain the irreversible phenomena in the empirical realm, one should appeal to mathematical models of the underlying mechanisms of these phenomena, which will be radically different from what is known from classical time-reversible physics (that is, it must be neither phase space S nor Hilbert space H).

This is a nontrivial consequence of Prigogine’s effort to solve the riddle of time, which makes it possible to reformulate the dualism about the nature of reality that was discussed above. One should now recognize how deep is the essential distinction between reversible and irreversible physical processes. They are different not only in their appearance in the empirical realm ER but also on the level of the underlying fundamental reality UR, which is supposed to be a logical and physical ground of these processes as observable in ER. It follows therefore that in order to understand the physics of the irreversible processes, one should change the fundamental descrip­tion of classical physics.

This change will amount to a substantial shift in our understanding of the physical world in general. We will not ascribe macroscopic irreversibility to a deficiency of our description. On the contrary, we have reason to insist that irreversibility demands consistent and coherent description (by using new mathematical concepts), which, however, leads us beyond the scope of classical physics. Rephrased in philosophical language, one needs an epistemology that can justify a new physics of irreversible processes. We intentionally use the term epistemology, not ontology, because we are aware that most of the models of underlying reality giving a fragment of a “theory” of irreversible phenomena are, by construction, far beyond the sphere of our immediate cognitive faculties and represent some ideas of physical discursive reason that tran­scend the world of phenomena, understood as a world of our physical experience ER.

In classical physics, we had a dualism between the variety of physical phenomena, including complexity and irreversibility (ER) and the underlying reality of perfect physical laws (UR). Now, following Prigogine, we have arrived at a more sophisticated dualism, which affirms that there are two complementary kinds of processes in the universe: (1) reversible processes, described in terms of ERrev ϵ ER and explained in terms of the corresponding URrev ϵ UR; and (2) irreversible processes as a differ­ent subclass of physical phenomena, described in terms of ERirr ϵ ER and explained, according to Prigogine, in terms of the new dynamics in URirr ϵ UR.

We feel intuitively that it is a fundamental feature of macroscopic reality to be in motion, to evolve, to pass in time, to produce novelty. We also intuitively feel that the future is open, that it is not fixed or determined in advance. This understanding stimulates our search for an ultimate cause of the passage of time. However, evolu­tion, irreversibility, passage of time always mocks and eludes our rational attempts to grasp everything by subordinating it to our empirical realism of classical physics; it leads us astray from the starting point of its search, from the experience itself. The epistemology that classical physics follows cannot provide a unified description of reversible and irreversible processes. In both cases, it was necessary to appeal to underlying conceptual realities, which by their construction should explain the processes in the ER. The new dualism, however, led to the split of the underlying real­ity into two distinct blocks. We can rearticulate that the new dualism has not removed the duality in views on the interplay between the observable phenomena and the fundamental physics that suppose to describe them from the underlying realm. The logic of Prigogine’s approach to the riddle of irreversibility of time brings us to a clear understanding that the irreversibility, if one wants to explain it in physical terms, demands that classical physics change first of all on the conceptual level. This change, however, leads to a split in the ontology of the underlying reality, manifesting thereby the irreducible nature of irreversible physics to one that is reversible in both the empirical and the intelligible realms.

We are inclined to argue that this indicates that the mystery of time’s irreversibility cannot be resolved by any theory. Any attempt to appeal to some underlying phys­ical mechanisms that are assumed to be existent ontologically and expressed conceptually through mathematics is doomed not to explain the problem but to shift it onto an underlying level, which will in turn demand its further explanation. The danger of this approach is that the advance toward conceptual realities that can underlie the empirically observable flow of time is probably unending, so that the ultimate term of the chain of intelligible causations that are assumed to describe empirical time cannot belong to the temporal series themselves, leading the search for its source outside physics to the sphere of philosophy and theology.

Let us pause on this last statement. Since UR in both views on nature cannot be observed directly, one might conjecture that there is only some kind of “causality of reason” that, after all, can bridge the difference between UR and ER. The belief that UR as the fundamental reality is responsible for the variety of the phenomena in ER is very close to the philosophical idea of “things-in-themselves” affecting our senses.423 It is interesting here that the difference in the empirical realm (as to reversible and irreversible processes) as a structure of the ER cascades down toward the underlying reality UR, which is now structured as the difference between URrev and URirr. The world of “things-in-themselves” (UR) is structured in the same way as the world of “things-for-us” (ER): we have two types of the empirical realm, which correspond to two types of the underlying reality. Thus we can argue that there are two types of causality of reason, which link two pairs of nonintersecting worlds: one that is applicable for justifying the reversible processes URrev → ERrev and another for irreversible processes URirr → ERirr.

