PART II: Goetheanism – Whence and Whither?
CHAPTER VIII – Dynamics versus Kinetics
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.
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.
Science, since Galileo, has been rooted in the conviction that the logic of mathematics is a means of expressing the behaviour of natural events. The material for the mathematical treatment of sense data is obtained through measurement. The actual thing, therefore, in which the scientific observer is interested in each case, is the position of some kind of pointer. In fact, physical science is essentially, as Professor Eddington put it, a ‘pointer-reading science’. Looking at this fact in our way we can say that all pointer instruments which man has constructed ever since the beginning of science, have as their model man himself, restricted to colourless, non-stereoscopic observation. For all that is left to him in this condition is to focus points in space and register changes of their positions. Indeed, the perfect scientific observer is himself the arch-pointer-instrument.
The birth of the method of pointer-reading is marked by Galileo’s construction of the first thermometer (actually, a thermoscope). The conviction of the applicability of mathematical concepts to the description of natural events is grounded in his discovery of the so-called Parallelogram of Forces. It is with these two innovations that we shall concern ourselves in this chapter.
Let it be said at once that our investigations will lead to the unveiling of certain illusions which the spectator-consciousness has woven round these two gifts of Galileo. This does not mean that their significance as fundamentals of science will be questioned. Nor will the practical uses to which they have been put with so much success be criticized in any way. But there are certain deceptive ideas which became connected with them, and the result is that to-day, when man is in need of finding new epistemological ground under his feet, he is entangled in a network of conceptual illusions which prevent him from using his reason with the required freedom.
A special word is necessary at this point regarding the term illusion, as it is used here and elsewhere. In respect of this, it will be well to remember what was pointed out earlier in connexion with the term ‘tragedy’ (Chapter II). In speaking of ‘illusion’, we neither intend to cast any blame on some person or another who took part in weaving the illusion, nor to suggest that the emergence of it should be thought of as an avoidable calamity. Rather should illusion be thought of as something which man has been allowed to weave because only by his own active overcoming of it can he fulfil his destiny as the bearer of truth in freedom. Illusion, in the sense used here, belongs to those things in man’s existence which are truly to be called tragic. It loses this quality, and assumes a quite different one, only when man, once the time has come for overcoming an illusion, insists on clinging to it.
As our further studies will show, the criticism to be applied here does not only leave the validity of measurement and the mathematical treatment of the data thus obtained fully intact, but by giving them their appropriate place in a wider conception of nature it opens the way to an ever more firmly grounded and, at the same time, enhanced application of both.
Our primary knowledge of the existence of something we call ‘warmth’ or ‘heat’ is due to a particular sense of warmth which modern research has recognized as a clearly definable sense. Naturally, seen from the spectator-standpoint, the experiences of this sense appear to be of purely subjective value and therefore useless for obtaining an objective insight into the nature of warmth and its effects in the physical world. In order to learn about these, resort is had to certain instruments which, through the change of the spatial position of a point, allow the onlooker-observer to register changes in the thermal condition of a physical object. An instrument of this kind is the thermometer. In the following way an indubitable proof seems to be given of the correctness of the view concerning the subjectivity of the impressions obtained through the sense of warmth, and of the objectivity of thermometrical measurement. A description of it is frequently given in physical textbooks as an introduction to the chapter on Heat.
To begin with, the well-known fact is cited that if one plunges one’s hands first into two different bowls, one filled with hot water and the other with cold, and then plunges them together into a bowl of tepid water, this will feel cold to the hand coming from the hot water and warm to the hand coming from the cold. Next, it is pointed out that two thermometers which are put through the same procedure will register an equal degree of temperature for the tepid water. In this way the student is given a lasting impression of the superiority of the ‘objective’ recording of the instrument over the ‘subjective’ character of the experiences mediated by his sense of warmth.
Let us now test this procedure by carrying out the same experiment with the help of thermometrical instruments in their original form, that is, the form in which Galileo first applied them. By doing so we proceed in a truly Goethean manner, because we divest the experiment of all accessories which prevent the phenomenon from appearing in its primary form.
To turn a modern thermometer into a thermoscope we need only remove the figures from its scale. If we make the experiment with two such thermoscopes we at once become aware of something which usually escapes us, our attention being fixed on the figures recorded by the two instruments. For we now notice that the two instruments, when transferred from the hot and cold water into the tepid water, behave quite differently. In one the column will fall, in the other it will rise.
