Physical Dimensions

A direct link to the above video is at http://www.youtube.com/watch?v=UUgeevkwoIs

(This entry completes a longer thought which encompasses 7 posts. If you're interested in seeing how I unfolded this argument, please read these blogs in the following order: Life is But a Dream, Time is in the Mind, Time and Schizophrenia, Consciousness in Frames per Second, Time and Music, Flow, and You are the Point.)

In "Life is But a Dream" we discussed the surprising conclusion that not just philosophy but quantum mechanics tells us each of us is an observer at the center of our own particular version of the universe. Likewise, cosmology tells us that we are at the center of the known universe, and this lovely new video from the American Museum of Natural History takes us on a journey from the planet earth out to the huge bubble of the cosmological horizon, the bubble that we are always at the center of.

A direct link to the above video is at http://www.youtube.com/watch?v=17jymDn0W6U

As it says in the above video at the 3:36 mark, this cosmological horizon is not only a 3D space object, but a 4D spacetime object. Because space and time are so intimately connected for us, we have to keep reminding ourselves of this important fact: we look out into space and it's so easy to forget that we are looking back in time as we do so. We've talked about this idea in blogs like An Expanding 4D Sphere, What's South of the South Pole and What's Around the Corner. Taking this idea even further leads to blogs like The Biocentric Universe Part 2, which is about a scientific theory stating that without life there is no time, space, or the cosmos, an idea which some people strongly dislike because it feels like a return to the geocentric model - hasn't it been proven long ago that the universe does not revolve around the earth? And yet the above animation shows that in a real sense it is true that we are at a point right at the center of the known universe, and that an observer ten billion light years away from here would have the same experience, seeing themselves to be right at the center of their own version of the universe.

Let's work through my approach to visualizing the spatial dimensions again keeping the above ideas in mind.

Zero - a Point
We start with a point of indeterminate size. Like the point we know from geometry, this point has no size, no dimension: which means we can think of it as being infinitely large, or infinitesimally small. What does it mean if we say a point's size is not just very very small or very very large, but indeterminate? If we consider every size of this point simultaneously, all of the possible values cancel each other out, and we end up in what physicists call the "underlying symmetry state": a perfectly balanced zero, which contains within it the unobserved potential of all other states. One good word to describe this "set of all possible states" when it's considered simultaneously like this is the omniverse.

Now, let's imagine that you are that point of no size, no dimension, and think about how a point is useful for indicating a position within a system, and how our universe or any other springs from a breaking of that underlying symmetry state.


One - a Line
You are a point on a one-dimensional line. Your options are very limited - you can move forward, you can move backward, there are only two directions you can travel. But here's another fact to consider: because you are a point of indeterminate size, you can imagine yourself as being an infinitely tiny point someplace on that line, or you can imagine yourself as an infinitely large point some place on that line, which means you would encompass the entire line. Since a line extends to infinity in both directions, making yourself this large would allow you to see how it doesn't really matter where you are on the line, because ultimately you can end up in the same place: the enfolded symmetry of all possible positions on that line considered simultaneously.

Now let's add some other spatial dimensions. But to keep our frame of reference, let's imagine that no matter how many other dimensions we add, this very first point on this very first one-dimensional line we've just looked at will always be the same one.


"Blue is blue and must be that, but yellow is none the worse for it"
Two - a Plane
Okay, so here we are now in a two-dimensional plane. Our point on our original line continues to have its forward and backward directions, but now there are two new directions at right angles to the first set that we can use to view that line and that point from. Regardless of where we go in our 2D plane, we can still always see that 1D line as a subset of that plane. And if we now imagine our point as being infinitely large it will encompass the entire plane and end up in that very same place once again - infinity, indeterminacy, the omniverse.

Way back in 1884, Edwin A. Abbott wrote a book called "Flatland: a Romance of Many Dimensions". In it, he introduced the world to the concept of imaginary creatures called "flatlanders" living in a flat, two-dimensional world.