We are now in a position to address whether something has changed in the epistemological status of the idea of time’s arrow after the new dualism in views about nature has been brought into physics by Prigogine’s ideas. Unfortunately, we have to state that nothing has changed. Despite the fact that his dynamics indicates a source of macroscopic irreversibility inherent in physical reality, the problem of the onto­logical status of URirr is unsolved. Since, from a philosophical point of view, we can­not point to any evidence of the objective existence of URirr – that is, such an existence that could be formulated in terms of physical space and time – we cannot claim that the source of time’s arrow belongs to the physical world.424 What we can do, and have done, is to invent two incompatible hypotheses concerning the nature of URirr. This leads us naturally to the view that the idea of the arrow of time can be treated only through the antinomian form of thought, setting out the limits of our capacities in tackling this problem of time. The justification for this comes from a simple Kantian formula: that since URirr is constructed in order to justify the tempo­ral series in ERirr, there must be some connection between them on the physical level so that the temporality of URirr cascades up toward temporality in ERirr. In this case, URirr, by logic of the argument, must belong to the same temporal series as does ERirr. On the other hand, since URirr is a purely intelligible object (that is, it does not belong to the temporal series of causation), the causation in the transition URirr → ERirr is purely intelligible; that is, the temporal series in ERirr are attempted to be explained by the jump to the ontological origin of this series in an atemporal world of intelligible forms. This situation can be formally described by the following “antinomy of time’s arrow”:

Thesis: The world is ruled from some unknown physical level URirr, whose existence is absolutely necessary for the existence of the arrow of time (macroscopic statistical irre­versibility) in the visible universe (ER).

Antithesis: There is simply no unknown fundamental-level URirr as a necessary cause of the arrow of time in the visible universe, either in the worid or out of it.

The presence of an antinomy in reasoning about the irreversibility of time indicates, in accordance with the logic established earlier in the context of Hawking’s cos­mology and Penrose’s conjecture, that any attempt to solve the mystery of time’s arrow – that is, to find its ultimate foundation in the physical world – leads human reason inevitably to a transcendence beyond the empirical physical world to the realm of intelligible physics, which is considered the foundation of the empirical flow of time. Prigogine’s attempt to construct a theory of the mechanism that is pushing time forward revealed with a new force the intuition that the foundation of time is not in the physical world and that theoretical advance in physics is amazingly similar to what is known from philosophy as an endless regressing in causations further from the observable physical world.

Finally, one can argue that Prigogine’s theory provides us with more evidence that physics, in its attempt to tackle the ultimate questions, has to deal with a dualistic structure of being (the dichotomy between sensible and intelligible), which, as we have established before, reflects the constitutive differentiation in the created world, its diaphora. The significance of this new articulation of the diaphora in Prigogine’s theory is that it was previously obscured by classical physics, which, by postulating dualism in two views of nature (reversible/irre­versible), was attempting to remove it in favor of a monistic description of the world, which was supposed to explain away the contingency of the created realm. It is interesting that Prigogine’s attempt to provide a fundamental description of irreversibility through the underlying physical mechanism is similar to the attempt of classical physics to reconcile the visible world with the invisible. What it proves, however, is that the gap between the reversible and irreversible processes is much deeper than was thought in classical physics and that the difference between empirical irreversible phenomena and their explanatory mechanisms in the intelligible realm is much more articulated in terms of the nonclassical and nonvisual nature of the latter.

The lesson of Prigogine’s theory strengthens even further the conclusion that the more we deal with the irreversible processes the less we understand their origin. If intrinsic irreversibility drives the life of complex structures, including such systems as the planetary biosphere and individual biological forms, the ultimate origin of these systems cannot be described in temporal terms, for, according to Prigogine, the past of these systems is detached from their present by an infinite entropy barrier, which cannot be overcome. This corresponds to our conclusion that what Prigo­gine’s theory of irreversible processes actually demonstrates is that the riddle of time cannot be explained away by constructing a particular mechanism; it remains the mystery of the whole constitution of the created world, including both the sensible and the intelligible realms – that is, finally it is linked to the problem of fundamental contingency of the world, its creation by God out of nothing.

