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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.