But neither does time exist without change; for when the state of
our own minds does not change at all, or we have not noticed its
changing, we do not realize that time has elapsed, any more than those
who are fabled to sleep among the heroes in Sardinia do when they
are awakened; for they connect the earlier "now" with the later and
make them one, cutting out the interval because of their failure to
notice it. So, just as, if the "now" were not different but one and
the same, there would not have been time, so too when its difference
escapes our notice the interval does not seem to be time. If, then,
the non-realization of the existence of time happens to us when we
do not distinguish any change, but the soul seems to stay in one
indivisible state, and when we perceive and distinguish we say time
has elapsed, evidently time is not independent of movement and change.
It is evident, then, that time is neither movement nor independent
of movement.

    We must take this as our starting-point and try to discover-since we
wish to know what time is-what exactly it has to do with movement.

    Now we perceive movement and time together: for even when it is dark
and we are not being affected through the body, if any movement
takes place in the mind we at once suppose that some time also has
elapsed; and not only that but also, when some time is thought to have
passed, some movement also along with it seems to have taken place.
Hence time is either movement or something that belongs to movement.
Since then it is not movement, it must be the other.

    But what is moved is moved from something to something, and all
magnitude is continuous. Therefore the movement goes with the
magnitude. Because the magnitude is continuous, the movement too
must be continuous, and if the movement, then the time; for the time
that has passed is always thought to be in proportion to the movement.

    The distinction of "before" and "after" holds primarily, then, in
place; and there in virtue of relative position. Since then "before"
and "after" hold in magnitude, they must hold also in movement,
these corresponding to those. But also in time the distinction of
"before" and "after" must hold, for time and movement always
correspond with each other. The "before" and "after" in motion is
identical in substratum with motion yet differs from it in definition,
and is not identical with motion.

    But we apprehend time only when we have marked motion, marking it by
"before" and "after"; and it is only when we have perceived "before"
and "after" in motion that we say that time has elapsed. Now we mark
them by judging that A and B are different, and that some third
thing is intermediate to them. When we think of the extremes as
different from the middle and the mind pronounces that the "nows"
are two, one before and one after, it is then that we say that there
is time, and this that we say is time. For what is bounded by the
"now" is thought to be time-we may assume this.

    When, therefore, we perceive the "now" one, and neither as before
and after in a motion nor as an identity but in relation to a "before"
and an "after", no time is thought to have elapsed, because there
has been no motion either. On the other hand, when we do perceive a
"before" and an "after", then we say that there is time. For time is
just this-number of motion in respect of "before" and "after".

    Hence time is not movement, but only movement in so far as it admits
of enumeration. A proof of this: we discriminate the more or the
less by number, but more or less movement by time. Time then is a kind
of number. (Number, we must note, is used in two senses-both of what
is counted or the countable and also of that with which we count. Time
obviously is what is counted, not that with which we count: there
are different kinds of thing.) Just as motion is a perpetual
succession, so also is time. But every simultaneous time is
self-identical; for the "now" as a subject is an identity, but it
accepts different attributes. The "now" measures time, in so far as
time involves the "before and after".

    The "now" in one sense is the same, in another it is not the same.
In so far as it is in succession, it is different (which is just
what its being was supposed to mean), but its substratum is an
identity: for motion, as was said, goes with magnitude, and time, as
we maintain, with motion. Similarly, then, there corresponds to the
point the body which is carried along, and by which we are aware of
the motion and of the "before and after" involved in it. This is an
identical substratum (whether a point or a stone or something else
of the kind), but it has different attributes as the sophists assume
that Coriscus" being in the Lyceum is a different thing from Coriscus"
being in the market-place. And the body which is carried along is
different, in so far as it is at one time here and at another there.
But the "now" corresponds to the body that is carried along, as time
corresponds to the motion. For it is by means of the body that is
carried along that we become aware of the "before and after" the
motion, and if we regard these as countable we get the "now". Hence in
these also the "now" as substratum remains the same (for it is what is
before and after in movement), but what is predicated of it is
different; for it is in so far as the "before and after" is
numerable that we get the "now". This is what is most knowable: for,
similarly, motion is known because of that which is moved,
locomotion because of that which is carried. what is carried is a real
thing, the movement is not. Thus what is called "now" in one sense
is always the same; in another it is not the same: for this is true
also of what is carried.

    Clearly, too, if there were no time, there would be no "now", and
vice versa. just as the moving body and its locomotion involve each
other mutually, so too do the number of the moving body and the number
of its locomotion. For the number of the locomotion is time, while the
"now" corresponds to the moving body, and is like the unit of number.

    Time, then, also is both made continuous by the "now" and divided at
it. For here too there is a correspondence with the locomotion and the
moving body. For the motion or locomotion is made one by the thing
which is moved, because it is one-not because it is one in its own
nature (for there might be pauses in the movement of such a thing)-but
because it is one in definition: for this determines the movement as
"before" and "after". Here, too there is a correspondence with the
point; for the point also both connects and terminates the length-it
is the beginning of one and the end of another. But when you take it
in this way, using the one point as two, a pause is necessary, if
the same point is to be the beginning and the end. The "now" on the
other hand, since the body carried is moving, is always different.

    Hence time is not number in the sense in which there is "number"
of the same point because it is beginning and end, but rather as the
extremities of a line form a number, and not as the parts of the
line do so, both for the reason given (for we can use the middle point
as two, so that on that analogy time might stand still), and further
because obviously the "now" is no part of time nor the section any
part of the movement, any more than the points are parts of the
line-for it is two lines that are parts of one line.

    In so far then as the "now" is a boundary, it is not time, but an
attribute of it; in so far as it numbers, it is number; for boundaries
belong only to that which they bound, but number (e.g. ten) is the
number of these horses, and belongs also elsewhere.

    It is clear, then, that time is "number of movement in respect of
the before and after", and is continuous since it is an attribute of
what is continuous.