Chapter 3: Temporal Order and Spatial Order: Their Differences and Relations by Milic Capek
Milic Capek is Professor of Philosophy at Boston University.
If we look at the subject catalogue of nearly any university library, we find that not only the books dealing with space and time are listed under the same heading, but also that in many of them both concepts are treated jointly as their very titles indicate: Space and Time, Space, Time and Matter; Space, Time and Motion; and even Space, Time and Deity, etc. This is certainly not accidental; nor is it accidental that with a few exceptions the word ‘space’ regularly appears in the titles before ‘time.’ This is due to the fact that the properties of space and time are, or at least appear to us, quite similar and, furthermore, that the spatial relations seem to us as somehow more fundamental, more solid, and easier to grasp than the elusive temporal relations. Hence our instinctive tendency to believe that the relations of succession can be adequately symbolized by geometrical relations.
The purpose of this paper is to trace the sources of this belief, its remarkable persistence through centuries of philosophical and theological speculation, and its disastrous influence not only on philosophy, but also on the interpretation of some recent and contemporary physical theories. Finally I want to show that an attentive analysis of both our introspective experience as well as of the revolutionary discoveries of twentieth-century physics indicates that, not only are temporal relations basic and irreducible to spatial relations, but also that spatial relations are of a derivative kind, being mere approximations or idealizations of those strata of experience in which the temporal aspect is less prominent and can be disregarded for practical purposes. Time, or more accurately, becoming seems to be more fundamental in the light of available evidence, while spatial relations are mere instantaneous cross-sections in what Whitehead called the ‘creative advance of nature’ and Bergson, before him, ‘true duration.’ Such instantaneous cuts have their usefulness and justification in our macroscopic and macrochronic perspective, but their pragmatic usefulness should not be confused with objective ontological status.
There are two approaches to the origin of the concept of time: on one side, Jean Piaget’s recent investigations of the formation of the notion of time in children; on the other side, the analysis of the development of the concept of time in adult humanity, more specifically, in the philosophical and scientific community. It is remarkable how complementary and convergent are the results obtained in two such apparently disparate areas -- child psychology and history of ideas. Piaget showed how young children (4-6 or even 7 years old) have considerable difficulty in differentiating temporal from spatial relations. Hence the succession is confused with spatial order; the duration of concomitant motions is judged erroneously from the distance covered by the moving bodies without taking into account the differences in speed; and the relation of simultaneity is not disentangled from spatial coincidence. Only gradually and after considerable groping and in a higher age (7-8 years) do children succeed in differentiating the temporal order from the spatial order, i.e., the temporal ‘before-after’ relation from the spatial ‘before-after.’ Similarly, the duration of motion is dissociated from the length of its trajectory, and the coincidence in time (i.e., simultaneity) is not confused with the coincidence in space. This is, of course, an extremely concise and simplified account. Piaget discovered that the formation of the notion of time proceeds by three successive stages, with the boundaries slightly different in different children; it is only in the third stage that the notion of duration is entirely freed from what Bergson called ‘the fallacy of spatialization,’ in the sense that it is understood how several different motions with different speeds and covering different distances can occur within one and the same interval of time. Thus the distinction is finally drawn not only between time and the spatial trajectory of motion, but also between time and motion itself (Piaget 1937).
It would be absurd to claim that there is a complete analogy between the formation of the notion of time in the child and the development of the concept of time in humanity. The situation is far more complex; yet, some interesting similarities do exist and they are hardly accidental. The early Pythagoreans identified time with the celestial sphere, that is, with the circular trajectories of the daily motion; later, time was identified with the rotating motion of the celestial sphere. The reference to the celestial sphere and its motion had far-reaching effects on the subsequent development of the concept of time: it focused the attention of philosophers on the regular periodicity of the celestial motions by which time can be measured and thus it deepened the distinction between the qualitative content of time and its metrical aspects; the correlation of time with spatial motion became the source of the relational theory of time, according to which "time is nothing by itself," as Lucretius wrote (De rerum natura, 1,495f.), and cannot be separated from concrete changes occurring in it; finally, the alleged inseparability of time from spatial displacements created the tendency to exaggerate the analogy between space and time and, eventually, to spatialize time entirely and thus virtually to eliminate it.
