Saturday, March 17, 2012

Gödel and the Constitution V: My Conjecture

I have long promised a final post in this series, containing my conjecture as to what Gödel's constitutional contradiction was. It is quite different from the other speculation I have seen. My delay has had several reasons:

  1. I have been immersed in doing my own mathematics.
  2. Really doing the homework on this requires a reasonable reading knowledge of German, something I do not have.
  3. Even given that I had done the homework, it was hard for me to imagine that others are impatient to hear my conjectures.
  4. Frankly, while I find the following convincing and interesting, my guess is most readers of the following will share the opinions of Einstein and Oskar Morgenstern and will be disappointed.

Without further ado, then, here is my conjecture:

  1. When the Nazis took over Austria, I conjecture that there was some after-the-fact justification in terms of Austrian constitutional law. I want to emphasize here that Gödel's concern would have been Austrian law -- *NOT* German law. I do not read German well and cannot follow up on this. It may be hard to find because even the lawyers who drafted it probably did not take it seriously.
  2. Gödel did take this after-the-fact justification seriously, and at face value. From Gödel's point of view, it would have explained why the Anschluss could and did happen.
  3. When Gödel studied the US Constitution, he found that a similar thing was possible under its terms.

I had already formed this conjecture before finding the Lost Morgenstern document, which contains the closest we will ever get to the exact wording of the conversation:
Gödel: "[Austria] was a republic, but the constitution was such that it was changed into a dictatorship."
Judge: "Oh! This is very bad. This could not happen in this country."
Gödel: "Oh, yes, I can prove it."

I cannot claim that the Morgenstern document proves my conjecture, but its language does track the conjecture exactly. And, if this conjecture seems unconvincing and uninteresting to you, note that that counts as evidence in its favor -- recall that, even though the story centers around it, Morgenstern and Einstein found Gödel's line of reasoning not worth repeating. Had it been something clearly convincing or interesting, presumably they would have passed at least a fragment of Gödel's argument on to posterity.

Tuesday, January 20, 2009

Gödel and the Constitution IV: Redisovery

In this post I tell how the Lost Morgenstern Document became lost, and finish the story of its rediscovery.  The Lost Morgenstern Document is the sole first-hand account of Kurt Gödel's citizenship hearing on 5 Dec 1947, at which Gödel, Albert Einstein, and Oskar Morgenstern went before Judge Phillip Forman.  On that occasion Gödel felt compelled to share with the judge his account of a proof he'd discovered -- that the U.S. could, quite legally, be converted into a dictatorship because of a logical contradiction in our Constitution.  Fortunately, Judge Forman was a friend of Einstein's.  Forman stopped Gödel short and forced the hearing to a successful conclusion.

After 1947, this story became a favorite.  It has been told and retold in many variations.  It's one of the better known Einstein stories, and probably the best-known story about Kurt Gödel.  In a draft dated 1971, Morgenstern wrote an authentic account up for publication.  This eventually became the Lost Morgenstern Document.

Judge Forman died in August 1978.  Judge Forman had bent some rules at the hearing, which may have made the others reticent.  But Forman outlived the other three.  Einstein had died back in 1955, Morgenstern the previous year, and Gödel a few months earlier, in January.

At some point, Dorothy Morgenstern, Oskar's widow, sent a copy of the Morgenstern Document to the Institute for Advanced Studies (IAS), where Morgenstern, Einstein and Gödel had all worked.  Presumably this was after Oskar's death, but even that is not totally certain.  Dorothy's cover note is dated "August 30".  She gives no year.

Dorothy Morgenstern probably sent the Morgenstern Document to the IAS before 1983, because on 17 October of that year, John Dawson interviewed her as part of his research for his biography of Gödel.  At that point, Dorothy no longer remembered where the Morgenstern Document was. The very thorough Dawson tried to locate it in Morgenstern's papers at Duke University and among Gödel's papers in Princeton's Firestone Library, but without success.  Dawson came to doubt that the Lost Morgenstern Document had ever actually existed.

Second-hand accounts of Gödel's hearing started to appear as early as 1978.  A 1986 account is especially striking, because it appears in Gödel's Collected WorksCollected Works is for almost all purposes a source so reliable that it can used with confidence to check the others.  It is quite willing to be dryasdust if that's what it takes to be absolutely meticulous.

All the more surprising, then, to find in Collected Works a version of the hearing with lively dialogue.  Only if the reader delves into the footnotes does he learn that this dialogue comes from a source which mislocated the hearing from Trenton to Washington.  The footnote goes on to admit that, since the source was in German, the dialogue must have been through a double translation, from English to German and back again.

In fact there was probably only one translation.  Because thanks to the Lost Morgenstern Document, we now know that the dialogue that appears in Collected Works was invented.

