Originally Posted by
PhilosopherStoned
As far as information goes, I would regard it as answers to questions. A question imposes a partition on the set of possible universes (as long as each can only assume one state simultaneously) with one section containing all the universes which are in a state that yields a particular answer to a question.
For example, think of our universes as being ordered sets of six symbols, five of which are 0 and one of which is 1. So they'll be something like 010000, 001000 and so on. There are six such universes. Take the question "Is the 1 in the first three spots?" This partitions the universe into the "yes" partition and the "no" partition, i.e {100000, 010000, 001000} and {000100, 000010, 000001}. So we could call it a binary question. Likewise for "Is the 1 in the first spot?"
As we ask questions, we are taking the intersection of the partitions on possible universes induced by those questions.
So I would regard information as being a set of possible universes that is kept as the "running" intersection induced by various questions.
We can think of usless questions as being those such that one partition induced by it contains that running intersection. For example, if we ask "Is the 1 in the first three spots" and get the answer yes, then we know that we're in one of the universes {100000, 010000, 001000}. The question "Is the 1 in the fourth spot" creates the partions {100000, 010000, 001000, 000010, 000001} and {000100}. The first partition contains our running intersection and so it's useless to ask "Is the 1 in the fourth spot?" after asking "is the 1 in the first three spots?" and getting a positive answer. Had we gotten a negative answer, then it would be useful and {0001000, 000010, 000001} intersects with but is not contained by {000010}.
This is an example of the general fact that the set of possible answers to a question is determined by what is already known. In this formalism, the set of possible answers to a question is the set of its partitions that intersect our running intersection. A question becomes useless when only one of its answers intersect our running partition because we can regard the answer as being known.
Is that at all clear?