Kurt Gödel had been on my mind and it looks like I wasn't the only one. His incompleteness theorems should be required study.
Posted on 06/15/2009 11:19:50 PM PDT by Maelstorm
If you travel two hours southeast of Fairfield County and 70 years back in time, you may come upon two old scientists taking a leisurely walk home from the Institute for Advanced Study in Princeton. You'd instantly recognize the one with the bushy mustache, suspenders and wild white hair — that's Albert Einstein. But who is that impeccably dressed, clean-shaven gentleman with the wire-rimmed glasses next to him?
That's mathematician and philosopher Kurt Gödel. In Einstein's later years, he once confided to a friend that his own research "no longer meant much" and that he came into work only "to have the privilege of walking home with Gödel."
Gödel, like Einstein, did his most famous work in his mid-20s — he published his two breakthrough incompleteness theorems at the age of 25 — but continued working throughout his life. For Einstein's 70th birthday, Gödel gave him this present: a new solution to Einstein's equations of general relativity, one that allowed time travel.
Most of their conversations were secret, so without a time machine, perhaps made possible using Gödel's solution to Einstein's equation, we'll never know what these two titans talked about on their walks home.
In the fall of 1947, Gödel took the U.S. citizenship exam. Gödel was a "very thorough man," in the words of Oskar Morgenstern, the same friend to whom Einstein confided his joy in walking with Gödel. In preparation for the exam, Gödel looked all through "the history of the settlement of North America by human beings," diving into matters of constitutional law and finally into ultra-local study about Princeton.
We know from Morgenstern's writings that in "looking at the Constitution," Gödel, "to his distress ... found some inner contradictions" that could show how, "in a perfectly legal manner, it would be possible for somebody to become a dictator and set up a Fascist regime, never intended by those who drew up the Constitution."
No one knows exactly what the flaw was that Gödel uncovered, though speculation is that it had something to do with amendments or additions.
Let's put ourselves in Gödel's mind. His biggest contributions to logic were his incompleteness theorems. Mathematicians were searching for a set of axioms from which all truth would flow. Gödel proved this search was impossible. There would always be truths that the formal system could not prove, and there was no way to make the system large enough to make that problem go away. If you adjust that idea to apply to government, you might think Gödel was a libertarian.
Back in 1946, most of today's government agencies hadn't even been authorized or hadn't grown to any sizable power. The first permanent agency, the Interstate Commerce Commission, was created in 1887. It regulated trains and it was, of course, a failure (though Congress didn't abolish it until 1995).
We don't hear much about agencies but they pass laws, adjudicate violations, punish transgressors and have their own courts and enforcement arms. And the only real oversight on them is the Administrative Procedure Act, a bill passed in 1946, the same year we are snooping on Gödel and Einstein. The APA came about because of Franklin Roosevelt's unprecedentedly copious births of new agencies. He was the political octo-mom of the 20th century. More than half of the 51 agencies in existence at that time came from FDR in a few years.
How many U.S. government agencies do you think we have today? I just counted them from www.usa.gov. There are 557, each an ugly appendix trying to solve the problem du jour. And we know that there will always be problems the government cannot solve.
Perhaps Gödel recognized that the path leads to a country where big companies regulate themselves at our expense, when powerful agencies answer only to the president. Welcome to 2009.
During Gödel's citizenship exam, he brought Morgenstern and Einstein as witnesses. The examiner asked him about the form of government of his homeland, Austria, and Godel replied that it was a republic but "the constitution was such that it finally was changed into a dictatorship." The examiner asserted that this could not happen in America. "Oh, yes," Gödel said. "I can prove it."
Fast forward 70 years and the proof is right there.
I’ve mentioned Godel’s remarkable observation a number of times on this forum but it seems to go unnoticed.
He was basically told to take his oath but otherwise keep his yap shut.
I personally think he is one of the most fascinating men in history and the importance of his theorems is in the humbling of the mind of man.
“Walking with Godel”.
I think I read that play,in college.
Whenever I ponder the breadth of human intellect, names like Feynman, Einstein and Godel are concentrated at one end while names like Obama and Clinton cluster at the other.
so how did it work?
I read it while I was waiting for somebody.
(Who never showed up!)
