It seems to me that, with increasing frequency, two books on the same or closely related subjects come out from different publishers almost simultaneously. I suspect an epidemic of corporate espionage. In 2003/4, did we really need two books with the identical title "Lincoln at Copper Union" about a pre-campaign speech in New York by the eventual president? Why was "The Empire of Tea" published within 6 months of "Tea: Addiction, Exploitation, and Empire"? (Perhaps they were tied to an epic mini-series that I missed.)
Kurt Gödel and his work have been largely ignored of late, yet now we suddenly have two books attempting to resurrect interest. Palle Yourgrau's "A World Without Time: The Forgotten Legacy of Gödel And Einstein" was published in January 2005, and "Incompleteness: The Proof and Paradox of Kurt Gödel" by Rebecca Goldstein just one month later.
Both are small-format books, and thus both attempt to squeeze already dense subject matter into unreasonably constricted space. Both use Gödel's personal and intellectual friendship with Einstein as a systematizing motif. Each author dedicates considerable time to rehearsing the history of The Vienna Circle, where Gödel spent formative years, and the Institute for Advanced Studies in Princeton, where Gödel and Einstein completed their careers. And both Goldstein (a mathematician and novelist) and Yourgrau (a professor of philosophy) attempt to give a summary of Gödel's important theorems that would make them accessible to the non-specialist.
However, the two books differ in important respects.
Goldstein, when dealing with Gödel's professional work, focuses almost exclusively on that concerned most directly with mathematical logic: his Incompleteness Theorems. That means Gödel's more cosmological exertions, which came after he joined the Institute, are left untreated. And Goldstein has a theorem or two of her own: that the implications of Gödel's work in mathematical logic and metaphysics were seriously misconstrued even in his own day, that such misunderstanding was a gnawing disturbance to the logician, and that it contributed greatly to his increasingly pathological alienation from his colleagues and the world at large.
Yourgrau is more interested in the validity and implications of Gödel's later philosophical (or cosmological) work on the nature of time. Yourgrau published an earlier monograph which the book jacket claims "sparked a resurgence of interest in Gödel's ideas about time and relativity." Yourgrau comes across as Gödel's self-appointed apologist, armed to defend the logician against claims that these later philosophical applications were amateurish and easily dismissed.
Both books, I felt, succeeded in gaining the reader's sympathy for their respective perspectives. But neither could be suitably comprehensive in the relatively few pages allotted them. For me, Goldstein did the slightly better job of explaining the Incompleteness Theorems.
(It would be beyond the skills of even the most accomplished popularizer to fit a truly satisfying explanation into these abbreviated books. The reader is subjected in both to sentences such as this one from Yourgrau: "The representation occurs via the arithmetization of the syntax of FA, so corresponding to a given syntactical truth Bew(x,y) of MFA, there is an arithmetical truth Bew(x,y) of IA that corresponds to a formula Bew(x,y) in FA that can be interpreted as saying that the sequence of formulas with Gödel number x is a proof of the formula with Gödel number y, and this formula, Bew(x,y), is a theorem of FA.")
You thus get from Goldstein a better grounding in what is considered Gödel's true legacy. But you have to look to Yourgrau to get even a basic sense of what Gödel later had to say about cosmology. In that sense, Yourgrau's book is the more thought-provoking.
Both authors are gifted writers, although Yourgrau seems to loose some control over his metaphors as he gets increasingly worked up about the lack of respect given to Gödel's cosmological contributions. As Yourgrau tells of a 1995 symposium on "Gödel's General Philosophical Significance", readers may feel they have stumbled into a metaphysical food-fight.
The fact that these two books were published at almost the same time shows that there must be a significant audience of non-specialist readers interested in an updated accounting of Gödel's life and work. It's unfortunate that such readers have to buy both these books and navigate through so much redundant material to get even the beginnings of a complete perspective.
