Number Nex

A Brief History of Number Nex
Many years ago, on a Sunday night, I decided to stop everything else in order only to look for the most primitive ideas in the world; ideas that would permeate all the metaphysical systems, that would be hidden deep in the heart of divine Philosophy, Mathematics, Logic... I spent almost the same time Ulysses did to go and come back, but finally I found what I was looking for. It's a terrible thing to find what you were searching for so long, except if you are a poet; reason is quit simple: only the poets are right. It's thrilling, but I also have here my scars from the boars. A complex simplicity, such are the most primitive ideas: naught, negation and uncertainty. Pure conquest of the human mind; nothing in the universe denotes them; to Wittgenstein we shouldn't even to talk about them. So, I started to look for their presence in Mathematics. I got surprised when I found them. From naught to the empty zero, it was a piece of cake. I thought negation would be even easier; fortunately, it was not. At first I turn to negative numbers, where negation is only a "kin mark", a sign; negation, the one I was looking for, isn't only a sign, a mark; it's also action, movement, as in Geometry. So, I flipped to the other possibility, that disturbs me since I was a teen: the rules of sign, where I found it. In the way I also found two attempts, separated by 1700 years, to demonstrate the same rule, just the most intriguing of all, the alchemist rule that transform negation into affirmation: (-)(-)=(+)(+). In spite of to like Diofantus' geometrical demonstration most, none of them convinced me, neither Diofantus, nor Birkhoff&Maclane's prove (arguments in text). Trying to overcome these difficulties I found a pure geometrical - and empirically falseable - model to all and each one of the rules of sign, whose finished product is Number Nex. Nex is the third; it can be false, nex or true. All these was hidden in a paper strip; it's so simple that will be difficult to explain. Meanwhile, what left from tenebrous Certainty, reigned sober, and bravely resisted up to 1930, when the young Gödel deciphers her, freeing the divine Mathematics and related systems, from this terrible burden, this firm ground. Up to the day I met Gödel in Venezia, to look for uncertainty in math wasn't an ease task; fortunately the Theorem of Incompleteness fitted perfect. As I had found all I were looking for, I wrote down my findings and took a break - and bought a boat and lived one year in Amazon river and some of its beautiful tributaries. Then I came back, set this site and invited you to look over. Hope you enjoy. Sik
PS. To a quick look on number nex, go to basic ideas (graphics)