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Fnord666 writes:

I came across an interesting blog post by Rudy Rucker from 2012 that I found quite interesting and thought I would share with my fellow Soylentils. It is titled "Memories of Kurt Gödel" and it is quite an interesting read.

Kurt Gödel was unquestionably the greatest logician of the century. He may also have been one of our greatest philosophers. When he died in 1978, one of the speakers at his memorial service made a provocative comparison of Gödel with Einstein ... and with Kafka.

Like Einstein, Gödel was German-speaking and sought a haven from the events of the Second World War in Princeton. And like Einstein, Gödel developed a structure of exact thought that forces everyone, scientist and layman alike, to look at the world in a new way.

The Kafkaesque aspect of Gödel's work and character is expressed in his famous Incompleteness Theorem of 1930. Although this theorem can be stated and proved in a rigorously mathematical way, what it seems to say is that rational thought can never penetrate to the final, ultimate truth. A bit more precisely, the Incompleteness Theorem shows that human beings can never formulate a correct and complete description of the set of natural numbers, {0, 1, 2, 3, . . .}. But if mathematicians cannot ever fully understand something as simple as number theory, then it is certainly too much to expect that science will ever expose any ultimate secret of the universe.

Wikipedia's page on Gödel's incompleteness theorems summarizes:

The first incompleteness theorem states that no consistent system of axioms whose theorems can be listed by an effective procedure (i.e., an algorithm) is capable of proving all truths about the arithmetic of the natural numbers. For any such formal system, there will always be statements about the natural numbers that are true, but that are unprovable within the system. The second incompleteness theorem, an extension of the first, shows that the system cannot demonstrate its own consistency.

Employing a diagonal argument, Gödel's incompleteness theorems were the first of several closely related theorems on the limitations of formal systems. They were followed by Tarski's undefinability theorem on the formal undefinability of truth, Church's proof that Hilbert's Entscheidungsproblem is unsolvable, and Turing's theorem that there is no algorithm to solve the halting problem.

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