THURSDAY, JUNE 3, 2021
Do you understand what gets said?: This very morning, our patience received its reward!
The New York Times finally reviewed the new book about Kurt Gödel—Stephen Budiansky's Journey to the Edge of Reason: The Life of Kurt Gödel.
Jennifer Szalai begins her review as shown. Do you understand what Szalai says? Hard-copy headline included:
SZALAI (6/3/21): Proof of a Brilliant, and Disturbed, Mind
In 1947, having left Nazi-occupied Vienna for the quaint idyll of Princeton, N.J., seven years before, the mathematician Kurt Gödel was studying for his citizenship exam and became preoccupied with the mechanisms of American government. A worried friend recalled Gödel talking about “some inner contradictions” in the Constitution that would make it legally possible “for somebody to become a dictator and set up a fascist regime.” Gödel started to bring this up at his actual examination, telling the judge that the United States could become a dictatorship—“I can prove it!”—before his friends (one of whom was Albert Einstein) managed to shut him up so that the naturalization process could go on as planned.
It’s the kind of unruly eruption that Stephen Budiansky showcases to potent and entertaining effect in “Journey to the Edge of Reason,” his account of Gödel’s life and work. Gödel’s “incompleteness theorem,” which he presented in 1930, when he was 24, upended his profession’s assumption that mathematics should be able to prove a mathematical statement that is true. Gödel’s proof landed on a mathematical statement that was true but unprovable.
Szalai begins with a familiar anecdote about Gödel’s trip to the citizenship office. Later in her review, she cites Einstein's statement describing Gödel as the greatest logician since Aristotle.
In the second paragraph of her review, Szalai gives the highlighted capsule account of what Gödel proved, discovered, demonstrated, showed or did. At age 24, his incompleteness theorem "upended his profession’s assumption that mathematics should be able to prove a mathematical statement that is true."
If a mathematical statement is true, mathematics should be able to prove it? At first glance, that doesn't seem like too much to ask.
On the other hand, it isn't completely obvious why upending that assumption would qualify someone as the greatest logician in 2500 years, or even as a logician at all. What exactly did Gödel show? And why would it make any difference?
We'd score Szalai's review as nearly a rave. That said, will the general reader for whom Budiansky's book is intended end up understanding what Gödel allegedly did?
Szalai doesn't guarantee that outcome as her review proceeds Meanwhile, as you may recall, Budiansky offers this capsule account of Gödel 's theorem in this, his book's opening paragraph:
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.
According to that initial capsule account, Gödel's theorem proved "that no formal mathematical system will ever capture every mathematical truth within its bounds."
Budiansky goes into much more detail as the book proceeds. But does he ever explain Gödel's allegedly brilliant and paradoxical theorem in a way the general reader will actually understand?
It's depressing to stand here "on the beach" watching Our Town slide away. On the brighter side, we expect to address that question about Budiansky's book next week.
It's hard to discuss the Post and the Times as they stand at present. As Elliott says when E.T. seems to have died, Look what they've done to you!
(For our money, it's one of the great movie quotes.)
For us, it's been Gödel in the afternoon of late. As the waters rise around Our Town, we're treating ourselves to nice things!
IMO it was never that likely that every true statement could be proved. E.g., take some irrational number such as π*e. Co0nsider two statement:ReplyDelete
A. In the decimal expansion of π*e, the percentage of 0's, 1's. 2's,... and 9's are all equal to 10% in the limit.
B. In the decimal expansion of π*e, the percentage of 0's, 1's. 2's,... and 9's are NOT all equal to 10% in the limit.
Either A or B must be true. Yet, it's far from clear that there's any way to prove either A or B.
And, one could state similar postulates for every irrational number. IMO it was implausible that every such statement could be proved or disproved.
So, IMO it's not unexpected that there are true, but unprovable, statements in mathematics However, what made Godel's work so impressive was that he proved that there are true but unprovable in mathematics.Delete
Also, Godel's novel approach was used to prove other theorems.
The world's greatest math book says it's unknown whether π*e is irrational. See "Open Questions":Delete
On the other hand, it's easy to construct an irrational number where the digits aren't all 10% in the limit.
I.e. one, zero, one, two zeroes, one, three zeroes, ...
Cleary irrational, almost all 0s, rare 1s, no others.
The Nazis did not occupy Vienna. Austria became an integral part of Germany in 1938, with the enthusiastic (and shameful) support of the Austrian people.ReplyDelete
People thronged the streets to welcome Hitler to Vienna.
Some people thronged the street. Others left Austria (if they could). Some Jews committed suicide out of despair over what would happen to them under Hitler. Not everyone had that same enthusiastic response.Delete
"On the other hand, it isn't completely obvious why upending that assumption would qualify someone as the greatest logician in 2500 years, or even as a logician at all. "ReplyDelete
You don't upend a profession by simply asserting something. Godel is great because he PROVED his assertion. People earn a reputation in mathematics and logic for what they prove, not their speculation or imagination.
"But does he ever explain Gödel's allegedly brilliant and paradoxical theorem in a way the general reader will actually understand?"ReplyDelete
The general reader isn't going to buy this book, much less read it. They are not the audience for it. The general reader has no idea who Godel was. This book was written for those who are familiar with his name, and have some notion of what he work was about and why it mattered.
Not every book is written for every reader. Our country is so large that there are niche markets and books written for very specialized segments of the book-buying public.
I'll bet that Somerby has never read a book by Nicholas Sparks, despite them reaching bestseller status. He wouldn't read them because they are not his type of book, and because he is underqualified to understand them, lacking empathy as he does. In fact, most of chick lit is out of his grasp. Does that mean that these are failed authors or that the books are useless or no good? Of course not.
The difference here is that Somerby apparently thinks he ought to be able to read this book about Godel, but he doesn't actually have the background for it and has little interest in trying to understand it. So he blames the book. He should instead consign it to the realm of geek studies and pursue something more his own speed, such as re-reading John Holt. Leave Godel to David and impCaesar.
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