The conversation touched on famous expressions, words carved in stone, in particular a saying of Kant which seeks to fix the foundation and the limits of knowledge. "Every science of Nature," the great philosopher of Königsberg had said, "contains just as much Truth as it contains mathematics." And since, ultimately. Nature includes everything--for a demarcation between physical and mental science no longer seems possible--then, if we follow Kant, we should have to regard mathematics as the sole measure of science. It is certainly not yet possible to enter into a discussion on this point with historians, medical or legal practitioners. They would be justified in refusing it, since, in their subjects, "truth" is not the sole factor, and because we cannot see at present how the conception of a comprehensive mathematical truth is to find a place in them. But when we question a physicist on this point, who unceasingly uses mathematics as his chief instrument, we should surely expect him to answer with an unconditional affirmative. At least, I should not have been surprised if Einstein had answered in this way, and if he had indeed claimed its validity for every branch of science. But Einstein considered this quotation to be true only conditionally, in that he accepted it as a principle, but did not regard it as universal. That is, he does not recognize mathematics as the only test of truth. "The sovereignty of mathematics," said Einstein, "is based on very simple assumptions; it is rooted in the conception of magnitude itself. Its dominant position is due to the fact that it gives us much more delicate means of distinguishing between infinitely varied possibilities than any other method of thought that expresses itself in language and is restricted to the use of words. The greater the field taken into consideration, the clearer does this become; but even in such a narrow range as 1 to 100, an estimate such as 27 is incomparably more exact than can be expressed in words in any other way. If we think of a series of sensations, ranging from pleasure to pain, or from sweet to bitter, we find that words leave us in an uncertain, confused state, and we do not succeed in fixing on a point of the series with the same precision as we above fixed on the 27 out of the 100. But when the theory of magnitude plays a part in the question, as, for example, in a series of tones, whose vibrations exhibit a mathematical sequence, we immediately attain a much higher order of precision by using numbers...."