We live smack in the middle of the IT age. Yet the foundations of the two reigning theories of information, Shannon's theory, and Kolmogorov's theory, require quantum indeterminacy. As far as I can tell, this is both true, and essentially unrecognized.
More, if we want to hold that information is "real," it forces us to abandon one of the three reigning interpretations of quantum mechanics, the beautiful Bohm version.
Why all of this stuff out of the blue?
Well consider Shannon's information theory. Shannon thought of an "information source" filled with different messages, e.g. (11111) and (01111) which messages might occur in different frequencies in the source. He then identified the "entropy of the source as minus the average of the logarithms of the probabilities i.e. - sum (Pi log2 Pi)." Next, one of these messages would be picked at random from the information source and sent traveling down the information channel, perhaps in the presence of noise, to a decoder.
But there is a BIG slight of hand here and it arises at two levels: 1) Notice that for the first "bit" in (11111) versus (011111) to carry a bit of information, it must be possible that the first bit can simultaneously possibly be 1 and simultaneously possible be "not 1" i.e. "0.") It is possible that either (11111) or (01111) will be sent down the channel.
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.
In Kolmogorov's theory, it is central that the bit symbol sequence could have been arbitrarily different. Like Shannon, Kolmogorov does not obey the Law of the Excluded Middle.
As I have blogged before, C.S. Pierce, late 19th Century American philosopher, pointed out that Actuals and Probables do obey Aristotle's law of the excluded middle. Possibles do not obey the Law of the Excluded Middle.
More classical physics, Newton to Einstein, does obey Aristotle's 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.
Recall that on Feynman's formulation of quantum mechanics, we have to think of a single photon approaching the two slit experiment as simultaneously through the left slit and also not passing through the left slit. Feynman's formulation of Quantum Mechanics evades Aristotle's Law of the Excluded Middle, and is interetatble as referring to Possibilities.
In a past blog, I proposed Res Potentia - realm of closed quantum behavior and Res Extensa, realm of the classical world, linked by the ever mysterious measurement "process."
Then information theory, to be ontologically real, must rest on something like Feynman's formulation of quantum mechanics.
And, startlingly, this seems to rule out the Bohmian interpretation of quantum mechanics in which the behavior of the total system is deterministic, but merely epistemologically unknowable. Here information would not be ontologically real.
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 ontologicallly real, I await elucidation.
I end by noting that information theory, Shannon or Kolmogove, 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.
In past blogs, on Free Will and the Poised Realm and Trans-Turing systems I have tried to lay a foundation for such an ontologically free will.
We may, after all, have to buy into Res Potentia and Res Extensia linked by quantum measurement. If not, it seems information cannot be ontologically real.