One should stress, however, that our conclusion about Prigogine’s model as rearticulating the contingency of the world upon the ground that is in its nonbeing, or its otherness, is made not as if Prigogine had proved the fundamental irreversibil­ity of everything implying contingency, but from a different perspective: by reducing the problem of time’s arrow to the problem of the basic differentiation in the created world between the sensible (with flow of time) and the intelligible (timeless, or with transcendent time).425 In other words, we treat the arrow of time as the expression of the split in creation between the sensible and the intelligible, which is the manifestation of the contingency of the world in a theological sense. In its essence, this con­clusion is similar to what we formulated in the context of Penrose’s model. Since the pattern of this split (that is, the basic diaphora), is applicable to both reversible and irreversible processes, both types are independently contingent on nonworldly factors. This implies that the link between irreversibility and contingency must not be absolutized; that is, any conjecture about the underlying laws of irreversible natural processes neither explains the contingency away in a monistic sense nor provides any direct evidence for it. This is why one should be cautious when making a distinction between contingency in a theological sense and contingency of processes as the unpredictability of their outcomes, on the one hand, and the lack of determinism in nature in general, on the other. This means that the famous question posed by W. Pannenberg to scientists – “Is the reality of nature to be understood as contingent, and are natural processes to be understood as irreversible?” – must be met with care, for it can give the impression that any display of irreversibility in nature points directly toward contingency in a theological sense.426 As we have seen in this chapter, the situation is much more complicated, for irreversibility can be caused by special initial conditions (Penrose’s case), which implies that it is not irreversibility itself that points toward contingency in this case but, rather, its original cause, which is the initial conditions in the universe. In this case, the whole of physics can be time reversible, but the observable universe will manifest the irreversibility. It is our inability to make a clear distinction between the effects of the remote initial condi­tions, on the one hand, and the outcomes of the dynamic laws acting here and now, on the other hand, that makes the problem of the link between contingency and irre­versibility hardly solvable on purely physical grounds. The confirmation to this was provided in an indirect way by the works of Prigogine and his group.

Prigogine, in his tremendous efforts, wanted to overcome this incompleteness of classical physics in order to restore the unity of the physical realm in such a way that both reversible and irreversible phenomena would be described within one concep­tual frame. This means that his new theories of irreversible processes were supposed to explain irreversibility in terms of new dynamics. But what does it mean to explain it? It means to explain the contingency of classical physics away! Yes, his world is irre­versible here and now – there is no strict determinism, apart from the statistical one – but there is internal dynamics behind this irreversibility, which means that on the level of ultimate physical reality, according to Prigogine, there is a law that drives irreversibility. This implies that, if we want to speak seriously about the contingency that follows from Prigogine’s explanation of irreversibility, we must explain the contingency of its underlying (new) physical laws. Irreversibility taken as a brute fact can point toward contingency only in the sense that there is the contingency of the underlying physical laws.

Finally, one can assert that the problem of the irreversibility of processes is linked to the unsolvable mystery of the irreversibility of time, which is not entirely decoded in the physics of these processes.427 T. Torrance expressed this thought as follows: “Real on-going time which, in metaphorical parlance ‘flows’, time which ‘passes’, is intrinsic to all contingent reality and must be interpreted as such, while in the nature of case it retains an open structure like all contingent forms of order. Time thus understood is elusive and cannot, of course, be objectified but requires appropriate modes of apprehension and articulation, and as such needs to be brought into scien­tific inquiry, not as a linear instrument for measuring velocities, but as an internal dynamic functioning of contingent order.”428

It is from the perspective of this vision of time as inherent in the contingent order that Torrance gives his view of Prigogine’s theory with the operator of time by saying that “while time is brought as an internal operator into physics, real time relations are still not built into the warp and woof of mathematical induction and explanation.”429

This implies that all modern attempts to give an accomplished physical descrip­tion of the irreversibility of time are doubtful, for the real effect of the proposed the­ories, if they are taken without careful philosophical and theological reflection, is not to provide further insights into the contingency of the world but to explain it away. Torrance and Pannenberg argue in a similar direction that a physics must be devel­oped that will incorporate the inevitability of irreversible time not through outwardly allocating a kind of function or operator as substitution for real time but by building time itself into the logic of the physics of contingent being.

In analyzing two attempts to tackle the riddles of irreversibility and time’s arrow, we have found similar results. In both cases considered in this chapter, physical reason has brought us to the edge of possible scientific explanation by suggesting mod­els of some ultimate underlying reality that is considered responsible for the observed macroscopic irreversibility of time. These models represent ideas that, while not being abstracted from experience, are at the same time not applicable to the data of sense intuition. These ideas transcend our ordinary experience in the sense that no objects are given, or can possibly be given, within experience that correspond to them. According to Kant, transcendental ideas are produced because of the natural tendency of the human mind to search for unconditioned principles of unity. The transcendental ideas exercise an important regulative function by suggest­ing scientific explanatory hypotheses; however, all attempts to use the ideas as a foun­dation of science involve us in logical fallacies and antinomies.

Current ideas about an underlying reality to explain the origin of time all stem from a general tendency of the human mind to look for the wholeness of scientific description beyond the sphere of immediate experience and to invoke the realities of the intelligible realm as the explanatory pattern. Using Kant’s method as a method­ological tool and placing it in a proper theological frame, we have revealed the mean­ing of the proposed models of temporal irreversibility as pointing toward its ultimate ground in the otherness of the world, in the transcendent sphere of the Divine.