This extreme tendency is conspicuous in the Eleatic school. Zeno’s four arguments against the reality of motion were based on the assimilation of time to a geometrical line. According to Zeno, temporal intervals are adequately symbolized by spatial segments: they both are divisible ad infinitum, and to the point-like extremities of linear trajectories correspond the durationless extremities of temporal intervals -- instants. From this the impossibility of building motion from the motionless positions, and durations from the durationless instants, followed naturally. Hence, in Zeno’s mind his teacher, Parmenides, ridiculed by his opponents for his denial of time and motion, was vindicated and avenged.
Eleatism was the metaphysics of timeless Being in its most radical form and, although it has never reappeared in its extreme form, it exerted a lasting influence on the subsequent development of Western thought. In truth, such systems as those of Spinoza and Bradley came very close to Eleatism; but instead of eliminating time, change and motion entirely, they half-heartedly retained them in treating them as mere ‘appearances,’ as having some sort of existence or rather semi-existence which was of an inferior and less dignified kind than that of immutable Being. In truth, it can be argued that even Parmenides treated change and motion at least as ‘appearances,’ as belonging at least to the illusory realm of phenomena and not as mere non-entities; otherwise the division of his poem into two parts -- "The Way of Truth" and "The Way of Opinion" -- would lose its meaning. But this is a historical question; what is important in this context is the fact that the subsequent development of Greek, medieval and modern philosophy was largely dominated by the contrast between the timeless realm of Being and the temporal realm of change; in this sense, it was a continuation of the dialogue between Parmenides and Heraclitus, with Parmenides having an upper hand. In most philosophical and theological systems Being was endowed with a more dignified status of the true reality, of which the temporal realm is merely a pale, shadowy replica. From Plato, who defined time as a moving (i.e., imperfect) image of eternity, down to St. Thomas, who stressed the perfect immutability of his Supreme Being in terms indistinguishable from the language of the Eleatic school, we can trace the same persistent theme -- a metaphysical dichotomy of Being and Becoming, of perfection and imperfection, of the timeless and the temporal realms. To this dichotomy corresponds the epistemological dichotomy of two kinds of knowledge -- the true knowledge of the all-embracing timeless truth which only God possesses and man’s imperfect knowledge confined to the temporal realm. The incompleteness of human knowledge is due to the temporal incompleteness of the realm to which it is confined. It is easy to see how the timelessness of God and of his knowledge led to the theological determinism, to the predestinationism of St. Augustine, St. Thomas and Calvin; for the abolition of time and becoming on the divine level eliminates entirely the ambiguity of the future which is uncertain only to our imperfect, time-bound insight, but which is in its completeness timelessly present in the mind of God.
This trend continued in modern philosophy and to some extent in modem science, in spite of the Copernican and Cartesian revolutions. Spinoza merely secularized the God of Aquinas and Calvin by equating him with the impersonal, but equally static and equally timeless, order of nature (Deus sive natura); and Laplace’s ‘omniscient mind’ is nothing but a secularized and depersonalized version of the God of the Scholastics and of the Protestant Reformation. This accounts for a "secret alliance of theological and naturalistic determinism" of which Professor Hartshorne once wrote (Hartshorne 1932, p. 429). I like to quote this because I regard it as one of the most insightful and also most neglected remarks concerning the history of ideas. There is no doubt that the preferential treatment of the concept of Being, with the concomitant tendency to debase the status of time, becoming and change continued until the last decades of the last century, when the first process philosophers -- Renouvier, Boutroux and Bergson in France, and William James in the United States -- tried to reverse the centuries-old trend. (I am not mentioning Hegel, since his status as a process thinker is rather ambiguous, as is shown by the two divergent interpretations of his philosophy -- that of Croce and J. N. Findlay, in contrast to the static interpretation of J. E. McTaggart.)