Humans and the rest of the matter in our universe are all made out of 3D atoms and molecules, so we often say that we live in a three-dimensional universe. If you were a 2D flatlander, you would have a much more limited range of motion - you could only move in four directions rather than the six that 3D people are used to, and if you were to look at a circle you would not be able to see inside it. In fact, because you would be living within this 2D plane, all that you would see as you looked around you would be lines all constrained within this flat 2D world: some of those lines would be near, some would be further away, and whatever shape was closest to you would keep you from being able to see any other shapes that were further away. The only way that you could deduce you were looking at a circle, then, would be to move around it and see it against the background of the other more distant shapes.


"No matter where you go, there you are".
Three - a Space
Now let's move to the dimension we're most familiar with, the third. If we go back to thinking about you as a point at that position we started from, there are now six directions you can view yourself from. You can still be infinitesimally small, but now when you expand you will become a 3D sphere that eventually grows so large that it encompasses infinity. You can think of that point as your awareness of the universe at this very specific "now", and that awareness can be as broad or as tight as you care to make it - because you are right at the center of this particular version of the universe, right at this very instant.

What we have just imagined is like a gigantic photograph of our universe at a particular instant. Because light takes a certain amount of time to get here, that photograph is different from what you see when you look through a telescope - because the light from those distant objects takes so long to get here, a telescope is like a way of looking back in time. The further away the star or the galaxy, the longer it took for the light to reach us. Thinking of you as a 3D point of infinitely large size requires us to think of something completely different - if a star is ten light years away, then the photograph we're thinking about here will show us how that star will look to us through a telescope ten years from now! This is a very important difference in what we're imagining here.


"Time may change me, but I can't trace time"
Four - a Line
Thinking of that entire snapshot of the universe as a single point, then, allows us to imagine how the fourth dimension would be a way of joining one snapshot, one "now", to another, and this is how some people come to think of the fourth dimension as being "time". There are two things wrong with that generalization - first of all, "time" is not a spatial dimension, it's just a way of describing change. At best, it's a direction, not a full dimension. And secondly, you can think of any dimension in a particular state, think of that dimension in a different state, and think of how the next dimension up would be how you change from one state to another. For a 2D flatlander, then,"time" would be one of the two possible directions in the third dimension, and it would be how our imaginary 2D creature changes from state to state.

For a 3D person, time is one of the two possible directions in the fourth spatial dimension, and the other opposing direction can be called "anti-time". If you are a point, you can be any place on that line, and you can be infinitesimally small, or you can be infinitely large, which once again would show you that ultimately this spatial dimension is just like all the others - you can imagine that eventually you can grow to encompass the same state at either end of the line, and we use words like infinity, eternity, and enfolded symmetry to discuss what you are heading towards in both directions.


"The further back one looks, the further ahead one can see"
Five - a Plane
As I've always said, my proposed way of visualizing the dimensions is not the explanation for string theory, but it does have many interesting tie-ins to various schools of thought. The starting point for string theory came from Theodor Kaluza back in 1919, when he proposed that the field equations from gravity and electromagnetism are resolved when they're calculated in the fifth dimension. Einstein eventually embraced this startling new theory and gave it his full support in 1921. With additional input from Oskar Klein, the resulting Kaluza-Klein theory became the starting point for the exploration of how our reality comes from extra dimensions that rose to dominance in the closing decades of the twentieth century.

Here's something to consider - if there really are ten spatial dimensions, then the fifth dimension is the halfway dividing point.

