From what we have here found we may expect that in order to explain the numerical relationships between natural phenomena (with which science in the past has been solely concerned), we by no means require the artificial theories to which the onlooker in man, confined as he is to abstract thinking, has been unavoidably driven. Indeed, to an observer who trains himself on the lines indicated in this book, even the quantitative secrets of nature will become objects of intuitive judgment, just as Goethe, by developing this organ of understanding, first found access to nature's qualitative secrets. (The change in our conception of number which this entails will be shown at a later stage of our discussions.)
1 Compare with this our account in Chapter X of the rise of the atomistic-kinematic interpretation of heat.
2 The following critical study leaves, of course, completely untouched our recognition of the devotion which guided the respective observers in their work, and of the ingenuity with which some of their observations were devised and carried out.
3 The assumption is that the wave-velocity differs from the group-velocity, if at all, by a negligible amount.
4 Once this is realized there can be no doubt that with the aid of an adequate mathematical calculus (which would have to be established on a realistic understanding of the respective properties of the fields of force coming into play) it will become possible to derive by calculation the speed of the establishment of light within physical space from the gravitational constant of the earth.
5 The grounds of Einstein's General Theory were dealt with in our earlier discussions.
CHAPTER XVIII
The Spectrum as a Script of the Spirit
The realization that Newton's explanation of the spectrum fails to meet the facts prompted Goethe to engage in all those studies which made him the founder of a modern optics based on intuitive participation in the phenomena. In spite of all that he achieved, however, he never reached a real solution of the riddle of the colour-phenomenon produced when light passes through a transparent body of prismatic shape. For his assumption of certain 'double images', which are supposed to appear as a result of the optical displacement of the boundaries between the Light-filled and the Dark-filled parts of space and the mutual superposition of which he believed to be responsible for the appearance of the respective colours, does not solve the problem.1