27. TIME AS NECESSARY, INFINITE, AND INFINITELY1 DIVISIBLE.—Of course, we all know something about time; we know it as past, present, and future; we know it as divisible into parts, all of which are successive; we know that whatever happens must happen in time. Those who have thought a good deal about the matter are apt to tell us that time is a necessity of thought, we cannot but think it; that time is and must be infinite; and that it is infinitely divisible.
These are the same statements that were made regarding space, and, as they have to be criticised in just the same way, it is not necessary to dwell upon them at great length. However, we must not pass them over altogether.
As to the statement that time is a necessary idea, we may freely admit that we cannot in thought annihilate2 time, or think it away. It does not seem to mean anything to attempt such a task. Whatever time may be, it does not appear to be a something of such a nature that we can demolish3 it or clear it away from something else. But is it necessarily absurd to speak of a system of things—not, of course, a system of things in which there is change, succession, an earlier and a later, but still a system of things of some sort—in which there obtain no time relations? The problem is, to be sure, one of theoretical interest merely, for such a system of things is not the world we know.
And as for the infinity5 of time, may we not ask on what ground any one ventures to assert that time is infinite? No man can say that infinite time is directly given in his experience. If one does not directly perceive it to be infinite, must one not seek for some proof of the fact? The only proof which appears to be offered us is contained in the statement that we cannot conceive of a time before which there was no time, nor of a time after which there will be no time; a proof which is no proof, for written out at length it reads as follows: we cannot conceive of a time in the time before which there was no time, nor of a time in the time after which there will be no time. As well say: We cannot conceive of a number the number before which was no number, nor of a number the number after which will be no number. Whatever may be said for the conclusion arrived at, the argument is a very poor one.
When we turn to the consideration of time as infinitely divisible, we seem to find ourselves confronted with the same difficulties which presented themselves when we thought of space as infinitely divisible. Certainly no man was immediately conscious of an infinite number of parts in the minute which just slipped by. Shall he assert that it did, nevertheless, contain an infinite number of parts? Then how did it succeed in passing? how did it even begin to pass away? It is infinitely divisible, that is, there is no end to the number of parts into which it may be divided; those parts and parts of parts are all successive, no two can pass at once, they must all do it in a certain order, one after the other.
Thus, something must pass first. What can it be? If that something has parts, is divisible, the whole of it cannot pass first. It must itself pass bit by bit, as must the whole minute; and if it is infinitely divisible we have precisely7 the problem that we had at the outset. Whatever passes first cannot, then, have parts.
Let us assume that it has no parts, and bid it Godspeed! Has the minute begun? Our minute is, by hypothesis, infinitely divisible; it is composed of parts, and those parts of other parts, and so on without end. We cannot by subdivision come to any part which is itself not composed of smaller parts. The partless thing that passed, then, is no part of the minute. That is all still waiting at the gate, and no member of its troop can prove that it has a right to lead the rest. In the same outer darkness is waiting the point on the line that misbehaved itself in the last chapter.
28. THE PROBLEM OF PAST, PRESENT, AND FUTURE.—It seems bad enough to have on our hands a minute which must pass away in successive bits, and to discover that no bit of it can possibly pass first. But if we follow with approval the reflections of certain thinkers, we may find ourselves at such a pass that we would be glad to be able to prove that we may have on our hands a minute of any sort. Men sometimes are so bold as to maintain that they know time to be infinite; would it not be well for them to prove first that they can know time at all?
The trouble is this; as was pointed8 out long ago by Saint Augustine (354-430) in his famous "Confessions," [1] the parts of time are successive, and of the three divisions, past, present, and future, only one can be regarded as existing: "Those two times, past and future, how can they be, when the past is not now, and the future is not yet?" The present is, it seems, the only existent; how long is the present?
"Even a single hour passes in fleeting9 moments; as much of it as has taken flight is past, what remains10 is future. If we can comprehend any time that is divisible into no parts at all, or perhaps into the minutest parts of moments, this alone let us call present; yet this speeds so hurriedly from the future to the past that it does not endure even for a little space. If it has duration, it is divided into a past and a future; but the present has no duration.
