A direct link to this video is at http://www.youtube.com/watch?v=kzlRuygMGHY
Here's another way of describing the Imagining the Tenth Dimension visualization that answers a commonly asked question: when we look around we see a three-dimensional world. Why do we need to think about any more than that? Isn't every dimension past those first three unnecessary? This time around we'll discuss that question.
So. Why do we need more than 3 dimensions? Because the third dimension is filled by the universe in its current state. We need to add a fourth dimension to get to the universe in some other state. The combination of these four dimensions is commonly called "space-time", but this project says that "time" is just one of the possible directions in the fourth dimension, and the accepted concept of time-reversal symmetry shows us that time's opposite direction is just as scientifically valid.
Then why do we need more than 4 dimensions? Because the fourth dimension is filled by the time line (or "world line" as physicists sometimes call it) representing our universe from its beginning to its end. We need to add a fifth dimension to get to the bush-like branching structure of possible futures and pasts that extend out from our universe in its current state. After spending two years pondering the idea of our observed reality being defined in five dimensions, Albert Einstein come out in full support of Theodor Kaluza's startling proof of that idea way back in 1921. This project uses its own logic to arrive at the same conclusion: our observed reality comes from the fifth dimension.
Then why do need more than 5 dimensions? Because the fifth dimension is filled by the world lines that are logically compatible with our universe in its current state, right from its beginning to its end. We need to add a sixth dimension to get to all of the events that physicists tell us are part of the over-all wave function for our universe but which are so unlikely they take longer than the beginning to the end of our universe to occur. This includes the version where one of us pops out of existence right now and reappears on the moon, and it also includes the version where it's 2008 and Madeleine L'Engle (the author of one of my favorite books from childhood, "A Wrinkle in Time") is still alive. A theory devised by German physicist Burkhard Heim was recently brought to my attention, and the original formulation of that theory was based on the idea of our four dimensions of spacetime being augmented by two more "timelike dimensions". To be clear, Heim Theory now has extended versions created by his associates which postulate 8 and even 12 dimensions, but as we discussed in a postscript to my blog entry "Time in 3 Dimensions" the idea of a scientific theory based upon dimensions four through six as being different parts of a wave function representing "time" in all of its possible expressions seems like a noteworthy connection for further exploration.
Okay. Why, then, do we need more than 6 dimensions? Because the sixth dimension is filled by all the world lines for all possible versions of our universe. We need to add a seventh dimension to get to the other universes that are completely decoherent to our own, that have a completely different fine structure constant and initial conditions. Once we get to one of those other universes, each will have its own unique expression within the first six dimensions, filling those six dimensions up with their own unique wave function patterns which will be completely inaccessible and decoherent to our own universe's wave function - much like tuning in a radio station, all of those other patterns continue to exist out there within timelessness, but each universe will be tuned into their own "channel", their own starting/ending position within the omniverse that creates their unique patterns in the dimensions below.
Then why do we need more than 7 dimensions? Because the 7th dimension is filled by all of the possible universes that, like our own universe, have locked-in fine structure constants. There are even more exotic universes possible, though, and that would be those strange and unlikely universes built from oscillating or gradually changing fine structure constants. In that sense, the eighth dimension can become like "time" for the seventh dimension: much as the fourth dimension gives the third dimension a way to change from one state to another, the eighth dimension can give a way for a point within the seventh dimension to change to (or within) different states. Garrett Lisi's E8 rotation also shows some interesting connections in that regard, as it appears an 8-dimensional geometry may be what provides an underlying structure that defines all possible subatomic particles for the universe we are in.
Then why do we need more than 8 dimensions? Because the eighth dimension is filled by all the possible physical expressions of matter and energy that could ever be expressed. We need to add a ninth dimension to get to the organizing patterns in the information that cannot be expressed as matter or energy, and the patterns that could become a reality but which exist only as potentials. Quantum physicists sometimes talk about a continuously burbling "quantum foam"as being the underlying structure for all reality, and that would be another way of thinking about the ninth dimension. This project has called those patterns that spring into existence in the ninth dimension the "big-picture memes" that can be used to define or select one pattern over another in the dimensions below.
Then why do we need more than 9 dimensions? Because the ninth dimension is filled by all of the organizing patterns and random fluctuations that could or could not become universes or coherent structures of any kind in the dimensions below. We need to add a tenth dimension to get to the enfolded symmetry state where all of those potentials are summed together and balance each other out, which gives us a logical and natural way to understand where our universe or any other universe or any other organizing pattern naturally comes from. In that sense, the tenth dimension is the Omniverse, or what Gevin Giorbran (in his acclaimed book Everything Forever) referred to as the Set of All Possible States for our universe, or for any other universe. As we discussed in my blog entry Time in Either Direction, physicists like Sean M. Carroll have shown us how this underlying symmetry state can be used to imagine how our universe (or any other universe) is really just a temporary deviation away from that perfectly balanced symmetry that exists both "before" the big bang, and "after" the end of the universe: a return to enfolded symmetry, the absolute zero that our universe's accelerated expansion is now moving us towards more and more quickly.
In entries like Hypercubes and Plato's Cave, we've talked about how the reality that we are witnessing down here in spacetime can be thought of as the shadows of higher dimensional shapes and patterns. As we've discussed here today, we can see how we move from the very general choices that are made from a starting point in the highest dimensions. Then, we can see how the patterns and shapes of each dimension below brings the shadows of those patterns into more and more specific focus, until we arrive at the sharply delineated reality which is the beautiful 3D universe we are witnessing in each quantum frame, one planck length after another. Fractals and helix shapes of the natural world, the universe as a hologram, the Poincaré Theorem's proof that our universe is the 3D surface of a 4D hypersphere, the Deutsch team's proof of the bush-like branching structure of parallel universes created through chance and choice being equivalent to the quantum wave function... these ideas and many more can be tied into this way of visualizing reality. And when you add in the mysteries of how consciousness, memes and spirit are also part of the specific observation of our 3D reality, the "now" that each of us is uniquely traveling within at this very instant, you have arrived at a very big idea indeed!
Why do we need more than 3 dimensions? To hold all of those possibilities. 3 dimensions are simply not big enough to hold the timeless whole of enfolded symmetry that our reality ultimately comes from.
Enjoy the journey,
Next: The Omniverse Almanac