I would like to conclude this digression into the history of ideas with the following words which Friedrich Nietzsche wrote in 1888:
You ask me which of the philosophers’ traits are really idiosyncracies? For example, their lack of historical sense, their hatred of the very idea of becoming, their Egypticism. They think that they show their respect for a subject when they de-historicize it, -- sub specie aeterni -- when they turn it into a mummy. All that philosophers have handled for thousands of years have been concept-mummies; nothing real escaped their grasp alive. When these honorable idolators of concepts worship something, they kill it and stuff it; they threaten the life of everything they worship. Death, change, old age, as well as procreation and growth, are to their mind objections -- even refutations. Whatever has being, does not become; whatever becomes does not have being. Now they all believe, desperately even, in what has being. . . .They place that which comes at the end -- unfortunately! for it ought not to come at all! -- namely, the ‘highest concepts’ which means the most general, the emptiest concepts, the last smoke of evaporating reality, in the beginning, as the beginning. This again is nothing but their way of showing reverence: the higher may not grow out of the lower, may not have grown at all. . . .
But Heraclitus will remain eternally right with his assertion that being is an empty fiction. The apparent world is the only one: the ‘true’ world is merely added by a lie (Nietzsche 1954, pp. 479-482).
This is a temperamental revolt against the perennial metaphysics of Being presaging the birth of process philosophy. (Curiously enough, Twilight of Idols, from which this passage is taken, was published only one month before Bergson wrote a preface to his first book.) But it is ironical to see how much Nietzsche, despite his furious attack on the metaphysics of Being, remained committed to it. He -- like some ancient Greek philosophers, perhaps even Heraclitus -- still accepted the idea of eternal recurrence, that is, in the words of Mircea Eliade, "Ontology uncontaminated by time and becoming." For, in the cyclical theory of time, what will be already has been, and what has been will be; the distinction between the past and the future -- and with it time itself -- is abolished. Another instance of spatialization of time.
The evolution of modern science in this respect was more ambiguous. On one side it exhibits the tendency similar to that which we observed in the history of modern philosophy. This is only natural, since modern science and modern philosophy have not developed independently, but have perpetually interacted and influenced each other; in truth, until the post-Kantian period they were so intertwined that it is difficult to speak of separate histories. This explains why certain ideas were shared by both scientists and philosophers. I have already mentioned Spinoza and Laplace, who were both equally intransigent in their insistence on rigorous determinism and equally explicit in their reduction of time to a mere illusory appearance. (What is less known is that Immanuel Kant in his Critique of Practical Reason expressed Laplace’s idea of timeless or becomingless determinism twenty-five years before Laplace wrote his famous passage in his Essai philosophique sur les probabilities.) I have already mentioned how the medieval theological determinism transformed itself into modern naturalistic determinism, which dominated modern science and a large part of modern philosophy. Emile Meyerson showed convincingly in a number of his books how an elimination of time was a theme common to both science and philosophy in the last three centuries. There is no question that the fact that time was symbolized by a geometrical line (t-axis), which had the role of an independent variable on which various physical quantities depend, greatly contributed to this view. For it is too easy to forget that even in this geometrical symbolism time is not represented by a static ready-made line, but by an incomplete line which is being continuously extended ‘into the future,’ as its terminal point, representing the present moment, is continuously moving; it is difficult to resist the notion that the future positions on the t-axis somehow pre-exist prior to their occupation by the moving present, and that all events -- present, past and future -- coexist on the ‘fourth dimension’ which is as complete and as static as the other three spatial dimensions. This view of time as the fourth dimension is usually associated with the theory of relativity, but it can be traced far back to the past pre-relativistic period: it was Descartes who called time a ‘dimension’ and d’Alembert who called it ‘the fourth dimension,’ while Lagrange called mechanics ‘geometry of four dimensions.’ In truth, the roots of this becomingless view go as far back as Zeno of Elea, who was probably the first who treated time and motion as a static geometrical line: his view that the allegedly flying arrow is motionless in all points of its trajectory has an obvious affinity with the strange view of some of our contemporaries according to which successive moments exist ‘tenselessly’ on the fourth dimension called ‘time.’