"Where, then, is the time that we may call long? Is it future? We do not say of the future: it is long; for as yet there exists nothing to be long. We say: it will be long. But when? If while yet future it will not be long, for nothing will yet exist to be long. And if it will be long, when, from a future as yet nonexistent, it has become a present, and has begun to be, that it may be something that is long, then present time cries out in the words of the preceding paragraph that it cannot be long."
Augustine's way of presenting the difficulty is a quaint11 one, but the problem is as real at the beginning of the twentieth century as it was at the beginning of the fifth. Past time does not exist now, future time does not exist yet, and present time, it seems, has no duration. Can a man be said to be conscious of time as past, present, and future? Who can be conscious of the nonexistent? And the existent is not time, it has no duration, there is no before and after in a mere4 limiting point.
Augustine's way out of the difficulty is the suggestion that, although we cannot, strictly12 speaking, measure time, we can measure memory and expectation. Before he begins to repeat a psalm13, his expectation extends over the whole of it. After a little a part of it must be referred to expectation and a part of it to memory. Finally, the whole psalm is "extended along" the memory. We can measure this, at least.
But how is the psalm in question "extended along" the memory or the expectation? Are the parts of it successive, or do they thus exist simultaneously14? If everything in the memory image exists at once, if all belongs to the punctual present, to the mere point that divides past from future, how can a man get from it a consciousness of time, of a something whose parts cannot exist together but must follow each other?
Augustine appears to overlook the fact that on his own hypothesis, the present, the only existent, the only thing a man can be conscious of, is an indivisible instant. In such there can be no change; the man who is shut up to such cannot be aware that the past is growing and the future diminishing. Any such change as this implies at least two instants, an earlier and a later. He who has never experienced a change of any sort, who has never been conscious of the relation of earlier and later, of succession, cannot think of the varied15 content of memory as of that which has been present. It cannot mean to him what memory certainly means to us; he cannot be conscious of a past, a present, and a future. To extract the notion of time, of past, present, and future, from an experience which contains no element of succession, from an indivisible instant, is as hopeless a task as to extract a line from a mathematical point.
It appears, then, that, if we are to be conscious of time at all, if we are to have the least conception of it, we must have some direct experience of change. We cannot really be shut up to that punctual present, that mere point or limit between past and future, that the present has been described as being. But does this not imply that we can be directly conscious of what is not present, that we can now perceive what does not now exist? How is this possible?
It is not easy for one whose reading has been somewhat limited in any given field to see the full significance of the problems which present themselves in that field. Those who read much in the history of modern philosophy will see that this ancient difficulty touching16 our consciousness of time has given rise to some exceedingly curious speculations17, and some strange conclusions touching the nature of the mind.
Thus, it has been argued that, since the experience of each moment is something quite distinct from the experience of the next, a something that passes away to give place to its successor, we cannot explain the consciousness of time, of a whole in which successive moments are recognized as having their appropriate place, unless we assume a something that knows each moment and knits it, so to speak, to its successor. This something is the self or consciousness, which is independent of time, and does not exist in time, as do the various experiences that fill the successive moments. It is assumed to be timelessly present at all times, and thus to connect the nonexistent past with the existent present.
I do not ask the reader to try to make clear to himself how anything can be timelessly present at all times, for I do not believe that the words can be made to represent any clear thought whatever. Nor do I ask him to try to conceive how this timeless something can join past and present. I merely wish to point out that these modern speculations, which still influence the minds of many distinguished18 men, have their origin in a difficulty which suggested itself early in the history of reflective thought, and are by no means to be regarded as a gratuitous19 and useless exercise of the ingenuity20. They are serious attempts to solve a real problem, though they may be unsuccessful ones, and they are worthy21 of attention even from those who incline to a different solution.