The problem of the irreversibility of time and processes is thus qualified as a theological problem of the creation of time in the context of the doctrine of creatio ex nihilo. Science itself cannot provide a consistent and accomplished theory of irreversibility, in the same way that it cannot explain away the contingency of nature in a theological sense. One can conclude, then, that both models of irreversibility of time – those of Penrose and Prigogine – provide invaluable material for a theological analysis, which uncovers in them the presence of implicit theological ingredients (such as diaphora in creation) that outline the similarity between the world at large and the anthropological constitution of humankind as the world in small (microcosm).

* * *

385

See, e.g., Isham and Polkinghorne, “The Debate over the Block Universe.”

386

N. O. Lossky, Sensible, Intellectual and Mystical Intuition.

387

For a general review, see Prigogine, From Being to Becoming; and Prigogine and Stengers, Order out of Chaos.

388

See also Nesteruk, “Temporal Irreversibility.”

389

See Philo of Alexandria On the Account of the Creation of the Worlds as Given by Moses 7, [ET: p. 6].

390

Mantzaridis, Time and Man, p.7. See the distinctions between aeon and aidion in the glossary of Palmer et al., eds., The Philokalia, under the rubric “Age.”

391

Maximus the Confessor Two Hundred Texts on Theology 86 [ET: p. 159].

392

Gregory the Theologian (Nazianzus) Orations 29.9 [ET: Norris, p. 250].

393

One can agree in this case with W. Pannenberg that “scientific knowledge participates in a certain sense, despite its position in time, in the perspective of eternity… Such participation in eternity… seems to be confirmed also in the function of knowledge which causes unity.” See Pannenberg, Toward a Theology of Nature, p. 102.

394

Compare with W. Pannenberg, who pointed out that “of the modes of time, the one closest to the eternal act of creation would not be the past but the future. From the future is the world, even with its already past periods of world process, created.” See Pannenberg, Toward a Theology of Nature, p. 102.

395

This can be illustrated by figure 5.4.

396

Barrow and Tipler, The Anthropic Cosmological Principle.

397

Prigogine, From Being to Becoming; Prigogine and Stengers, Order out of Chaos. We will analyze Prigogine’s program later in this chapter. See also Nesteruk, “Temporal Irreversibility.”

398

See, e.g., Ellis, “Modern Cosmology and the Limits of Science,” p. 11.

399

Penrose, “Singularities and Time-Asymmetry”, p. 586.

←400

Prigogine, From Being to Becoming.

←401

Penrose, “Singularities and Time-Asymmetry”, p. 588.

←402

Prigogine and Stengers, Order out of Chaos.

←403

Penrose, “Singularities and Time-Asymmetry”.

←404

This hypothesis was originally formulated by R. Penrose in “Singularities and Time-Asymmetry” and reproduced later in a series of papers and books. See, e.g., The Emperor's New Mind.

←405

Penrose, “Singularities and Time-Asymmetry,” p. 632.

←406

Penrose, “Singularities and Time-Asymmetry,” p.633.

←407

Penrose, The Emperor’s New Mind, p. 344.

←408

Penrose et al., The Large, the Small and the Human Mind, p. 2.

←409

Compare with the reasoning of St. Athanasius that we considered in chapter 2.

←410

The notion of contingency is applied only to the form of the world, not to its substance. See Kant, Critique of Pure Reason, p. 522. The idea of the wise cause of the world cannot have its object (p. 518). Kant denies any causation between an idea and its hypothetical object because he denies logical predetermination, or the existence of a forming principle of object.

←411

For example, the many-worlds interpretation of quantum mechanics or chaotic inflation in the context of the strong anthropic principle.

←412

Kant, Critique of Pure Reason, p. 415.

←413

It is similar to what was affirmed by Maximus the Confessor on the mediation between sensible and intelligible realms. See the discussion in chapter 4.

←414

Prigogine, “What Is Time?”

←415

Prigogine, “La redécouverte du temps,” p. 6.

←416

Poincaré, Methods nouvelles de la mécanique céleste.

←417

See Arnold and Avez, Ergodic Problems of Classical Mechanics.

←418

Prigogine, “La redécouverte du temps.”

←419

For more technical details, see, e.g., Prigogine, “Why Irreversibility?”

←420

Prigogine, From Being to Becoming; Prigogine and Stengers, Order out of Chaos.

←421

See, e.g., Barrow and Tipler, The Anthropic Cosmological Principle.

←422

Petrosky and Prigogine, “Thermodynamic Limit.”