Godel never revealed the details of his observation. He only hinted that within the legal framework of the Constitution it was possible for a malevolent politician to legally usurp power and become a dictator. When Einstein and Morgenstern heard of this they basically told him in no uncertain terms that it would be unwise to piss off the oath examiner and bite his tongue.
bookmark for later
It’s also interesting to note that Harry Mudd’s androids were evidently unaware of Godel’s work.
Oh, yes, and Godel proved the existence of God. Well, not exactly (given the limitations of the systems within which he was working, which he himself had circumscribed). But he did codify the Ontological argument for the existence of God into formal symbolic logic and set theory, and discovered both to his delight and dismay that his (atheist) friend Bertrand Russell was right - it was far more powerful than it appeared.
He was also a closet Lutheran, but not a churchgoer, who read the Bible on Sundays in bed with his wife. She didn't divulge that one until after his death. It wouldn't have fit the image, one supposes...not that Godel would have remotely cared. Fascinating fellow.
When the Constitution was written honor meant everything.
Now it means a good deal less.
Who needs to do it legally WHEN THE MEDIA AND THE COURTS IGNORES ALL THE ILLEGAL STUFF?!?!?!
LEGAL???? I’m afraid Marx and Stalin had a little bit of an edge on this guy.
I bet the flaw has something to do with Czars
Im pretty sure from watching MSNBC that Einstein was stupid
Since the Supreme Court moves slowly, establishing a dictatorship would be fairly simple as citizens and law enforcement are prone to obey the law.
That law can be made to be too complex for the average person to understand and passed so quickly as to give the dictator sweeping powers for a long enough time to seize control of the Supreme Court or render it powerless.
All political allegiances aside, we live in the scariest of times.
Franklin’s description of the new government as a “... a republic, if you can keep it ...” still applies. There’s no substitute for an informed and pro-active electorate. Expecting any document written by human hands (even the best) to protect our liberties in some automatic fashion - that’s probably the road to the exact type of fascism to which Godel was referring.
The entire workings of our system was revealed to me once by the seemingly innocuous phrase “we have the best government money can buy”.
What?
And for a good while later as well... How many duels was Andrew Jackson involved in? And how many people fled to avoid dying in a duel with Jackson?
Care to guess what would have happened to a "comedian" who made a joke like the one Letterman made at Sara Palin's expense?
Mark
It shouldn't take a Gödel or an Einstein to noodle that one. The solution is to ignore the Constitution. All that is necessary to accomplish that are people willing to exchange America’s Republic for a Democracy. With the consent of the majority, ignoring laws is but a trifle.
I have always found Feynman’s work and life very interesting. He had a way of looking at things from a very different perspective, but I guess that is what made him so successful in his field. He was definitely not what you would call a dry and boring person, though.
Details, please?
Cheers!
When the Constitution was written honor meant everything.
Now it means a good deal less...."
That may have been the post of the year.
Oh God No!
While he is not my type of personality, the guy had a lot of a lot of things in spades. It his book “Surely You’re Joking Mr. Feynman”, there were two parts that completely amazed and amused me.
In one chapter, he talks about being at Los Alamos and somehow getting interested in safe cracking. He found that it is pretty much a myth to crack a safe cold. But what he DID find was there were lots of ways to cheat at it to get some components of the combinations. He found that one could often find out the last number while a safe was open and being used, which if you knew one of the numbers, mathematically it made the problem of mechanically trying combinations much easier. Or, you could simply use human engineering to determine it by finding out where on their desk they wrote the combination. Or, if you got to know the brand of safe, many people left it on the default factory combination. It was as funny as could be. He developed a reputation as a safecracker, which amused him greatly. He did like to see untalented hacks put in their place, and would torture them with ruses like this...
The other thing was when he served on the school textbook committee for a school district (textbook quality was a pet peeve of his) he had them deliver a big crate of all books under consideration to his house, and he went through all of them, outlining, highlighting, making notes, categorizing and analyzing. When he went to the meeting to choose the books, he was shocked to find out that it was all a corrupt scam...they already knew what books were going to be chosen in advance due to kickbacks, bribes and such to the members of the committee. In his naivete, he had no idea!
He was quite a guy.
Never fear, Mr. SpaceBar... 
