“A Day Dawns” W. Zeitler [Piano]
Order of Chivalry: Truth W. Zeitler [Organ]
One of the major mathematicians of the 20th century was Kurt Gödel (1906–1978), who dropped a major thought bomb right in the middle of mathematics much like Einstein (1879-1955) dropped one in the middle of physics.
There were two major questions in Math World at the beginning of the 20th century, and they had implications for Science since you can’t do Science without major math. The first was: is math complete? Do we have just the right number of axioms to start with (not too many, not too few) to derive all the math we’ll ever need? The second was: is math consistent? We’re starting from some axioms (like geometry in high school) and deriving all this stuff, but are we going to derive some self-contradiction at some point? In 1930, a 25-year-old Gödel blew both questions out of the water with very unexpected results: 1) no math-system can ever be complete, even if you had an infinite computer that could derive more math infinitely fast, because incompleteness is baked into the very nature of math itself. And 2) no math-like system can prove its own consistency. And Gödel PROVED them both mathematically. (Think about that — it’s twisty!)
Gödel’s work wasn’t entirely without practical application: to prove his famous theorem he invented a ‘logic machine’ which he used in his papers. Others took his idea and began fleshing out how to build a working version, thereby founding Computer Science.
Gödel was born in Austria and went to the prestigious University of Vienna, where his monumental proof was his doctoral thesis! In 1933 Hitler came to power, and although Gödel was Lutheran, he LOOKED Jewish and associated with Jews, and that was more than enough to get you in serious trouble with the Nazis. Many of his colleagues left for England and America, but Gödel delayed too long. By the time he decided to leave, Germany was at war and the Atlantic was closed to Germans. The only way out was through Russia. Hitler and Stalin had signed an alliance (which Hitler would break in a few months by invading Russia). With powerful friends in America wrangling all the necessary visas in this last brief window of escape, Gödel and his wife Adele were able to travel EAST, taking the Trans-Siberian railway across Russia, and by ship from Japan to San Francisco (the U.S. wasn’t yet at war with Japan). The entire journey took six weeks. Gödel ended up at the Institute of Advanced Studies in Princeton, where Einstein was. They became good friends, taking long walks together daily.
Of course Gödel didn’t stop at his so-called Incompleteness Theorem. Gödel was deeply expert on Einstein’s Relativity, and demonstrated that if Relativity is true, then Time is an illusion. Einstein and the physics community couldn’t find fault with Gödel’s reasoning. Later, Stephen Hawking proposed an amendment to the Laws of Physics to make Gödel’s universe impossible.
Another paper, more to our interest, was a proof of the existence of God. He based it on the Ontological Proof for the existence of God, first articulated by Anselm of Canterbury in 1078. The gist of it is to show that assuming there isn’t a God leads to absurd conclusions, therefore there must be One. Gödel, who self-identified as a Lutheran, supercharged Anselm’s argument by recasting it in modern rigorous mathematical logic.
There are many instances of people who’s minds are so powerful in one direction that they are deeply fragile in others, and Gödel is a member of that set. He never had a strong constitution, and then paranoia set in. He was particularly fearful of being poisoned. Gödel trusted his wife implicitly, and she taste-tested all his food, nevertheless he was chronically undernourished. Finally, Adele herself had to enter hospital for an extended period, and Gödel starved to death, weighing 65 pounds at his passing. He was 72.