←423

This is just a vague analogy, for the things-in-themselves in the Kantian sense are beyond any expe­rience, including the mathematical one that attempts to model UR.

←424

It should be stressed, however, that an accomplished model of URirr , which, according to Prigogine’s results, should be a radical modification of phase space and Hilbert space, does not yet exist.

←425

See the discussion in chapter 5 on the Neoplatonic theory of time.

←426

Pannenberg, Toward a Theology of Nature, p. 21.

←427

Pannenberg, Toward a Theology of Nature, p. 21.

←428

Torrance, “Creation, Contingent World-Order, and Time,” p. 220.

←429

Torrance, “Creation, Contingent World-Order, and Time,” p. 220.

←430

R. Swinburne defines human life as the embodiment of conscious creatures. He makes a clear dis­tinction between animal life and the life of the human conscious being, who possesses free will, which is not rooted in the laws of nature. See his “Argument from the Fine-Tuning of the Universe.”

←431

For more on theological vision of the distinct position of humans in the universe, see K. Ware, Through the Creation to the Creator, pp. 15 – 23.

←432

See Barrow and Tipler, The Anthropic Cosmological Principle, p. 305, where it is mentioned that the value of αe together with the ratio mp/me = 1837 (mp is the mass of a proton) provides a strict condition for the possibility for the replication of DNA.

←433

This point will be discussed intensively later.

←434

Barrow and Tipler, The Anthropic Cosmological Principle, pp. 565 – 566. This estimate has been made on the basis of Carter’s formula, derived from the assumption that life is improbable in the universe. The accuracy of this estimate is dependent on our accurate knowledge of many factors that sustain the stability of the biosphere, in particular, the physics of the atmosphere’s stability.

←435

Dyson, “Time without End,” p. 447.

←436

A similar way of thinking was developed later by F. Tipler. See, e.g., Barrow and Tipler, The Anthropic Cosmological Principle, ch. 10.

←437

Krauss and Starkman, “Life, the Universe, and Nothing.”

←438

See Leslie, The End of the World, and the references therein. On the latter issue, see pp. 108 – 122.

←439

Compare with Leslie, Value and Existence, in which the author argues that the ultimate reason and values of all existing things belong to the realm of Platonic ides, which cause the things to exist.

←440

The list of references on this topic is vast. The main systematic source before 1988 is Barrow and Tipler, The Anthropic Cosmological Principle; a list of different published papers before 1991 can be found in Balashov, “Resource Letter AP-1.” See also Leslie, Universes, and the references therein.

←441

See pp. 16 – 23.

←442

Barrow and Tipler, The Anthropic Cosmological Principle, p. 16.

←443

See, e.g., Kane et al., “The Beginning and the End of the Anthropic Principle.”

←444

R. Swinburne asserts that there cannot be a scientific explanation for the occurrence of conscious­ness. See Swinburne, “Argument from the Fine-Tuning of the Universe,” p. 163. See also Swinburne, The Evolution of the Soul, p. 10.

←445

Barrow and Tipler, The Anthropic Cosmological Principle, p. 21 (emphasis added).

←446

See, e.g., Carr, “On the Origin, Evolution and Purpose of the Physical Universe”; and Leslie, “The Anthropic Principle Today.” Leslie makes a point that in spite of the AP sounding like a tautology its explanatory and predictive power is very limited, but he affirmed that the AP can enter the explanation and prediction (p. 295, p. 301).

←447

Barrow, Between Inner Space and Outer Space, p. 19.

←448

For details, see, e.g., Nicolis and Prigogine, Exploring Complexity.

←449

See, e.g., Polkinghorne, Belief in God in an Age of Science, ch. 3.

←450

The well-known example is the refutation of Maxwell’s demon in thermodynamics. See, e.g., Brilluoin, Science and Information Theory.

←451

Polkinghorne, Belief in God in an Age of Science, p. 63.

←452

Haught, God after Darwin, p. 76.

←453

Haught, God after Darwin, p. 76.

←454

Leslie, “The Anthropic Principle Today,” p. 296.

←455

See Torrance, Divine and Contingent Order.

←456

E. McMullin, in his critical appraisal of the SAP, points out that the problem with it is in the phrase “must be,” which appears in its formulation. He argues that if “must be” is understood in the sense “that, antecedently, the universe had to be of the sort that would make the appearance within it of observers unavoidable, then it is not just strong, it is entirely groundless.” See McMullin, “Fine-Tuning the Universe?” p. 112.

←457

Carr, “On the Origin, Evolution and Purpose of the Physical Universe,” p. 152.

←458

This makes all claims of physics and cosmology about the position of humankind in the universe limited and insufficient in principle. This follows from a separation, typical for natural sciences, of what is supposed to be described as objective reality from the subject, who affirms this reality, who hypostasizes this reality as existing in the knowledge of this subject.

