"In terms of the infinite continuum of reality, where does choice fall in the D.U.C.?" Commenter Lambness pointed out the term "recursion" and the concept of "discrete infinity".
All rather dizzying, no?
So, I will attempt to explain my view of this, starting from my primary hypothesis that the D.U.C. tastes just like chicken. (And tofu. And dust. And quark-poo.)
To understand what I am about to express, we will have to agree that the usual perspective that we, as physical human beings, have on Time and Space is just that -- A perspective.
Let's say that Time . . . . . perhaps . . . . (I include that "perhaps" for the explorationally timid) . . . . is not really linear. Let's say that all moments in Time are actually concurrent, and that we are choosing to perceive and experience Time as linear.
My favorite metaphor is -- a great novel -- perhaps you've already read it, perhaps you haven't read it -- but it's sitting on your desk, bookshelf, or in the basket on the back of your toilet. Let's say it's a novel that you read before, and you loved it. (If you "don't read" -- and I know some people who do not, and hold this as a point of pride -- simply substitute "move" for "novel" and "watch" for "read")
Jeez, I can't believe I just included that -- but I did.
Anyway, back to that great novel that you've read before --
Why in the world would you read it again?
But you do.
You read it again, even though you already know how it turns out.
You read it again, and perhaps, even enjoy it more than the first time you read it, because now, you're not all about how it turns out, but about how it unfolds. You notice nuances and structure and meaning that were not apparent in your first fascinated reading of the novel, because your focus has change.
And every time you read this great novel, the novel itself is changed by the fact that you read it.
(If you can't handle paradox, you should probably stop reading now, or take two aspirin. Or four.)
In other words -- all the possible novels of this Universe have already been written, but every time any one of those novels is read/perceived/experienced (for the first time or the non-nillionth time) that novel is expanded and transformed.
This may seem counter-intuitive -- how can a novel be changed by being read? Well, even at the most physical, matter-based level, when you pick up a book and thumb through its pages, oils and residual tissue from your fingertips join with the pages -- that's why historians wear gloves when handling very ancient or valuable texts. If you sneeze while your reading, this matter exchange escalates even further -- or if you read it in the rain at the bus-stop, or while you're slouched over a table at Mickey Dee's. Perhaps now you're grasping the true spiritual depth of the ancient Koan: "I CAN HAZCHEEZBURGER?"
"MY CHEEZBURGER. YOU NO CAN HAZ."
The point is, even when you put the book back on the shelf, or in your garage sale -- even if you never read that book -- the book still exists.
The notion that all possible stories of the Universe already exist may lead some to conclude that things are "pre-destined" -- but if Time is not linear but rather, concurrent, nothing can be "pre"-destined, as there is no "pre" and no "post".
So, the D.U.C. is like the owner (and author) of an infinite library of stories about Itself. In Its fully unified state, there's really no reason to "read" the books. So, It chooses to mitose into various forms and levels of enfolding intelligence, some of which (human, for example) are designed to forget that the entire library already exists, and so begin to read the stories one at a time (incarnation), in a linear direction (past to future).
Then, where is Choice? Well, there's one little thing I neglected to point out. Each of these novels is really a choose-your-own-path book -- you know -- if you want to find out what happens to character A, skip to page 73, if you want to find out what happens to character B, skip to page 91, etc..
This is the place(for me) that the concept of parallel universes comes in -- but that is a whole 'nother can of worms that is too big to stuff into this post -- perhaps another time (scratch that -- in some reality, I've already written it, and in some reality, I never will).
It kind of hurts my brain to think about this stuff sometimes, and I believe that is because the brain is actually designed as a tool to perceive Time in a manner (linear/finite) that doesn't fully represent its true state (concurrent/infinite). If you want to read something that takes you to a more transcendent, experiential version of these concepts, try reading Jorge Borges' The Library of Babel (What luck -- the entire text online!), or Donald Barthelme's excellent "Nothing is Not a Nail".
I want to point out that I don't believe that the human perception of linear time is necessarily the only way the the D.U.C. is playing with itself. I think it's entirely possible that other species and/or constructs are designed to play with various aspects of paradox and apparent limitation/separation in entirely different ways.
Some people say, for example, that animals do not (and perhaps, can not) perceive linear Time. Since I don't speak dolphin or turtle or snake or spider or cow (yet), I'm not ready to make a conclusion about this.
I will say that, so far, it's my experience that human beings are the only known earthly creatures who obsess on measuring Time and carving it up into calendar squares, hours, minutes, second, nano-seconds, etc.. It's almost as if by divvying it up, we're trying to make more of it. Which, if my hypothesis about time is correct, is an impossible (but interesting and, ironically, time-consuming) endeavor.
To sum up -- in my cosmology, there is Choice -- but the choice rests exclusively in which story to read/re-read, and how to interpret it. Since Time doesn't truly exist as linear, you might say that your consciousness of your own existence and the choices that you make in interpreting that experience are, literally, the concurrent creation of the Universe in "real time".
How 'bout those aspirin, now? Or, for being a dutiful reader and plowing through this post, you can hazcheezburger. Or not.
Yes, and Yes. However, separate from the D.U.C. only in the sense that you have the ability to entertain the notion of separation (and I'm quite convinced it's a notion that is essential to making the game more fun -- I also believe that the ability to perceive the notion of separation is tied in, somehow, with the ability to perceive Time as linear).
Definitely a "cell" in the body -- or perhaps, to give it the proper scale, a quark in a cell of the body (although I suspect you are closer to being located somewhere in the "apple" cells of the D.U.C.'s eye ;). )
These seeming "paradoxes" are what the Big Game is all about.
If you have not seen "What the #$*! Do We (K)now!?," do so, post haste. This movie was self-described as "a quantum fable."
Regtarding your "novel" analogy: There is a book that I read for the first time when I was 16. And, have read it a total of 13 times. Between the 12th and 13th reading was a 10 gap. When I read this book for the 13th times, every single character has changed. The noble had become insipid. The strong and selfish female protagonist had become a wise and noble heroine. How did this happen? What an amazing experience.
If you don't mind me indulging in a little bit of my own theories ...
I see repetition as the fundamental creative power in the universe. In my theory, recursion is the unifying thread that acts on all systems in the universe, from the smallest to the largest.
EM waves oscillate to create the illusion of matter. Cells divide over and over to create a human. Systems of galaxies expand and contract. Each state is dependent on the previous one. Each turn transforms both the system and its observer.
The first time you lift something, is a completely different experience than when you lift it for the 10,000th time. Besides the transformation of yourself (and likely what you are lifting) ... what is learned from that 10,000th time is completely different. Your mind is stripped of doubt. Your movement is economized. You are free to explore the nuance of the activity.