Ocean Lover
bean
ONE MORE....what will the 4,000th one be?????
This better be good BR...we've been waiting for days!
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BR's Beatin' Down...
- Thread starter Miss Kitty
- Start date
This better be good BR...we've been waiting for days! 
Beach Runner
beats on hood
In 1931 the Czech-born mathematician Kurt G?del demonstrated that within any given branch of mathematics, there would always be some propositions that cannot be proven either true or false using the rules and axioms of that mathematical branch itself (G?del's Incompleteness Theorem). One might be able to prove every conceivable statement about numbers within a system by going outside the system in order to come up with new rules and axioms, but by doing so one will only create a larger system with its own unprovable statements. The implication is that all logical systems of any complexity are, by definition, incomplete; each of them contains, at any given time, more true statements than it can possibly prove according to its own defining set of rules.
One metaphorical analog to G?del's Theorem which I find provocative suggests that ultimately, we cannot understand our own mind/brains. Just as we cannot see our faces with our own eyes, is it not inconceivable to expect that we cannot mirror our complete mental structures in the symbols which carry them out? All the limitative theorems of mathematics and the theory of computation suggest that once the ability to represent your own structure has reached a certain critical point, that is the kiss of death. It guarantees that you can never represent yourself totally.
Think about it. There are some things that are true that are unprovable. For example, just because we can't prove that there is a God, based on the limitations of our minds, that does not mean that there is no God. I find it very comforting that one of the most brilliant humans of the twentieth century has acknowledged his limitations as a human being.
One metaphorical analog to G?del's Theorem which I find provocative suggests that ultimately, we cannot understand our own mind/brains. Just as we cannot see our faces with our own eyes, is it not inconceivable to expect that we cannot mirror our complete mental structures in the symbols which carry them out? All the limitative theorems of mathematics and the theory of computation suggest that once the ability to represent your own structure has reached a certain critical point, that is the kiss of death. It guarantees that you can never represent yourself totally.
Think about it. There are some things that are true that are unprovable. For example, just because we can't prove that there is a God, based on the limitations of our minds, that does not mean that there is no God. I find it very comforting that one of the most brilliant humans of the twentieth century has acknowledged his limitations as a human being.
Miss Kitty
Meow
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seacrestkristi
Beach Fanatic
Now that's a helluva 4000, BR!!!
Ocean Lover
bean
Congrats to our mathy friend! 
