Knowing how things are doesn’t make you see them correctly, doesn’t stop you from seeing things incorrectly. Stare at the image as much as you like, it’s all in vain. It will never surrender the truth, not to your naked eyes; you have to go in armed with a straightedge.

I know that most men, including those at ease with problems of the greatest complexity, can seldom accept even the simplest and most obvious truth if it be such as would oblige them to admit the falsity of conclusions which they have delighted in explaining to colleagues, which they have proudly taught to others, and which they have woven, thread by thread, into the fabric of their lives.

—Leo Tolstoy, What Is Art?

In an article in Science magazine in 2000—one of those links emailed to me by my father—the novelist David Foster Wallace writes:

Modern math is like a pyramid, and the broad fundament is often not fun. It is at the higher and apical levels of geometry, topology, analysis, number theory, and mathematical logic that the fun and profundity start, when the calculators and contextless formulae fall away and all that’s left are pencil & paper and what gets called “genius,” viz. the particular blend of reason and ecstatic creativity that characterizes what is best about the human mind. Those who’ve been privileged (or forced) to study it understand that the practice of higher mathematics is, in fact, an “art” and that it depends no less than other arts on inspiration, courage, toil, etc.… but with the added stricture that the “truths” the art of math tries to express are deductive, necessary, a priori truths, capable of both derivation and demonstration by logical proof.

A metaphor is useful only for transforming what happens, enriching it in some way. It never tells you what actually happened, how it happened, or why it happened.

I am reminded of what Einstein said on the death of his friend: He has departed from this strange world a little ahead of me. That means nothing. For us believing physicists, the distinction between past, present and future is only a stubborn illusion.