←459

The reader can find these diagrams in many books. See, in particular, Barrow,’ The Artful Universe, p. 49, p. 53; and Barrow, Between Inner Space and Outer Space, p. 20. See also Penrose et al., The Large, the Small and the Human Mind, p. 5.

←460

The difference between natural and hypostatic in human constitution can be illustrated in terms of space and time. Indeed, is it possible for a human individual to exist at different places at the same time? If human beings are considered only as physical bodies animated by soul, it seems inconceivable. If, how­ever, by its hypostatic constitution, human beings are related to God, and through him to the whole world, its physical presence here and now does not exhaust its potential from being present everywhere in the universe by the power of relation to it, which is not so much epistemological as ontological (not based on the substance of nature).

←461

See a bright exposition of this view in Dennet, Consciousness Explained.

←462

In Greek Patristic literature, it was a prevailing view that the state of human being as it exists in the natural environment includes the body, soul (including the dianoia as an analytical part of the soul), and spirit, which had never been dissociated from the Holy Spirit. Human spirit stands here for the nous (spir­itual intellect, the organ of faith), linking the human person to its dynamic relationship to God and to the world. It is natural congeniality with God, which is articulated by the presence of the Holy Spirit in human being. But the Holy Spirit is the creator of both body and soul, whose unity forms a particular human per­son. The presence of the Holy Spirit in human constitution thus makes the human person open upward through its calling to the Divine as its destiny. Without the Spirit, the Greek Fathers assert, the human being is incomplete and imprisoned through the conditions of the created nature. V. Lossky reaffirms this point by saying that “the distinction between person and nature reproduces in humanity the order of divine life, expressed by the dogma of the Trinity.” See V. Lossky, Orthodox Theology, p. 128.

←463

The acquisition of personhood can be achieved only in community. This is the meaning of what J. Zizioulas calls the ecclesial existence. See Zizioulas, Being as Communion.

←464

For a better understanding that the hypostasis of human beings relates not purely to their cogni­tive faculties or to consciousness but represents an ontological, existential notion, it may be useful to comment on its meaning by using the language of E. Levinas. Levinas, in his approach to hypostasis, starts with the ontological notion of one’s existing. He writes: “It is thus the being in me, the fact that I exist, my existing, that constitutes the absolutely intransitive element, something without intentionality or rela­tionship. One can exchange everything between beings except existing. In this sense to be is to be isolated by existence. Inasmuch as I am, I am a monad. It is by existing that I am without windows and doors, and not by some content in me that would be incommunicable.” In order to overcome the isolation of the exis­tent in its existing – that is, for the existent to come into existence – there must be, according to Levinas, an ontological event when “the existence contracts its existing.” Levinas calls this event hypostasis. See Levinas, Time and the Other, pp. 42 – 43.

In the language used in this chapter, this thought could be rephrased as that the existent, who was brought into being as the composite of the body and soul, contracts its existing in the hypostatic event, when the unity of the body and soul of a particular individual is related to a similar unity of another indi­vidual not naturally, but hypostatically (that is, when the existing of the one becomes the existence for the other).

←465

One should note that the idea of man as microcosm in Maximus is a Christian transformation of the old pagan idea of man as microcosmos, which recapitulates in itself all natural elements of the universe.

←466

ET: p. 196. The words in brackets are imported from the Russian translation of the same text, which better clarify the sense of Maximus’s assertion. See Maximus the Confessor, Collected Works, vol. 1 (in Russian) (Moscow: Martis, 1993), pp. 167 – 168.

←467

It should be mentioned here that, despite the nonscientific origin of the idea that the reality of the universe is brought into existence through the process of its contemplation and knowledge, the articulation of this idea has at least been attempted in modern physics by J. A. Wheeler, who proposed the so-called participatory anthropic principle. Discussion of the PAP can be found later in this chapter.

←468

This expresses the essence of the Bohr’s principle: “No elementary phenomenon is a phenomenon until it is a registered (‘observed’) phenomenon.” See, e.g., Bohr, Atomic Physics and Human Knowledge.

←469

See McLaughlin, “Kantian Epistemology as an Alternative to Heroic Astronomy.” See also Balashov, “Transcendental Background to the Anthropic Reasoning in Cosmology.”

←470

Temple, “The New Design Argument,” p. 137.

←471

For the variety of different theories of multiple universes, see Leslie, Universes, ch. 4.

←472

Barrow and Tipler, The Anthropic Cosmological Principle, p. 22.

