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.)