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New More on Gödel.
Gödel:

On December 5, 1947, Einstein and Morgenstern accompanied Gödel to his U.S. citizenship exam, where they acted as witnesses. Gödel had confided in them that he had discovered an inconsistency in the U.S. Constitution that could allow the U.S. to become a dictatorship. Einstein and Morgenstern were concerned that their friend's unpredictable behavior might jeopardize his application. Fortunately, the judge turned out to be Phillip Forman, who knew Einstein and had administered the oath at Einstein's own citizenship hearing. Everything went smoothly until Forman happened to ask Gödel if he thought a dictatorship like the Nazi regime could happen in the U.S. Gödel then started to explain his discovery to Forman. Forman understood what was going on, cut Gödel off, and moved the hearing on to other questions and a routine conclusion.[19][20]


Zooks!!

Cheers,
Scott.
New Kurt has always been my hero.
Some 42 years ago, when I was in high school, I first read this. Although a non-technical account (interestingly, I just discovered this text is used in some university math courses as a textbook today!), it permanently and fundamentally changed the way I think about mathematics. The one thing I wanted out of my university study of mathematics was a comprehensive, technical understanding of The Incompleteness Theorems. I was endlessly frustrated by the fact that none - and I mean none - of my professors would discuss them with me.

Finally, in grad school I had the opportunity to take a grad level Number Theory course. A few weeks before the class started, I was in the bookstore looking at the assigned Number Theory textbook and I was delighted to see a chapter dedicated to The Incompleteness Theorems about two-thirds of the way into the book. Just as I found that chapter, the late Dr. L (who was scheduled to teach the class and was a member of my graduate committee) came down the aisle and said to me, "Don't read too far ahead in that book. I can't have you knowing more about this than me on the first day of class."

We went through the leading chapters and ended a week on the chapter immediately preceding the chapter I could not wait to start. Monday rolls around and I'm pretty excited. There were roughly 25 students in the class and as was my custom, I was seated in the front row. Dr. L announced the chapter we'd be studying and it was the chapter after the Incompleteness Theorems. I could not contain myself. I said, "Wait! What's going on here? You can't skip that chapter! That chapter is the only reason I enrolled in this course!" Dr. L replied, "You already know about The Incompleteness Theorems, Mike." I protested, "Not sufficiently. I don't yet have a full technical understanding of all the proofs." Dr. L replied, haughtily - so much so it passed for contempt in the eyes of the other students (or so they said after class), "You know enough! You understand the proofs and you know exactly what are the implications." I said, "But there other students in here who might not have ever encountered Goedel because you and I both know how loath mathematics professors are to address those implications." He, I will always believe was truly angry at this point said, "Well, that's just great, Mike. Yes. By all means let's face The Incompleteness Theorems. Is that what you want? Okay. Let's do that. Then we can throw away all the mathematics books, calculus, differential equations, all of it while we wait breathlessly for you to come up with a system of mathematics that is both complete and consistent. But please hurry. Because none of us in the field of mathematics will have anything to do until you're finished. Shall we do that then?"

That was over 25 years ago and it still stings. Needless to say, we did not study The Incompleteness Theorems in that Number Theory class.

If you haven't heard of Greg Chaitin, you might be interested in this. Quite some time ago, I actually got to exchange a few emails with him about his work and it's relation to Goedel's.
bcnu,
Mikem

It's mourning in America again.
New a Bully Stand! and impeachable only (via the sleazy sarcasm employed?)
Shall return, follow-up on this topic anon as/when domiciles n'such have become less Jello-like in consistency. While my math chops are quite inadequate to 'testing Proofs of' say, (irony so delicious? as:) sorta verifying the Incompleteness of Anything ..to an extent which scares Math Profs into er, cowardice !?

Maybe why I latched on to The Relief of-absolute-Cant, I thought) brought us by Kurt.
Dunno if there be any useful similarities re the Non-denumerable (but Comparable!) "Infinities"/first grammatically-correct use of a plural there?? as also must have shattered some sets of 4 x 5" card-sets so oft seen in lectures du My jour.

..to be continued. Don't sweat such 'stings' as you say; yours *was* the braver, Truthier path and you Stayed.. as the Roman signature-Marathon-runner opined/just before he is said to have fallen dead from exhaustion:

Rejoice! We Conquer!!

;^>
New It's alive! Good to see you
--

Drew
New Go have a shower, you're all sooty and reek of smoke. Been playing with matches again?
Great to see you!
New Thanks! And VERY GLAD to know you're safe.
bcnu,
Mikem

It's mourning in America again.
New Missed Y'All.. while plotting courses: !=orange-glow-in-sky direction.
New Math-Man after my own heart:

“A clearly written and witty look at a difficult subject. . . . Chaitin explains with infectious enthusiasm how mathematics doesn't equal certainty.” –Science News



Look at [Nothing] as a personal-Noun, for a minute.. as one incorporates 'math' into er, Actual Life?
.
.
Nothing can save you
.
.
Nothing matters..
.
.
Nothing ... [the Only "entity" "who" Can say?] is Certain.



Rest case, for now.
Curl grad V=0 ;^>
New Mathematics is an interesting game. Too bad it's so broadly misapplied and misunderstood. ;0)
bcnu,
Mikem

It's mourning in America again.
     Think arithmetic is "basic"? Think again. - (drook) - (15)
         Neat. -NT - (Another Scott)
         Russell, Whitehead and later Goedel showed me arithmetic isn't easy. ;0) -NT - (mmoffitt) - (10)
             Early on the page they mention being inspired by Russell's "Principia" - (Another Scott) - (9)
                 More on Gödel. - (Another Scott) - (8)
                     Kurt has always been my hero. - (mmoffitt) - (7)
                         a Bully Stand! and impeachable only (via the sleazy sarcasm employed?) - (Ashton) - (4)
                             It's alive! Good to see you -NT - (drook)
                             Go have a shower, you're all sooty and reek of smoke. Been playing with matches again? -NT - (CRConrad)
                             Thanks! And VERY GLAD to know you're safe. -NT - (mmoffitt) - (1)
                                 Missed Y'All.. while plotting courses: !=orange-glow-in-sky direction. -NT - (Ashton)
                         Math-Man after my own heart: - (Ashton) - (1)
                             Mathematics is an interesting game. Too bad it's so broadly misapplied and misunderstood. ;0) -NT - (mmoffitt)
         Makes me miss Ben Tilly. -NT - (static)
         And no mention of Nicolas Bourbaki? :) - (a6l6e6x) - (1)
             Mea Culpa and thanks! -NT - (mmoffitt)

Anyone who would spend $5000 on a laptop is either Todd, or out of his mind.
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