In 1997 Dawson published Logical Dilemmas.  Confronted with the problem of trafficking in hearsay, Collected Works had chosen to dive in face first.  Dawson was more prudent.  He restricted himself to what Dorothy Morgenstern had told him.  Her knowledge was second-hand, and we now know that on this matter her memory was not good, but of all the possible second-hand sources she could be thought to be the least bad -- she certainly must have heard Oskar tell the story many times.  Until 2008 Dawson remained the only careful source for Gödel's citizenship hearing, and Logical Dilemmas remains the most reliable source for Gödel biography.

In Spring 2006, the IAS Letter published an account of Gödel's citizenship hearing with this unpromising beginning:  "On September 13, 1971, Oskar Morgenstern recorded the following memory of Kurt Gödel’s 1948 Trenton interview with an official of the Immigration and Naturalization Service (INS)."  Whoever wrote that sentence knew little about the hearing. While Gödel took the oath of citizenship in 1948, his hearing was in 1947.  And the hearing took place before a District Court Judge, not an INS official.  But we now know that the first part of this sentence was correct, and that the sentence indeed introduced an edited version of the Lost Morgenstern Document.

John Dawson saw this account in the IAS Letter and passed it over as yet another second-hand account of the hearing masquerading as the real thing.  The Letter appeared on the Web, and a version of its account of the hearing made its way onto another IAS web page.

In November 2008, I edited the account of the hearing on Wikipedia's Gödel page.  I changed it to follow what was then by far the most reliable version of the story -- the one in Dawson's biography.  Following up, I used Google to search for Web links on the hearing, and found an IAS Web page with the Morgenstern account.  For my Wikipedia edit, I'd reread Dawson.  I had seen his mention of a supposed Lost Morgenstern Document, a document which Dawson was not convinced had ever existed.  On careful reading, I realized that, despite its erroneous first sentence, the account on the IAS web page was probably what it claimed to be.  Morgenstern's Lost Document not only existed, I was reading it.

To confirm my idea, on November 23, 2008, I emailed John Dawson, who I'd never previously contacted.  I drew his attention back to the IAS account, pointing out that if it was not authentic, then it was an improbably expert and painstaking forgery.  The next day, Dawson replied.  He'd contacted the IAS, and confirmed that the account on the IAS website was in fact based on the Lost Morgenstern Document, which they still had in their possession. Dawson sent me the PDF that I have put on the Web.

Alas, the no longer Lost Morgenstern Document gives no definite answer as to what Gödel's proof was.  In my concluding post, I'll discuss what it does say.

Tuesday, January 6, 2009

Gödel and the Constitution III: Psych-out

On 5 December 1947, Albert Einstein set himself the task of psyching out the world's greatest mathematician. His partner and wheel-man in this venture was Oskar Morgenstern, the co-inventor of game theory.

Their motive was not frivolous. The target was Kurt Godel, whose citizenship hearing was scheduled in Trenton, New Jersey for that day. In studying for the questions he would be asked at the hearing, Gödel decided that he had discovered a contradiction in the U.S. Constitution. Gödel believed this contradiction would allow the U.S. to be turned, quite legally, into a dictatorship. Gödel was sure that this discovery needed to be shared.

Einstein and Morgenstern were sure that Gödel's citizenship hearing would turn into a world-class fiasco if he were to start proving logico-philosopical contradictions in Constitutional Law before the wrong judge. And more was at stake than bureaucratic delay. Gödel was an Austrian citizen, the Cold War was starting up, and there were Russian occupation troops in Austria. Gödel might talk his way into a real bind.

On the newsreels, Einstein looks like a genial, harmless eccentric. That's one side of him, and it's the side he liked the public to see. But Einstein was shrewd about people and politics, and he could be ruthless if he thought the situation justified it.

"Are you really well prepared for this examination?" Einstein said to Gödel once they were on the way to Trenton. Gödel has sat in the back, and Einstein turned around as he said it. From behind the steering wheel, Morgenstern noticed the effect.  Gödel was very worried, which was just what Einstein intended. Einstein's next task was to keep Gödel just as upset all the way to Trenton.

Einstein abruptly changed the subject away from the upcoming hearing, to a book he had just read -- a very detailed study on the history of the Russian Church. Gödel wanted to talk about his upcoming hearing, but a sardonic Einstein always turned the conversation back to the religious history of the Russias. As they neared Trenton, Morgenstern threaded them through the increasingly dense traffic, while Einstein wove more detail into his tapestry of theology and statecraft.

Listening to Einstein's tale of a Russian Church steering its way between Roman Catholicism and Eastern Orthodoxy, Gödel grew more and more worried about whether he'd pass the examination. He became less and less interested in proving theorems about the U.S. Constitution.  By the time the three came before the judge, Einstein and Morgenstern had Gödel where they wanted him.

