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
"Our Town just doesn't reason real well"ReplyDelete
You can say that again. Look at the cretins who comment here trying to toe the line of idiot us vs. them propaganda which rules the internet and cable TV.
Don't forget AM talk radio and Congress.Delete
OK I won't forget you're on the level of Sean Hannity. Great.Delete
There is a direct line from us vs. them propaganda and the January 6 Capitol attack.ReplyDelete
I know - you're in league with QAnon. Fantastic job.Delete
"The goal of our exploration is this:ReplyDelete
To see if Budiansky can explain Gödel's "Incompleteness Theorem." More specifically, to see if Budiansky can make this topic accessible to "general readers.""
When you read any biography or autobiography, the goal should be to understand the subject of that bio as a person, to get instead his head and explore his own motives, to see how he or she achieved what made them famous enough to earn a biography, and to understand the times in which they lived and worked in order to understand the forces that shape great men and women.
If Somerby wants to understand Godel's Incompleteness Theorem, you don't read trade books about people's lives. You study mathematics and logic and computer science.
At least Somerby admits he is not reading the book with an open mind. He is playing a game of gotcha, because he cannot stand it when someone else is more famous than he is, much like his idol, Trump.
"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."ReplyDelete
Do I need to understand electricity from a physics standpoint in order to appreciate reading about Thomas Edison's life? Clearly no. Do I need to understand the intricacies of musical composition in order to appreciate reading about Mozart's life? Clearly no. Why then, should I have to understand logic to appreciate reading about the life and troubles of Godel?
Somerby is being an asshole because he wishes to discredit not only Godel's work, but also those who dare to write about his life.
Somerby himself has written many times about Trump's purported craziness, without knowing thing 1 about psychology, much less psychiatry. He routinely writes about despairing anthropologists without knowing anything at all about what anthropologists do. He even writes about NAEP scores without any background in education theory, testing, or measurement of cognitive abilities, only classroom experience, and it has never bothered him to do so. But now he criticizes Budiansky for not devoting a biography (for God's sake) to discussing what the Incompleteness Theorem means. What an asshole!
"Indeed, did he ever prove anything at all?"ReplyDelete
Why isn't it enough for Somerby that actual mathematicians, logicians, philosophers and computer scientists believe he did?
This extreme disbelief is one reason why I think Somerby's purpose here is to himself undermine reason and faith in expertise. If Godel's theorem can be discounted, in the face of so much support for it, then anything can be and that opens the door to the kinds of lies and disinformation spread by the right. Up can be down, if a charismatic figure like Trump says so, because any lazy undereducated buffoon like Somerby can call Godel wrong, simply because he (like Howard Hughes and quite a few others) suffered from paranoid dementia at the end of his life.
Somerby should be ashamed of himself, but like most Republicans these days, he has no shame.
"That work there is often quite poor."ReplyDelete
How would Somerby know?
"that no formal mathematical system will ever capture every mathematical truth within its bounds"ReplyDelete
Yeah, that's pompous bs, obviously.
But since you, dear Bob, sound like you already know that the book is crap, why don't you just stop reading it? Use it for starting fire in your fireplace.
Seriously, reading crap in order to criticize it? We feel there's something masochistic in it, dear Bob. Incidentally, same goes for religiously watching your dembot shows and reading dembot websites. Well, your own business, of course.
Somerby thinks we're all in trouble because a biographer with an M.S. in Applied Science cannot get every reader of his book to understand a theorem that I only encountered in a graduate level course in computational modeling?ReplyDelete
Why is this a matter of IQ and not acquired (crystallized) knowledge?ReplyDelete
The media is the propaganda arm of corporations.ReplyDelete
If it wasn't they'd point out, on a daily basis, the Republican Party is an anti-democratic cabal dedicated to a white supremacy oligarchy.
A real media criticism blog would be continuously banging the drum about this fact.Delete
This is not a real media criticism blog. It is a blog devoted to the worship of DJT and the defense of Roy Moore, Ron Johnson, Devin Nunes and Matt Gaetz. In short, it is a blog full of sound and fury, told by a Trumptard, signifying nothing.Delete
'Our Town is in a lot of trouble. Meanwhile, as various experts have noted, Our Town just doesn't reason real well,ReplyDelete
Certainly your town of hardcore, malignant Trumptards is in a lot of trouble. That doubtless explains Somerby's depression and his going even further off the rails.
This comment has been removed by the author.ReplyDelete
“Our Town is in a lot of trouble.“ReplyDelete
No, Our Country is in a lot of trouble.
But thanks for taking the tribal view, Somerby.
When Bob completely abandons the stated subject matter of the blog, you may get something useful. The problem is even he is exhausted trying to shore up his “both sides” arguments. That much reason tells us. These are chilling days. The Republicans will not agree to a bipartisan report on Trump’s rape of the Capitol for an obvious reason: better than half the party is complicit in the criminality. Thinkers like Bob helped create this situation when he made the conscious, hardly rational choice that only the left deserved critiquing. And he has never been able to admit much that he was wrong.ReplyDelete
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