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.

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.

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.

We now turn to the second theorem which speaks of an outwardly similar relationship between forces. As is well nown, 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.

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.

History relates that on making the discovery he exclaimed: 'La natura è 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?

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.

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.

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.