But things unraveled with Judge Philip Forman's very first question. "What kind of government did you have in Austria?", he asked.

Gödel told Forman that it had been a republic but had been turned into a dictatorship.  Einstein and Morgenstern squirmed.

"Oh! This is very bad," said Judge Forman. "This could not happen in this country."

"Oh, yes," Gödel answered, "I can prove it."

That they had come before Judge Forman was a stroke of luck. Forman was a friend of Einstein's.  After a brief discussion, Forman told Gödel that he need not go into more detail on the dictatorship issue and force-marched the hearing to a successful end.

This account of the hearing comes from a first hand account by Oskar Morgenstern. This account was lost for many decades, but in November 2008 I rediscovered it. In my next post, I'll finish the story of how the Lost Morgenstern Document came back to light.

Wednesday, December 10, 2008

Gödel and the Constitution II: The Lost Morgenstern Document

The great mathematician Kurt Gödel thought he found a contradiction in the U.S. Constitution. He came upon it in 1947, while preparing for the questions he would be asked at his citizenship hearing, and became obsessed with it to the point where it seemed likely to torpedo his chances at citizenship. Gödel's friends, Albert Einstein and Oskar Morgenstern joined forces to prevent this from happening.

Until November 2008, there was a major obstacle to taking this story seriously as history. We know that Gödel had a citizenship hearing in 1947. Judge Philip Forman presided and Einstein and Morgenstern were there as witnesses. But the rest of the story depended completely on hearsay.

All participants at the hearing have been dead for 30 years. We had no first-hand account of the hearing from any of them. According to John Dawson, Gödel's very capable and thorough biographer, Morgenstern claimed to have written up an account for publication. But Dawson couldn't find it. To me that meant fuhgeddaboudit. But on Nov 23, 2008, much to my own surprise, I found the Lost Morgenstern Document.

By coincidence, I've written a novel that revolves around the serendipitous finding of lost Gödel documents. In The God Proof, the main character is sitting in his office when a woman shows up carrying a briefcase with $20,000 in cash and two long missing Gödel notebooks. The woman is famous, rich, mysterious, beautiful and in trouble. Unfortunately, that's not how I found the Lost Morgenstern Document. A shame, too, since I could use the cash.

My real-life discovery of the Lost Morgenstern Document started with Wikipedia's article on Kurt Gödel. I'd revised its account of the citizenship hearing to stick to the facts as related in Dawson's biography. While Googling around, I hit upon a page that struck me as odd.

At first glance, it was Yet Another Retelling of the citizenship hearing, a bit more shaky than most. It described itself as an account of "Gödel's 1948 Trenton interview with an official of the Immigration Service." The hearing did take place in Trenton, but it was in front of a U.S. District Court Judge. And while Gödel took his citizenship oath in 1948, the hearing took place on 5 December 1947.

I'm not sure why I kept on reading. Possibly I wanted to check out how another writer handled the "lost document" trope. The "false document" method is a very powerful way to tell a story, but hard to do right. On one hand, it takes work to make the fictional document seem authentic. On the other hand, for the story to read well, the fictional document has to avoid the gaps, detours and general clumsiness of real-life documentation.

This writer was very convincing, but his story-telling was awkward. Which struck me as strange. Good yarnsmanship is not rare. Less common is the ability to catch the voice of someone like Morgenstern. This writer had Morgenstern nailed. What if the writer was Morgenstern?

Going back to the account, I looked for three signs of genuineness. First, if this was the Lost Morgenstern Document, I'd expect the writer to be perfect on any facts that Morgenstern would know. And, except for that screwy first sentence, the writer knew what Morgenstern knew. But the opening sentence used the third person and was outside of the quote marks. It could have been an introduction, added by another writer.

The second sign was detail not in previous accounts. This writer had lots of it. The writer said that he drove and that he picked up Gödel first. Gödel sat in back. He then drove to Mercer Street to pick up Einstein. The hearing was in a "big room". Gödel sat between Einstein and Morgenstern. And so on.

The third sign was the clincher. I looked for something which was unexpected but which seemed "right" in hindsight. And I found something new in the story which, once I thought about it, fit perfectly.

None of the retellings of the citizenship hearing story make the contest of intellects between Einstein and Gödel sound right. The Einstein in the hearsay versions was wishy-washy, the affable Einstein of the newsreels. The Einstein in the Lost Morgenstern Document was the real Einstein, brilliant and quite capable of ruthlessness when he thought it was important and in a good cause.

In my next post, I'll tell the story of Einstein and the Gödel psych-out.

