Incompleteness incompletely explained: As we noted a few weeks back, we’ve conducted a long love affair with bad explanation.
The affair may have begun in September 1965, when we enrolled in Professor Nozick’s “Problems in Philosophy” class.
Who are these “problems” problems for, we found ourselves brightly wondering.
Years later, we began to suspect that the course had been designed to ensure that no one would major in philosophy. In fairness, though, that was pure conjecture.
Whatever! In recent weeks, we’ve been spending our spare time with Professor Goldstein’s 2005 book, Incompleteness: The Proof and Paradox of Kurt Godel. We’re going to make a lover’s confession:
We’re fascinated by the book’s mastery of bad explanation.
Who the Sam Hill is Kurt Godel, you ask. Early on, Professor Goldstein links him to Einstein and Heisenberg as a revolutionary thinker of the last century.
“His work was, in its own way, as revolutionary as Einstein’s,” Professor Goldstein writes (page 21). Godel’s work should “be grouped along the small set of the last century’s most radical and rigorous discoveries, all with consequences seeming to spill far beyond their respective fields, percolating down into our most basic preconceptions.”
According to Professor Goldstein, Godel’s incompleteness theorem (or theorems) “is the third leg, together with Heisenberg’s uncertainty principle and Einstein’s relativity, of that tripod of theoretical cataclysms that have been felt to force disturbances deep down in the foundations of the ‘exact sciences.’ ”
As far as we know, these are highly conventional judgments—hence the professor’s book. If Godel’s incompleteness theorem is as significant as is commonly said, it makes sense to write an accessible book explaining what he discovered, devised or invented.
That’s what Professor Goldstein set out to do. Her book is designed for non-specialists, for rubes like you and us. Indeed, the three blurbs on the back on the book stress how “accessible” it is:
Professor Pinker says that Professor Goldstein “offers us...a lucid exposition of Godel’s brainchild.” Professor Greene, of “Einstein made easy” fame, credits the book with “a detailed yet remarkable accessible account [Godel’s] most stunning breakthrough.”
Professor Lightman makes it three, crediting Professor Goldstein with a “penetrating, accessible, and beautifully written book.”
After all that, you open the book and start reading. But we don’t think that what you find is “remarkably accessible” at all!
According to us, you find something quite different—you find a fascinating compilation of wonderfully bad explanations. And, as we’ve already confessed, we’ve conducted a love affair with this literary form for perhaps four decades now.
Within the academy, Godel is famous, revered, regarded as deeply important. Does Professor Goldstein’s book offer “a lucid exposition” of his thought? Are her presentations “remarkably accessible?”
To the contrary! We’d say her work is fascinatingly muddled. In line with our true confessions, this attracts us all the more.
In our spare time, we’ll be doing some posts on Professor Goldstein’s book. In part, here’s why:
Our national discourse is virtually defined by bad explanation. Journalists rarely seem to notice, and professors like Professor Goldstein rarely intervene.
The professors leave us to twist in the wind. Left to themselves, they produce brilliantly muddled work which gets praised by gangs of their colleagues.
Before you know it, parents are paying tuition fees to expose teenagers to their work. And we know this! It happened to us!