[snarks_when_bored]

This is another review of two books noted on previous FR threads:

Gödel and Einstein: Friendship and Relativity [an excerpt from Palle Yourgrau's book]

Truth, Incompleteness and the Gödelian Way [a review of Rebecca Goldstein's book]

GÖDEL AND THE NATURE OF MATHEMATICAL TRUTH [6.8.05] - A Talk with Rebecca Goldstein

GÖDEL AND THE NATURE OF MATHEMATICAL TRUTH II [7.27.05] - A Talk with Verena Huber-Dyson

Having now read both Yourgrau's and Goldstein's books, I must concur with Moore's judgment that Yourgrau's appears to be the more accurate account of what Gödel was attempting to accomplish with his two great Incompleteness theorems, and also with his work on General Relativity during the 1940's. Goldstein has a literary sensibility, but doesn't convince her reader that she really has a grip either on the technical aspects of Gödel's work or on what Gödel's inner life must have been like. A novelist's imagination proved insufficiently powerful to see into the heart of what Gödel accomplished and who he was.

On the other hand, Verena Huber-Dyson's book, Gödel's Theorems; a workbook on Formalization, is a relentlessly detailed exploration of the formal logic and mathematics needed to really grasp Gödel's theorems. If I had a year or so of free time, I'd be tempted to work my way through the exercises. In another life, perhaps...

[snarks_when_bored]

Gödel ping

I've pinged everybody who showed up on any of the four earlier threads I've posted on Gödel, with the idea that a previously displayed interest might be a reliable sign of continuing interest.

[ThePythonicCow]

I recall when Godel died, in January of 1978. I had to give a talk the next day at Georgia Tech, and began the session by announcing his death, and asking for a moment of silence.

The great ones speak with a clarity that is delightful.

[Flightdeck]

In a slight change of topic, has anyone posted that article from the latest Popular Science that mentions freerepublic?

[aculeus]

Thanks for the ping.

[GOPJ]

Goldstein has a literary sensibility, but doesn't convince her reader that she really has a grip either on the technical aspects of Gödel's work or on what Gödel's inner life must have been like. A novelist's imagination proved insufficiently powerful to see into the heart of what Gödel accomplished and who he was.

Math, the truest language for describing reality, falls flat when describing humans. For now...

[Lancey Howard]

BUMP

[sauropod]

mark

[grey_whiskers]

If I had a year or so of free time, I'd be tempted to work my way through the exercises. In another life, perhaps...

All too true, mate.

In the meantime, don't feel so bad. I once read that David Hilbert turned down an offer to work on Fermat's last theorem, on the grounds he didn't want to spare the three (!!) years it would take him to get up to speed on the background.

Cheers!

[Allan]

More Godel.

[IslandJeff]

Bookmarked. Thanks for the ping.

[Ichneumon]

This is another review of two books noted on previous FR threads:

Yet another book on the subject:

d) the whole idea of universal truths is a misunderstanding based on a limited philosophical system?

Again, "universal truths" is one of those "everyone knows what I mean" terms that nonetheless start to feel like nailing Jell-o to a wall when you actually begin to try to pin it down. Half the room will agree to a particular meaning, and the other half will object strenuously (*whichever* of dozens of possible ways you try to define it).

One of (hell, *THE*) best books for the layman on these types of issues (as well as many others) is "Godel, Escher, Bach: An Eternal Golden Braid", by Douglas Hofstadter. Truly one of the great books in the history of mankind. And no, I'm not exaggerating. In a step-by-step, understandable, *entertaining* manner, he walks the reader on a grand tour through (using Amazon.com's subject list for the book):

Topics Covered: J.S. Bach, M.C. Escher, Kurt Gödel: biographical information and work, artificial intelligence (AI) history and theories, strange loops and tangled hierarchies, formal and informal systems, number theory, form in mathematics, figure and ground, consistency, completeness, Euclidean and non-Euclidean geometry, recursive structures, theories of meaning, propositional calculus, typographical number theory, Zen and mathematics, levels of description and computers; theory of mind: neurons, minds and thoughts; undecidability; self-reference and self-representation; Turing test for machine intelligence.

And unlike most books on any/all of these topics, the material is not "dumbed down" -- anyone who works through the book will get a *real* appreciation and working understanding of these subjects.

And as the "braid" in the title promises, the author delivers on showing the intimate interconnections between these topics. In a sense, although the book is about *all* those things, it's really all about the *same* thing. And the book itself is so tightly constructed that it sometimes feels that if one sentence were accidentally removed, the whole book would unravel like a snagged tapestry. Even when it seems that the author is starting a new chapter on an entirely different topic, at some point you'll find that your brain suddenly goes, *oooooooohh*...., as you realize that he has managed to weave another "thread" into the very same subject matter that the last chapter covered.

A truly remarkable book, and I'm not the only one to think so. It won the Pulitzer Prize, an amazing achievement for a book in this genre. There are better books on the subject for a technical audience, of course, but this one's excellent for a layman who has little or no prior background. It starts from "the ground up", but climbs to amazing heights for a book of its type.

[monkey]

Are you familiar with Gödel's slingshot?

[Blind Eye Jones]

>
The Great Frankenstein Einstein Debate at Princeton

Little known fact: the Frankenstein Einstein debate at Princeton in the late 30s. Frankenstein was coming off a few hit horror films with Dracula and bought his way into Princeton. The high point was a math debate at the student union hall where Einstein said, "pi r2" and Frankenstein rebutted with, "No! Pie are round!" It caused a big stir amongst the faculty and they chased Frankenstein back to the dorm with pitchforks and torches.

[RightWhale]

Goldstein's philosophy classes might be interesting, but like many who teach philosophy she is no Hegel [that is a hard act to follow]. What it comes down to is that the student has to develop his own understanding. The teacher can only point the way, or several ways or possible points of departure, and maybe one of them will be a sufficient spark. If Chomsky can do it, there is hope that all of us can do it.

[Blind Eye Jones]

Forgive me for that picture S_W_B, Halloween is around the corner and I couldn't resist. All The Best!

[snarks_when_bored]

Hey, folks, I've pinged you because you've evinced an interest in Kurt Gödel and his work on past threads. FYI, the current (April, 2006) issue of the Notices of the American Mathematical Society is devoted in its entirety to Gödel. Each article is a PDF file and must be downloaded individually.

Here's the link:

Kurt Gödel special edition of the Notices of American Mathematical Society

Enjoy!

[Billthedrill]

A Godel BTT. He and Einstein were walking buddies at the Institute for Advanced Studies. The story I heard is that no one else would walk with them because no one else had the faintest idea what they were talking about.

I'm guessing it wasn't "Hey, yo, how 'bout them Packers, baby?"...