`A Part May Be Equal to the Whole'

“Were you reading this book from the last page to the first some six or eight billion years ago? And did the people of that time produce fried chickens from their mouth, put life into them in the kitchen, and send them to the farm where they grew from adulthood to babyhood, finally crawled into eggshells, and after some weeks became fresh eggs?”

How many books that we read as children remain readable today, and on their own merits, not merely as nostalgic indulgences? My list: Robinson Crusoe, Gulliver’s Travels, The Bible, Kim, some Stevenson. Not one American product among them, and that surprises me but confirms my sense that writerly England from Chaucer to Larkin is my true home. But let me add another title, written by a latter-day American, a Russian Jew born in Odessa (like Isaac Babel, but ten fortunate years later): One, Two, Three.. . Infinity: Facts and Speculations of Science (1947) by the theoretical physicist and cosmologist George Gamow. I read it as a Signet paperback with a gold-colored spine while in the seventh grade, in 1964 or 1965. At the time, I hardly distinguished between literary and non-literary, high culture or low. It’s not irrelevant that I was still reading science fiction but would soon put it away with other childish things.

The passage quoted above – part cartoon, part Borges -- is drawn from Gamow’s final paragraph. Often while reading Gamow again I’ve been reminded of Borges and his fascination with infinity (as in “The Library of Babel”). Gamow adapts his title from Georg Cantor’s theory of multiple infinities, which he explains with a mathematician’s matter-of-fact coolness: “According to our rule of comparing infinities we must say that the infinity of even numbers is exactly as large as the infinity of all numbers. This sounds, of course, paradoxical, since even numbers represent only a part of all numbers, but we must remember that we operate here with infinite numbers, and must be prepared to encounter different properties.” I admire the sangfroid of that final clause, and suspect Borges would have as well. His story “The Aleph” is probably an allusion to Cantor’s use of the Hebrew letter aleph to represent transfinite sets. Gamow himself is not above Borgesian pranks, as when he notes that “in the world of infinity a part may be equal to the whole!” Then he tells an anecdote attributed to the German mathematician David Hilbert, with this footnote attached:

“From the unpublished, and even never written, but widely circulating volume: `The Complete Collection of Hilbert Stories’ by R. Courant.”

I’ve never bought the idea that science and math are on one side (of the brain, of the universe), and art on the other. They overlap like a Venn diagram and share a common source in the imagination. Gamow consistently gives the impression that he’s having a good time playing with mathematical ideas without trivializing them, and that he’s happy sharing his enthusiasms without dumbing them down (yes, he includes some equations). Gamow rekindles my interest in topology, recreational mathematics and the work of the late Martin Gardner (who was much appreciated by Nabokov). Here is the sentence that follows the one quoted above and closes One, Two, Three. . . Infinity:

“Interesting as they are, such questions cannot be answered from the purely scientific point of view, since the maximum compression of the universe, which squeezed all matter into a uniform nuclear fluid, must have completely obliterated all the records of the earlier compressive stages.”