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.
Wednesday, December 10, 2008
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.
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?"):
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.
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.
Tuesday, February 19, 2008
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