The mechanical formulas of science are admirably adapted to the purpose for which they were designed, that is, the handling of matter, but they are misleading as applied to living beings, and especially to the human mind, which is the farthest removed from the realm of material mechanics. Here is true freedom and initiative.

The advocate of free will always gets beaten in the argument with the determinist when he meets him on his own ground, for adopting the spatial conception of time and the dynamic conception of motives, reduces man to a machine and, of course, makes him amenable to the ordinary laws of mechanics. If it is correct to represent the future as two crossroads in front of the undecided individual and he pulled to right and left by "motives" on either side, then the determinist has it all his own way. The case has been conceded to him in advance, and the libertarian can only flinch from his logic. But Bergson holds that when the determinist pretends to talk about the future, he really is regarding it as already past, as definitely mapped and virtually existent.

As Bergson's first book, "Time and Free Will", was devoted to the overthrow of the metaphysical argument for determinism, so his second, "Matter and Memory", was devoted to the overthrow of the psychological argument, which is that the mind and the brain are merely different aspects of the same thing (monism) or that their action is parallel so that a certain state of consciousness always corresponds to a certain molecular motion (dualism). Since the activities of the brain are presumably controlled by the physical and chemical laws, then must be also the mental activities identical or inseparably connected with them. But Bergson, taking the position of an extreme dualist, argues that the mind is distinct from matter and only in part dependent upon it, that memories are not altogether stored in the brain or anywhere in space, and that the brain is essentially nothing more than an instrument of action.

The same is true of our senses, of our bodily organism in general. They are made for practical, not speculative, purposes. The things nearest to us are seen largest and clearest. The eye is useful because its vision is limited. If it were susceptible to all rays, like our skin, we should get, not vision, but sunburn. Now the understanding, also having a pragmatic origin, limits our knowledge just as the eye limits our vision, and for the same purpose.

Let me give a few examples of this limitation of our senses and of our intellect. Suppose we are looking at a horse or automobile going past in the street. We get an immediate sense of the movement very decidedly, but the motion itself we cannot see. We must first analyze the motion; that is, take it apart, break it up into something that is not motion. This we can do with a kinetoscope camera which takes snapshots at the rate of fifty a second. These successive pictures do not give the motion, no matter how rapidly they are taken. Each represents the object standing still, or if not quick enough for that, the picture is blurred; but show these still-life photographs to us in quick succession, and we no longer perceive them as separate views but as continuous motion. Why can the camera so deceive us? Simply because our eyes work in the same way. They are cameras, and the exposure time of the retina is about the same as that of the moving picture films. A moving object looked at steadily is merely a blurred band. But if we wink rapidly, we can catch glimpses of the legs of the horse or the spokes of the wheel, thus like the kinetoscope transforming motion into immobility by intermittent attention.

Look closely at a portrait in this book, and you will see that it consists of pure black and white. Needless to say that the face portrayed was not composed of black spots of various sizes on a white ground. In the original there were no black, no white, and no dots. There were only even shadings, lighter and darker. The picture is an absolute misrepresentation. Yet viewed with the naked eye at sufficient distance to put the dots out of sight, it imitates the shading of the original well enough to be called a "half-tone plate", although there is really not a half tone in it, nothing but black and white.

Now this trick of decomposing continuous motion into successive pictures like the kinetoscope and decomposing continuous space into successive spots like the printing process, is the way we do our thinking. The mind goes by jerks like the eye. When we think of the course of history we break it up into blocks of handy size, comparing century with century, year with year. This is perfectly justifiable, very useful, in fact inevitable, and quite innocent, provided we realize that it is a logical fiction, adapted to practical purposes merely. The trouble has come from not recognizing this. People generally, and especially scientists and philosophers, have been inclined to regard this process of rationalization as the way of getting at reality, instead of as a mere tool for handling reality.

Long ago, when men first began to think hard, they discovered the inadequacy of mere thinking. Zeno of Elea propounded among other puzzles that of Achilles and the tortoise, which has kept the world guessing for twenty-four centuries. While Achilles is making up his handicap, the tortoise has gone on a bit farther, and when Achilles has covered this distance, the tortoise is not there, but still ahead, and since space is conceived as infinitely divisible, Achilles would take an infinity of time to catch up. I do not suppose the experiment was ever tried. That was not the way of the Greeks. They placed too much reliance upon their brains and too little on anything outside of them to put a theory to the test of experiment. But it has been agreed everywhere, always and by all, that Achilles would catch the tortoise, and a considerable proportion of each generation have tried to explain how he could, often succeeding to their own satisfaction, but rarely to the satisfaction of other people. For the point to this puzzle is not to get the answer, but to say why it puzzles us, and to this point philosophers from Aristotle to Bergson have devoted much study; and doubtless the end is not yet.

I remember well the day when that ancient jest was first sprung upon me in the University of Kansas, by the instructor in philosophy, a bright young man just on from Harvard, who had the Eleatics at his finger tips. Several of the boys volunteered to explain it, but I, having the longest arm and snappiest fingers, got the floor. I suggested that we substitute a greyhound chasing a jack rabbit for Achilles and the tortoise, who must be tired of running so long. Both greyhound and jack rabbit progress by jumps, and I argued, with the aid of a piece of chalk, that these could be measured and laid off on the prairie, here represented by the blackboard, and so the whole thing figured out. But the instructor denied my petition for a change of venue. He stuck to Greece and refused to meet me on my native soil, so I retired discomfited. I thought him unaccommodating at the time, but I see now that he was merely wise. Wariness is often so mistaken for disobligingness. The paradox is solved by science and by common sense by assuming that Achilles and the tortoise move by jumps instead of continuously and then comparing these jumps, for they are of finite length and number.

In short, we know what motion is by common sense, by feeling, by intuition, but when we come to reason about it, and especially when we come to talk about it, we have to substitute for it something that is not motion, but is easier to handle and near enough like it, so that ordinarily it serves just as well. It is as much like it as the short, straight lines, substituted by the mathematician, are like the segments of the curve he is trying to solve. What is true of motion is true in a way of all our definitions, formulations, laws, and categories; they are not the real things, but merely handy surrogates. They represent some particular phase of reality more or less satisfactorily. These formulas are not designed to pick all the locks of Nature's treasure chests. They are good for the lock they are designed for and sometimes others, not all. The master key to all locks either does not exist or is too cumbrous to be wielded by man.