←473

E. McMullin mentions in this context that the MW hypothesis represents simply a shift in a much wider metaphysical indifference principle, in which our mediocre location in space is replaced by our mediocre membership in the ensemble of universes. See McMullin, “Fine-Tuning the Universe?” p. 109.

←474

De Witt, “Quantum Mechanics and Reality,” p. 33.

←475

Everett, “Relative State Formulation of Quantum Mechanics,” p. 459.

←476

A certain philosophical approach known as modal realism can be used to clarify the above-mentioned distinction between the actual and the possible in the context of MWI. See, e.g., Lewis, On the Plurality of Worlds.

←477

Compare with Penrose’s phase space of all possible initial conditions of the universe, which was discussed in chapter 6.

←478

See, e.g., Leslie, “Modern Cosmology and the Creation of Life.”

←479

Temple, “The New Design Argument,” pp. 134 – 135.

←480

Barrow and Tipler, The Anthropic Cosmological Principle, p. 22.

←481

Carr, “On the Origin, Evolution and Purpose of the Physical Universe,” p. 158.

←482

Wheeler, “On Recognising Law without Law,” p. 404.

←483

Wheeler, “On Recognising Law without Law,” p. 404.

←484

Wheeler, “How Come the Quantum?” p. 310.

←485

Wheeler, “How Come the Quantum?” p. 310.

←486

Wheeler, “How Come the Quantum?” p. 311.

←487

See Wheeler, “World as a System Self-Synthesized by Quantum Networking.”

←488

See, e.g., Wheeler, At Home in the Universe, p. 307.

←489

See, e.g., Wheeler, At Home in the Universe, p. 293.

←490

Wheeler, At Home in the Universe, p. 300; Wheeler, “How Come the Quantum?” p. 313.

←491

See Wheeler, “How Come the Quantum?” p. 305.

←492

See Wheeler, “World as a System Self-Synthesized by Quantum Networking.”

←493

Gregory of Nyssa On the Making of Man 16.1 ET: quoted in O. Clément, On Human Being, p. 34.

←494

The affirmation of this community aspect of human existence in relation to the Father is mani­fested in the “Lord’s Prayer,” whose entry words “Our Father…” signify the positioning of all human beings with respect to their common source of origin, thus making all beings to be the same, that is, to be the community, which is formed through the communion with God.

←495

Gregory of Nyssa On the Making of Man 16.17 [ET: p. 406].

←496

Irenaeus of Lyons Against the Heresies 5.16.2 [ET: Scandal, p. 56].

←497

Irenaeus of Lyons Against the Heresies 3.18.7 [ET: Scandal, p. 58].

←498

Irenaeus of Lyons Against the Heresies 3.13.1 [ET: Scandal, p. 59].

←499

Temple, Readings in St. Johns Gospels.

←500

Ellis, “The Theology of the Anthropic Principle,” pp. 396 – 397.

←501

Zizioulas, Being as Communion.

←502

Torrance, Space, Time and Incarnation.

←503

A similar relation is established in the humankind-event, which being finite in space and time, is related through human apprehension to the whole universe.

←504

Origen Contra celsum 4 [ET: Bettenson, p. 213].

←505

Origen, Contra celsum 1 [ET: Chadwick, p. 187]

←506

Athanasius of Alexandria De incarnatione verbi Dei 8 [ET: p. 33].

←507

On the receptacle and relational notions of space in theology, see Torrance, “The Relation of the Incarnation to Space in Nicene Theology.” See also Torrance, Space, Time and Incarnation.

←508

Athanasius of Alexandria De incarnatione verbi Dei 16 [ET: p. 45].

←509

Athanasius of Alexandria De incarnatione verbi Dei 12, 14 [ET: p. 39, p. 42]. In modern terms, it means that any natural theology is insufficient in order to know truth about God.

←510

Athanasius of Alexandria De incarnatione verbi Dei 14 [ET: p. 42].

←511

See the quote in chapter 2.

←512

Torrance, “The Relation of the Incarnation to Space in Nicene Theology,” p. 365.

←513

See., e.g., Barrow and Tipler, The Anthropic Cosmological Principle, p. 260.

←514

Pannenberg, Jesus – God and Man, p. 166.

←515

Maximus the Confessor The Church’s Mystagogy 7 [ET: pp. 196 – 197].

←516

Maximus the Confessor The Church’s Mystagogy 7 [ET: p. 188].

←517

Compare with Zizioulas, Being as Communion, pp. 119 – 120.

←518

Athanasius of Alexandria Contra arianos 3.23 [ET: pp. 369 – 370] (emphasis added).

←519

Torrance, “The Relation of the Incarnation to Space in Nicene Theology,” p. 371.

←520

See, e.g., Leslie, The End of the World.

←521

Berdyaev, “Man and Machine,” p. 157.

←522

Berdyaev, “Man and Machine.”