It is important to note that by this treatment of the two instruments we have not changed the way in which they usually indicate temperature. For thermometrical measurement is in actual fact never anything else than a recording of the movement of the indicator from one level to another. We choose merely to take a certain temperature level – that of melting ice or something else – as a fixed point of reference and mark it once for all on the instrument. Because we find this mark clearly distinguished on our thermometers, and the scales numbered accordingly, we fail to notice what lies ideally behind this use of the same zero for every new operation we undertake.
What the zero signifies becomes clear directly we start to work with thermometers not marked with scales. For in order to be used in this form as real thermometers, they must be exposed on each occasion first of all to some zero level of temperature, say, that of melting ice. If we then take them into the region of temperature we want to measure, we shall discern the difference of levels through the corresponding movement of the column. The final position of the column tells us nothing in itself. It is always the change from one level to another that the thermometer registers – precisely as does the sense of warmth in our hands in the experiment just described.
Hence we see that in the ordinary operation with the thermometers, and when we use our hands in the prescribed manner, we are dealing with the zero level in two quite different ways. While in the/two instruments the zero level is the same, in accordance with the whole idea of thermometric measurement, we make a special arrangement so as to expose our hands to two different levels. So we need not be surprised if these two ways yield different results. If, after placing two thermometers without scales in hot and cold water, we were to assign to each its own zero in accordance with the respective height of its column, and then graduate them from this reference point, they would necessarily record different levels when exposed to the tepid water, in just the same way as the hands do. Our two hands, moreover, will receive the same sense-impression from the tepid water, if we keep them in it long enough.
Seen in this light, the original experiment, designed to show the subjective character of the impressions gained through the sense of warmth, reveals itself as a piece of self-deception by the onlooker-consciousness. The truth of the matter is that, in so far as there is any subjective element in the experience and measurement of heat, it does not lie on the side of our sense of warmth, but in our judgment of the significance of thermometrical readings. In fact, our test of the alleged proof of the absolute superiority of pointer-readings over the impressions gained by our senses gives us proof of the correctness of Goethe’s statement, quoted earlier, that the senses do not deceive, but the judgment deceives.
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.
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
The following description will show that, directly we free ourselves from the onlooker-limitations of our consciousness in the way shown by Goethe – and, in respect of the present problem, in particular also by Reid – the ideal relationship between the two theorems is seen to be precisely the opposite to the one expressed in the above statement. The reason why we take pains to show this at the present point of our discussion is that only through replacing the fallacious conception by the correct one, do we open the way for forming a concrete concept of Force and thereby for establishing a truly dynamic conception of nature.
Let us begin by describing briefly the content of the two theorems in question. In Fig. 1, a diagrammatical representation is given of the parallelogram of movements. It sets out to show that when a point moves with a certain velocity in the direction indicated by the arrow a, so that in a certain time it passes from P to A, and when it simultaneously moves with a second velocity in the direction indicated by
b, through which alone it would pass to B in the same time, its actual movement is indicated by c, the diagonal in the parallelogram formed by a and b. An example of the way in which this theorem is practically applied is the well-known case of a rower who sets out from P in order to cross at right angles a river indicated by the parallel lines. He has to overcome the velocity a of the water of the river flowing to the right by steering obliquely left towards B in order to arrive finally at C.
It is essential to observe that the content of this theorem does not need the confirmation of any outer experience for its discovery, or to establish its truth. Even though the recognition of the fact which it expresses may have first come to men through practical observation, yet the content of this theorem can be discovered and proved by purely logical means. In this respect it resembles any purely geometrical statement such as, that the sum of the angles of a triangle is two right angles (180°). Even though this too may have first been learnt through outer observation, yet it remains true that for the discovery of the fact expressed by it – valid for all plane triangles – no outer experience is needed. In both cases we find ourselves in the domain of pure geometric conceptions (length and direction of straight lines, movement of a point along these), whose reciprocal relationships are ordered by the laws of pure geometric logic. So in the theorem of the Parallelogram of Velocities we have a strictly geometrical theorem, whose content is in the narrowest sense kinematic. In fact, it is the basic theorem of kinematics.
We now turn to the second theorem which speaks of an outwardly similar relationship between forces. As is well known, this states that two forces of different magnitude and direction, when they apply at the same point, act together in the manner of a single force whose magnitude and direction may be represented by the diagonal of a parallelogram whose sides express in extent and direction the first two forces. Thus in Fig. 2, R exercises upon P the same effect as F1 and F2 together.
Expressed in another way, a force of this magnitude working in the reverse direction (R’) will establish an equilibrium with the other two forces. In technical practice, as is well known, this theorem is used for countless calculations, in both statics and dynamics, and indeed more frequently not in the form given here but in the converse manner, when a single known force is resolved into two component forces. (Distribution of a pressure along frameworks, of air pressure along moving surfaces, etc.)