Mister Peabody and I will use the wayback machine to go back and make sure everyone on Free Republic knows without any shadow of a doubt that you quoted Kurt Gödel numerous times!
Gadzooks! That Sherman is some boy, isn't he, Space? And... 
the little peckerwood makes one hell of a martini!
bite me bender.
But of course -
Well, it seems perfectly obvious to me. ;-)
HERE is the source article with more English words and fewer squiggly lines. Mathematicians only use them to piss people off anyway. And don't get me started on the dang Greek alphabet...
Hehehe...that has a certain ‘ring’ to it.
Actually MSNBC has convinced me that Einstein was an extraordinarily intelligent man ... involved in a secret homosexual relationship with Godel.
/sarc
This reminds me of Phil Zimmerman's description of his PGP (Pretty Good Privacy) encryption tool.
As far as encryption algorithms go it was among the best of breeds when it came out, so why did he only call it "pretty good"?
Because you could hack into computer files through finding the password written down, using the default password, guessing at a password, monitoring the key clicks, tricking the user into giving you the password, etc.
God bump
I have long believed that we should take the park in Weehauken, NJ, where Burr shot Hamilton, and turn it into our National Dueling Ground. It would solve a lot of problems.
Money quote from that thread:
"These developments have lead to a new physics in which the dynamics of the 3-space have been formulated, together with the required generalisations of the Maxwell equations (as first suggested by Hertz in 1890 [3])"
And your first term had what looked like a D'Alembertian, so I was thinking, "WTFrick are they doing with a D'Alembertian in 3-space?"
So, thanks for posting, I'm happily in over my head as usual with your information.
Cheers!
It'd be interesting to see how he reconciled the claims of morality as absolute but transcendent, or whether God was "necessary" to morality, given his eponymous theorem.
Cheers!
Totally agree.
St. Anselm's ontological argument, in its most succinct form, is as follows: "God, by definition, is that than which a greater cannot be thought. God exists in the understanding. If God exists in the understanding, we could imagine Him to be greater by existing in reality. Therefore, God must exist."
But is it the case that God exists in the understanding? I would suggest that the expression "exists in the understanding" might well belong with the systematically ambiguous expressions "is definable", "is nameable", "is satisfiable", and so on. Check out this Berry Paradox article.
As for the implication, "if God exists in the understanding, we could imagine Him to be greater by existing in reality", this would not be true if reality bites.
Hey, maybe Lickspittle Chrissy Matthews is onto something...I think I feel a tingling in my leg... ;-)
Thank you for brightening my day.
(I’m writing some obituary and eulogy type stuff and it is not very happiness inducing.)
Killed the thread. Way to go!
And of course it leaves out the fact that one can arbitrarily invent a new symbol to denote almost anything -- "The artist formerly known as Prince" comes to mind:
Just to make it creepier, he *does* hail from Minneapolis (his recording studios are in Chanhassen); and he converted to be a Jehovah's Witness of all things.
Cheers!
Cheers!
17
Or the understatement, unfortunately.
“There’s only one real flaw in the Constitution. It relies on the honor of political parties to vet their own candidates.”
The Constitution as originally written did not anticipate party politics as all.
“The presidential election of 1800 was one of the most dramatic in history. Jefferson had chosen Aaron Burr to be his vice presidential Democratic-Republican party running mate against the Federalist party’s John Adams. Jefferson’s seventy-three electoral votes in the electoral college easily defeated John Adam’s sixty-five, but Aaron Burr also received seventy-three electoral votes. The electoral college had not been set up for formal party politics and to determine which candidate, Burr or Jefferson, would be president, the election was sent to the House of Representitives to be resolved.
“The Federalists in Congress favored Burr over Jefferson and for six days neither received a majority vote in the house. Not until Alexander Hamilton, in spite of his opposition to Jefferson, supported him over his fellow New Yorker, Burr, whom he bitterly disliked, calling him “deficient in honesty,” and “the last man in the United States to be supported by the Federalists” was the election finally resolved with Jefferson’s election on February 17, 1801, with Burr named as Vice President.”
It is, as a matter of fact, party politics that has destroyed the possibility of a republican form of government intended by the Constitution. I agree with Jefferson, “If I could not go to heaven but with a party, I would not go there at all.”
Hank
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