Information Needs Quantum Indeterminacy?

Information Needs Quantum Indeterminacy

S. Kauffman

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.

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.

Information Needs Quantum Indeterminacy

S. Kauffman

 In short, if we think information is ontologically real, we seem stuck with its base in quantum mechanics and quantum ontological Possibiles. If we do not think information is ontologically real, I await elucidation.

I end by noting that information theory, Shannon or Kolmogrov, assumes a free willed agent who can possibly create the symbol sequences (11111) or possibly (01111), then also possibly choose to send ONE of these OR the other, down the channel.

I got all excited, when I read this a decade ago.  S. Kauffman, in an interview about the article, said it was just a "way to think about it" and he wasn't invested.

Still, the bolded part above: is what I believe, that reality includes a nexus of real-world probabilities (as information objects) with some independence of their presence in a fixed time or physical location.