CHAPTER XII

19. The memory also contains the principles and the unnumbered laws of numbers and dimensions. None of these has been impressed on the memory by a physical sense, because they have neither color nor sound, nor taste, nor sense of touch. I have heard the sound of the words by which these things are signified when they are discussed: but the sounds are one thing, the things another. For the sounds are one thing in Greek, another in Latin; but the things themselves are neither Greek nor Latin nor any other language. I have seen the lines of the craftsmen, the finest of which are like a spider’s web, but mathematical lines are different. They are not the images of such things as the eye of my body has showed me. The man who knows them does so without any cogitation of physical objects whatever, but intuits them within himself. I have perceived with all the senses of my body the numbers we use in counting; but the numbers by which we count are far different from these. They are not the images of these; they simply are. Let the man who does not see these things mock me for saying them; and I will pity him while he laughs at me.