In the original tenth dimension logo we see the "zero" and the "ten" as being the two extremes of a line, and if we were to think of that line as being like a guitar string then the "five" would exactly divide that string in half, with 1,2,3, and 4 being part of a wave below, and 6,7,8 and 9 being part of a complimentary but opposing wave above. Persons familiar with my book will recognize the following diagrams. The three images below were accompanied by the following text:

a. The concept of "harmonics" might be more familiar to anyone who has played a stringed instrument. When you pluck a string on a guitar or violin, the action is not as simple as you might imagine. While it might appear to your eye that the string is simply moving back and forth to describe a gentle curve that is widest at the middle of the string, there are other vibrational patterns that are also part of the string's motion, and the proportion of those other vibrational patterns is what gives each instrument its unique timbre.
b. We can more clearly see the other competing patterns by lightly touching the string at various points along the string when we strike it, and we call these other vibration modes "harmonics" or "partials'. So, by touching the string at its half way point we cause the perceived note to jump up an octave, and a high speed photograph would show us that the string is now vibrating in a pattern that describes two equal curves rather than one, with each curve occupying half the length of the string. The point we touched in the middle of the string would now appear to not be vibrating, and we can call that point a node.
c. Now, if we touch the string at the one third point we can create a note which is an octave and fifth higher, which would be the next harmonic, and our high speed photograph would show the string now vibrating with two nodes dividing the string into three equal sections. Dividing the string at the one-quarter mark produces a note two octaves up, and so on up through a series of harmonics, all of which are part of the main vibration of the open string when we pluck it.

Looking at the second of the three images above then, helps us to imagine the symmetry we're thinking about here - when the left hand side of that waveform is going up, the right hand is going down, and so on. But let's be clear here: even when the string is vibrating freely as in the top image, all those other vibration modes are happening. A high-speed strobe light set to very specific frequencies would be able to reveal (though interference between the frequency of the strobe and the patterns of the vibrating string) the other vibration modes such as the two we're picturing here.

What does all this have to do with the fifth dimension? In entries like The Flipbook Universe, Slices of Reality,and The Holographic Universe, we keep returning to the idea that our reality is not continuous, and our experience of the fifth dimension is divided into planck-unit-sized "frames" (which is what leads some physicists to say that the fifth dimension is "curled up at the planck length"). Those planck frames are the "strobe light" that reveals how freely moving patterns that exist across the dimensions contain a node at the fifth dimension, the strongest harmonic as pictured in the middle of the above three images. Since holograms are observed through interference, when a cosmologist says "our spacetime universe is the shadow of a fifth dimensional hologram" that is what we're talking about here.

Imagining then, that anything above the fifth dimension is how we get to the other versions of our universe that don't connect to the one we're currently in, and to the other universes that have different basic physical laws, and even the patterns of information that are not part of our underlying reality, is all part of what this particular visualization should help us to hold in our minds.

And likewise, just as we did with the previous dimensions and could continue to do with each additional spatial dimension beyond this one, we can imagine how the "point" that represents us in our current state within the fifth dimension could be infinitesimally small, or infinitely large, or some place in between, and this is how I suggest our reality is really connected together in ways that seem much less mysterious when we realize that what we are observing is defined at the fifth dimension rather than the fourth. For more about all that from a variety of perspectives, please check out blog entries like The Fifth Dimension is Spooky, Creativity and the Quantum Universe, The Statistical Universe, and Now vs. the Future.

Enjoy the journey!

Rob Bryanton

Next: Placebos Becoming More Effective?

A direct link to the above video is at http://www.youtube.com/watch?v=1K_MgAfeZkk

Last time, in "A Hug From Another Dimension", we returned to Edwin Abbott's imaginary 2D creatures, the flatlanders, and the idea that a 3D person passing through the flatlander's plane would appear very strange indeed to the flatlander. It has been rightly pointed that in my original 11 minute animation I show the flatlander world not as they would see it, but as we would see it viewing from "above" their plane. While that perspective is boggling enough, the "lines all in the same plane" that a flatlander would really see is even more difficult for people new to these concepts to try to imagine.

Why do we talk about flatlanders? Because with this project we're talking about spatial dimensions: the ways that our 3D reality relates to the flatlander's 2D reality gives us some useful clues to the relationship between any spatial dimension and the next. Since the extra dimensions beyond spacetime that physicists talk about are all spatial dimensions (or "space-like" as some prefer to say), thinking about how the simplest spatial dimensions relate one to another gives us tools for imagining the more complex ones. The key to remember with all this is that each additional spatial dimension is at "right angles" to the one before: so each new dimension allows an observer to see "around the corner" in a way that was unattainable from the previous dimension. This time, let's work through the dimensions with that idea in mind.