29. WHAT IS REAL TIME?—From the thin air of such speculations as we have been discussing let us come back to the world of the plain man, the world in which we all habitually22 live. It is from this that we must start out upon all our journeys, and it is good to come back to it from time to time to make sure of our bearings.
We have seen (Chapter V) that we distinguish between the real and the apparent, and that we recognize as the real world the objects revealed to the sense of touch. These objects stand to each other in certain relations of arrangement; that is to say, they exist in space. And just as we may distinguish between the object as it appears and the object as it is, so we may distinguish between apparent space and real space, i.e. between the relations of arrangement, actual and possible, which obtain among the parts of the object as it appears, and those which obtain among the parts of the object as it really is.
But our experience does not present us only with objects in space relations; it presents us with a succession of changes in those objects. And if we will reason about those changes as we have reasoned about space relations, many of our difficulties regarding the nature of time may, as it seems, be made to disappear.
Thus we may recognize that we are directly conscious of duration, of succession, and may yet hold that this crude and immediate6 experience of duration is not what we mean by real time. Every one distinguishes between apparent time and real time now and then. We all know that a sermon may _seem _long and not be long; that the ten years that we live over in a dream are not ten real years; that the swallowing of certain drugs may be followed by the illusion of the lapse23 of vast spaces of time, when really very little time has elapsed. What is this real time?
It is nothing else than the order of the changes which take place or may take place in real things. In the last chapter I spoke24 of space as the "form" of the real world; it would be better to call it a "form" of the real world, and to give the same name also to time.
It is very clear that, when we inquire concerning the real time of any occurrence, or ask how long a series of such lasted, we always look for our answer to something that has happened in the external world. The passage of a star over the meridian25, the position of the sun above the horizon, the arc which the moon has described since our last observation, the movement of the hands of a clock, the amount of sand which has fallen in the hourglass, these things and such as these are the indicators26 of real time. There may be indicators of a different sort; we may decide that it is noon because we are hungry, or midnight because we are tired; we may argue that the preacher must have spoken more than an hour because he quite wore out the patience of the congregation. These are more or less uncertain signs of the lapse of time, but they cannot be regarded as experiences of the passing of time either apparent or real.
Thus, we see that real space and real time are the plan of the world system. They are not things of any sort, and they should not be mistaken for things. They are not known independently of things, though, when we have once had an experience of things and their changes, we can by abstraction from the things themselves fix our attention upon their arrangement and upon the order of their changes. We can divide and subdivide27 spaces and times without much reference to the things. But we should never forget that it would never have occurred to us to do this, indeed, that the whole procedure would be absolutely meaningless to us, were not a real world revealed in our experience as it is.
He who has attained28 to this insight into the nature of time is in a position to offer what seem to be satisfactory solutions to the problems which have been brought forward above.
(1) He can see, thus, why it is absurd to speak of any portion of time as becoming nonexistent. Time is nothing else than an order, a great system of relations. One cannot drop out certain of these and leave the rest unchanged, for the latter imply the former. Day-after-to-morrow would not be day-after-to-morrow, if to-morrow did not lie between it and to-day. To speak of dropping out to-morrow and leaving it the time it was conceived to be is mere nonsense.
(2) He can see why it does not indicate a measureless conceit29 for a man to be willing to say that time is infinite. One who says this need not be supposed to be acquainted with the whole past and future history of the real world, of which time is an aspect. We constantly abstract from things, and consider only the order of their changes, and in this order itself there is no reason why one should set a limit at some point; indeed, to set such a limit seems a gratuitous absurdity30. He who says that time is infinite does not say much; he is not affirming the existence of some sort of a thing; he is merely affirming a theoretical possibility, and is it not a theoretical possibility that there may be an endless succession of real changes in a real world?
(3) It is evident, furthermore, that, when one has grasped firmly the significance of the distinction between apparent time and real time, one may with a clear conscience speak of time as infinitely divisible. Of course, the time directly given in any single experience, the minute or the second of which we are conscious as it passes, cannot be regarded as composed of an infinite number of parts. We are not directly conscious of these subdivisions, and it is a monstrous31 assumption to maintain that they must be present in the minute or second as perceived.
