I saw a video the other day that piqued my interest, about imagining the tenth dimension -- and I figured, "What the heck, let's give it a shot -- even though it's almost 12 minutes long." Well, I watched it all, and was impressed with how clear they were able to make it. My thoughts spun for the rest of the afternoon, making little thought experiments about this new abstract way of thinking. Of course, my thoughts quickly turned theological, and I was amazed how the Christian concept of a personal God fits perfectly into what the scientists and philosophers came up with here -- not only that, but (as it usually does) a higher understanding of science leads one to a heightened view of how awesome God really, truly is. In short, this is an abridged map of where my brain went in thinking about this:
We human creatures are bound by the fourth dimension (i.e. time) -- we cannot move freely about the time dimension (either forward or backward, despite the best intentions of creative minds like H. G. Wells to imagine the possibility), but are rather "swept up" in its current such that our consciousness, so to speak, moves in a positive direction along the fourth-dimension axis at a constant rate, until we cease to be. We can certainly, to a degree, control our physical position in the three spatial directions -- but we can only experience "now", like being a single point along the line of time. And "now" is lost to us forever before we can even think about it.
Now, from what the Christians know of God, we know that He is not bound by the Fourth Dimension -- "He knows the end from the beginning." Thus, we imagine God as looking at the whole time/space existence of the universe from outside of it. This, by the way, essentially blows away any skeptical arguments about whether or not human beings really have free will if God knows what we're going to do before we do it; to say it in these terms betrays a paradigm that assumes that God exists in time like we do, and He certainly does not. He doesn't know what I'm going to do before I do it -- but since to him "tomorrow" is the same as "today", all moments in time are "now" to Him. It's not that He knows what I'm going to do before I do it -- it's that what I am going to do tomorrow has already happened for Him, and he's watched me do it already. Weird, huh? XD
But God is even higher than that. He is not bound either by the Fifth Dimension either, which is the dimension that connects all of the different possibilities of what could possibly happen to anything, anywhere, at any time in the universe. From our human point of view, I can imagine several possible states of the universe, depending (for instance) on the choices I make today: if I got in my car and drove away, never to return to my house or my family or anything, and set up camp somewhere else, the universe tomorrow would look different than it will look if I did not do these things. And the lines that connect my present state to those two possible states in the future are drawn in the Fifth Dimension.
God must know all of these possibilities, for nothing surprises Him -- it's the only way He could tell Isaiah with confidence what the Messiah is going to be like, in detail, over 700 years before Jesus was born. And thus, it wouldn't make sense for God to be bound by the Sixth Dimension either, for He can go freely and instantaneously between all these infinite possibilities any time He wants to.
When we move on and think about the Seventh Dimension (and, then and on, into the Ninth Dimension), we find that God is not bound here either. Our universe (its constants, its initial conditions, etc) is a single point in the Seventh Dimension -- thus, to imagine another point to which to draw a line in that dimension, we have to think of another universe entirely -- one, for instance, where gravity is stronger than in ours, or where there is no such thing as magnetism. Obviously, since God created the universe and set these initial conditions as He pleased, he must be outside the Seventh Dimension -- in other words, He could have made the universe any way He wanted to, and so He must be in a plane that gives Him command over these several possibilities before deciding to create the "heavens and the earth". And, just like in the first three spatial dimensions (the dimensions are grouped into threes), you can quickly jump from understanding a line (1D), to understanding a figure made of several lines (2D), to a body made up of several figures (3D). So, in short, the Ninth Dimension is like a 3-dimensional space, where each point in it is a completely different universe, and one can freely move between them and make other bodies that combine them in ways that you would combine six squares to make a cube. This is obviously very abstract, and we can't really get our head around it :) But basically, the Ninth Dimension is, pretty much, Infinity: Every possibility of everything.
Now, here's where philosophers and scientists stop -- they say there cannot be anything higher than the Tenth Dimension (wherein the whole of Infinity, or the Ninth Dimension, is a single point). What else could there be? However, as a Theist, I began wondering if there could be higher dimensions than the Tenth :P
Now, our concept of a universe is spatial -- our universe exists spatially, i.e. it takes up space. It seems to me (in my days-old concept of this idea of the Tenth Dimension) that all of the universes in the Ninth Dimension also have some reliance on the three spatial dimensions (1,2, and 3) -- in other words, I don't see any scientists so far imagining a universe that has no space. I thought, what if there were a universe of spirits? Many of us think of heaven in this way -- not as a place that is bound by space, but as some transcendent "somewhere" that doesn't really have "matter" in it at all. (For the record, I don't think this idea of heaven is Biblical, but I'll go with it as a thought experiment.) If one could imagine such a world -- with no space, no matter, etc. -- could this be a point in the Ninth Dimension? Or would it be even higher than that? Would a space-less, matter-less universe that yet has some sort of incorporeal "spirit" life in it fit into this space of Infinity that we've imagined? Or not?
Of course I can't answer that question right now, just thinking out loud :) So, having reached the end of my thought in the higher dimensions, I began wondering: Are there dimensions lower than us? (i.e. Is there a dimension lower than the First Dimension?) I can certainly imagine there being such dimensions (it seems there'd have to be at least three) -- I got the idea from imagining myself in the Seventh Dimension, moving in all directions along the time/possibility axes to different cross-sections of our universe. From that vantage point, the "actual" fate of our universe would be a single point, which would be like a single story: If I'm writing a novel, that is a universe whose time I am not bound in -- I can move anywhere in the story and explore any possible outcomes of my story simply by "thinking" about it. Thus, it seems to be that a being who lived in the Seventh Dimension looking at our lives bound by the Fourth Dimension would see all the possibilities of our universe as the possible plots of a storyline -- and by "writing" that story, he would be identifying a single point in his "three-dimensional" space.
So, since we can reason, since we can imagine universes and stories and things with perfect ease, maybe the realm of "reason" or "thought" should get its own triplet of dimensions (Dimensions -2, -1 and 0). This only works if you assume that thought is real, and not just some "fake" phenomenon that's a byproduct of synapses firing in the brain. But what if thought was a real part of the universe? As a Christian, the idea doesn't seem too far off -- God thinks and reasons (He gave us a shadow of this ability in making us rational creatures), and He created our universe (our point in the Seventh Dimension) simply by "speaking" it into existence, much like we would "speak" a story or a mental image into existence with perfect ease. So, who's to say that when I envision a story, or a character, or even an entire universe (what's to keep me from this?), I'm actually identifying a single point in an infinite field of possible thoughts, each of which has a three-coordinate position in some "three-dimensional" "thought space" -- a space that actually exists?
This is as far as I've been able to think so far :)