Lecture I

And then there is the third thing which we do, still before reaching outer Nature. I am referring to what we do in “Phoronomy” so-called, or Kinematics, i.e. the science of Movement. Now it is very important for you to be clear on this point,—to realize that Kinematics too is, fundamentally speaking, still remote from what we call the “real” phenomena of Nature. Say I imagine an object to be moving from the point \(a\) to the point \(b\) (Figure 1a). I am not looking at any moving object; I just imagine it. Then I can always imagine this movement from \(a\) to \(b\), indicated by an arrow in the figure, to be compounded of two distinct movements. Think of it thus: the point \(a\) is ultimately to get to \(b\), but we suppose it does not go there at once. It sets out in this other direction and reaches \(c\). If it then subsequently moves from \(c\) to \(b\), it does eventually get to \(b\). Thus I can also imagine the movement from \(a\) to \(b\) so that it does not go along the line \(ab\) but along the line, or the two lines, \(ac\) and \(cb\). The movement \(ab\) is then compounded of the movements \(ac\) and \(cb\), i.e. of two distinct movements. You need not observe any process in outer Nature; you can simply think it—picture it to yourself in thought—how that the movement from \(a\) to \(b\) is composed of the two other movements. That is to say, in place of the one movement the two other movements might be carried out with the same ultimate effect. And when in thinking I picture this. The thought—the mental picture—is spun out of myself. I need have made no outer drawing; I could simply have instructed you in thought to form the mental picture; you could not but have found it valid. Yet if in outer Nature there is really something like the point \(a\)—perhaps a little ball, a grain of shot—which in one instance moves from \(a\) to \(b\) and in another from \(a\) to \(c\) and then from \(c\) to \(b\), what I have pictured to myself in thought will really happen. So then it is in kinematics, in the science of movement also; I think the movements to myself, yet what I think proves applicable to the phenomena of Nature and must indeed hold good among them.