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We commonly hold several beliefs about time:

1. The past no longer exists.

2. The future does not yet exist.

3. Only in the present do we actually live, and move, and have our being.

We also believe that time travels in just one direction. The popular metaphor "arrow of time," coined by Sir Arthur Eddington in 1928, describes the apparent one-way path time takes as it flies from the past, through the present, to the future.

At first glance, there seems to be little in our everyday experience that would lead us to challenge these beliefs. Yesterday is gone, although memory gives us at least a shadowy impression of what it was like. Today we actively engage the world through our senses. Tomorrow is yet to come, but we can at least imagine what it holds in store.

Such beliefs provide us with a certain level of comfort and security, and we are likely to resist any suggestion that something so fundamental to our worldview as time may not be entirely what it seems. There may be good reasons, however, to question what appears to be self-evident.

Remembrance of Things Past

Our belief in the past rests precariously on the assumption that memory provides us with a more or less accurate picture of what used to be but now no longer exists. In order to prove conclusively that memory is what we think it is, however, we would have to demonstrate that it has in some sense actually recorded the past. Here we meet with seemingly insurmountable difficulties, for if the source of our remembered impressions--the past--no longer exists, it is impossible to demonstrate just what, if anything, memory might have recorded about it.

We simply have no way of making a corroborative comparison between the fleeting "something" we remember and the "nothing" to which the unidirectional progress of time has apparently reduced the past. If we attempted to express such a comparison in the simplest mathematical terms, we would end up with the ratio x/0, which is neither defined nor permitted. We are left to cope with an alleged copy of an alleged original that no longer exists.

Can this problem be resolved with the help of some form of objective physical evidence? What about photographs, for example? They, too, are taken to be records of the past. However, if the past no longer exists, there is still no possibility of corroborative comparison and hence no absolute proof that our photographs have actually recorded anything either.

There are, however, numerous physical objects we "remember" that are actually present to our senses: our tattered but favorite bathrobe; the ancient oak tree growing in our backyard; the century-old church we sometimes attend on Sundays; the hill on the edge of town where we used to go sledding. That we can both remember these things from the past and perceive them as objective realities in the present appears to contradict our belief that the past no longer exists. Indeed, the so-called "past" actually seems to penetrate the present so pervasively that it is virtually impossible to tell where the one ends and the other begins.

In this light, our notion that time flies straight as an arrow along a unidirectional axis seems unaccountably out of sync with observable facts: past and present actually seem to coexist in some strange but familiar sense in the here and now. Is this "evidence" that time is merely illusory? For Argentine literary luminary Jorge Luis Borges, this was surely the case:

Time, if we can intuitively grasp such an identity, is a delusion: the difference and inseparability of one moment belonging to its apparent past from another belonging to its apparent present is sufficient to disintegrate it. (Borges, 227)

We are particularly struck by this curious admixture of past and present in certain historic cities, like Rome, whose rich architectural heritage is an essential and inseparable component of the contemporary urban fabric.

The Roman Forum, 1982

Fig. 1. View of Roman Forum, summer, 1982

Literature and architecture are not alone in calling our attention to what post-modernists have variously described as "the presence of the past." Marcel Duchamp's Nude Descending a Staircase, No. 2 is a startling attempt to depict motion through a series of some twenty cubistic figures that appear to overlap in time, in effect collapsing past and present into a single visual entity. Ironically, this "futurist" work--one of the most widely known icons of modernism--anticipates the post-modern subversion of time and place by nearly fifty years.

Duchamp,

Fig. 2 Marcel Duchamp, Nude Descending a Staircase, No. 2 (1912)

The Paradoxical Present

What, then, is the "here and now," the present? We might begin to answer this question by posing another: "Does the present have any duration?" If it has none, we may be hard pressed to explain how a series of temporally insubstantial instants manage, in successive combination, to form extended units of time--seconds, minutes, hours, days, months, years, and so on.