But even if we do not forget that in the geometrical diagram ‘the t-line’ is perpetually being extended by the continual forward motion of its terminal point, representing the present moment, the risk of serious confusions is hardly lessened. For, to confuse time with motion is only slightly less misleading than to confuse it with the trajectory of motion. In other words, in speaking of time, the kinematic metaphors are hardly better than the static and geometrical ones. How many confusions were and are still caused by an assimilation of time to motion! The metaphorical expressions, ‘direction of time,’ and ‘time arrow,’ are very fashionable and are justified to a certain extent. They express in kinematic terms the basic asymmetry of time, the distinction between past and future. The image of time as a ‘flow’ was used already by early Greek thinkers -- let us only remember of Heraclitus -- and was retained even by sober Newton in his Principia. But as soon as this kinematic metaphor is taken literally, serious difficulties arise. We may ask, for instance: "Whence and whither does time flow?" The conventional answer, "From the past to the future," seems to satisfy most people. Time thus becomes a metaphysical river whose source is in the infinitely distant past and its estuary in the infinitely distant future. More abstractly, but not in an essentially different way, time is described as a motion along a straight line; the moving point stands for the present instant, the path already covered corresponds to the past, the points not yet occupied correspond to the future events. But as every motion in space is relative and can be transformed into a rest by an appropriate change of the frame of reference, it is permissible to regard the present moment as stationary and future events as moving toward the past with an equal and opposite velocity, to wit, opposite with respect to the velocity of the present moment in the first picture. Instead of the present’s advancing toward the future, future events retreat toward the motionless present, pass through it, and then sink into the deeper and deeper past. Now which of these descriptions is correct? Does time flow forwards, from the past to the future, or backwards, from the future to the past?
The only possible answer is that both descriptions are equally inadequate; both are metaphorical attempts to translate into spatial and kinematic terms the elusive and essentially incomplete nature of time. As soon as we try to illustrate the nature of time by comparing it to motion, the principle of kinematic relativity of motion will sooner or later sneak into our illustrations and diagrams; hence two apparently contradictory answers concerning the alleged direction of time. If, however, we forget that the word ‘direction’ is borrowed from geometry and kinematics and therefore can be applied to time only in a metaphorical sense, we may thoughtlessly draw all consequences from the alleged analogy between ‘movement of time’ and movement of bodies. Thus we may think that, as the direction of motion in space may change, the time direction may change too; as a material particle may reverse its motion and pass again through the positions previously occupied, ‘the moving present’ can also return to the past; or as the motions in space may be circular, the course of time may be circular too. Both the theory of reversible time and the theory of eternal recurrence are based on such false kinematic analogies. As I tried to show in my first book (Capek 1969) as well as in some of my articles, such theories, when closely analyzed, cannot be even stated in a self-consistent language, since they use alternately and surreptitiously two incompatible temporal descriptions. Such antagonistic and contradictory descriptions are merely clumsy translations into geometrical and kinematic terms of the basic irreversibility of becoming which cannot be meaningfully separated from the very nature of time.
