“The first incompleteness theorem states that no consistent system of axioms whose theorems can be listed by an ‘effective procedure’ (essentially, a computer program) is capable of proving all facts about the natural numbers. For any such system, there will always be statements about the natural numbers that are true, but that are unprovable within the system . . .“The second incompleteness theorem shows that if such a system is also capable of proving certain basic facts about the natural numbers, then one particular arithmetic truth the system cannot prove is the consistency of the system itself . . .” http://en.wikipedia.org/wiki/Godel’s_incompleteness_theorems
Old Doc could ramble before he had his latté.
Network theory feels like home to me. My thoughts flow through and around it, examples are everywhere, and they are of every size and activity. Kurt Gödel’s work, in contrast, is older but stranger, important because it centers on our believing mathematical things that can’t be proven to exist or proven not to exist. A part of me wants to unite Gödel’s ideas with what I understand of networks and women. Another part of me can’t handle the confusion.
Gödel, a philosopher born to be a Czech but in love with being an Austrian, wrote in German and did for mathematics what a different Czech, Franz Kafka, did for literature. Gödel upset a lot of mathematicians when he demonstrated that there is no area of mathematics—one that involves a certain amount of arithmetic—that is free of beliefs that can be neither proved nor disproved. It’s as if invisible holes and imagined platforms exist when you count from one to ten. Of course, you know that Kafka told us what it’s like to wake up as a beetle.
I sometimes think of women as Gödel’s angels who spin proofs, myths, and superstitions to anchor their faith and they pretend to do so with what they “know” to be facts. Thus, every conversation with a woman will not be about true or false but about her ideas that she wants you to accept as true or false; the conversation is her test that shows you do or don’t believe what she believes and that you share the platforms and holes in her thoughts. Agree and she stays; disagree and she leaves. Agree today and disagree tomorrow and she will shriek that you’re a liar.
Eve, our first woman, did a female-network thing when she trained Adam. First, she formed a weak link with a smooth talker named Satan while she ignored Adam’s strong link with God.
She next addled Adam when she told him, “This sentence is a lie.” She also formed a second weak link when she trained him early and often to say “Yes, dear.” “Yes dear,” of course, means “I agree with whatever you say, I want to watch NASCAR.”
Doc still doesn’t know what Gödel would say about Eve unless she could perform a certain amount of arithmetic . . .