Augustine of Hippo (354-439) subscribed to the belief in a present without duration to avoid what he thought was an untenable paradox--a present that contained its own past and future:

If an instant of time be conceived, which cannot be divided into the smallest particles of moments, that alone is it, which may be called present. Which yet flies with such speed from future to past, as not to be lengthened out with the least stay. For if it be, it is divided into past and future. The present hath no space. (Augustine of Hippo, 241)

Augustine's own temporal paradox--a present without duration (i.e., "space")--is actually compounded by his insistence that that past and future do not exist:

That I measure time, I know; and yet I measure not time to come, for it is not yet; nor present, because it is not protracted by any space; nor past, because it now is not. (Ibid., 248)

Thus, Augustine's time has no duration, either in its nonexistent portions (past and future) or in the "instant" he defines as the present. The threefold present he does propose, however, still admits the past and future in the form of memory and expectation:

What now is clear and plain is, that neither things to come nor past are. Nor is it properly said, "there be three times, past, present, and to come": yet perchance it might be properly said, "there be three times; a present of things past, a present of things present, and a present of things future." For these three do exist in some sort, in the soul, but otherwise do I not see them; present of things past, memory; present of things present, sight; present of things future, expectation. (Ibid., 243)

We find a modern echo of this sort of thinking in Schopenhauer (1788-1860):

The form of the phenomenon of the will . . . is really only the present, not the future nor the past. The latter are only in the conception of knowledge, so far as it follows the principle of sufficient reason. No man has ever lived in the past, and none will live in the future; the present alone is the form of all life, and is its sure possession which can never be taken from it. (Welt als Wille und Vorsellung, I, 54). (Borges, 233)

This formulation returns us to the prevailing assumptions about time enumerated at the beginning of this paper, which the enormously prolific Saint Augustine helped to shape not long before the fall of the Roman Empire. But let us now consider something akin to the "protracted" present that Augustine expressly rejected.

Because such a present would logically have to have a beginning and an ending in time, we might represent these as points situated a certain distance apart on our familiar unidirectional time axis (Fig 3). The present is thus shown as a line segment beginning at point x and ending at point y, with a theoretically infinite number of points lying between these two termini. Such a present could be subdivided into a series of "microscopic" moments, thus encompassing a potentially infinite number of pasts and futures--precisely the sort of paradox that Augustine wanted to avoid.

Paradoxical Present

Fig. 3. A Paradoxical Interpretation of the Present

Such temporal paradoxes were widely propounded in the Classical world. In his Adversus mathematicos, the skeptical physician Sextus Empiricus (c. 200 A.D.) denies

the existence of the past, that which already was, and the future, that which is not yet, and argues that the present is divisible or indivisible. It is not indivisible, for in such a case it would have no beginning to link it to the past nor end to link it to the future, nor even a middle, since what has no beginning or end can have no middle; neither is it divisible, for in such a case it would consist of a part that was and another that is not. Ergo, it does not exist, but since the past and the future do not exist either, time does not exist. (Ibid., 232)

Nearly two millennia later, Einstein's equally paradoxical theory of special relativity rocked the scientific world and captured the popular imagination. In essence, Einstein demolished the notion of an absolute, universal present by demonstrating that two events that apparently take place simultaneously from one vantage point may actually take place at different times when viewed from different vantage points.

Conjuring the Future

The argument is often made that if time's arrow really could be reversed, we might remember the future instead of the past. This, however, is misleading, for by definition memory is a faculty for recollecting the past--even if time should run "backwards" and the past swapped places with the future! Any human faculty capable of predicting the future would more properly be called "foresight."

