c8p33 chapter_8_text

c8p33

With the help of the definition of force as the product of mass and acceleration it seems possible, indeed, to derive the parallelogram of forces from that of accelerations in a purely logical manner. For it is necessary only to extend all sides of an a parallelogram by means of the same factor m in order to turn it into an F parallelogram. A single geometrical figure on paper can represent both cases, since only the scale needs to be altered in order that the same geometrical length should represent at one time the magnitude a and on another occasion ma. It is in this way that present-day scientific thought keeps itself convinced that the parallelogram of forces follows with logical evidence from the parallelogram of accelerations, and that the discovery of the former is therefore due to a purely mental process.

c8p49 chapter_8_text

c8p49

The same method which has enabled us to restore its true meaning to the formula connecting mass and force will serve to find the true source of man’s knowledge of the parallelogram of forces. Accordingly, our procedure will be as follows.

c8p65 chapter_8_text

c8p65

Thus it became man’s fate in the first phase of science, which fills the period from Galileo and his contemporaries up to the present time, that the very faculty which man needed for creating this science prevented him from recognizing its true foundations. Restricted as he was to the building of a purely kinematic world-picture, he had to persuade himself that the order of interdependence of the two parallelogram-theorems was the opposite of the one which it really is.

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c8p2 chapter_8_text

c8p2

At the present time the human mind is in danger of confusing the realm of dynamic events, into which modern atomic research has penetrated, with the world of the spirit; that is, the world whence nature is endowed with intelligent design, and of which human thinking is an expression in terms of consciousness. If a view of nature as a manifestation of spirit, such as Goethe and kindred minds conceived it, is to be of any significance in our time, it must include a conception of matter which shows as one of its attributes its capacity to serve Form (in the sense in which Ruskin spoke of it in opposition to mere Force) as a means of manifestation.

c8p18 chapter_8_text

c8p18

Let it be repeated here that what we have found in this way does not lead to any depreciation of the method of pointer-reading. For the direct findings of the senses cannot be compared quantitatively. The point is that the idea of the absolute superiority of physical measurement as a means of scientific knowledge, in all circumstances, must be abandoned as false.

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c8p34 chapter_8_text

c8p34

Since the parallelogram of forces is the prototype of each further mathematical representation of physical force-relationships in nature, the conceptual link thus forged between it and the basic theorem of kinematics has led to the conviction that the fact that natural events can be expressed in terms of mathematics could be, and actually has been, discovered through pure logical reasoning, and thus by the brain-bound, day-waking consciousness ‘of the world-spectator. Justification thereby seemed to be given for the building of a valid scientific world-picture, purely kinematic in character.

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c8p50 chapter_8_text

c8p50

We shall engage two other persons, together with whom we shall try to discover by means of our respective experiences of force the law under which three forces applying at a common point may hold themselves in equilibrium. Our first step will consist in grasping each other by the hand and in applying various efforts of our wills to draw one another in different directions, seeing to it that we do this in such a way that the three joined hands remain undisturbed at the same place. By this means we can get as far as to establish that, when two persons maintain a steady direction and strength of pull, the third must alter his applied force with every change in his own direction in order to hold the two others in equilibrium. He will find that in some instances he must increase his pull and in other instances decrease it.

c8p66 chapter_8_text

c8p66

The result of the considerations of this chapter is of twofold significance for our further studies. On the one hand, we have seen that there is a way out of the impasse into which modern scientific theory has got itself as a result of the lack of a justifiable concept of force, and that this way is the one shown by Reid and travelled by Goethe. ‘We must become as little children again, if we will be philosophers’, is as true for science as it is for philosophy. On the other hand, our investigation of the event which led Galileo to the discovery that nature is recorded in the language of mathematics, has shown us that this discovery would not have been possible unless Galileo had in a sense become, albeit unconsciously, a little child again. Thus the event that gave science its first foundations is an occurrence in man himself of precisely the same character as the one which we have learnt to regard as necessary for building science’s new foundations. The only difference is that we are trying to turn into a deliberate and consciously handled method something which once in the past happened to a man without his noticing it.

c8p3 chapter_8_text

c8p3

The present part of this book, comprising Chapters VIII-XI, will be devoted to working out such a conception of matter. An example will thereby be given of how Goethe’s method of acquiring understanding of natural phenomena through reading the phenomena themselves may be carried beyond his own field of observation. There are, however, certain theoretical obstacles, erected by the onlooker-consciousness, which require to be removed before we can actually set foot on the new path. The present chapter will in particular serve this purpose.

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c8p19 chapter_8_text

c8p19

We now turn to Galileo’s discovery known as the theorem of the Parallelogram of Forces. The illusion which has been woven round this theorem expresses itself in the way it is described as being connected ideally with another theorem, outwardly similar in character, known as the theorem of the Parallelogram of Movements (or Velocities), by stating that the former follows logically from the latter. This statement is to be found in every textbook on physics at the outset of the chapter on dynamics (kinetics), where it serves to establish the right to treat the dynamic occurrences in nature in a purely kinematic fashion, true to the requirements of the onlooker-consciousness.1