De Natura Temporis

By Austin Cagle

12-7-04

Time has been one of the greatest metaphysical dilemmas ever contemplated. Its existence is instinctual yet its nature is elusive. It does not lend itself to the direct empirical studies of science. Studies of its essence, and even its existence, have been almost completely isolated to the realm of philosophy and its sisters. Experience tells us that we are more likely to hear the nature of time from a priest than a physicist. Most of the statements presented on time are elusive in their meaning, but some philosophers, like Rabbi Abraham Heschel, seek to provide real answers to the questions of time. Heschel says, “When closing our eyes in moments of intellectual concentration we are able to have time without space. But we can never have space without time. To the spiritual eye space is frozen time, and all things are petrified events.”[1] Even the most highly religious will recognize and acknowledge the similarities and relation between this empirical enigma and that which science has been seeking to master as long as it has existed, namely space. “In the beginning God created the heavens and the earth.”[2] There is a relation that exists between time and space that cannot be avoided. It is in contemplating the nature of time that a philosopher is overwhelmed with the desire to become a physicist. One cannot properly understand time without a proper understanding of space, and the understanding of space is a life long pursuit of its own. It will be helpful, however to draw upon the similarities that are known between space and time to better understand the complex natures of these dimensions. The connections are related to each other enough to allow an easy flow one to the other. First are the ideas of finitude and density. Secondly there is the measurement of time which leads to the notion of the “movement of time.” This in turn is strongly related to causality and the perception of the direction of time. Each of these ideas will be discussed in light of space and time and in the context of each other.

Density and Infinity

The concepts of finitude and infinity pose the first difficulty for time. Van Inwagen says ‘Both space and time are (or seem to be) composed of infinitely many dimensionless points.”[3] One of the qualities that time appears to have is its infinity or boundless nature. It certainly shares this with space. It is unavoidable that Zeno’s paradox come up in this topic. Russell quotes him saying of Achilles and the tortoise, “the slower will never be overtaken by the swifter, for the pursuer must first reach the point whence the fugitive is departed, so that the slower must always necessarily remain ahead.”[4] The idea is that before Achilles can get to the tortoise, he must go to the point the tortoise just left. Since he is in constant motion, there is an infinite amount of departure points for the tortoise. Here we have a classic representation of a seemingly endless distance that, as experience has taught us, is actually a finite amount. It is usually quite easy to think of the infinite as larger than the finite, but this analogy seeks to understand the infinite within the confines of the finite. Certainly space and time share this unique quality. Though they are bound by finite numerical measures, there is an infinite amount of numerical measures between them. This idea is what is called density. All relational aspects of time and space are dealing with density and the measures between the points. Van Inwagen says,

“Between any two points in space there is an interval that has (or is assumed to have) a ‘measure’, such as 3.2 meters or six light years. Between any two points in time, there also is an interval that has (or is assumed to have) a measure, such as a nanosecond or a billion years. Both space and time (at least as we conceive them) have a property called density: between any two points in space, there are other points in space; between any two points in time, there are other points in time.”[5]

No one has as of yet determined the topology of time. Is time finite or infinite? It seems that it can be classified as infinite within the bounds of its nature. In other words, even if time has a finite beginning and finite ending, the concept of infinity can be found within the framework of this finitude. Though there is a set amount of time for the earth to rotate once on its axis, there is an infinite amount of smaller measures or units of time within that finite. Just as there are an unending amount of numbers between 1 and 2, so there are also an infinite amount of moments between the beginning and the end.

Time and Movement

The sense of the motion of time, the perception that time is moving, is a common phenomenon that adds to the difficulty in understanding what it is. Russell says that “the concept of motion is logically subsequent to that of occupying a place at a time, and also that of change.”[6] For example: at time x the ball is in the hand of the pitcher, and at time y it is in the hand of the catcher. Therefore, the ball has been in motion. If we are seeking the motion of time, how is it possible to determine at what place in time a moment of time occurs? It is absurd to think this possible. Similarly, when motion is introduced the concept of rate is a necessary presence. Rate is mathematically defined as the distance in relation to the time. The problem is quite apparent. To give a rate of time in relation to time is utterly meaningless. What is to be done with this perception? Many philosophers have given answers to this question, one of which will be looked at shortly. Let’s think of this idea in relation to space and see what conclusions can be discovered. When dealing with rate in space we do not speak of space moving, but of objects moving within space. We measure distance (i.e. amount of space) in relation to time and call it rate of motion. Objects move in space because they occupy space. It would seem that space and time again share similarities in this regard. It does not seem possible that time itself could move. Rather whatever occupies time in the way objects occupy space will have the sense of motion in time in a similar fashion to the motion of objects in space. It seems most plausible that the entities which occupy time are what we refer to as events. The philosopher/rabbi Abraham Heschel previously quoted agrees, “To the spiritual eye space is frozen time, and all things are petrified events.” (p.97) He continues,