Whether we accept anecdotal "evidence" supporting the existence of foresight is probably as much a matter of personal belief as our acceptance of memory. Even the God-fearing Augustine, who accepted the faculty of memory and was certainly aware of prophecy in the Judeo-Christian tradition, was not at all sure about foresight:

Although when past facts are related, there are drawn out of the memory, not the things themselves which are past, but words which, conceived by the images of the things, they, in passing, have through the senses left as traces in the mind. Thus my childhood, which now is not, is in time past, which now is not: but now when I recall its image, and tell of it, I behold it in the present, because it is still in my memory. Whether there be a like cause of foretelling things to come also; that of things which as yet are not, the images may be perceived before, already existing, I confess, O my God, I know not. This indeed I know, that we generally think before on our future actions, and that the forethinking is present, but the action whereof we forethink is not yet, because it is to come. (Ibid., 242)

If the future does not yet exist, we find ourselves in the Cassandra-like predicament of being unable to prove that what we allegedly "foresee" will come to pass. Nor can we prove, if the past no longer exists, that the prediction we recall writing down yesterday (or at any time in the past) is actual evidence of prognostication. We see that something written exists "now" that may (or may not) accurately describe unfolding events, but we are unable to provide corroborative comparison with the past that our alleged prediction even existed before the present.

If we take the view, as previously suggested, that the past is to a significant degree coextensive with the present, the distinction between foresight and "ordinary" sight becomes as blurred as the distinction between remembrance and "ordinary" sight.

Since the present stands in relation to the past in much the same way that the future stands in relation to the present, it is possible to think of the present penetrating the future just as the past seems to penetrate the present (see Fig. 1):

The possibility exists that the future and the past are already communicating with the present. The tiny quantum wave of probability and its behavior in spacetime, already implies that information can flow from past to present and from future to present. Thus it implies the existence of both the past and the future "simultaneously" with our own time. (Wolf, 205)

Dream Time

Augustine observed that both foreseeing the future and remembering the past are activities that take place in the present, dismissing the idea that past or future have any real existence independent of human consciousness. For visionaries, writers, and artists, however, past and future sometimes appear to be inextricably entwined with the present.

In the fourteenth century, the heretical Meister Eckhart (c. 1260-c. 1328) preached a radically different view from that of Augustine:

A day, whether six or seven ago, or more than six thousand years ago, is just as near to the present as yesterday. Why? Because all time is contained in the present Now-moment.

To talk about the world as being made by God tomorrow, or yesterday, would be talking nonsense. God makes the world and all things in this present now. Time gone a thousand years ago is now as present and as near to God as this very instant. (Rucker, 136)

Emerson, who abjured the cloth early in his career, married past to present in a more poetic but robustly secular manner:

Old and new make the warp and woof of every moment. There is no thread that is not a twist of these two strands. (Emerson, 285)

Panta rei: all things are in flux. It is inevitable that you are indebted to the past. You are fed and formed by it. The old forest is decomposed for the composition of the new forest. The old animals have given their bodies to the earth to furnish through chemistry the forming race, and every individual is only a momentary fixation of what was yesterday another's, is today his, and will belong to a third tomorrow. (Ibid., 300)

This intimate interpenetration of past, present, and future takes on special significance upon consideration of the fact that we spend roughly a third of our lives in sleep, and a significant portion of that time dreaming. Among the many peculiar properties of dreams is the frequent suspension of time as a logical succession of events. In the dream state, we may imagine ourselves aged and decrepit one moment, only to revert to childhood and youthful vigor in the next.

In The Interpretation of Dreams, Freud observed that dreams also "reproduce logical connection by simultaneity in time," in a manner analogous to Raphael's "School of Athens." In this celebrated tableau, the painter represents a convocation of scientists, philosophers, and artists from the seventh century B.C. through the sixteenth century A.D.--distilling nearly two thousand years of intellectual experience into a single view (Freud, 349).

Raphael,

Fig. 4. Raphael, "The School of Athens"

