MONDAY, JULY 11, 2022
Took it but seem to have failed: To us, it felt like a four-day weekend. Also, the weather in the Baltimore/Washington area was unseasonably superb.
Under the circumstances, we did what anyone else would have done over the recent July 4 weekend. We gifted ourselves with the ongoing pleasures of "The Gödel Challenge," resulting in this report.
Major figures have taken the Gödel Challenge. In its simplest form, the challenge consists in this:
At its simplest, the challenge consists in the attempt to explain Kurt Gödel's incompleteness theorem(s) in a way the general reader can understand.
As the days and weeks pass, we'll add a bit to that description of the Gödel Challenge. That said, major figures have taken the challenge. In our view, they seem to have failed.
Question! Since almost no one has ever heard of Kurt Gödel, why should such folderol matter?
Given the way the world really works, it doesn't matter at all! Given the way we might wish the world worked, it matters for this reason:
Kurt Gödel (1906-1978) has often been described as "the greatest logician since Aristotle." Given the role logic is said to play in idealized pictures of human life, you'd almost think we'd want to know what he showed or proved.
Alas! We know of no one who has been able to explain that matter in a way the general reader can hope to understand. Today, we present a roster of some major figures who have taken the Gödel Challenge—who have taken the challenge and failed:
Professor Rebecca Goldstein:
Rebecca Goldstein took the challenge in her well-received book, Incompleteness: The Proof and Paradox of Kurt Godel.
The book appeared in 2005, part of a larger series aimed at general readers. It was festooned with blurbs from leading intellectuals who testified to its lucidity.
At the time, Goldstein was a philosophy professor at Barnard. She graduated as valedictorian from Barnard in 1972, then received her doctorate in philosophy from Princeton.
Aside from her work in philosophy, Goldstein is also a well-regarded novelist. In 2014, she received a MacArthur genius grant.
Biographer Stephen Budiansky:
In 2021, Stephen Budiansky took the challenge in a similar biography aimed at general readers. His book was called Journey to the Edge of Reason: The Life of Kurt Gödel.
The book was favorably reviewed. Budiansky benefited from access to a wide array of private papers which has previously been inaccessible to Gödel scholars.
Professors Nagel and Newman:
Longer ago and farther away, Ernest Nagel and James Newman also took the challenge. Initially, they did so in an article for Scientific American.
Nagel and Newman were highly regarded scholars in their respective fields. Later, their article was expanded into a short book, Gödel's Proof.
The book appeared in 1958, becoming an instant classic. In 2001, New York University Press published a slightly revised edition of the original text, describing the book as shown:
An accessible explanation of Kurt Gödel's groundbreaking work in mathematical logic
In 1931 Kurt Gödel published his fundamental paper, "On Formally Undecidable Propositions of Principia Mathematica and Related Systems." This revolutionary paper challenged certain basic assumptions underlying much research in mathematics and logic. Gödel received public recognition of his work in 1951 when he was awarded the first Albert Einstein Award for achievement in the natural sciences—perhaps the highest award of its kind in the United States. The award committee described his work in mathematical logic as "one of the greatest contributions to the sciences in recent times."
However, few mathematicians of the time were equipped to understand the young scholar's complex proof. Ernest Nagel and James Newman provide a readable and accessible explanation to both scholars and non-specialists of the main ideas and broad implications of Gödel's discovery. It offers every educated person with a taste for logic and philosophy the chance to understand a previously difficult and inaccessible subject.
New York University Press is proud to publish this special edition of one of its bestselling books. With a new introduction by Douglas R. Hofstadter, this book will appeal students, scholars, and professionals in the fields of mathematics, computer science, logic and philosophy, and science.
According to NYU Press, Gödel's Proof provides non-specialists with "a readable and accessible explanation of the main ideas and broad implications of Gödel's discovery." The overview notes that the new edition of the book included "a new introduction by Douglas R. Hofstadter."
"What is Gödel's work about?" Hofstadter asks at one point in that introduction. That said, Hofstadter was already very well known, and highly regarded, for having taken the challenge at an earlier point.
Professor Douglas Hofstadter:
Perhaps the best-known attempt at the Gödel Challenge came from Professor Hofstadter in his 1979 book, Gödel, Escher and Bach.