It will now be our task to examine the logical link which is believed to connect one theorem with the other. This link is found in the well-known definition of physical force as a product of ‘mass’ and ‘acceleration’ – in algebraic symbols F=ma. We will discuss the implications of this definition in more detail later on. Let us first see how it is used as a foundation for the above assertion.
The conception of ‘force’ as the product of ‘mass’ and ‘acceleration’ is based on the fact – easily experienced by anyone who cycles along a level road – that it is not velocity itself which requires the exertion of force, but the change of velocity – that is, acceleration or retardation (‘negative acceleration’ in the sense of mathematical physics); also that in the case of equal accelerations, the force depends upon the mass of the accelerated object. The more massive the object, the greater will be the force necessary for accelerating it. This mass, in turn, reveals itself in the resistance a particular object offers to any change of its state of motion. Where different accelerations and the same mass are considered, the factor m in the above formula remains constant, and force and acceleration are directly proportional to each other. Thus in the acceleration is discovered a measure for the magnitude of the force which thereby acts.
Now it is logically evident that the theorem of the parallelogram of velocities is equally valid for movements with constant or variable velocities. Even though it is somewhat more difficult to perceive mentally the movement of a point in two different directions with two differently accelerated motions, and to form an inner conception of the resulting movement, we are nevertheless still within a domain which may be fully embraced by thought. Thus accelerated movements and movements under constant velocity can be resolved and combined according to the law of the parallelogram of movements, a law which is fully attainable by means of logical thought.
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.
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.
The line of consideration we shall now have to enter upon for carrying out our own examination of what is believed to be the link between the two theorems may seem to the scientifically trained reader to be of an all too elementary kind compared with the complexities of thought in which he is used to engage in order to settle a scientific problem. It is therefore necessary to state here that anyone who wishes to help to overcome the tangle of modern theoretical science must not be shy in applying thoughts and observations of seemingly so simple a nature as those used both here and on other occasions. Some readiness, in fact, is required to play where necessary the part of the child in Hans Andersen’s fairy-story of The Emperor’s New Clothes, where all the people are loud in praise of the magnificent robes of the Emperor, who is actually passing through the streets with no clothes on at all, and a single child’s voice exclaims the truth that ‘the Emperor has nothing on’. There will repeatedly be occasion to adopt the role of this child in the course of our own studies.
In the scientific definition of force given above force appears as the result of a multiplication of two other magnitudes. Now as is well known, it is essential for the operation of multiplication that of the two factors forming the product at least one should exhibit the properties of a pure number. For two pure numbers may be multiplied together – e.g. 2 and 4 – and a number of concrete things can be multiplied by a pure number – e. g. 3 apples and the number 4 – but no sense can be attached to the multiplication of 3 apples by 4 apples, let alone by 4 pears! The result of multiplication is therefore always either itself a pure number, when both factors have this property; or when one of the two factors is of the nature of a concrete object, the result is of the same quality as the latter. An apple will always remain an apple after multiplication, and what distinguishes the final product (apples) from the original factor (apples) is only a pure number.
If we take seriously what this simple consideration tells us of the nature of multiplication, and if we do not allow ourselves to deviate from it for whatever purpose we make use of this algebraic operation, then the various concepts we connect with the basic measurements in physics undergo a considerable change of meaning.
Let us test, in this respect, the well-known formula which, in the conceptual language of physics, connects ‘distance’ (s), ‘time’ (t), and ‘velocity’ (c). It is written
c = s / t, or s = ct.
In this formula, s has most definitely the meaning of a ‘thing’, for it represents measured spatial distance. Of the two factors on the other side of the second equation, one must needs have the same quality as s: this is c. Thus for the other factor, t, there remains the property of a pure number. We are, therefore, under an illusion if we assume the factor c to represent anything of what velocity implies in outer cosmic reality. The truth is that c represents a spatial distance just as s does, with the difference only that it is a certain unit-distance. Just as little does real time enter into this formula – nor does it into any other formula of mathematical physics. ‘Time’, in physics, is always a pure number without any cosmic quality. Indeed, how could it be otherwise for a purely kinematic world-observation?
We now submit the formula F=ma to the same scrutiny. If we attach to the factor a on the right side of the equation a definite quality, namely an observable acceleration, the other factor in the product is permitted to have only the properties of a pure number; F, therefore, can be only of the same nature as a and must itself be an acceleration. Were it otherwise, then the equation F=ma could certainly not serve as a logical link between the Velocity and Force parallelograms.
