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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.

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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.

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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.

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By way of this procedure we shall arrive at a sequence of figures such as is shown in Fig. 3.

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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.

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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?

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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.

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