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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.)

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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.

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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.

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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.

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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.

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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.

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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.