“There are two points of view from which time can be sensed: from the point of view of space and from the point of view of spirit. Looking out of the window of a swiftly moving railroad car, we have the impression that the landscape is moving while we ourselves are sitting still. Similarly, when gazing at reality while our souls are carried away by spatial things, time appears to be in constant motion. However, when we learn to understand that it is the spatial things that are constantly running out, we realize that time is that which never expires, that it is the world of space which is rolling through the infinite expanse of time. Thus temporality may be defined as the relation of space to time.” [7]

Whatever other difficulties Heschel presents with this view, he gives a strong picture of the occupants of moments of time. Namely, that events occupy time in the way that objects occupy space. The only difference is that these events forever occupy the moment in which they occur. These moments of time can be measured by the events that occupy them. The question may be posed, “If the motion of objects in space constitute motion in space, how can set events move to bring motion in time?” One possible response to this question is Heschel’s view that it is space as a whole that moves through time.

Another response to this question can be understood using Bertrand Russell’s view of time. In his book “The Principles of Mathematics” Russell presents a view of motion (i.e. the relation of objects in space and time) which relies on a rather unique method of describing time. His most concise rendering of his view is still rather lengthy and it is therefore helpful to use the aid of those who have presented his view clearly. Russell begins by denying the concept that the present moment as an entity which floats through time. Russell believed that most of the difficulties that we have in contemplating time comes from this idea of the elusive present moment. He believed it complicates the study by making a word with a vague meaning the focal point of discussions on time. By eliminating the word from our vocabulary for time he allows a more precise search into its true nature. He then presents a vocabulary which can be used in describing the relation between the events in time while avoiding as much as possible the differing of tense at all. Van Inwagen presents Russell’s view as having primitive terms which he states are:

“x is before y (where x and y are moments of or points in time), and

A occurs at x (where A is an event and x is a moment in time)

We now define three terms we shall find it easier to work with than our two primitive terms. In these definitions, ‘A’ and ‘B’ both refer to events.

‘A occurs before B’ is defined as the moment at which A occurs is before the moment at which B occurs.

‘A occurs after B’ is defined as the moment at which B occurs is before the moment at which A occurs.

‘A and B are simultaneous’ is defined as the moment at which A occurs is the moment at which B occurs.”[8]

In actuality Russell’s vocabulary makes the motion of the present an impossibility. In fact, in regards to this idea Van Inwagen says, “We can do no better than ‘Various events occur before various other events,’ which hardly seems to involve the idea of movement.”[9] Some may be uneasy about denying the reality of the present moment as an entity, but again a spatial example may settle this unease. Van Inwagen tells how some advocates of Russell’s theory draw the parallel between “hereness” in space and “nowness” in time. “One does indeed pick out a place each time one says ‘here,’ but ‘here’ simply means ‘the place at which this utterance—or thought—occurs.”[10] In the same light “nowness” in Russell’s terms is ‘the time at which this utterance—or thought—occurs.’ All references to time in Russell’s vocabulary are shown as the relation between the events occurring within the moments of time. Let’s assume for the sake of discussion that a moment of time is equal to the amount of time filled by an event. In this way we can say that the time it takes for the earth to rotate once around its axis is a moment, and the time it takes for the earth to orbit the sun is also a moment. Assuming that God is outside of time completely, and can therefore see all of time at once, it is possible to call all of time one moment and all of history past, present, and future, one event. Using Russell’s vocabulary, it seems that if time is seen as a finite creation which has a logical beginning and a logical end, it can be reduced to a single moment, and all existence becomes a single event occupying that single moment. We, as creatures of time experience the infinite within the finite. We can break down the universe into infinitely small pieces of time and study it by breaking the events into smaller individual events. Van Inwagen consents that Russell’s view allows for a logical explanation of static time. He says, “If Russell’s theory is correct, the seeming movement of time (or of whatever it is that is supposed to move) is a mere seeming, a feature of appearance and not reality: in fact, an illusion. What the theory does not seem to be able to do is explain the source of the illusion.”[11] Van Inwagen does not want to give up on his instinctual conception of time. It seems, though, that Van Inwagen can be given an answer to the source of the illusion of movement. The cause of this illusion is that our perception of time is largely dependent on causality and what Stephen Hawking has labeled the arrows of time.

