I had a feeling once about Mathematics - that I saw it all. Depth beyond depth was revealed to me - the Byss and Abyss. I saw - as one might see the transit of Venus or even the Lord Mayor's Show - a quantity passing through infinity and changing its sign from plus to minus. I saw exactly why it happened and why the tergiversation was inevitable but it was after dinner and I let it go.
Next you'd see a raft sliding by, away off yonder, and maybe a galoot on it chopping. . . you'd see the ax flash and come down-you don't hear nothing; you see the ax go up again, and by the time it's above the man's head then you hear the k'chunk!-it had took all that time to come over the water.
See skulking Truth to her old cavern fled, Mountains of Casuistry heap'd o'er her head! Philosophy, that lean'd on Heav'n before, Shrinks to her second cause, and is no more. Physic of Metaphysic begs defence, And Metaphysic calls for aid on Sense! See Mystery to Mathematics fly!
Wherefore, I beseech you let the dog and the onions and these people of the strange and godless names work out their several salvations from their piteous and wonderful difficulties without help of mine, for indeed their trouble is sufficient as it is, whereas an I tried to help I should but damage their cause the more and yet mayhap not live myself to see the desolation wrought.
That Logic has advanced in this sure course, even from the earliest times, is apparent from the fact that, since Aristotle, it has been unable to advance a step, and thus to all appearance has reached its completion.
I'm always interested in understanding the math of things and understanding as much as I can about all aspects of business. And what I learn today may be useful to me two years from now. That's really the wonderful thing about investments is your knowledge is cumulative.
We come now to the question: what is a priori certain or necessary, respectively in geometry (doctrine of space) or its foundations? Formerly we thought everything; nowadays we think nothing. Already the distance-concept is logically arbitrary; there need be no things that correspond to it, even approximately.