"For Turing it wasn't quite so bad. ...uring could see that the solution is to understand that mathematics was computational all along. ...For instance pi in classical mathematics is a value. It's also a function, but it's the same thing. In computation, a function is only a value when you can compute it, and if you cannot compute the last digit of pi, you only have a function. You can plug this function into your local sun, let it run until the sun burns out... This is it. This is the last digit of pi you will know. But it also means that there can be no process in the physical universe, or in any physically realized computer that depends on having known the last digit of pi. ...Which means that there are parts of physics that are defined in such a way that cannot strictly be true, because, assuming that this could be true leads into contradictions."
More by Joscha Bach
See allResonant Thoughts
"I do not now make any comment upon the mode in which this country has been put into possession of India. I accept that possession as a fact. There we are; we do not know how to leave it, and therefore…"
Explore Further
Related Quotes
"Let us all be men and women in full. Let us expect from ourselves more than we think we can give, more than…"
— Michael Mullen"May I therefore acknowledge the tender glow of health induced by reading, as I sat here in the morning sun,…"
— James McNeill Whistler"I know it's a very human thing to say 'Is there anything I can do', but in this case I would only entertain…"
— Terry Pratchett"This applies to family horror and to horror in general, but there was a real aversion in our business to th…"
— Dan Angel"Errors of knowledge are not breaches of morality; no proper moral code can demand infallibility or omniscie…"
— Ayn Rand"Unless we have a Government with capable officers to run it, then our Government will fall tomorrow. I want…"
— Jomo Kenyatta