The 777-page book won the Pulitzer Prize for general non-fiction and the National Book Award for Science Hardcover. Hofstadter's explanation of Gödel's work was one of the building-bocks of the book—and Hofstadter didn't stop there.
In 2001, Hofstadter took the challenge again, writing that preface to the latest edition of the Nagel and Newman book. Again, he tried to explain what Gödel had done in a way which would be accessible to the general reader.
Others have taken the Gödel Challenge over the many long years. That said, we'll be focusing on the efforts listed above as we attempt to discern if anyone has successfully taken this challenge.
Above, you see our roster. We've cited five highly-regarded scholars and writers who have taken the Gödel Challenge. But has anyone succeeded at this daunting task?
We're inclined to say that the answer is no. As we noted in our earlier post, we'll raise a related set of questions as we continue along with our quest. Our questions will go like this:
Do Gödel's theorems even make sense? Yes, the theorems are hard to explain. But is it possible that these famous theorems don't even make good sense, judged on their own terms?
That may seem like a ridiculous thought. For reasons we'll note as we proceed, we can't necessarily say that we automatically agree.
Our reasons for doubt will follow. We think this 20th-century story is wonderfully comic. It's anthropology all the way down!
Coming next: Expanding the terms of the Gödel Challenge
Earlier in this continuing series:
TOOK THE GODEL CHALLENGE: To their credit, they took the challenge! See THE DAILY HOWLER, 7/5/22.
ERRORS: We pivot away from our tribe's mistakes in search of some comic relief! See THE DAILY HOWLER, 7/7/22.
"Do Gödel's theorems even make sense?"ReplyDelete
But of course it does, dear Bob.
"Yes, the theorems are hard to explain."
But this one is not hard to explain, dear Bob. In any formal system of axioms and inference rules there are sentences that can be neither proved nor disproved, within that system.
What can be easier to explain, dear Bob? If you want complicated shit, try calculus...
Here we see that Mao isn't stupid. He (or she) is an educated Russian troll.Delete
Hello and a warm greeting, to be sure!Delete
A word of friendly advice - beware the whispering fanny. It can become volatile and release noxious gas, clearing a room in ten seconds flat! If you have a whispering fanny, you may not have many friends at a social gathering.
There are two homeless people on every other street corner. As the Federal Reserve attempts to slow down the economy, how many new homeless people will be there tomorrow?ReplyDelete
A. The system is more important than the people
B. A homeless person is just a lazy worker
C. Put the homeless on a bus to another state
Yeah. Back in the 1920s, the unemployment rate was quite low. As low as 2.5%, in some years.Delete
...and then, in 1930, suddenly it was 25%...
Life can be complicated...
The homeless aren’t stupid either. They put themselves on buses to CA where the winters are mild and there are better services.Delete
I checked Anon @5:27 and his talking point comes from a California politician, who said the majority were from out of state. Politifact called it pants on fire: "70 percent had lived in the city; 22 percent in another California county and 8 percent out-of-state. Of that 70 percent, more than half, or 55 percent, reported living in San Francisco for a decade or more before losing their home. Just 6 percent said they had lived in the city for less than a year."Delete
San Francisco’s own homeless surveys contradict this. They show a large majority reported living in the city before becoming homeless, and just a fraction coming in from out-of-state.
Newsom’s office pointed to data from San Francisco’s bus ticket program for homeless people. But that defense doesn’t hold up. It shows just a small fraction, less than 7 percent, left for Texas, and doesn’t demonstrate that they originally came to San Francisco from that state.
In the end, we found Newsom made a ridiculous claim.
We rated it Pants on Fire."
1. I was not talking about any comment made by Newsom.Delete
2. I was not talking about San Francisco specifically.
3. Homeless have been coming to California since the Dust Bowl in the 1930s (see Grapes of Wrath, written by Steinbeck, who lived in Monterey).
4. Reagan was initially responsible for high homelessness in the early 1970 related to closing mental hospitals and failure to help returning Viet Nam veterans. That was exacerbated by big increase in use of street drugs in later 1970s & 80s.
