One of the leading mathematicians of the 20th century, Kurt Gödel is considered by many to have been the most sophisticated logical thinker the world has ever seen. His best known work, Gödel’s theorem, highlighted a fundamental inconsistency in the basic structure of mathematics. Of more interest to the general reader, however, is Gödel’s Loophole – which performs much the same trick for the Constitution of the United States: “He could show how in a perfectly legal manner it would be possible for somebody to become a dictator and set up a fascist regime”.

Of course, many people worry that a fascist takeover is just around the corner, but it’s something Gödel had experienced at first hand. His native Austria was annexed by the Nazis in 1938, and the following year he fled to America. He got a job at the Institute for Advanced Study in Princeton, where he befriended two other European refugees – the physicist Albert Einstein and the economist Oskar Morgenstern. They encouraged Gödel to apply for U.S. citizenship, and that’s when his study of the Constitution began in earnest. By the time he was ready to take his citizenship examination, in December 1947, he had discovered the “inner contradictions” that are now known as Gödel’s Loophole.

It never seems to have occurred to Gödel that – whether he was right or wrong – he ought to keep his mouth shut about this particular point. As Morgenstern says (in the only first-hand account of Gödel’s Loophole):

I tried to persuade him that he should avoid bringing up such matters at the examination before the court in Trenton, and I also told Einstein about it: he was horrified that such an idea had occurred to Gödel, and he also told him he should not worry about these things nor discuss that matter.

Many months went by and finally the date for the examination in Trenton came. […] The examiner first asked Einstein and then me whether we thought Gödel would make a good citizen. We assured him that this would certainly be the case, that he was a distinguished man, etc. And then he turned to Gödel and said, Now, Mr. Gödel, where do you come from?

Gödel:Where I come from? Austria.

The examiner:What kind of government did you have in Austria?

Gödel:It was a republic, but the constitution was such that it finally was changed into a dictatorship.

The examiner:Oh! This is very bad. This could not happen in this country.

Gödel:Oh, yes, I can prove it.So of all the possible questions, just that critical one was asked by the examiner. Einstein and I were horrified during this exchange; the examiner was intelligent enough to quickly quieten Gödel and broke off the examination at this point, greatly to our relief.

So what was Gödel’s Loophole? The truth is no-one knows – the details of his reasoning are as lost to history as the proof of Fermat’s Last Theorem. That hasn’t prevented people from speculating, of course, but all the suggestions I’ve seen are of the “sledgehammer to crack a nut” variety – for example a series of amendments that would end up in complete opposition to the original spirit of the Constitution. That strikes me as too blunt and straightforward to be worthy of Gödel. If there’s a common theme running through his work, it’s a profound obscurity and counter-intuitiveness. He was a bit like Einstein in that respect – arguably more so.

Gödel’s penchant for finding logical flaws in things (such as mathematics and the U.S. Constitution) even extended to Einstein’s own theory of General Relativity. Gödel was the first person to find a solution of Einstein’s equations – the Gödel Metric – which permitted time travel into the past. As far as he was concerned this proved Einstein was wrong, because of the paradoxical situations that would inevitably follow. Einstein himself wasn’t convinced, though – he felt that Gödel had simply shown that time, as it is usually perceived, was an illusion all along.

Another example of Gödel’s logic – at its most obscure – is his ontological proof of the existence of God (reproduced in the image below). Whether it’s right or wrong, it clearly requires a high degree of intellectual sophistication just to understand what he’s on about. Let’s hope the logical proof of Gödel’s Loophole – showing how a tyrannical dictatorship could be set up within the terms of the U.S. Constitution – is in a similar vein. After all, politicians aren’t renowned for their intellectual sophistication, are they?