Conservation Of Information?

Posting again on a subject I don't understand and never will: what physicists mean by "information." My brain balks at mathematical symbols, but I'm good at concepts; so my guess is that if some articulate physicist were to wander by, he or she could explain "conservation of information" in a way that doesn't totally leave me at sea. Wikipedia hasn't succeeded*, but this passage from the entry on "Black hole information paradox" is useful:

There are two main principles in play:

--Quantum determinism means that given a present wave function, its future changes are uniquely determined by the evolution operator.
--Reversibility refers to the fact that the evolution operator has an inverse, meaning that the past wave functions are similarly unique.

The combination of the two means that information must always be preserved.

What I gather from this is that: (i) any present "state" must have a unique past; you can't have two pasts leading to the same present; and (ii) the present can't lead to multiple futures. Am I interpreting this right? So a quantum waveform (?) version of a Laplace Demon** could reconstitute the past or forecast the future (or maybe, this being quanta, could reconstitute past probability wave something-or-other and forecast future probability wave something-or-other) based on what's known now. Hence information is preserved. So, however you twist it, you'll always have the same information.

( Black holes seem to pose a problem for the principle )

The question I posed last time is, "When physicists say that information is preserved even after everything's been absorbed into black holes that have subsequently evaporated, do they mean that, e.g., 'The test tomorrow is at 1:00 PM' is preserved?" Certainly in my everyday use of the term "information," "the test tomorrow is at 1:00 PM" is information. So I can simplify my question down to this:

Is "The test tomorrow is at 1:00 PM" preserved (by the principle of conservation of information)? If not, what is preserved?

( Changed my mind since last time )

I continue to have little idea what I'm talking about. But right now I'd reformulate the question as:

If all physical information is preserved, how can "The test tomorrow is at 1:00 PM" not be preserved?

And a corollary to that one would be:

If all physical information is preserved, and this — somehow — does not include "The test tomorrow is at 1:00 PM" being preserved, then how is it possible that "The test tomorrow is at 1:00 PM" exists even now?

So, to convince myself that all information can be preserved while "The test tomorrow is at 1:00 PM" is not preserved, I'd have to have an explanation for why "The test tomorrow is at 1:00 PM" isn't preserved. And to do that, I'd have to have an explanation for how it can exist now without being physical information. We as physical beings sure seem to have the information that the test tomorrow is at 1:00 PM. So far I can't counter this, can't come up with an explanation of how physical beings can have nonphysical information, or what "nonphysical information" would even mean. I don't think physicists, to the extent that they've thought about it, disbelieve that "mental" and "cultural" information can be conveyed by physical information, or that the latter two sorts of information are different in kind from the former. Actually, I don't know what they think. But how would they even potentially explain the existence of "cultural information" at all if such information is not conveyable physically?

That's what I would need to explain, if I wanted to preserve the principle of "conservation of information" while denying the conservation of "The test tomorrow is at 1:00 PM." Not that I necessarily want to deny that "The test tomorrow is at 1:00 PM" can be preserved. What I'm saying is that I don't know how not to preserve it without destroying the principle of conservation of (physical) information — which for all I know is a wrong principle, but to half understand what physicists mean by it, I'm acting as if it's right. Quantum physics guys seem to believe it needs to be right. So, for the moment at least, I'm counting "The test tomorrow is at 1:00 PM" as physical information, hence preservable by "conservation of information."

So, to reiterate, I think the crucial question here, this time in bold, is: How can "The test tomorrow is at 1:00 PM" exist now without being physical information?

I'm deciding for the time being that it can't, and that therefore it is physical information.

( No dif in physical status between things and conventions )

( Social info has same physical status as any other info )

( Footnotes )