Sunday, November 30, 2008

Gödel and the Constitution I: The Fatal Contradiction

On 5 December 1947, Kurt Gödel, the man Time magazine called the last century's greatest mathematician, had his citizenship hearing. One of Gödel's witnesses was the man the same issue of Time called the century's greatest person, Albert Einstein. The other witness was Oskar Morgenstern, co-inventor of game theory.

At the hearing, the prospective citizen has to answer a few basic questions. Not a big deal, you'd think, for the second greatest mind in the world, especially when he's got number one there to vouch for him. But Gödel, for better and for worse, was not like other people. In mathematics, Gödel could do the impossible. In the rest of life, Gödel had a way of making the easy difficult. Sixty years later, Gödel's citizenship hearing is legendary. Now, in 2008, decades after all the participants in that meeting have died, there's an important discovery about it.

Uniquely among mathematicians, Gödel was known for surprises. Most mathematicians prove things already believed to be true. Occasionally mathematicians prove things that other mathematicians weren't one hundred percent sure about. Rarely does a mathematician prove something most of the others thought must be false. And no mathematician had made a career of that kind of proof until Kurt Gödel came along.

When it came to this citizenship hearing, Einstein and Morgenstern were in no mood for surprises. So when Gödel told them he'd found a contradiction in the U.S. Constitution, one that would allow the U.S. to be turned into a dictatorship, they told him to forget it. But Gödel seemed to feel the need to share his discovery. If Gödel started expounding on defects in the U.S. Constitution to the wrong kind of judge, Einstein and Morgenstern knew there could be trouble.

In the decades since 1947, the tale of what happened at the hearing was told and retold, each time with differing incident and dialog. Certainly, there was a citizenship hearing. Probably Gödel had some kind of proof about the US constitution, one which had Morgenstern and Einstein worried. More than that I didn't think we'd ever know.

Not that there weren’t lots of stories. When I was a grad student, Gödel was still alive. In the halls and offices, I heard many a tale of Gödel's eccentric behavior. Over the years, I’ve learned that every one of those stories was unfounded and probably false.

I expected that none of the various recountings of the citizenship hearing was to be trusted. Faculty room yarnsmanship had "improved" them to the point where they were useless. I also expected that the hearsay versions omitted a lot of important details.

Now, to my surprise, we can know. I have discovered Morgenstern's original account of Gödel's citizenship hearing, lost to scholarship for decades. How I found it, I'll describe in my next post.

Thursday, August 21, 2008

Dawkins Revisit: A Compromise between Survival and Increase?

This blog post is a long delayed reply to a question Harshad asked in a comment to "Dawkins #5: 'As Much As Possible' is Vacuous". We're talking about Richard Dawkins's theories, set out in the popular The Selfish Gene and the scholarly The Extended Phenotype. Dawkins refutes the idea that natural selection can be competition of species or even individuals. He makes the case that natural selection is driven by competition between genes. In my series of posts, I take Dawkins arguments as a starting point but find that Dawkins is ambiguous about the goal of the "selfish genes".

Specifically, most of the time Dawkins says that genes are trying to maximize their chances of "survival" (The Extended Phenotype, p. 233) but sometimes he says they are trying to increase in number (Phenotype, p. 84). When Dawkins gives examples, the genes are usually trying to increase the number of "germline" genes. (Germline genes are those actually in reproductive lineages.)

This distinction (survival vs. increase) is not a verbal quibble. The two goals produce different mathematical models and these will usually make different predictions, probably including testably different predictions. I went on to try to settle the issue of survival vs. increase, looking at the internal coherence of the two ideas, and their consistency with Dawkins methodology. Here Harshad had questions. I had decided one of the two goals was probably right, and the other wrong. Harshad wondered whether some combination of the two might be at work.

Dawkins' materialist method is the major reason for thinking survival vs. increase must be decided entirely for one goal or the other. Natural selection is driven by "selfish genes", but (from my "Dawkins #1: Are His Genes Selfish Enough?"):
Closely related to the "increase" vs. "survival" question, is the question of the exact nature of "the unit of selfishness". It's the "gene", but "the gene" can either be the collection of all genes with the same phenotype at the same place in the chromosome (which I'll call the gene-type), or one individual member of that collection (which I'll call the gene-copy). While the English language is ambiguous, Dawkins is not. His examples and his more detailed explications clearly show that he thinks the gene-type is what is "selfish", and that gene-copies subordinate their individual interests to the gene-type.
If the gene-copy is the "unit of selfishness", survival is the goal. If the gene-type is the "unit of selfishness", increase is the goal. A mechanism where the two cooperate on some sort of shared goal can't be excluded, but it is hard to see how they can share responsibility in materialist terms.

The above brutally summarizes my previous Dawkins posts. I make these arguments much more carefully in them and I also examine the kind of combined goals Harshad suggests in detail.