But no such single experience of duration constitutes what we mean by real time. We have seen that real time is the time occupied by the changes in real things, and the question is, How far can one go in the subdivision of this time?
Now, the touch thing which usually is for us in common life the real thing is not the real thing for science; it is the appearance under which the real world of atoms and molecules32 reveals itself. The atom is not directly perceivable, and we may assign to its motions a space so small that no one could possibly perceive it as space, as a something with part out of part, a something with a here and a there. But, as has been before pointed out (section 26), this does not prevent us from believing the atom and the space in which it moves to be real, and we can represent them to ourselves as we can the things and the spaces with which we have to do in common life.
It is with time just as it is with space. We can perceive an inch to have parts; we cannot perceive a thousandth of an inch to have parts, if we can perceive it at all; but we can represent it to ourselves as extended, that is, we can let an experience which is extended stand for it, and can dwell upon the parts of that. We can perceive a second to have duration; we cannot perceive a thousandth of a second to have duration; but we can conceive it as having duration, i.e. we can let some experience of duration stand for it and serve as its representative.
It is, then, reasonable to speak of the space covered by the vibration33 of an atom, and it is equally reasonable to speak of the time taken up by its vibration. It is not necessary to believe that the duration that we actually experience as a second must itself be capable of being divided up into the number of parts indicated by the denominator of the fraction that we use in indicating such a time, and that each of these parts must be perceived as duration.
There is, then, a sense in which we may affirm that time is infinitely divisible. But we must remember that apparent time—the time presented in any single experience of duration—is never infinitely divisible; and that real time, in any save a relative sense of the word, is not a single experience of duration at all. It is a recognition of the fact that experiences of duration may be substituted for each other without assignable limit.
(4) But what shall we say to the last problem—to the question how we can be conscious of time at all, when the parts of time are all successive? How can we even have a consciousness of "crude" time, of apparent time, of duration in any sense of the word, when duration must be made up of moments no two of which can exist together and no one of which alone can constitute time? The past is not now, the future is not yet, the present is a mere point, as we are told, and cannot have parts. If we are conscious of time as past, present, and future, must we not be conscious of a series as a series when every member of it save one is nonexistent? Can a man be conscious of the nonexistent?
The difficulty does seem a serious one, and yet I venture to affirm that, if we examine it carefully, we shall see that it is a difficulty of our own devising. The argument quietly makes an assumption—and makes it gratuitously—with which any consciousness of duration is incompatible34, and then asks us how there can be such a thing as a consciousness of duration.
The assumption is that we can be conscious only of the existent, and this, written out a little more at length, reads as follows: we can be conscious only of the now existent, or, in other words of the present. Of course, this determines from the outset that we cannot be conscious of the past and the future, of duration.
The past and the future are, to be sure, nonexistent from the point of view of the present; but it should be remarked as well that the present is nonexistent from the point of view of the past or the future. If we are talking of time at all we are talking of that no two parts of which are simultaneous; it would be absurd to speak of a past that existed simultaneously with the present, just as it would be absurd to speak of a present existing simultaneously with the past. But we should not deny to past, present, and future, respectively, their appropriate existence; nor is it by any means self-evident that there cannot be a consciousness of past, present, and future as such.
We fall in with the assumption, it seems, because we know very well that we are not directly conscious of a remote past and a remote future. We represent these to ourselves by means of some proxy—we have present memories of times long past and present anticipations35 of what will be in the time to come. Moreover, we use the word "present" very loosely; we say the present year, the present day, the present hour, the present minute, or the present second. When we use the word thus loosely, there seems no reason for believing that there should be such a thing as a direct consciousness that extends beyond the present. It appears reasonable to say: No one can be conscious save of the present.