1. Alcibiades (451/0-404/3 B.C.); 2. Aristotle (384-322 B.C.); 3. Averroes (1126-98); 4. Diogenes (412-323 B.C.);

5. Epicurus (341-270 B.C.); 6. Euclid (fl. 300 B.C); 7. Federico II, Duke of Mantua (1500-1540);

8. Francesco Maria della Rovere, Duke of Urbino (1490-1538); 9. Heraclitus (535-475 B.C.); 10. Plato (429-347 B.C.);

11. Ptolemy (fl. 2d century A.D.); 12. Pythagoras (c. 582-c. 507 B.C.); 13. Raphael Sanzio (1483-1520);

14. Socrates (469-399 B.C.); 15. Giovanni Antonio Bazzi Sodoma (1477-1549); 16. Giorgio Vasari (1511-74);

17. Xenophon (c. 430-c. 355 B.C.); 18. Zoroaster (c.628-551 B.C.)

The oneiric obliteration of the boundaries between past, present, and future is hardly a phenomenon confined to the West or even to the unconscious. Central to the culture of the Australian aborigines, who evidently do not have a word for "time" in the abstract conceptual sense, is the "Dreaming," a sacred, heroic state in which man and nature come to be that has no fixed place in past or present. (Davies, Time, 26)

Timeless Laws or Lawless Times?

Interestingly enough, Raphael's painterly vision seems to resonate with mainstream scientific theory. Physicists tend to look upon past, present, and future as if they were equally real, laid out together as a multidimensional landscape (or "timescape") in block form. (Davies, Time, 70-77)

As physicist Frank Tipler matter-of-factly reminds us:

All fundamental physical theories advanced in the past three centuries--Newtonian mechanics, general relativity, quantum mechanics, string field theory--have insisted there is no fundamental distinction between past, present, and future. (Tipler, xii)

In fact, physical theory is basically time-symmetric: its equations show no prejudice in favor of any particular temporal direction. Although the metaphorical "arrow of time" receives marked emphasis in certain areas of modern physics--notably thermodynamics, radiation, and cosmology, it should by no means be taken as evidence that time actually "flies" (or "flows" or "passes" or "moves") in any direction whatsoever.

What is more, there is nothing that absolutely forbids certain physical processes from being reversed in time. There is simply an exceedingly low probability--particularly at the macroscopic scale of human perception--that phenomena we anthropocentrically regard as occurring in one temporal direction will reverse themselves and "run backwards" like a film showing the pieces of a shattered vase reassembling themselves.

At the microscopic quantum scale, it is a different matter. "Quantum events seem to be yelling at physicists that the universe has no intrinsic arrow of time, but most refuse to listen." (Stenger, 5)

The macroscopic observation that in nature all things tend to become dispersed and disorderly is the basis of the second law of thermodynamics, which predicts that entropy will always increase. Although the second law ultimately seems to be responsible for the arrow of time, it is not sufficient in itself to abrogate the temporal symmetry demanded by classical physical theory. Indeed, various theories have been advanced in an attempt to reconcile the often jarring clashes that have arisen between the two.

Fearful Symmetries

In the 1960s Thomas Gold proposed that, whereas the expansion of the universe is responsible for the thermodynamic arrow of time, that arrow will eventually change direction as entropy decreases and the universe collapses in a "Big Crunch." This suggests that, given a long enough time, temporal asymmetries will counterbalance one another, and underlying symmetry will be restored.

The problem with this interpretation is that contraction does not necessarily result in decreasing entropy--although that possibility is not entirely ruled out. It simply is not clear if there is enough matter in the universe to bring about a "Big Crunch." If such is the case, however, the future will actually lie in the direction of decreasing entropy, and the end of the universe may actually be indistinguishable from the beginning.

Ludwig Boltzmann, the "father" of statistical mechanics, had already envisioned something of the sort in the late nineteenth century when he proposed that entropy increases not just in the direction of the future but also in the direction of the past. However, this attempt to ensure fundamental symmetry posed some formidable problems. If the entropy gradient increased towards the past, why did it not decrease towards the future? What, indeed, was so "special" about the present that resulted in such a relatively high level of order and correspondingly low level of entropy?

Boltzmann reasoned that across the axis of time, at whose extremes the infinitely remote past and infinitely distant future were both close to a state of maximum entropy, there were intermittent probabilistic fluctuations that now and then produced periods of comparative order and stability. The present happened to correspond to such a fluctuation, making it possible for creatures such as Homo sapiens to come into being.

