Re: What is Information?
Forgive me if I don't see much connection between "what is information?" and questions about faith - unless we're simply going to define "taking something on faith" as "assuming something is true before we have enough information to prove it."
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Here's how I begin to think about it: Information is observed order.
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This is actually a good way of putting it into plain English.
The usual measure of order and disorder, in science and mathematics, is entropy: in principle, we count the number of possible states of a system that are consistent with what we know about it. The larger this number is, the more there is about that system that remains unknown to us; if we succeed in reducing this count to 1, we have managed to completely specify every last detail of the system.
For any practical purpose, the numbers involved are huge; usually we take logarithms but even then the numbers for a 'big' system are still huge. There are also extensions of the idea to cover things varying continuously over a range.
But to answer the question "what is information," we don't much care about the absolute size of this number, or care whether we are taking logs, or logs of logs, or any other 1-1 function of this number. Information about a system is anything which causes you to reduce this count.
In poker, hearing a predictable player raise means that we cross 72o off the list of possible hands he could hold. Discovering for the first time that the sky is blue places constraints on what gases are present in the upper atmosphere. If you already know the exact compositon of the atmosphere this isn't new information; but in the days after the basic laws of optics were known but before high-altitude aircraft and rockets were invented, this imparted a great deal of new information to scientists.
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(snip) So, where does this common ground come from?
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If I receive new information about the world, my list of possible states of the system -- speaking loosely, my list of possible ways the world can work, or possible explanations for alleged miracles or whatever -- gets shorter.
If you receive new information, your list gets shorter.
One way we can make both of our lists shorter is to compare our lists, and strike out anything which appears on only one of the two lists... since the true state of things, whatever that might be, has to be consistent with *everything* that *anyone* observes.
Scientists and mathematicians spend some of their time making new observations and deductions - one way to shorten their lists - and some of their time attending conferences, publishing papers, and reading other people's publications. Every time we speak or publish we shorten someone else's list; every time we read someone else's article, attend someone else's lecture, or receive editorial comments on an article we submit, we shorten our own list.
What you call "common ground" is simply an artifact of the fact that, as time goes on, the most obvious pieces of information get passed around to almost everyone, so the most ridiculous explanations get crossed off of almost everyone's list. We are all trying to peel our lists down to a single explanation of the life, the universe, and everything.
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So then: Where does order come from? It seems to neither be imposed upon nature by Man’s conditioned mind (2.) nor hidden in nature for Man to discover by God (1.)…
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"Order" is simply a name for observing that a given system exhibits a lower number of states that might have been expected based on the number of elements it contains.
By extension of this general idea, mathematicians speak of partial orderings and total orderings to refer to particular types of restrictions on the way the elements of a set can be arranged, and of various types of measures which can be used to compare the sizes of sets, the entropies of systems, and so on.
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Anyway, just some thoughts…I think this is a key element in my favorite question: What is a Soul?
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Forgive me if I can't see much of a connection between "what is information" and "what is a soul."
Returning to the question of faith - it does indeed seem like a natural definition of "belief" or "faith" is "to voluntary confine one's attention to a subset of one's list, " pretending to have stricken off some items from that list when you haven't actually received information telling you that you can. This can be a valuable hypothetical exercise as long as you remember you've done it. If however you discard those other items outright, you risk having accidentally crossed off the one true state of the system from your list and made a mess of the entire exercise.
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