Our present investigation has done no more than grant us an insight into the process of thought whereby the consciousness limited to a purely kinematic experience has deprived the concept of force of any real content. Let us look at the equation F=ma as a means of splitting of the magnitude F into two components m and a. The equation then tells us that F is reduced to the nature of pure acceleration, for that which resides in the force as a factor not observable by kinematic vision has been split away from it as the factor m. For this factor, however, as we have seen, nothing remains over but the property of a pure number.
Let us note here that the first thinker to concern himself with a comprehensive world-picture in which the non-existence of a real concept of force is taken in earnest-namely, Albert Einstein – was also the first to consider mass as a form of energy and even to predict correctly, as was proved later, the amount of energy represented by the unit of mass, thereby encouraging decisively the new branch of experimental research which has led to the freeing of the so-called atomic energy. Is it then possible that pure numbers can effect what took place above and within Nagasaki, Hiroshima, etc.? Here we are standing once again before one of the paradoxes of modern science which we have found to play so considerable a part in its development.
To find an interpretation of the formula F=ma, which is free from illusion, we must turn our attention first of all to the concepts ‘force’ and ‘mass’ themselves. The fact that men have these two words in their languages shows that the concepts expressed by them must be based on some experience that has been man’s long before he was capable of any scientific reflexion. Let us ask what kind of experience this is and by what part of his being he gathers it.
The answer is, as simple self-observation will show, that we know of the existence of force through the fact that we ourselves must exert it in order to move our own body. Thus it is the resistance of our body against any alteration of its state of motion, as a result of its being composed of inert matter, which gives us the experience of force both as a possession of our own and as a property of the outer world. All other references to force, in places where it cannot be immediately experienced, arise by way of analogy based on the similarity of the content of our observation to that which springs from the exertion of force in our own bodies.
As we see, in this experience of force that of mass is at once implied. Still, we can strengthen the latter by experimenting with some outer physical object. Take a fairly heavy object in your hand, stretch out your arm lightly and move it slowly up and down, watching intently the sensation this operation rouses in you.2 Evidently the experience of mass outside ourselves, as with that of our own body, comes to us through the experience of the force which we ourselves must exert in order to overcome some resisting force occasioned by the mass. Already this simple observation – as such made by means of the sense of movement and therefore outside the frontiers of the onlooker-consciousness – tells us that mass is nothing but a particular manifestation of force.
Seen in the light of this experience, the equation F=ma requires to be interpreted in a manner quite different from that to which scientific logic has submitted it. For if we have to ascribe to F and m the same quality, then the rule of multiplication allows us to ascribe to a nothing but the character of a pure number. This implies that there is no such thing as acceleration as a self-contained entity, merely attached to mass in an external way.
What we designate as acceleration, and measure as such, is nothing else than a numerical factor comparing two different conditions of force within the physical-material world.
Only when we give the three factors in our equation this meaning, does it express some concrete outer reality. At the same time it forbids the use of this equation for a logical derivation of the parallelogram of forces from that of pure velocities.
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.
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.
This, however, is all that can be learnt in this way. No possibility arises at this stage of our investigation of establishing any exact quantitative comparison. For the forces which we have brought forth (and this is valid for forces in general, no matter of what kind they are) represent pure intensities, outwardly neither visible nor directly measurable. We can certainly tell whether we are intensifying or diminishing the application of our will, but a numerical comparison between different exertions of will is not possible.
In order to make such a comparison, a further step is necessary. We must convey our effort to some pointer-instrument – for instance, a spiral spring which will respond to an exerted pressure or pull by a change in its spatial extension. (Principle of the spring balance.) In this way, by making use of a certain property of matter – elasticity – the purely intensive magnitudes of the forces which we exert become extensively visible and can be presented geometrically. We shall therefore continue our investigation with the aid of three spring balances, which we hook together at one end while exposing them to the three pulls at the other.
To mark the results of our repeated pulls of varying intensities and directions, we draw on the floor on which we stand three chalk lines outward from the point underneath the common point of the three instruments, each in the direction taken up by one of the three persons. Along these lines we mark the extensions corresponding to those of the springs of the instruments.
By way of this procedure we shall arrive at a sequence of figures such as is shown in Fig. 3.
This is all we can discover empirically regarding the mutual relationships of three forces engaging at a point.
