Information Needs Quantum Indeterminacy

S. Kauffman

S. Kauffman

Quote:Now recall Artistotle's Law of the Excluded Middle: Either "A" is true or "Not A" is true, there is nothing in the middle. Hence, "A and Not A" is a contradiction.

But the claim, central to information theory, that the first bit can possibly be 1 and simultaneously possibly be 0 does not obey Aristole's law of the excluded middle. Nor does the premise that possibly (11111) or possibly (01111) will be chosen to send down the channel. This too does not obey the Law of the Excluded Middle.

Quote:Now start a purely classical, say Laplacian universe going, with all positions and momenta of all particles known to a vast computer in the sky. Using Netwon's laws, says Laplace, this computer could know the entire future and past of the universe.

But that means that either the symbol sequence (11111) or the symbol sequence (011111) was predestined to come into existence. Not "possibly both." In classical physics, even with deterministic chaos, it is not true that both (11111) and (011111) can have come into existence deterministically.

But this seems to mean that at the very heart of information theory, we need to appeal to quantum uncertainty.

'Historically, we may regard materialism as a system of dogma set up to combat orthodox dogma...Accordingly we find that, as ancient orthodoxies disintegrate, materialism more and more gives way to scepticism.'

- Bertrand Russell

- Bertrand Russell