The criticism of the confusion of time with motion represented another trend in the development of physics which was clearly incompatible with the trend just described. This is why I said that the development of physics, unlike that of philosophy, was far more ambiguous. One of the first instances of such criticism is to be found in Aristotle’s Physics. Although Aristotle insisted on the inseparability of time and motion, he was careful not to identify them. He did not fail to observe that the motions with different velocities and covering different distances can take place within one and the same interval of time, so that none of them could be identified with time itself. It is true that there is, according to Aristotle, one privileged motion -- the rotation of the sphere of the fixed stars -- which measures accurately the objective flow of time; in its insistence on the close correlation of time with the universal celestial clock, Aristotle’s theory of time remained relational. But there are certainly the shades of Newton in it. What prevented him from reaching Newton’s conclusion about the independence of time from its concrete physical content was, besides the Eleatic influences, his belief in the universal cosmic clock which was, so to speak, a physical embodiment of the oneness and uniformity of time. When the astronomical revolution of the sixteenth century -- in which the Italian philosophers of the Renaissance played a far more important role than historians of science admit -- removed the universal cosmic clock, there were two alternative ways open to physics and philosophy of nature: either to retain the relational theory of time and to hold with Bruno (Bruno 1879, p. 144) that "there are as many times as there are the stars" (tot tempora quot astra), since there is no body possessing a privileged rotation motion, and the only body which allegedly had it -- the sphere of the fixed stars -- has been swept away; or to save the unity and homogeneity of time by separating it from any particular motion -- and this is what Newton did, anticipated in this respect by Isaac Barrow and, in particular, Gassendi. Thus the absolute theory of time -- and with it classical physics itself -- was born.
In the eyes of a philosopher, time has acquired in classical physics a strangely ambiguous character. The name of both Newton and Laplace belong to classical physics. Yet, these two giants of the classical era had entirely different views of time. According to Newton, time is ultimately real, even on the divine level; this is why he regarded it as sensorium dei. In it everything exists, even space; for space endures in time, and what we call ‘enduring space’ is really nothing but a continuous succession of instantaneous spaces. According to Laplace, time is merely the fourth dimension of space, as static as the other three dimensions; its apparent incompleteness is illusory, being merely, as Bergson observed, "the infirmity of a mind that cannot know everything at once (Bergson 1944, p. 45). Who then was right, Newton or Laplace?
Today it is tempting to say that they were both wrong, since they both belong to the classical era which is now definitely over. But such a bare negative statement will certainly not satisfy a philosopher interested in the ultimate status of time and becoming. When the relativity theory came into existence, there was at first the widespread tendency to regard it as another confirmation of the Laplacean view of time as the additional fourth dimension. Long was the list of those -- not only of popularizers, but philosophers as well, and even some physicists -- who interpreted Minkowski’s four-dimensional continuum not as the four-dimensional process, essentially incomplete, but as a sort of a four-dimensional hyperspace, whose fourth dimension exists in its completeness as much as the three spatial dimensions. Although this misinterpretation had been effectively criticized, not only by philosophers such as Bergson, Meyerson, Whitehead and Reichenbach, but also by a number of physicists -- among them Einstein himself, Langevin, Eddington, etc. -- it was again revived recently by Costa de Beauregard, Adolf Gruenbaum, and J. J. Smart, and apparently accepted by W. Quine. I criticized this revived misinterpretation in a number of previous articles (Capek 1951, 1955, 1965, 1966) and in both my books (Capek 1969, esp. Ch. XI, XVII, and Append. I, II; 1971, pp. 226-256). Hence I prefer to restate the main arguments against the static misinterpretation in a concise form only. They are as follows:
1. To a historian of ideas, it is clear that this misinterpretation is another instance of the perennial tendency to spatialize time which can be traced to the very dawn of Western thought. This in itself would not be a decisive argument against it, but it acquires its significance in conjunction with other arguments, in particular with the unsolvable epistemological difficulty to which such elimination of time leads.
2. The most plausible argument for the static interpretation is the relativization of simultaneity and succession. But this relativization is far from being unqualified and, when attentively analyzed, it leads to an elimination of instantaneous space without weakening in any sense the ontological status of becoming.
3. Finally, the static interpretation does not eliminate becoming; it merely relegates it into the subjective, ‘phenomenal’ realm. But in this way it creates an intolerable dualism of two completely heterogeneous realms without any attempt to relate them in some intelligible way.