We start with a point of indeterminate size. We can imagine this point to be any size we choose, and it can exist in any dimension. Let's say that's all you really are - a point. What will it be like for you to exist within each of the spatial dimensions?

You are a point on a one dimensional line. You can look in either direction on your line, but whatever's nearest to you obscures your ability to see anything beyond. If there were nothing else on your line to get in the way, you would be looking towards infinity in either direction.

What if you wanted to see what lies beyond any nearby objects on your line? You would need a way to move on your line. For you, "time" would be a direction in the second spatial dimension, and it would be what you use to change from state to state, from position to position, which would allow you to see "around the corner" to what lies beyond. Think about what the third dimension would be like for you on this one dimensional line - it would be omni-directional, all around you.

Now you're a point on a two-dimensional plane. You can look in four directions on your plane, and the new directions are at "right angles" to the previous ones. If there were nothing else on your plane, you would be looking towards infinity in four directions.

What if there were nearby objects that were obstructing your view and you wanted to see around them? You would need a way to move within your plane. For you, "time" would be a direction in the third spatial dimension, and it would be what you use to change from state to state, from position to position, which would allow you to see "around the corner" to what lies beyond. Think about what the fourth dimension would be like for you on this two dimensional plane - it would be omni-directional, all around you.

Now you're a point within a three-dimensional space. You can look in six directions from within your space, and the new directions are at "right angles" to the previous ones. If there were nothing else within your space, you would be looking towards infinity in six directions.

What if there were nearby objects that were obstructing your view? Since we're already living in a 3D world, this is the easiest for us to picture. If that object were a building, for instance, and you wanted to see what was on the other side of the building, you would need a way to move within your space. For you, "time" would be a direction in the fourth spatial dimension, and it would be what you use to change from state to state, from position to position, which would allow you to see "around the corner" to what lies beyond. Think about what the fifth dimension would be like for you within this three dimensional space - it would be omni-directional, all around you.

Up to now this has been fairly simple to visualize, because we're so familiar with these dimensions from our basic day-to-day experience. But this logic continues to work all the way up. Understanding what that means to us is an important key to understanding the connections between the quantum world, Everett's Many Worlds Interpretation, and the multiverse landscape.

Now you're a point within a four-dimensional "hyperspace". You can look in eight directions from within your hyperspace and the new directions are at "right angles" to the previous ones. If there were nothing else within your hyperspace, you would be looking towards infinity in eight directions.

What if there were nearby objects that were obstructing your view and you wanted to see around them? You would need a way to move within your hyperspace. For you, "time" would be a direction in the fifth spatial dimension, and it would be what you use to change from state to state, from position to position, which would allow you to see "around the corner" to what lies beyond. Think about what the sixth dimension would be like for you within this four dimensional hyperspace - it would be omni-directional, all around you.

If we think of the quantum wave function for our spacetime as existing within the fourth spatial dimension, we are in one of the "worlds" of Everett's Many Worlds Interpretation, and another phrase for what obstructs our view beyond our spacetime would be the cosmological horizon. For people who believe there is nothing more than the fourth dimension, it can be easy to assume that free will does not exist and that there is only one "world", one inevitable version of our universe which exists from its beginning to its end. If there's really nothing more beyond the fourth dimension then we are all like riders on a train, unable to change whatever we're about to observe. What if we wanted to get off that train track and see what lies beyond, see what other "parallel universe" versions of our universe are out there? The same logic continues to apply, so that's the fifth dimension. Because those other worlds are causally connected to our current one by the probabilities of the quantum wave function along with the choices that are made, let's call the fifth dimension our "probability space".

Now you're a point within a five-dimensional probability space. You can look in ten directions from within your probability space and the new directions are at "right angles" to the previous ones. If there were nothing else within your probability space, you would be looking towards infinity in ten directions.