Because we evidently live in a period of increasing entropy, and memory itself is subject to its effects, time seems to move in the direction we think of as the future. But since the direction of time is a subjective phenomenon dependent on the relative presence or absence of entropy, under other circumstances, time itself might be perceived very differently.

Boltzmann's theory seems to fail because it is not only extremely improbable that Homo sapiens exists but that order exists on such a vast, universal scale. Although entropy has taken a toll on our records, monuments, and collective memories, how can it be that so much of our so-called past seems to have been preserved in tact? Statistically speaking, the sum total of human knowledge ought to have been reduced to little more than an indecipherable muddle, but somehow civilization has managed to develop and man has evolved into a highly complex organism. More importantly, in direct contradiction of Boltzmann's explanation, modern cosmological theory suggests that entropy actually decreases in the direction of the distant past, all the way back to the initial singularity before the Big Bang.

In part as a consequence of his colleagues' critical rejection of his ideas, Bolztmann succumbed to severe mental disorder, and in 1906 he committed suicide.

Paradox Lost or Paradox Regained?

In more recent times, controversy has arisen because certain leading physicists have evidently swept time-symmetric physical theory under the rug and accepted the arrow of time as an inescapable cosmological given. Nowhere has this been more evident than in the case of Stephen Hawking, arguably the most celebrated scientific personality since Albert Einstein. After first embracing the concept of a contracting universe in which entropy would decease, he reversed his opinion and concluded that disorder would increase without affecting the direction of the thermodynamic (and psychological) arrow of time.

Hawking was called to task, however, by logician Huw Price, who accused him of failing to explain why entropy could be low near the Big Bang and not near the final singularity of the Big Crunch, a necessary condition of time-symmetric physical theory:

This then is the dilemma: either we have to admit reversal of the thermodynamic arrow of time in the case of local or universal gravitational collapse; or temporal asymmetry turns out to be inexplicable after all, since we can't account for the low initial entropy of the universe as a more or less inevitable consequence of our best physical theory of the universe as a whole. (Price, Point, 3)

Price further challenges the notion that the Big Bang should be regarded as the beginning of the universe, since time-symmetric physical theory might just as well allow us to consider it to be the end of the universe.

Physicist Victor Stenger describes what would be required to eliminate the discrepancies Price has identified:

The idea is to maintain underlying time symmetry while allowing "localized" violations, a trick that has worked for other symmetries in particle theory. Like those symmetries, time symmetry becomes a global rule that is locally broken, where by "local" . . . I am referring to the region of spacetime occupied by our universe since the beginning of the big bang. (Stenger, 2)

He proposes an alternate explanation of the Big Bang which allows for time-symmetric inflation on both sides of the time axis, resulting in two conjoined universes, "one with its time arrow forward in conventional time and one with its time arrow going in the opposite direction."

Meanwhile, Nobel laureate Ilya Prigogine and Isabelle Stengers have put forth a radical reinterpretation of the second law of thermodynamics, whereby entropy does not necessarily lead to disorder but may, under the right conditions, give rise to increased order. Their work addresses not only the contradictions in physical theory between classical time-symmetry and the asymmetric "arrow of time," but also the significant clash between evolutionary theory--which predicts increasing biological order and complexity--and the disordered homogeneity foreshadowed by thermodynamic entropy.

Alvin Toffler explains:

By insisting that irreversible time is not a mere aberration, but a characteristic of much of the universe, they subvert classical dynamics. . . . Of course, reversibility still applies (at least for sufficiently long times)--but in closed systems only. Irreversibility applies to the rest of the universe.

Prigogine and Stengers also undermine conventional views of thermodynamics by showing that, under nonequilibrium conditions, at least, entropy may produce, rather than degrade, order, organization--and therefore life. . . .

While certain systems run down, other systems simultaneously evolve and grow more coherent. This mutualistic, nonexclusive view makes it possible for biology and physics to coexist rather than merely contradict one another. (Prigogine and Stengers, xxi)

Perhaps the most radical solution of all, however is that recently revisited by physicist Julian Barbour: time simply does not exist at all!