Let me comment on these three points.
Re 1. This point has been already lengthily and sufficiently covered and there is no need to return to it.
Re 2. This point requires rather lengthy discussion. The relativization of simultaneity and succession has been and still is regarded as an argument against the objectivity of time and/or becoming. If there is no objective ‘Now’ unambiguously separating the past from the future -- in other words, if what is simultaneous for one frame of reference is not so for another system -- is it still meaningful to uphold the objectivity of succession and the reality of becoming? This is how the argument is usually formulated and in this form it was accepted by Quine when he wrote that the principle of relativity "leaves no reasonable alternative to treating time as space-like." But despite its superficial plausibility, the argument collapses under a closer scrutiny.
In the first place, it is simply not true that simultaneity and succession are unqualifiedly relativized. What is relative is only the simultaneity of the events occurring at different places; the simultaneity of the isotopic events (i.e., occurring at the same place) remains a simultaneity for any conceivable observer. It is true that, strictly speaking, there are no such events: as long as they remain different they cannot be exactly at the same point; and as long as they are rigorously isotopic, they merge into a single event. Thus the thesis is reduced to the apparent triviality that each event is simultaneous with itself But it ceases to be trivial if we add that each event is simultaneous only with itself That this is not trivial is obvious from the fact that it was denied, for instance, by Kurt Goedel (1949, pp. 560-561), who accepted the possibility of self-intersecting world-lines -- that is, the possibility of a Wellsian trip to the past and back to the present. Thus we would have an event which, besides being simultaneous with itself, would be also simultaneous with its future descendant. Even if we disregard the difficulty of stating this view in a self-consistent language, its incompatibility with relativity theory is obvious. For in the relativistic universe no body can move with a velocity greater than that of light; in the language of the relativistic space-time diagram, it can never enter the forbidden zone of ‘Elsewhere’ outside of its own causal future; a fortiori it cannot cross the Elsewhere region and re-enter its own past. Here we see the relevance of Eddington’s insightful remark that, in the relativistic world, the past is separated from the future even more effectively than in the universe of Newton (Eddington 1925, p. 178). (In the Newtonian universe the past is separated from the future by an ‘infinitely thin’ layer of instantaneous space which contains all events objectively simultaneous with Here-Now; in the universe of Einstein the separation is effected by the four-dimensional region of Elsewhere.) Goedel’s hypothesis shows also a disastrous effect of false geometrical analogies; apparently the fact that there are some curves (e.g., lemniscate or Descarte’s leaf) which intersect themselves in the so-called singular points is for some mathematical minds a sufficient reason to believe that ‘the curve of time’ can behave in a similar way. This is a fallacy of geometrization or spatialization at its worst; it is certainly revealing that Goedel is proudly aware of the philosophical tradition to which he belongs -- that of Parmenides and McTaggart, whose names he mentions.
Equally important -- probably even more important -- is the limited extent to which succession is relativized. As early as 1911, Paul Langevin pointed out that only the succession of causally unrelated events can be changed into a simultaneity or even be reversed by an appropriate change of the frame of reference; the succession of causally related events remains qualitatively (though not metrically) invariant for any conceivable observer. Here is what, in my view, is philosophically the most significant result of relativity: that while there are no juxtapositions of events which would remain justapositions in all frames of reference, there are certain types of succession which preserve their character of succession for any possible observer. This certainly cannot be described as any weakening of the objective status of becoming; but it does away with the classical notion of instantaneous space defined as a three-dimensional layer of objectively (absolutely) simultaneous events.
