All consistent axiomatic formulations of number theory include undecidable propositions.
If anyone can let me know where the first one comes from, let me know, k?
I met a man who loved butterflies so much that he travelled the world in search of them. When he found a butterfly, he would kill it, preserve it, and display it as a wonderful example of his own skill.
But the skill was not his. The work was not his own. And the true beauty of each butterfly died as murdered in a jar, leaving a thin shell of the earlier wonder and a hollow memory of its glory.
I spoke to that man, asking him why -- he shrugged "Beacuse it's my job." I broke his jar, tore his net, sent his specimens scattering, the pages of his notebook adrift on the breeze.
Then he took up his pen, looked carefully at me, and asked, "Pardon me, what was that you just said? I really just must write it down."
You sense my loneliness, my bitterness at being shut out of life. My bitterness that I'm evil, that I don't deserve to be loved yet I love hungrily. My horror that I can never reveal myself to mortals. But these things don't stop me. As you said yourself once, I am very good at being what I am. These things merely now and then make me suffer, that's all.
--Anne Rice, The Vampire Lestat
There is no god but man.
Man has the right to live by his own law -- to live in the way that he wills to do: to work as he will: to play as he will: to rest as he will: to die when and how he will.
Man has the right to eat what he will: to drink what he will: to dwell where he will: to move as he will on the face of the earth.
Man has the right to think what he will: to speak what he will: to write what he will: to draw, paint, carve, etch, mold, build as he will: to dress as he will.
Man has the right to love as he will.
Man has the right to kill those who thwart these rights.
--The Equinox: A Journal of Scientific Illuminism, 1922 (edited by Aleister Crowley)
--as quoted in The Illuminatus! Triology by Robert Shea and Robert Anton Wilson
A human being should be able to change a diaper, plan an invasion, butcher a hog, conn a ship, design a building, write a sonnet, balance accounts, build a wall, set a bone, comfort the dying, take orders, give orders, cooperate, act alone, solve equations, analyse a new problem, pitch manure, program a computer, cook a tasty meal, fight efficiently, die gallantly. Specialization is for insects.
All men are created unequal.
Democracy is based on the assumption that a million men are wiser than one man. How's that again? I missed something.
Autocracy is based on the assumption that one man is wiser than a million men. Let's play that over again, too. Who decides?
Be wary of strong drink. It can make you shoot at tax collectors -- and miss.
Certainly the game is rigged. Don't let that stop you; if you don't bet, you can't win.
There is no conclusive evidence for life after death. But there is no evidence of any sort against it. Soon enough you will know. So why fret about it?
Delusions are often functional. A mother's opinions about her children's beauty, intelligence, goodness, et cetera ad nauseam, keep her from drowning them at birth.
I walked by Michael's office around sundown, just before I left home for a shower and a snack before coming back to stomp the bugs. He was playing a game on his monitor that I'd never seen before.
I asked him what it was and he told me it was something he had designed himself. It was a game about a beautiful kingdom on the edge of the world that saw time coming to an end.
However, the kingdom had found a way to trick God. It did this by converting its world into code -- into bits of light and electricity that would keep pace with time as it raced away from them. And thus the kingdom would live forever, after time had come to an end.
Michael said the citizens of the kingdom were allowed to do this becuase they had made it to the end of history without ever having had the blood of war spill on their soil. He said it would have been an affront to all good souls who had worked for a better world over the millennia not to engineer a system for preserving the finer thoughts after the millenium arrived and all ideologies died and people became animals once more.
-- Douglas Coupland, microserfs
Godel's Theorem V1:
To every omega-consistent recursive class kappa of formulae there correspond recursive class-signs r, such that neither v Gen r nor Neg (v Gen r) belongs to Flg (Kappa) (where v is the free variable of r).
Actually, it was in German, and perhaps you feel that it might as
well be in German anyway. So here is a paraphrase in more normal
English:
All consistent axiomatic formulations of number theory
include undecidable propositions.