There is nothing at all about motion here. All that we have done is to measure lengths. We have made a kind of counterpoint, _X_-points against _Y_-points, but we have not even made a curve. We connect the points _A_, _B_, _C_, _D_, _E_, etc., by means of short, straight lines, and then we may connect together these short lines, and, if we plot a number of intermediate points between those that we have already obtained and join these, the points may be so close together that they may seem to be indistinguishable from a curve. Yet, no matter how numerous they may be, they can never be connected together so as to form a curve; we therefore draw a curved line freehand through them, and at once, in so doing, we abandon our intellectual methods, for our curve depends on our intuition of _continuously changing direction_. But if we think about it we shall find that we can form no clear intellectual notion of continuity and we can only measure the curvature of a line _at a point in_ the line by drawing a tangent to the curve at this point, and then by measuring the slope of the tangent. The curve itself we obviously leave out of consideration. We cannot conceive of the point moving along the locus _OD_. We can think of it only as _at_ the places _O_, _A_, _B_, _C_, _D_, _E_, etc., but we must neglect the intervals _OA_, _AB_, _BC_, _CD_, _DE_, and so on, or we can divide them into smaller intervals by supposing the point to have occupied the positions _f_, _g_, _i_, _j_, between the points _A_ and _B_, for instance. Yet, no matter how many these intervals may be, we can only think of the point as being _at_ the places _O_, _A_, _B_, _C_, _D_, _E_, or at _f_, _g_, _i_, _j_, and so on. We never think of the intervals themselves, and, if all we think about is the _position_ of the point, we do not really think of it as in motion at all. We can _see_ it in motion, but we cannot form an intellectual concept of its motion. It is not really necessary that we should in the affairs of everyday life, but for the adequate treatment of problems involving rates of change science had to wait for the invention of the methods of the infinitesimal calculus before this disability of the human mind could be circumvented. But the moving point occupies _successively_ a number of different positions in space. If it is a material point that we observe to move from one place to another, we perceive that a certain interval of our duration corresponds with the change of position of the point. Duration was not used up in the occupancy of the different positions _O_, _A_, _B_, _C_, _D_, _E_, and so on, nor in that of the occupancy of the indefinitely numerous other positions in which we may place the moving point, but in the intervals themselves. We have said “duration” and not “time,” using Bergson’s term. By duration and time we understand different things.