[Note: this post is somewhat related to an ongoing discussion about "interestingness" and "complexidynamics" that was initially inspired by Sean Carroll's FQXi presentation and has been subsequently discussed by Scott Aaronson (see here and here) and Charlie Bennett.]
We know how to measure information (both classical and quantum), we know how to encode information, and we know how to transmit information. But do we really know what it is?
Consider the following example. Imagine a painter who paints an exquisite painting. Is the painting itself information? Certainly we can encode it in bits and qubits, but is the encoding of the painting the same thing as the original painting? In other words, is information the same thing as that which it represents? I can get plenty of copies of the Mona Lisa, but they aren’t the Mona Lisa.
Now suppose our painter never shows anyone else and the painting is eventually lost in a fire. The painter forgets about it and eventually dies. No record of this painting ever existed (after the fire) outside of the painter’s own head and he/she eventually died. To use a turn of phrase from a novel I’m currently reading (Murakami’s 1Q84), quite clearly something – who knows what – was “irretrievably lost” once that painter died. Now this raises some interesting questions.
If we take Wheeler’s “it from bit” seriously, then information is the core component of the universe. While the physical atoms of the painting and the painter are, of course, not lost, the specific “macrostate” (“message”), if you will, that they represented, is clearly gone. The same can be said if we merely say that information represents reality rather than constructs it and even if we say it merely encodes reality.
Given recent results concerning information causality and our penchant for referring to entropy as a measure of information, this should raise some intriguing questions. Now, even if you postulate an infinite universe or a multiverse to compensate for the lost information (if that is indeed what is lost), there’s still a problem: the fact remains that that painting in that particular universe (or part of an infinite universe) was destroyed (I suppose there are some subtle distinguishability issues that this raises).
The ongoing discussion about “interestingness” and complexidynamics aside, I think this raises a very thorny issue: just what exactly is information anyway?