Clippings

First, take a deep breath. Assume Shakespeare’s account is accurate and Julius Caesar gasped “You too, Brutus” before breathing his last. What are the chances you just inhaled a molecule which Caesar exhaled in his dying breath? The surprising answer is that, with probability better than 99 percent, you did just inhale such a molecule.

For those who don’t believe me: I’m assuming that after more than two thousand years the exhaled molecules are uniformly spread about the world and the vast majority are still free in the atmosphere. Given these reasonably valid assumptions, the problem of determining the relevant probability is straightforward. If there are N molecules of air in the world and Caesar exhaled A of them, them the probability that any given molecule you inhale is from Caesar is A/N. The probability that any given molecule you inhale is not from Caesar is thus 1 − A/N. …if you inhale B molecules, the probability that none of them is from Caesar is approximately (1 − A/N)^B. Hence, the probability of the complementary event, of your inhaling at least one of his exhaled molecules, is 1 − (1 − A/N)^B. A, B (each about 1/30th of a mole, or 2.2 × 10²²), and N (about 10⁴⁴ molecules) are such that this probability is more than .99.

Why is it, incidentally, if all the 3,838,380 ways of choosing six numbers out of forty are equally likely, that a lottery ticket with the numbers 2 13 17 20 29 36 is for most people much preferable to one with the numbers 1 2 3 4 5 6? This is, I think, a fairly deep question.

“There’s a place where it’s always light,” the woman said. “Bright, everywhere. No place dark. Bright like a mist, like something falling, always, every second. All the colors of it. Towers you can’t see the top of, and the light falling. Down below, they pile up bars. Bars and strip clubs and discos. Stacked up like shoe boxes, one on top of the other. And no matter how far you worm your way in, no matter how many stairs you climb, how many elevators you ride, no matter how small a room you finally get to, the light still finds you. It’s a light that blows in under the door, like powder. Fine, so fine. Blows in under your eyelids, if you find a way to get to sleep. But you don’t want to sleep there. Not in Shinjuku. Do you?”

… “No,” Chia heard herself say…

“No,” the woman agreed, “you don’t. I know. But they make you. They make you. At the center of the world.” And then she put her head back, closed her eyes, and began to snore.

And it came to me then. That we were wonderful traveling companions but in the end no more than lonely lumps of metal in their own separate orbits. From far off they look like beautiful shooting stars, but in reality they’re nothing more than prisons, where each of us is locked up alone, going nowhere. When the orbits of these two satellites of ours happened to cross paths, we could be together. Maybe even open our hearts to each other. But that was only for the briefest moment. In the next instant we’d be in absolute solitude. Until we burned up and became nothing.

Let the mystery writ upon the jaguars die with me. He who has glimpsed the universe, he who has glimpsed the burning designs of the universe, can have no thought for a man, for a man’s trivial joys or calamities, though he himself be that man. He was that man, who no longer matters to him. What does he care about the fate of that other man, what does he care about the other man’s nation, when now he is no one? That is why I do not speak the formula, that is why, lying in darkness, I allow the days to forget me.

Abercrombie was a man of his time…. He was the author of two works that were universally admired: Principles of Meteorological Prediction/Forecasting, with its 63 pages of text and its 65 illustrations, including six color plates; and a book called simply The Weather (472 pages, 96 illustrations), which had become since publication one of the standard references on the subject. Abercrombie possessed the kind of personal courage that impresses the simpleminded and astounds foreigners: One day, in the smoking room of the Meteorological Society of Edinburgh, while debating a member who believed that human fate was absolutely predetermined and that human will would never amount to anything, Abercrombie accidentally severed the tip of his pinkie with a cigar cutter. While applying a tourniquet, made from his own handkerchief, he had countered, to the amazement of his opponent, with a brilliant refutation that had carried the day. Men such as Abercrombie do not change.

“The future historian of science concerned with the development of mathematics in the late nineteenth and the first half of the twentieth century will undoubtedly state that several branches of mathematics are highly indebted to Hilbert’s achievements for their vigorous advancement in that period,” Alfred Tarski has written. “On the other hand, he will have to note, perhaps with some wonder, that the influence of this man appears equally strong and powerful in some other domains which do not owe any exceptionally important results to Hilbert’s own research. An example of this kind is furnished by the foundations of geometry. I am far from underestimating the value of Hilbert’s contributions … in his [Foundations of Geometry], but I think that his most essential merit was the impulse he gave to organized research in this domain. A still more striking example is presented by metamathematics. Occasional considerations in this field preceded Hilbert’s Paris address; the first positive and really profound results appeared before Hilbert started his continuous work in this domain … [and] one does not immediately associate with Hilbert’s name any definite and important metamathematical result. Nevertheless, Hilbert will deservedly be called the father of metamathematics. For he is the one who created metamathematics as an independent being; he fought for its right to existence, backing it with his whole authority as a great mathematician. And he was the one who mapped out its future course and entrusted it with ambitions and important tasks.”