THURSDAY, MAY 27, 2021
The IQ of Our Town: For ourselves, we've been allowing ourselves to have nice things, at least in the afternoons.
We're allowing ourselves to spend some time with Stephen Budiansky's new book, Journey to the Edge of Reason: The Life of Kurt Gödel.
The goal of our exploration is this:
To see if Budiansky can explain Gödel's "Incompleteness Theorem." More specifically, to see if Budiansky can make this topic accessible to "general readers."
How is Budiansky doing so far? At this point, we'll only say this:
Even before he starts Chapter 1, Budiansky offers a six-page Prologue. In the main, he uses notes from Gödel's psychiatrist to describe Gödel's terrible psychiatric state in the years before his death in 1978, at age 71.
(Gödel, who was 5 feet 7 inches tall, weighed 65 pounds at the time of his death, largely due to something resembling self-starvation.)
Gödel was gripped by paranoia and delusional thinking in, let's say, the last decade of his life. In his Prologue, Budiansky focuses on this terrible state of affairs.
That said, he offers a brief overview of Gödel intellectual work in his book's first paragraph. In this, the first paragraph of his Prologue, Budiansky offers this first brief account of that work:
MARCH 1970. The psychiatrist moved his pen swiftly across the yellow sheets of lined notebook paper, recording facts, strange and mundane, about his new patient. Einstein had called him "the greatest logician since Aristotle," and even in Princeton, the town with more Nobel Prize winners than traffic lights, his otherworldly genius had stood out. The work he had done forty years earlier, at age twenty-four, had brought fame and recognition from around the world—"the most significant mathematical truth of the century," a staggeringly brilliant and paradoxical proof that no formal mathematical system will ever capture every mathematical truth within its bounds.
But now he was tormented by demons, of failure and persecution...
As described in that opening paragraph, Einstein had referred to Gödel as "the greatest logician since Aristotle." Also, Gödel had proven "that no formal mathematical system will ever capture every mathematical truth within its bounds."
According to that brief capsule statement, Gödel—the greatest logician in 2500 years—had proved that no formal mathematical system will ever capture every mathematical truth within its bounds.
Will a general reader have any idea what that formulation means? Without meaning this as a criticism of Budiansky, we'll note that the answer is clearly no.
The general reader will have no idea what a "formal mathematical system" is. For that reason, the reader will have no idea how some such system can "capture a mathematical truth," let alone how it can "capture every mathematical truth within its bounds."
What does it mean for a mathematical truth to be "within the bounds" of a "mathematical system?" The general reader will have no idea! Meanwhile, how could such a demonstration have qualified Gödel as "the greatest logician since Aristotle?"
The general reader won't know that either! Whether we're willing to notice or not, here come those crickets again!
In the opening paragraph of his book, Budiansky provides an account of Gödel's work which general readers won't understand. That doesn't mean that this material won't be clarified later on. For now, though, the general reader will have no idea what Budiansky is talking about.
At present, we're scouring Budianky's book to see if he ever makes this matter clear.
What did Gödel actually prove? Indeed, did he ever prove anything at all? Our training, along with advice from experts, teaches us that the answer to that latter question may not even be yes!
We wouldn't sweat that the greatest logician proved anything at all! But as we let ourselves have nice things in the afternoon, we're trying to see if Budiansky can explain what Gödel is alleged to have proven:
We're trying to see if Budiansky can explain the Incompleteness Theorem in a way a general reader, a rube like us, can actually understand.
We're letting ourselves have those nice things, but only in the afternoons. In the mornings, we're thrown to the mercy of Our Town's greatest newspapers.
That work there is often quite poor. This morning's New York Times, for example, offers an array of articles which largely function as a series of muddles inside a large mud puddle.
Last weekend, this same muddle-minded newspaper tackled a very important topic. Forgive us if we wait till tomorrow to report what Reverend Barber said, or to visit Kristof and Healy.
Our Town is in a lot of trouble. Meanwhile, as various experts have noted, Our Town just doesn't reason real well, especially on topics like this.
Also, what did Gödel actually prove? Did Gödel prove anything at all?
Experts say these puzzles are interrelated. It's love in the afternoon(s)!
Tomorrow: What Reverend Barber said