godel.

"You can't put everything into boxes. Everything doesn't just fit into neat little shoeboxes."

She said it, angry at me, angry that someone could still believe in such an unenlighetened idea as the shoeboxes. I guess she was angry at me, she was angry at most everyone. She was arguing with someone else, but as a believer in the shoeboxes, I felt attacked just the same.

Godel's Theorem has many profound implications, both for science and for philosophy. ...

Godel believed in the shoeboxes, I'm sure of it, though if I ever said that to the math teacher that told me about Godel and his theorem, she'd think I was crazy. Actually, it was Godel that was crazy.

I didn't defend myself, didn't defend the shoeboxes. Maybe I looked like I wasn't even listening to the two people arguing, one my friend, the other a bi-polar water faucet that ran scalding or freezing, so I could never do more than dip my toe before jerking back and hiding in the corner. I didn't want to look like I was listening - I wanted to look detached from them, as I if I were quietly having my own deep thoughts. I saw no point in contributing. It's not like I could change anyone's mind on such a faith-based idea as that of the shoeboxes.

Godel's message is that mankind will never know the final secret of the universe by 'finitistic' or constructivistic thought alone;

No one believed Godel either. Not because he wasn't right, but because no one wanted to. People spent their whole careers looking for the shoeboxes, and then he went and said they didn't exist. In Godel's time, it was still very popular to believe in the shoeboxes. It was American to believe in the shoeboxes. Godel was German.

Now it's my time, and believing in the shoeboxes is almost a sign of unintelligence to those intelligent enough to not believe in them. "If you believe in them, then you obviously haven't thought about it, because I have, and that's not the conclusion I came up with." She never said that, and if you asked her, she would deny feeling that way, but she felt that way just the same. I had thought about it, years ago when it first occured to me that there may not be shoeboxes after all. And maybe I wasn't smart enough, because I did not come to the same conclusion as she did when she thought about it.

it's impossible for human beings ever to formulate a complete description of the natural numbers.

Poor Godel, he was one of those who spent his career looking for the shoeboxes, but he was the methodical type. One step at a time, that was the way to the shoeboxes. The first step was to simply prove the shoeboxes existed. But then Godel proved the opposite, and the rest of the steps became pointless.

I was listening to them, though. The fact that I remember the evening at all shows that. It was at night, a mid-summer night without the dreams. We sat on the edge of the parking lot next to the soccer field. It was early in the evening, before curfew beause I was never the kind to break curfew. I was pretending not to listen and looking out into the field, watching rabbits as they hopped around, nibbled, and thought nothing about shoeboxes.

There will always be arithmetic truths that escape our ability to fence them in by any kind of finite analysis.

Godel thought about shoeboxes, though he didn't know it. The shoeboxes are a philosophical idea, or maybe a metaphor for a philosophical idea, and Godel was a mathematician. The two things don't overlap much. I wasn't good with philosophy. That's why I studied math, to avoid it. To avoid those conversations where I listen and don't say much, not because I don't have anything to say, but because I can't say it well enough to come across as an intelligent human being. Well, sometimes I don't have anything to say. Either way, I don't say much.

And I never said a word that night. I never stood up and yelled a defense of my beliefs so forceful and eloqent that the rabbits didn't even run away, but applauded their little rabbit paws. Staying out of the discussion was as characteristic of me as never breaking curfew. Predictable, aloof, safe, boring.

As Rudy Rucker has expressed it, Godel's Theorem leaves scientists in a position similar to that of Joseph K. in Kafka's novel 'The Trial'. We scurry around, running up and down endless corridors, buttonholing people, going in and out of offices, and, in general, conducting investigations. But we will never achieve ultimate success; there is no final verdict in the court of science leading to absolute truth.

My math teacher used Godel as an example of the price of brilliance. After Godel disproved the existence of the shoeboxes, he went crazy. He screwed up the beliefs of so many mathematicians, himself included, that I guess it got to him. He starved himself to death because he thought everyone was trying to poison him and would not eat. I'd like to be brilliant without the price. If I could find the IQ with the maximum amount of intelligence and the minimum amount of mental and emotional instability, I'd like to have that. But I suppose it's too late for all that now.

She wasn't a math person. I suppose she was good at math, because she was probably smart enough to be good at everything. But she was interested in saving the world, social issues and deep thoughts and other things I didn't care about. I doubt if she knew anything about Godel. I didn't know anything about Godel then either, and wouldn't know for another four years or so. I'm glad she didn't know because I would have hated to hear her use Godel as evidence. Godel would've hated it too.

However, Rucker notes, "To understand the labyrinthine nature of the castle [i.e., court] is, somehow, to be free of it."

Really, Godel didn't prove that there were no shoeboxes. Godel's Incompleteness Theorem, such a great name for a theorem, proved that there was no way to represent mathematics in its entirety by a simple set of axioms or truths. You can't take half a dozen or even half a million true statements and derive the rest of math from them. If anything, he proved that there were no shoeboxes when it came to math. But if mathematics doesn't fit into shoeboxes, how can life, the universe, everything?

And there's no understanding of the court of science that digs deeper into its foundations that the understanding given by Godel's Theorem.

Maybe it's the same, and maybe it isn't. Maybe there are shoeboxes, neat little shoeboxes that Someone could put the whole world into. Maybe the likes of she and of I and of Godel are too small and too simple to see them. For all our intelligence, we don't know everything. Maybe there are shoeboxes, and therefore Someone large enough to put us all into our place. She doesn't know for sure, I don't know for sure, thought we're both arrogant enough to think we do.

I guess Godel knows now, but he's not telling.



From Casti, J.L. "Searching for Certainty", Abacus, London. (pp.381-383)

Godel's Incompleteness Theorem