5. No one cares about what is in your pants.
https://silo.tips/download/article-for-rescue-magazine-by-betsy-degeorge (this article says that 56% of homeless stay in one area, while disputing seasonal migration among homeless people, contradicting its own conclusions)
Another study concluded that homelessness is homegrown, but cites similar stats for migration by homeless people: "L.A.H.S.A.’s 2019 homeless count found that 64 percent of the 58,936 Los Angeles County residents experiencing homelessness had lived in the city for more than 10 years. Less than a fifth (18 percent) said they had lived out of state before becoming homeless.
In San Francisco, 43 percent of the homeless said they had lived in the city for more than 10 years."
So this seems to be a matter of degree and needs to be compared to migration patterns by non-homeless people. These have changed with the increase in cost of living in CA.
Ah yes I seem to have been caught spreading bullshit let me backtrackDelete
"a matter of degree" like the degree you don't have in statistics or sociologyDelete
Well, to butt in I don't like the phrasing of the original question.Delete
"There are two homeless people... how many new homeless people will be there tomorrow?"
So I want to give a numeric answer. And the question doesn't seem to leave open the possibility that the number reduces. Unless you'll except negative numbers as answers.
He wasn't talking about San Francisco when he said "CA where the winters are mild and there are better services."Delete
Where is San Francisco folks?
How many people know that? Anon didn't.
“Is it possible that these famous theorems don't even make good sense, judged on their own terms?”ReplyDelete
Why doesn’t Somerby actually look at Gödel’s own work? How can he judge whether the other reviewers have gotten it right?
It’s like trying to decide what Hamlet is about or if it’s any good by reading reviews of it.
Has Somerby ever attempted to go to the source? He is being remarkably unfair to Gödel otherwise.
I doubt he read the assigned philosophers when he was in college either. I cannot fathom why Somerby was a philosophy major when he is so reluctant to engage in actual thought along with the major figures he would surely have been assigned to read.Delete
The only notion he seems to have absorbed is a kind of nihilistic "maybe it is, maybe it isn't, no one can know for sure, anything is possible" dodge that evades engagement with any idea.That is far from what philosophy is about or how it reasons. It does seem like a juvenile posture for evading taking a position and being responsible for any opinion, that maybe even seems a bit zen to unwary hippies of the mid-60s, especially those experimenting with drugs.
Somerby cannot be that stupid, so this has to be some sort of Andy Kaufmanesque joke on those who read his blog. Meanwhile, Godel's reputation doesn't hinge on anything Somerby says about him. His place in history is firm and he has had his influence on others already, including Einstein and Turing -- bigger names than Somerby. So I don't see any point engaging with Somerby while he pretends to write a blog here each day. As Mao has pointed out, there are actual social problems people could be discussing more profitably than Somerby's opinion of Godel's work, as filtered through better minds than his own.
So what's the point here, are you both suggesting to fulfill The Gödel Challenge which is to explain Gödel's work in a way a general reader can understand, that one need look no further than Gödel's own writings? Can you see that the Hamlet comparison is not applicable?Delete
The general reader is not going to understand Godel's work fully, It takes a mathematical background to do that. Somerby's demand is unreasonable. A skilled writer who understand Godel can explain his work to a lay audience in simpler terms, but the reader will not gain a full understanding. That simpler explanation is not enough for Somerby, although it is fine for those who read the books he has listed.Delete
The unreasonableness of Somerby's demands is the point here, not Godel. Those who are interested have already the books listed. The rest of us are not interested in knowing more about Godel. Somerby's continued harping on an unreasonable demand makes no sense in the context of this blog or anywhere else.
Since many of us are watching the hearings, Somerby's demand that Godel be explained so that a layperson can understand it fully, in all of its depth, logic and implications, is akin to Trump's demand that he be permitted a second term, even when everyone told him that was not possible. Somerby is throwing a Trump-like tantrum, by returning to this same demand, time and time, even when it has been explained to him that he must have some background himself to understand technical material. Somerby is autistic about this because he doesn't read his comments, where the explanations and attempts to reason with him have been provided on many past occasions.
So, this is an exercise in futility, a waste of everyone's time, an insult to blog readers, and a rejection of how communication is supposed to work (no reciprocity, no feedback, repetition to no purpose, nonsensical content and lack of meaning, etc.). Somerby is being an asshole.
"The general reader is not going to understand Godel's work fully..."Delete
Fully being the operative word. I disagree with the premise that one needs "a mathematical background" to understand his work on a fundamental level.
