A haunted thinker and his legacy

Page 2 of 2 -- In a 1949 paper Gödel used general relativity to theorize universes in which time travel is possible. Einstein declared the paper ''an important contribution," and the questions it brings up are as fascinating as they are thorny: If the past is always accessible in these hypothetical universes, then the past must coexist with the present, and if so, how can time as we understand it exist? And if time doesn't exist in any of these so-called Gödel universes, how can it in ours?

ADVERTISEMENT

Yourgrau covers much of the same ground Goldstein does. Occasionally he fills in details Goldstein misses; occasionally the case is otherwise. Once in a while they contradict each other. ''Gödel was at heart an ironist," writes Yourgrau; ''Gödel, unlike his friend Einstein, did not have a well-developed sense of the ironic," writes Goldstein. Unfortunately, neither author answers the question I'd most hoped they would: What emotional, physical, and intellectual journey did Gödel undertake in producing his famous proof?

It's not really the biographers' fault. The problem is, a finished proof, by its very nature, no longer shows the struts and scaffolding that went into its construction. The sweat of its creator is rinsed away, and all we're left with are the clean lines of math, and the breathtaking result. Goldstein comes as close as she can get when she writes, ''It must have been an extraordinarily exhilarating experience." That's about all we get.

Maybe, though, Alan Lightman offers a glimmer of that exhilaration in his book of collected essays, ''A Sense of the Mysterious." After making a minor discovery about the theoretical properties of high-temperature gases, he recalls, ''I experienced a kaleidoscope of emotions. . . . I had found something new . . . something that no one had ever known before me, and I felt elated and powerful with knowledge." Lightman's new book is worth a look for many reasons, especially an essay entitled ''Metaphor in Science," written within the system of language about the limitations of that system, something Gödel, ironist or not, might have enjoyed. About his own small discovery, Lightman writes, ''I had shed light on a small corner of nature. Other scientists had illuminated larger corners. But there were almost certainly vast chambers and ballrooms that remained in the dark."

You can't help but wonder what kaleidoscope of emotions Gödel passed through when he arrived, at 24, at a mathematical proof that would irrevocably change human thought. I wonder if he saw how beautiful it was, if he realized, early on, how his work could creep beneath any fence you tried to put around it, exceeding mathematics, exceeding logic, radiating into the humanities, into the philosophy of the mind, the mysteries within human reach, and the ones still in shadow.

Anthony Doerr is the author of ''The Shell Collector" and ''About Grace."