What if there were nearby objects that were obstructing your view and you wanted to see around them? You would need a way to move within your probability space. For you, "time" would be a direction in the sixth spatial dimension, and it would be what you use to change from state to state, from position to position, which would allow you to see "around the corner" and see what lies beyond. Think about what the seventh dimension would be like for you within this five dimensional probability space - it would be omni-directional, all around you.

So what does "obstructing your view" mean when we're in a five dimensional probability space? Here's a couple of examples. Because the probabilistic outcomes for our universe's wave function of possible state are causally connected, no matter where we are in the fifth dimensional version of our universe there are going to be parallel universe versions which are "around the corner" and can't be seen from our current position. For instance, the version of our universe where it's 2010 and Elvis is still alive must exist within the set of all possible states, but no amount of choice or chance will allow us to see that version from here - it's just like our inability to see what lies on the other side of a building, we need to use the next dimension up to move to a different position if we want to be able to see that version of our universe. Also, quantum physicists talk about the wave function of our universe including the possibility of extremely unlikely events -- like one of us now disappearing here and reappearing on the moon. Why do we never see such events? Because they are like seeing the other side of a building: we need to move through the sixth dimension to be able to see that version of our universe, because those events lie outside of our cosmological horizon.

For we spacetime creatures our actual "now" is always really a point in the fifth dimension, being observed one planck frame at a time. This is why physicists suggest that the fifth dimension is "curled up at the planck length": not because the fifth dimension is small, but because the granular nature of spacetime only allows us to view the fifth dimension through our tiny little planck-length window. We look around us and see what feels like a solid, continuous reality, but physicists are now proving that this is an illusion. The fact that our spacetime reality is divided into planck-length "frames" is also part of the recent theories suggesting that our 4D universe is actually the shadow of a 5D hologram!

Now, as we move on to think about the sixth dimension we are thinking about the wave function for All Possible States for our particular universe. This wave function includes all the possible states for our universe, including those which are not causally connected to each other: the version of universe where it's 2010 and dinosaurs aren't extinct should have some possibility of existing, but that version is not connected to our own version of 2010. Because both chance and choice are participants in choosing what version of the universe we observe, this 6D space for our universe also would include versions of the universe that each of us would never choose to observe (like the one where I go crazy and kill my neighbors). And as we said, it also includes the states which we can't observe because the event is so unlikely it would take longer than the existence of the universe for the event to occur (like the version where one of us now disappears from here and reappears on the moon).

Now you're a point within a six-dimensional wave function space. You can look in twelve directions from within your wave function space and the new directions are at "right angles" to the previous ones. If there were nothing else within your wave function space, you would be looking towards infinity in twelve directions.

What if there were nearby objects that were obstructing your view and you wanted to see around them? You would need a way to move within your wave function space. For you, "time" would be a direction in the seventh spatial dimension, and it would be what you use to change from state to state, from position to position, which would allow you to see "around the corner" and see what lies beyond those nearby obstructions. Think about what the eighth dimension would be like for you within this sixth dimensional wave function space - it would be omni-directional, all around you.

What's outside of our wave function space? By the time we've imagined every possible state for our universe, no matter how unlikely some of those states might be, haven't we got everything covered? In other words, what's hidden from view within a point in the sixth dimension? Now we're starting to think about the multiverse landscape of other universes with different basic physical laws from our own. Up to now, no matter how we twisted and turned in the dimensions we were in, we were always confined to our universe, with its specific value for gravity, its specific planck length and speed of light. To look "around the corner" and see one of those other universes, we need to move through the seventh dimension.


Now you're a point within a seven-dimensional multi-universe space. You can now look in fourteen directions, and the new directions are at "right angles" to the previous ones. If there were nothing else within your multi-universe space, you would be looking towards infinity in fourteen directions.

What if there were nearby objects that were obstructing your view and you wanted to see around them? You would need a way to move within your space. For you, "time" would be a direction in the eighth spatial dimension, and it would be what you use to change from state to state, from position to position, which would allow you to see "around the corner" and see what lies beyond. Think about what the ninth dimension would be like for you within this seventh dimensional space - it would be omni-directional, all around you.

