OF TIME
27. TIME AS NECESSARY, INFINITE, AND INFINITELY 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 _annihilate_ 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
demolish 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 infinity 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 precisely 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 pointed 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 fleeting moments; as much of it as has
taken flight is past, what remains 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 quaint 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 mere limiting point.
Augustine's way out of the difficulty is the suggestion that, although we
cannot, strictly speaking, measure time, we can measure _memory_ and
_expectation_. Before he begins to repeat a psalm, 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
simultaneously? 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 varied 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 touching our
consciousness of time has given rise to some exceedingly curious
speculations, 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 distinguished 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 gratuitous and useless
exercise of the ingenuity. They are serious attempts to solve a real
problem, though they may be unsuccessful ones, and they are worthy 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 habitually 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 immediate 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 lapse 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 spoke 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 meridian, 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 indicators 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
subdivide 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 attained 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 conceit 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 absurdity. 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 monstrous 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 molecules 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 vibration 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 incompatible,
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 anticipations 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
discourse 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.
III. PROBLEMS TOUCHING THE MIND