He suddenly felt nothing, or rather Nothing, a pre-tornadic stillness of zero sensation, as if he were the very space he occupied.
But if we play it safe, the problem is that we may be losing out, and I believe we are.
As Hamlet tells his friend, ``There are more things in heaven and earth, Horatio, than are dreamt of in your philosophy. '' Well then, we must try harder to dream!
So in the end it wasn't Gödel, it wasn't Turing, and it wasn't my results that are making mathematics go into an experimental mathematics direction, in a quasi-empirical direction. The reason why mathematicians are changing their working habits is the computer. I think that this is an excellent joke!
Bertrand Russell started off as a mathematician and then degenerated into a philosopher and finally into a humanist; he went downhill rapidly!
A random sequence is one that cannot be algorithmically compressed : the shortest description of a random sequence is simply the sequence itself.
In a way, math isn't the art of answering mathematical questions, it is the art of asking the right questions, the questions that give you insight, the ones that lead you in interesting directions, the ones that connect with lots of other interesting questions -the ones with beautiful answers.
You see, for me [art]'s not one of life's ornaments, rococo relaxation to be greeted affably after a day of hard work; I'm inverted on this : for me it's my very breath, the one thing necessary, and all else is excretion and a latrine.
Mankind are greater gainers by suffering each other to live as seems good to themselves, than by compelling each to live as seems good to the rest.
Meanwhile, followers of Eastern religions are sitting in the middle of their minds, experiencing a bliss and a level of consciousness that Western man can't begin to approach.
I was born in Memphis. There was music all around me, really deep and special music. I heard all these great masters at a young age. There was a great genius in my town, Phineas Newborn, who is one of the greatest pianists ever on the planet. He took me under his wings at about 9 and he put me on the right track.