It should be remembered, however, that the generous present of common discourse36 is by no means identical with the ideal point between past and future dealt with in the argument under discussion. We all say: I now see that the cloud is moving; I now see that the snow is falling. But there can be no moving, no falling, no change, in the timeless "now" with which we have been concerned. Is there any evidence whatever that we are shut up, for all our immediate knowledge, to such a "now"? There is none whatever.
The fact is that this timeless "now" is a product of reflective thought and not a something of which we are directly conscious. It is an ideal point in the real time of which this chapter has treated, the time that is in a certain sense infinitely divisible. It is first cousin to the ideal mathematical point, the mere limit between two lines, a something not perceptible to any sense. We have a tendency to carry over to it what we recognize to be true of the very different present of common discourse, a present which we distinguish from past and future in a somewhat loose way, but a present in which there certainly is the consciousness of change, of duration. And when we do this, we dig for ourselves a pit into which we proceed to fall.
We may, then, conclude that we are directly conscious of more than the present, in the sense in which Augustine used the word. We are conscious of time, of "crude" time, and from this we can pass to a knowledge of real time, and can determine its parts with precision.
[1] Book XI, Chapters 14 and 15.
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infinitely
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| adv.无限地，无穷地 | |
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annihilate
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| v.使无效；毁灭；取消 | |
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demolish
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| v.拆毁(建筑物等)，推翻(计划、制度等) | |
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mere
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| adj.纯粹的；仅仅，只不过 | |
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infinity
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| n.无限，无穷，大量 | |
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immediate
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| adj.立即的；直接的，最接近的；紧靠的 | |
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precisely
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| adv.恰好，正好，精确地，细致地 | |
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pointed
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| adj.尖的，直截了当的 | |
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fleeting
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| adj.短暂的，飞逝的 | |
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remains
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| n.剩余物，残留物；遗体，遗迹 | |
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quaint
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| adj.古雅的，离奇有趣的，奇怪的 | |
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strictly
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| adv.严厉地，严格地；严密地 | |
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psalm
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| n.赞美诗，圣诗 | |
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simultaneously
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| adv.同时发生地，同时进行地 | |
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varied
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| adj.多样的，多变化的 | |
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touching
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| adj.动人的，使人感伤的 | |
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speculations
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| n.投机买卖( speculation的名词复数 )；思考；投机活动；推断 | |
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distinguished
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| adj.卓越的，杰出的，著名的 | |
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gratuitous
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| adj.无偿的，免费的；无缘无故的，不必要的 | |
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ingenuity
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| n.别出心裁；善于发明创造 | |
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worthy
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| adj.(of)值得的，配得上的；有价值的 | |
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habitually
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| ad.习惯地，通常地 | |
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lapse
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| n.过失，流逝，失效，抛弃信仰，间隔；vi.堕落，停止，失效，流逝；vt.使失效 | |
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spoke
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| n.（车轮的）辐条；轮辐；破坏某人的计划；阻挠某人的行动 v.讲，谈（speak的过去式）；说；演说；从某种观点来说 | |
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meridian
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| adj.子午线的；全盛期的 | |
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indicators
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| （仪器上显示温度、压力、耗油量等的）指针( indicator的名词复数 )； 指示物； （车辆上的）转弯指示灯； 指示信号 | |
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subdivide
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| vt.细分（细区分，再划分，重分，叠分，分小类） | |
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attained
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| （通常经过努力）实现( attain的过去式和过去分词 )； 达到； 获得； 达到（某年龄、水平、状况） | |
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conceit
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| n.自负，自高自大 | |
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absurdity
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| n.荒谬，愚蠢；谬论 | |
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monstrous
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| adj.巨大的；恐怖的；可耻的，丢脸的 | |
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molecules
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| 分子( molecule的名词复数 ) | |
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vibration
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| n.颤动，振动；摆动 | |
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incompatible
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| adj.不相容的，不协调的，不相配的 | |
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anticipations
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| 预期( anticipation的名词复数 )； 预测； （信托财产收益的）预支； 预期的事物 | |
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discourse
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| n.论文，演说；谈话；话语；vi.讲述，著述 | |
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