(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.