oodles more godels

Godel, for example, knew that math was fucked. It's the best kept secret of the eggheads. Consider, for a moment, the numeral zero.

For those of you who pay no attention to the things that rule your lives (don't think the numeral zero rules your life? What's the difference between a millionaire and a billionaire?) the numeral zero didn't exist for the majority of human history. Okay, numerals didn't really exist as such for the majority of human history either, but the numeral zero didn't exist for the majority of the history of numerals. It was invented in Arabia or Persia or somewhere like that, in, um, the seventh century. Or the fifth, or maybe 280 BC. It's not important.

The sneaky tricky thing, though, is that the numeral zero has a secret identity. In normal everyday usage it is fundamentally just a place-holder for a better way of organizing numbers (most protonumeric societies just used a rote system which eventually, somewhere between fifteen and a hundred, terminated with a catch all word that signified =a lot.= Roman numerals are a half-assed attempt to systematize counting). With zero holding the place representing a double handfull (as one hand is used to keep track of handfulls you count first by extending each finger of one hand and then the thumb in turn and then by turning them down again, hence at =ten= the counting hand is a curled up fist, the origin of the cipher symbol) the enumeration system can be maintained indefinately with only nine numerals.

However, when zero is treated as a numeral itself and you try to do something normal (numeral?) with it like divide by it or take it's square root you inevitably end up with itself or else an irrational explosion of value, an approach to infinity. In this the secret identity of zero as the so-called empty set is revealed. Per Parmenides, the existence of nothing itself is in dispute, revealing why all equations involving zero are either self-reflexive or of an indeterminate value. Like I said, math is fucked.

klik if you demand tedious explanations of every little thing.