My quest to make some sense out of randomness, logic and Islam led me to the Theory of Incompletion. It is a beautiful theory on its own. It says how any theory or any law that we might have now can be nullified with new discoveries and invention and goes on to state that logic in itself does not exist: which did not lead to randomness (randomness itself had been known for a long time) but made it completely unavoidable in modern day Physics.
I hope, if you are still reading this, know that you can not predict exactly what’s going to happen because nature itself is non-deterministic: you can only predict probabilities. Thats where randomness becomes just so important. Poor Einstein, he was never able to prove that there are some hidden variables which could perhaps bring back the good old days of deterministic Newtonian Physics. Einstein was a physist, he was never scared of randomness but he still firmly believed that there must be something that could eliminate randomness, a true challenge to the Theory of Incompletion.
My own research that I have often been whining about is about randomness in time series and I somehow stumbled upon something else which can possibly be used to quantify the Theory of Incompletion: The number of wisdom.
So what is the number of wisdom? Chaitin discovered a number (called Ω, ‘Omega’) with the amazing property that it is “perfectly well-defined mathematically, but you can never know its digits, you can never know what the digits in the decimal expansion of this real number are. Every one of these digits has got to be from 0 to 9, but you can’t know what it is, because the digits are accidental, they’re random. The digits of this number are so delicately balanced between one possibility and another, that we will never know what they are!” (OK, I myself dont know wat I just said!!! 😛 )
Lets track back a lil and see what it actually is: In simple words, Chaitin is only trying to say that if we can find the exact digits of the ‘number of wisdom’, all sorts of randomness can be eliminated and also prove that mathematics has no limits (we already know that Theory of Incompletion says that mathematics is incomplete and has boundaries: wat is true within one boundary will be false in some other boundary)
I am intrigued, fascinated, to say the least! 😀