He came out of this trance of thought hungry, and with a full bladder. He felt quite sure there was some real potential in the work. And that was giving him some ideas.
He got up stiffly, went to the bathroom, came back. It was midafternoon already. If he left soon he would be able to hack through the traffic to his apartment, eat quickly, then go out to Great Falls. By then the day’s blanching heat would have started to subside, and the river’s gorge walls would be nearly empty of climbers. He could climb until well past sunset, and do some more thinking about this algorithm, out where he thought best these days, on the hard old schist walls of the only place in the Washington D.C. area where a scrap of nature had survived.
II
In the Hyperpower
Mathematics sometimes seems like a universe of its own. But it comes to us as part of the brain’s engagement with the world, and appears to be part of the world, its structure or recipe.
Over historical time humanity has explored farther and farther into the various realms of mathematics, in a cumulative and collective process, an ongoing conversation between the species and reality. The discovery of the calculus. The invention of formal arithmetic and symbolic logic, both mathematicizing the instinctive strategies of human reason, making them as distinct and solid as geometric proofs. The attempt to make the entire system contained and self-consistent. The invention of set theory, and the finessing of the various paradoxes engendered by considering sets as members of themselves. The discovery of the incompletability of all systems. The step-by-step mechanics of programming new calculating machines. All this resulted in an amalgam of math and logic, the symbols and methods drawn from both realms, combining in the often long and complicated operations that we call algorithms.