So then the rest of your comment is built on a series of premises I entirely disagree with, so I can't comment further. We're at an impasse.
First of all, anon 2:32, you would have to agree that Somerby is correct about those he listed. Did they really fail the Gödel challenge?Delete
Secondly, it is quite clear that Somerby is suggesting (and has suggested in the past) that Gödel’s theorems actually don’t make sense. You may not think that is what he is saying, because he is being coy about it, but read his past blog entries. He is indeed saying that, just as he suggests that all philosophy is idiotic “word games”, as he likes to tell us Wittgenstein said.
And just as you cannot judge Hamlet “on its own terms” by reading other people’s writing about, how can you judge Gödel’s? Somerby is specifically not judging Gödel on his own terms.
No you're not following. There is a difference between being useless and not making sense. And Hamlet is still a poor comparison because the language is not that tricky to decipher, not like Gödel’s theorems. And the challenge is for someone else to explain them, that's just how it's stated. So difficult to continue this discussion considering all those issues, there's nothing left to address that you've presented here except you don't like Somerby.Delete
FWIW I really liked the Nagel and Newman book. I found it accessible. Of course, I studied a lot of math. It's a really good explanation of the clever proof. The nature of the proof is valuable, aside the value of knowing what it shows. (I wonder if Bob really read this whole book and how hard he thought about it.)ReplyDelete
The Hofstadter explanation of Godel's proof was not quite as clear for me. However, EVERYBODY should read it. Depending on your background, you may not understand all of it, but that's OK. You will understand a lot of it. It has chapters on Bach as well as Escher. It's remarkable! Reading it will make you a smarter person.
"A new New York Times/Siena poll finds a remarkable educational divide among Republican votes with college graduates preferring Ron DeSantis over Donald Trump as the 2024 nominee, 32% to 28%, while non-college graduates overwhelmingly prefer Trump, 58% to 21%."ReplyDelete
Not surprising. I think everyone knows DeSantis doesn't have a chance. The question is will the Dems go with someone with more popularity than Biden.Delete
It's a shame that college graduates are still allowed to vote. Their brains are irreparably damaged.Delete
It is so sad to see how the republican party establishment is stabbing Trump in the back. That DeSantis is one sly little weasel, making his move now while Trump is getting hammered daily with the 1/6 committee lynch mob hearings. I guess politics ain't beanbag.Delete
Dems have been wishing for Trump's downfall via various means for some time now. He'll get impeached... criminally charged... undone by DeSantis...Delete
We're still stuck with him. But is it that bad? The guy is an idiotic con artist and maybe Dems should say he *is* the candidate they want to face in the election. But a winning strategy would need to be developed, how to point out what a clown he is in a way that doesn't feed the black hole that sucks in all logic and reason and makes him stronger...
It's just sad watching Trump get pummeled day after day without any republicans standing up for him and DeSantis stabbing him in the back. Even here on this blog we see David in Cal has abandoned Trump and is jumping on the DeSantis bandwagon. So sad.Delete
If you compromise your own integrity in attacking those that already have, what exactly are you left with?Delete
Men can't get pregnant.ReplyDelete
Is this something you spend a lot of time thinking about? First world problems I guess.Delete
Males can be mothers and females can be fathers.Delete
"Someone argue with me because my mommy didn't hug me enough and now I'm like this"Delete
Wanted: non-propagandist, non-ideological extremist comments that want to discuss things logically instead of reciting boring party talking points over and overReplyDelete
Pay: unfortunately, zero
Statement from Donald J. TrumpReplyDelete
"The failing New York Times is down 40% year-to-date because they are Fake News. Their reporters are dishonest, and their front page has become a work of total fiction, not news. They hate our Country, and they hate reporting the truth, which is why America is not respected and our Nation has never been weaker. Instead, they obsess over January 6, just like they did over Impeachment Hoax #1, Impeachment Hoax #2, the Mueller Witch Hunt, and Russia, Russia, Russia. The New York Times will continue to decline because people no longer believe their reporting is even close to being true. Fake polls, phony stories, and made up quotes—they are a disgrace to journalism and have set it back many many years. THE NEW YORK TIMES IS TRULY THE ENEMY OF THE PEOPLE!"
The NY Times is a Right-wing rag, owned by a corporation which wants tax breaks.Delete