←523

Tipler, “The Omega Point Theory”; Tipler, “The Omega Point as Eschaton”; and Tipler, The Physics of Immortality.

←524

Barrow and Tipler, The Anthropic Cosmological Principle, ch. 10.

←525

Barrow and Tipler, The Anthropic Cosmological Principle, p. 23.

←526

Barrow and Tipler, The Anthropic Cosmological Principle, p. 659.

←527

Tipler, “The Omega Point Theory,” p. 317.

←528

Tipler, “The Omega Point as Eschaton,” p. 223.

←529

Barrow and Tipler, The Anthropic Cosmological Principle, p. 660.

←530

See, e.g., Stoeger and Ellis, “A Response to Tipler’s Omega-Point Theory.”

←531

Nesteruk, “The Final Anthropic Cosmology as Seen by Transcendental Philosophy.”

←532

See the argument on this in Nesteruk, “The Final Anthropic Cosmology as Seen by Transcenden­tal Philosophy.”

←533

See Nesteruk, “The Metaethical Alternative to the Idea of Eternal Life in Modern Cosmology”; Nesteruk, “Ecological Insights on the Anthropic Reasoning in Cosmology”; and Nesteruk, “The Idea of Eternal Life in Modern Cosmology.”

←534

Philip Sherrard argued strongly along similar lines that the desanctification of nature takes place as the result of the dehumanization of humankind, so that the ecological crisis is in its essence anthropological and manifests the spiritual disorientation of human beings. See Sherrard, The Rape of Man and Nature; and Sherrard, Human Image: World Image.

←535

See, e.g., Mathews, The Ecological Self.

←536

See, e.g., some examples from ethnology in Lévi-Strauss, Structural Anthropology.

←537

It is worth pointing out W. Heisenberg’s modern treatment (probably a little anachronistic) of the famous conflict of Galileo with the Roman Catholic Church, in which he made an interesting connection between a change in the world outlook induced by scientific and technological progress and the problem of stability of the society whose integrity is based upon a particular view of reality based on tradition (for example, religious tradition). Heisenberg linked new cosmological perspectives on humankind’s place in the universe following from Copernicus’s and Galileo’s (arguably just or not) with the risk of obscuring the vision of the whole in the consciousness of the individual, so that the living community could suffer and be threatened with decay. See Heisenberg, “Science and Religious Truth,” p. 225.

←538

On “The Lure of the Cosmos,” see Berdyaev, Slavery and Freedom, pp. 93 –102.

←539

See, e.g., Wilkinson, Alone in the Universe, p. 144.

←540

Tipler, “The Omega Point Theory,” p. 314.

←541

Sherrard, The Rape of Man and Nature, p. 43.

←542

Gregory of Nyssa On the Making of Man 22 [ET: p. 412].

←543

See Gregory of Nyssa On the Making of Man 23 [ET: p. 413]. There is a deep contrast between the Christian eschatological vision of being and that of Hellenistic philosophy, in which the whole world was in a steady, cyclic motion, that is, in a mode of endless repetition of its states. The eschatology is not pos­sible in the Hellenistic world, for it cannot be the end of the world if it did not have the beginning. On a detailed account of the Christian eschatology versus Hellenistic cosmology, see Florovsky, “The Patristic Age and Eschatology.”

←544

Gregory of Nyssa On the Making of Man 23 [ET: p. 413].

←545

See Mantzaridis, Time and Man, pp. 100 – 105.

←546

See Torrance, Space, Time and Resurrection, p. 99.

←547

This was one of Athanasius’s main arguments in his De incarnatione verbi Dei 21 [ET: p. 51].

←548

Torrance, Space, Time and Resurrection, p. 94.

←549

Gregory the Theologian (Nazianzus) Orations 45.21 [ET: NPNF, pp. 430 – 431].

←550

Hapgood, ed., Service Book, p. 204.

←551

Hapgood, ed., Service Book, p. 204.

←552

See Zizioulas, “The Eucharist and the Kingdom,” pt. 1, 6.

←553

See Zizioulas, “The Eucharist and the Kingdom,” pt. 3, 12.

←554

Gregory the Theologian (Nazianzus) Orations 45.5 – 9 [ET: pp. 424 – 426].

←555

Gregory the Theologian (Nazianzus) Orations 10 [ET: pp. 203 – 204].

←556

Füglister, “The Biblical Roots of the Easter Celebration,” pp. 24 – 26.

←557

Füglister, “The Biblical Roots of the Easter Celebration,” p. 26.


Источник: Light from the East: Theology, Science, and the Eastern Orthodox Tradition / A.V. Nesteruk - Minneapolis : Fortress Press, 2003. - 287 p. ISBN 0800634993

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