Causality and the Illusion of Motion

All events can be classified as either a cause or an effect. The philosopher Leibniz called this idea the principle of sufficient reason. He said that the principle of sufficient reason means, “that nothing happens without its being possible for one who has enough knowledge of things to give a reason sufficient to determine why it is thus and not otherwise.” This principle implies that time is infinite because there is always a prior cause for the effect at hand. One way to avoid this dilemma is to assume a first cause as a necessary being. If the first cause is a necessary being than its cause is itself. Let’s assume this is the case for the present study. God is the first cause, the Great cause. Everything that occurred after God’s initial cause, creation, is an effect first and foremost. Thus all of time can be referred to as the Great Effect. This is not to say that created things cannot be causes, only that they are not the first cause and will always be the effect of a prior cause first. It is certainly possible, and indeed very likely that any given effect become a cause as well. However, if looked at in its totality, creation is best described as the Great Effect. This is due to the fact that all the causes that are present within it only cause things within creation itself. God is the only cause that was not first an effect. There is a natural and logical link between a cause and effect. This link is one of the factors in the illusion of motion in time. The flow of one event to another can be compared to the falling of dominoes in a line. Does the movement that we see along the whole line of dominoes consist in the dominoes, or does it follow along the top of them? Is it possible that the movement of the whole is an illusion based upon the first causing the second and the second causing the third and so on? If understood this way there is no overall motion. It is merely an illusion. It seems plausible that the motion of time is an illusion following a similar idea. The illusion of motion is strengthened by the remembrance of great events which happened before and the expectation of great events which happen after this utterance. This phenomenon can be explained by Hawking’s description of the arrows of time.

The Arrows of Time

One of the more interesting distinctions between time and space is directional movement. It is completely natural to think about moving in space in any particular direction. It is done in the most mundane daily exercises; getting up in the morning, walking to the coffee maker, walking back to the bedroom, etc. Time, on the other hand, is quite one directional. The idea of seeing pieces of glass on the floor collect themselves together in the form of a mug and jump up onto a table strikes our minds as absurd. However it is quite natural to see a mug fall from the table and shatter on the ground. Hawking says,

“The explanation that is usually given as to why we don’t see broken cups gathering themselves together off the floor and jumping back onto the table is that it is forbidden by the second law of thermodynamics. This says that in any closed system disorder, or entropy, always increases with time. In other words, it is a form of Murphy’s law: Things always tend to go wrong! An intact cup on the table is a state of high order, but a broken cup on the floor is a disordered state, One can go readily from the cup on the table in the past to the broken cup on the floor in the future, but not the other way around.”[12]

The increase of disorder with time is one example that Hawking gives of an arrow in time. It is something that distinguishes past events from future events giving time a perceived direction. Hawking identifies three different types of arrows in time.

“First, there is the thermodynamic arrow of time, the direction of time in which disorder or entropy increases. Then, there is the psychological arrow of time. This is the direction in which we feel time passes, the direction in which we remember the past, but not the future. Finally there is the cosmological arrow of time. This is the direction of time in which the universe is expanding rather than contracting.”[13]

Hawking points out that the thermodynamic arrow and the psychological arrow will always point the same way. This is due to the fact that the psychological arrow of time is determined by the thermodynamic arrow of time. Hawking says, “Just as a computer, we must remember things in the order in which entropy increases…Disorder increases with time because we measure time in the direction in which disorder increases.” Time appears to be moving forward because we are limited by the thermodynamic arrow to remember the past and expect the future.

Conclusion

Time is an elusive creature that always manages to evade those who seek to capture her. As new discoveries are made concerning space, perhaps more will be understood concerning time. The relatively recent validation of Einstein’s theory of relativity speaks to the nature of time, though its application is not necessary to spell out here. The interconnected nature of the studies of space and time means that philosophers will always be following on the heels of physicists in new theories of time. It is only through the working of both fields that a valid theory of time can ever be presented, as was shown earlier by Hawking’s presentation of the arrows of time aiding in discovering the source of the illusion of time’s motion. As we begin to understand the concepts of finitude and density more completely when applied to space, the mysteries of time will also begin to reveal themselves. Perhaps we will find that space is a single point as time is a single moment. Or perhaps Heschel will be proved correct in theorizing that the events of space move through eternal, static time. In the end it appears that space holds all the answers to time, but only time will tell.

Works Cited

Hawking, Stephen. A Brief History of Time: From the Big Bang to Black Holes. New York, Bantan, 1988.

Heschel, Abraham Joshua. The Sabbath. New York, Farrar, Straus, and Giroux, 1979.

Russell, Bertrand. The Principles of Mathematics. New York, W. W. Norton and Company, 1996.

The Student Bible, New International Version. Michigan: Zondervan, 1996.

Van Inwagen, Peter. Metaphysics. Colorado, Westview Press, 2002.

[1]Abraham Joshua Heschel, The Sabbath (New York: Farrar, Straus, and Giroux, 1979) 96-97.

[3] Peter van Inwagen, Metaphysics, (Colorado: Westview Press, 2002) 56.

[4] Bertrand Russell, The Principles of Mathematics, (New York: W. W. Norton and Company, 1996) 350.

[5] Peter van Inwagen, Metaphysics, (Colorado: Westview Press, 2002) 56

[6] Bertrand Russell, The Principles of Mathematics, (New York: W. W. Norton and Company, 1996) 350.

[7]Abraham Joshua Heschel, The Sabbath (New York: Farrar, Straus, and Giroux, 1979) 97.

[8] Peter van Inwagen, Metaphysics, (Colorado: Westview Press, 2002) 61

[12] Stephen Hawking, A Brief History of Time: From the Big Bang to Black Holes (New York: Bantan, 1988) 144-145