Let us now heed the fact that nothing in this group of figures reveals that in each one of these trios of lines there resides a definite and identical geometrical order; nor do they convey anything that would turn our thoughts to the parallelogram of velocities with the effect of leading us to expect, by way of analogy, a similar order in these figures. And this result, we note, is quite independent of our particular way of procedure, whether we use, right from the start, a measuring instrument, or whether we proceed as described above.
Having in this way removed the fallacious idea that the parallelogram of forces can, and therefore ever has been, conceived by way of logical derivation from the parallelogram of velocities, we must then ask ourselves what it was, if not any act of logical reason, that led Galileo to discover it.
History relates that on making the discovery he exclaimed: ‘La natura Ã¨ scritta in lingua matematica!‘ (‘Nature is recorded in the language of mathematics.’) These words reveal his surprise when he realized the implication of his discovery. Still, intuitively he must have known that using geometrical lengths to symbolize the measured magnitudes of forces would yield some valid result. Whence came this intuition, as well as the other which led him to recognize from the figures thus obtained that in a parallelogram made up of any two of the three lines, the remaining line came in as its diagonal? And, quite apart from the particular event of the discovery, how can we account for the very fact that nature – at least on a certain level of her existence – exhibits rules of action expressible in terms of logical principles immanent in the human mind?
To find the answer to these questions we must revert to certain facts connected with man’s psycho-physical make-up of which the considerations of Chapter II have already made us aware.
Let us, therefore, transpose ourselves once more into the condition of the child who is still entirely volition, and thus experiences himself as one with the world. Let us consider, from the point of view of this condition, the process of lifting the body into the vertical position and the acquisition of the faculty of maintaining it in this position; and let us ask what the soul, though with no consciousness of itself, experiences in all this. It is the child’s will which wrestles in this act with the dynamic structure of external space, and what his will experiences is accompanied by corresponding perceptions through the sense of movement and other related bodily senses. In this way the parallelogram of forces becomes an inner experience of our organism at the beginning of our earthly life. What we thus carry in the body’s will-region in the form of experienced geometry – this, together with the freeing and crystallizing of part of our will-substance into our conceptual capacity, is transformed into our faculty of forming geometrical concepts, and among them the concept of the parallelogram of movements.
Looked at in this way, the true relationship between the two parallelogram-theorems is seen to be the very opposite of the one held with conviction by scientific thinking up to now. Instead of the parallelogram of forces following from the parallelogram of movements, and the entire science of dynamics from that of kinematics, our very faculty of thinking in kinematic concepts is the evolutionary product of our previously acquired intuitive experience of the dynamic order of the world.
If this is the truth concerning the origin of our knowledge of force and its behaviour on the one hand, and our capacity to conceive mathematical concepts in a purely ideal way on the other, what is it then that causes man to dwell in such illusion as regards the relationship between the two? From our account it follows that no illusion of this kind could arise if we were able to remember throughout life our experiences in early childhood. Now we know from our considerations in Chapter VI that in former times man had such a memory. In those times, therefore, he was under no illusion as to the reality of force in the world. In the working of outer forces he saw a manifestation of spiritual beings, just as in himself he experienced force as a manifestation of his own spiritual being. We have seen also that this form of memory had to fade away to enable man to find himself as a self-conscious personality between birth and death. As such a personality, Galileo was able to think the parallelogram of forces, but he was unable to comprehend the origin of his faculty of mathematical thinking, or of his intuitive knowledge of the mathematical behaviour of nature in that realm of hers where she sets physical forces into action.
Deep below in Galileo’s soul there lived, as it does in every human being, the intuitive knowledge, acquired in early childhood, that part of nature’s order is recordable in the conceptual language of mathematics. In order that this intuition should rise sufficiently far into his conscious mind to guide him, as it did, in his observations, the veil of oblivion which otherwise separates our waking consciousness from the experiences of earliest childhood must have been momentarily lightened. Unaware of all this, Galileo was duly surprised when in the onlooker-part of his being the truth of his intuition was confirmed in a way accessible to it, namely through outer experiment. Yet with the veil immediately darkening again the onlooker soon became subject to the illusion that for his recognition of mathematics as a means of describing nature he was in need of nothing but what was accessible to him on the near side of the veil.
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.
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.
Need we wonder that we are challenged to do so in our day, when mankind is several centuries older than it was in the time of Galileo?
1 As to the terms ‘kinetic’ and ‘kinematic’, see Chapter II, page 30, footnote.
2 For the sake of our later studies it is essential that the reader does not content himself with merely following the above description mentally, but that he carries out the experiment himself.
- THE IDEA OF COUNTERSPACE
- CHAPTER IX – Pro Levitate