Suppose we accept the quantum universe is static and timeless. How can we reconcile that with actually seeing motion and remembering the past? In fact, besides the direct sensing of change of one kind or another, the only direct evidence we have for time and the past comes from records, which include memories. Now records, either natural like fossils or man made, are so ubiquitous we can easily forget how remarkable their existence is according to the current understanding of classical mechanics. This is the problem of the extraordinarily low entropy of the universe. It was emphasized a century ago by Boltzmann. In the modern context of general relativity, Roger Penrose keeps on pointing out what a huge problem it is. All statistical arguments based on classical mechanics suggest the universe ought to have a vastly higher entropy and exist in a state in which records simply cannot form. Penrose wants to explain the low entropy and the arrow of time by a new physics which is explicitly time-asymmetric and comes with a built-in arrow of time and forces the universe to begin in a highly uniform state. My own view is that, paradoxically, the arrow of time may be easier to explain in a theory in which there is no time at all. (Brockman)

* * *

After a lifetime of reflection, Einstein conceded, "The distinction between past, present and future is only an illusion, even if a stubborn one." (Davies, Time, 70) Our persistent conceits about time confound our understanding, illuminating the corridors of consciousness with a dazing spectral glare. Even as time's arrow whizzes by, as if shot by some invisible marksman, we can only wonder from what quiver it was drawn and towards what target it flies.

Or could it be that it has entirely missed its mark?


REFERENCES

  1. Augustine of Hippo. Confessions. Book 11: Of God and the Nature of Time. Translated by Edward Bouverie Pusey. Reprint, Franklin Center [Pennsylvania]: The Franklin Library,1982.
  2. Borges, Jorge Luis. "A New Refutation of Time." In Labyrinths: Selected Stories and Other Writings, edited by Donald A. Yates and James E. Irby, with a preface by André Maurois, 217-334. New York: New Directions, 1964.
  3. Brockman, John. "The End of Time: A Talk with Julian Barbour." Edge 60, 20 September 1999. Reprint available online at:
  4. "The End of Time: A Talk with Julian Barbour"
  5. Davies, Paul. About Time: Einstein's Unfinished Revolution. New York: Simon and Schuster, 1995.
  6. __________. "That Mysterious Flow." Scientific American, vol. 287, no. 3 (September 2002).
  7. Emerson, Ralph Waldo. "Quotation and Originality." In The Portable Emerson, selected and arranged with an introduction and notes by Mark van Doren, 284-303. New York: The Viking Press, 1965.
  8. Freud, Sigmund. 1953. The Interpretation of Dreams. Vols. 4-5. Translated and edited by James Strachey. London: Hogarth Press, 1953. Reprint (2 vols. in 1), New York: Avon Books, 1972.
  9. Hall, Marcia, ed. Raphael's School of Athens. Masterpieces of Western Painting. Cambridge: Cambridge, 1997.
  10. Price, Huw. "A Point on the Arrow of Time." Nature, 20 July 1989, 181-82. Reprint available online at:
  11. Huw Price Publications
  12. __________. Time’s Arrow and Archimedes’ Point: New Directions for the Physics of Time.New York: Oxford, 1997.
  13. Rucker, Rudy. The Fourth Dimension: A Guided Tour of the Higher Universes. Boston: Houghton Mifflin, 1984.
  14. Stenger, Victor J. "Time's Arrows Point Both Ways: The View from Nowhen." Skeptic, vol. 8, no. 4, 92-95. Reprint available online at:
  15. "Time's Arrows Point Both Ways: The View from Nowhen"
  16. Tipler, Frank J. The Physics of Immortality: Modern Cosmology, God and the Resurrection of the Dead. New York: Doubleday, 1994.
  17. Toffler, Alvin. Foreword to Order Out of Chaos: Man's New Dialogue with Nature, by Ilya Prigogine and Isabelle Stengers. New York: Bantam Books, 1984.
  18. Wolf, Fred. Parallel Universes: The Search for Other Worlds. New York: Simon and Schuster, 1988.

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