Gödel, Escher, Bach

Gödel, Escher, Bach

Gödel, Escher, Bach by Douglas Hofstadter is a most wittily written work. It’s rather long (at 700+ pages) but it is the most interesting informative book I have ever read. Note that I use “informative” rather than “nonfiction,” as half the chapters are nonfiction and the other half fiction—the fiction is where most of the fascination is at.

It is also where the self-descriptor of the book kicks in: “A metaphorical fugue on minds and machines in the spirit of Lewis Carroll”—a writer whose nonsensical style any follower of this blog should know. Indeed, Hofstadter’s dialogs (the fiction parts) consist of absurd, comical scenes which are intended to both inform and amuse. And the nonfiction parts are good as well, covering a gamut of subjects, a nice dab into everything. The three people listed in the title, after all, are a mathematician, an artist, and a composer. Some major points of discussion include Gödel’s incompleteness theorems, logic, and Artificial Intelligence.

What’s more amusing is the subtle humor present in many of the nonfiction parts. Even in one of the most serious parts of any book—the bibliography—Hofstadter manages to squeeze in an imaginary work titled Copper, Silver, Gold: an Indestructible Metallic Alloy. This is alluded to several times in the fictional parts of the book, and is of course an imitation of the book’s own title: Gödel, Escher, Bach: an Eternal Golden Braid. The supposed author of Copper, Silver, Gold is Egbert B. Gebstadter, whose initials match those of “Eternal Golden Braid,” and Gebstadter is of course a spoof of Hofstadter. Moreover, to contrast Hofstadter’s publisher Basic Books, Gebstadter publishes with Acidic Books.

Hofstadter’s Law

Hofstadter’s Law: It always takes longer than you expect, even when you take into account Hofstadter’s Law.

(And it has right now a Wikipedia page that directly links to itself. Even the “Recursion” page does not do this.)

Hofstadter’s Law is a self-referential (or recursive) statement coined by Douglas Hofstadter in his magnum opus Gödel, Escher, Bach. It is a statement about time-taking projects, which seem to take more time than expected, even when the expected time is adjusted for delays.

Hostadter includes this at the end of a chapter on recursion, and particularly on a topic in which he shows how chess is analyzed recursively. He then recounts how programmers once (in the mid 1900s) thought chess could be mastered by a computer within ten years, but ten years later, it was still not even close to mastered, and it would seem to take even longer than ten years still!

Here is my illustration of Hofstadter’s Law:

Hofstadter's Law

The subtlety is of course that the graph is self referential. That is, Hofstadter’s Law as in the title of the graph refers to the last bar, “Actual Time.” At first you might expect that Hofstadter’s Law is present only in the fourth bar, but it is really the fifth bar that is Hofstadter’s Law. In fact, the “Actual Time” would be the “Worst Case Estimate, Taking Into Account Hofstadter’s Law” Taking Into Account Hofstadter’s Law. This leads to an infinite regress, as now the “Actual Time” is the new “Worst Case Estimate, Taking Into Account Hofstadter’s Law.”