Gödel's Proof

Nagel’s book is the most understandable explanation I’ve found about one of the most cosmically seminal math proofs: Godel’s incompleteness theorem.

It takes the idea of recursion and self-reference to the ultimate conclusion about truth, understanding, and boundaries of existence. This may sound hootie-tootie, but think of the sequence of abstraction in math: arithmetic, algebra, calculus, etc.

Once you add in recursion (self-reference), you’ve got the most important concepts underlying true understanding and productivity in software – something never discussed in computer science, and certainly not in practical programming.

Think about the so-called Von Neumann computer architecture, which underlies all… show more.

I attended Caltech my freshman year of college, expecting to learn the tools to help me find the answer to any question I had about the nature of reality. Before the first quarter started, I purchased a copy of Gödel’s Proof. This describes that given any logical system at least as complex as the axioms for arithmetic, there will be at least one statement that makes perfect sense that can neither be proven nor disproven from the axioms of that system. Some axioms for arithmetic, for example, are that for any two numbers a and b, a=a and a+b=b+a.… show more.