This means that it is far more accurate to characterize Minkowski’s fusion of space with time as a temporalization or dynamization of space than as a spatialization of time. Minkowski’s universe is a network of the irreversible causal lines (‘world-lines’), but without any instantaneous, i.e., purely spatial, connections. This is a deeper meaning of the relativization of simultaneity, whose more correct term should be elimination of simultaneity; once we realize that the terms ‘class of simultaneous events’ and ‘instantaneous space’ are entirely synonymous, we shall also see that a negation of one implies a negation of the other. The four-dimensional becoming contains the regions of causal independence (the so-called regions of ‘Elsewhere’ which could be equally well called ‘Elsewhen’); it contains topologically invariant successions, but it does not contain any instantaneous transversal cuts, any purely spatial distances. As Whitehead observed, since the advent of relativity, "spatial relations must stretch through time" (Whitehead 1925, p. 6); in other words, there are only spatio-temporal, but no merely spatial distances. If we furthermore consider the space-time of the general-theory of relativity, with its locally variable and changing curvature, and, in particular, if we consider the expanding space of modern cosmogony, we will agree that the term ‘dynamization of space’ is not inappropriate and that we can even speak of incorporation of space into becoming. In any case, nothing is left of the traditional space since its fundamental constituting feature -- the relation of coexistence (juxtaposition, Kantian auseinander or nebeneinander) -- has no physical basis. Briefly: if we take relativity seriously, we must deny the reality of space in the sense of simultaneous juxtaposition of points.
Two objections will come immediately to our mind. First, is it not true that nothing is left of the Newtonian concept of time as well? It cannot be denied that the classical concept of time is also profoundly modified. The time of relativity is neither a uniformly flowing metaphysical river, nor is it an immaterial invisible clock in God’s mind, as Newton imagined. Yet, as Whitehead (1920, p. 17) observed as early as in 1920, the variety of metrically discordant temporal series is entirely compatible with one single underlying ‘creative advance of nature,’ or, in less poetic words, with universal becoming. Thus one basic feature of Newtonian time remains intact: its incompleteness. This, too, can be proved rigorously and without any appeal to metaphors by drawing another consequence from Minkowski’s same formula. It can be shown that no event which is still unreal for me, i.e., which is still in my causal future, can be included in the causal past of any possible observer. (By ‘possible observer’ I mean any observer located either in my causal past or anywhere in my Elsewhere region.) Since the inclusion of the events in the causal past of some observer is a necessary condition of their observability, it means that future events are intrinsically unobservable and thus it is entirely superfluous to postulate their existence. It is far more natural to regard them as genuinely future. i.e., as actually not yet existing. The physical emptiness of the future is another inevitable consequence of special relativity.
The second objection is the following: is it not true that the character of spatiality is in some sense preserved in Minkowski’s time-space? This is certainly true provided that we carefully distinguish between spatiality in a broader sense and the classical notion of static instantaneous space. The four-dimensional world process consists of an enormous number of world-lines which occasionally interact, but which mostly run independently of each other. In this sense, the world process has a certain transversal width, since it contains contemporary parts. But ‘contemporary’ is not co-instantaneous! This is more than a mere terminological difference. As said before, the four-dimensional becoming does not yield to any instantaneous cuts. In other words, there is no simultaneity of instants. But, as Bergson observed, the relativistic universe does not exclude the simultaneity of intervals, i.e., contemporaneity of temporal series, even if they are metrically discordant. Minkowski’s time-space is, to use another of Bergson’s terms, ‘extensive becoming’ (Bergson 1944, p. 265; 1965, pp. 52-53), which cannot be properly decomposed into one-dimensional time and three-dimensional instantaneous space. Such decomposition was possible in the classical space-time and this precisely distinguishes it from the relativistic time-space.
Commenting on both the relativity and quantum theories, Whitehead (1925, p. 54) observed in 1925 that "nature is nothing at an instant." If this is difficult to our visual imagination, Whitehead, following again in this respect Bergson, tried to remove the difficulty by using an auditory model: "In an analogous way, a note of music is nothing at an instant, but it also requires its whole period in which to manifest itself." The fact that melody does not exist at an instant does not make it unreal; on the contrary it shows the fictitious character of durationless instants. Similarly, time-space does not cease to be real because it does not yield to any instantaneous, purely spatial, cuts. But this impossibility of instantaneous cuts is entirely compatible with the transversal width of becoming, i.e., with the co-presence, or rather, co-becoming of the world-lines. In an analogous way, there are different melodies co-present within a polyphonic pattern. In this respect an auditory model is free of the limitations of visual models and geometrical diagrams.
