Dear James,
What would be the metric here? I think it may be a tricky question. Take Bennett's logic depth and the obvious answer is that the complexity of the world (which you may want to match with 'amount of information') obviously increases, it couldn't be otherwise. But it all depends on the definition of information, if you are matching information with matter/energy my answer may or may not contradict thermodynamics (but note that the current theory of the universe also contradicts thermodynamics at the point where the physical laws we know does not longer apply). If it is Shannon information it may be misleading because Shannon's entropy inherits the caveats of probability (that is that one cannot talk about the information content of individual objects, nor meaning associated to information) but it may leave thermodynamics laws intact. While in algorithmic information one can define individual information content and characterize lack of meaning as random or trivial (i.e. as carrying very little or no information). In this case, I think information has evolved from an early state (when the universe was so dense that everything looked random) into the current more organized forms that we see today (e.g. it is almost certain that in the early universe there was no life, because it seems life requires a long computing period to emerge). So my first answer would be that the process of symmetry breaking actually creates but also also destroys information.
Concerning the typical definition of analog, I find your view interesting and I agree with you that there are certainly different ways to conceive an analog world. From general relativity (GR), for example, it is matter who has to cover a continuum (otherwise GR seems to collapse into classical mechanics) and as such even if one may not be able to divide matter the exercise is to think that relativity theory somehow implies that matter is infinitely divisible (a way to say that it cover a continuum). But if that wouldn't really be the case (that one can think of matter as infinitely divisible) I wonder whether this matter wouldn't actually be better described as being discrete. But if what you conceive to be continuum is an abstract conception of space as an indivisible entity that may be another legitimate definition of analog world.
And that is one of my points, the fact that one cannot even agree on what an analog world may be, while the digital view is basically crystal clear (in a digital world computational power is also well defined). You are right when saying that proving that something resembles to something else doesn't rule out other possibilities. Unfortunately (for the analog worldview supporters I think) we have been incredibly successful modeling the world with digital approaches, while we don't seem to be sure how to really tackle the question or even compare our world to whatever an analog world may mean. My argument is why would someone believe that something is what doesn't look to be rather that what it looks to be. And when I say 'look' I mean something more than only the semantic of the word, because I try to scientifically quantify how much the world looks like an algorithmic (digital) one, and the methodology is described in the essay with references to some of my papers.
Thanks.