Re. 3. The epistemological difficulty of the static interpretation of space-time can be dealt with briefly. As stated above, becoming and succession cannot be simply denied, but only confined to the subjective realm, to be made, in Gruenbaum’s words, ‘mind-dependent.’ This is the meaning of his statement that "coming into being is only coming into present awareness" (Gruenbaum 1963, p. 329; italics his). This can mean -- if it means anything at all -- only one thing: that what I experience as a new present moment existed prior to and independently of my deceptive temporal experience timelessly -- or, as it is fashionable now to say, tenselessly -- in the becomingless physical world. There are thus two realms: the realm of physical reality devoid of becoming in which all events that appear to us in succession are ‘tenselessly’ juxtaposed, and our private ‘stream of consciousness’ where there is a genuine succession and becoming. This is a dualism far more extreme than that of Descartes, for in Cartesian dualism, mind and matter, in spite of their heterogeneity, both shared at least the general temporal character. But for those who deny the reality of physical becoming the difficulty is doubled, since their two realms do not even share this temporal character! No attempt is even made to relate such altogether heterogeneous realms; no explanation is offered why and how the becomingless reality manifests itself in a gradually unfolding temporal form in the subjective realm. The difficulty is only increased by the physicalistic leanings of J. J. Smart, Quine and Gruenbaum himself, for if the subjective realm itself is a part of the becomingless physical reality, we should not have even the illusion of becoming, since the successive character of our stream of consciousness would become impossible! Briefly, the static interpretation of physical reality is nothing but a relapse into a strange Eleatic myth with all its oddities and contradictions, not only completely divorced from our immediate experience, but incompatible with contemporary physical science properly interpreted.
We are now returning after a long detour to the results of Piaget’s investigations. It appears that the fallacy of spatialization of time is committed by young children and -- quite a number of philosophers! This conclusion may sound offensive and disrespectful; but it is far less offensive than it sounds. Not all the features of a child’s mind are objectionable. Did not, for instance, Aristotle say that a proper trait of a philosopher’s mind is the capacity of wonder -- which children certainly have more than an average adult? In one of his other studies Piaget (1957) discovered that the children’s minds in their earliest stage, when not yet shaped by the influence of macroscopic environment, have no notion of a permanent object and are thus closer to the microphysical world of the impermanent ‘particles’ than an average adult mind. But the case of the spatializing fallacy is amusingly different. Children gradually realize that their confusions of time with spatial trajectory contradicts their own experience -- sensory and, especially, introspective -- and they give up spatialization; philosophers, while they are fully aware of the same contradiction, retain spatialization and deny experience -- and are even proud of it!
The question why the fallacy of spatialization does not entirely disappear with childhood would require another paper. Let me only indicate a sketch of the answer, which only a biological, evolutionary theory of knowledge can provide. Human mind and organism are adjusted to the realm of middle dimensions and middle velocities, in which Euclidian geometry, Newtonian mechanics and classical determinism very approximately hold. Perceptible motions of our bodies and of surrounding objects are very slow with respect to the velocity of light and gravitation -- a velocity which for us is practically infinite. Thus the motions of macroscopic bodies appear on the background of the network of practically instantaneous interactions. By the further natural process of abstraction and idealization, the notion of space as a network of instantaneous connections and as the container of everything existing emerges. It is not accidental that for c = oo the transformation of Lorentz passes over into that of Galileo. Hence a persistent tendency to translate every experience into visual and spatial terms -- even at the price of distorting, or even eliminating it.
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