String theory suggests that our universe is embedded in a seventh-dimensional "brane". What if you moved to a different seventh dimensional brane to observe a completely different universe? Would that be the same as moving to a different 7D "point" within this way of visualizing the dimensions? That's what I'm suggesting. A different "point" might define a universe with a different strength for gravity, or a different speed of light. So once we defined any arbitrary second "point" there would be a line that passes through our point and this second one, but there would still be a huge number of other universes that would not be on the unique line we had just created. To get to those other universes not on our 7D "line" (a line that exists within a space defined by 7 pairs of directions all at right angles to each other!) would require us to travel through the 8th dimension. By the time we get to the 8th dimension, then, we are able to consider all possible universes that could have a physical expression, so what we're talking about by now is also sometimes called the "multiverse landscape".

Now you're a point within an eight-dimensional multiverse space. You can look in sixteen directions from within your multiverse space and the new directions are at "right angles" to the previous ones. If there were nothing else within your space, you would be looking towards infinity in sixteen directions.

What if there were nearby objects that were obstructing your view and you wanted to see around them? You would need a way to move within your space. For you, "time" would be a direction in the ninth spatial dimension, and it would be what you use to change from state to state, from position to position, which would allow you to see "around the corner" and see what lies beyond. Think about what the tenth dimension would be like for you within this eight dimensional space - it would be omni-directional, all around you.

Although Garrett Lisi's E8 rotation is not usually described as being a way to represent actual spatial dimensions, I think it's fascinating that his theory also suggests that interlocking 8 dimensional patterns would be able to describe any particle in our universe. What do we need to go beyond the 8th dimension for? Because there are still other ways of organizing the information that becomes reality that don't actually become physical realities (for more about the "Information Equals Reality" concept, look up digital physics).

That's why it's useful to think of the ninth dimension as being our information space.
Now you're a point within a nine-dimensional information space. You can look in eighteen directions from within your information space and the new directions are at "right angles" to the previous ones. If there were nothing else within your information space, you would be looking towards infinity in eighteen directions.

What if there were nearby objects that were obstructing your view and you wanted to see around them? You would need a way to move within your space. For you, "time" would be a direction in the tenth spatial dimension, and it would be what you use to change from state to state, from position to position, which would allow you to see "around the corner" and see what lies beyond. But because there are no actual physical objects within this nine-dimensional space, only information patterns, things are much more open-ended here, and in that sense the tenth dimension is also all around, and omni-directional to the ninth dimension.

In this way of visualizing the dimensions, we sometimes talk about the ninth dimension as being where the "big picture memes" reside: these would be the general organizing patterns that could result in a universe as specific as ours, or it could be an organizing pattern that expresses a preference towards one kind of order over another, or one kind of universe over another. Michael Shermer, well-known editor of Skeptic Magazine, has said that he is quite willing to accept this as a new way of thinking about what "God" could really be - an organizing pattern that chooses one kind of universe over another.

Now you're a point of indeterminate size in the tenth dimension, which some people call the Omniverse. As soon as you try to move, or observe any aspect of the Omniverse, you are spilled back into the dimensions below. In that sense, the tenth dimension is the infinity that all of our other directions were pointing towards, no matter what direction and no matter what dimension we were considering.

The tenth dimension as described in this way of visualizing the dimensions is "outside the system" in the sense that
Gödel used the phrase. It's the unobserved wave function of all possible information states, all patterns, all universes, and it's the enfolded symmetry state that exists both "before" and "after" our universe or any other, as physicist Sean Carroll likes to say. As Gevin Giorbran described it, it's also like a big, beautiful, perfectly balanced "zero" which is not empty, but full of all the other possible states. This means that our universe, like any others, is just a temporary deviation from that symmetry, and symmetry breaking is what makes any universe more interesting than this unobserved whole.


I hope you've enjoyed our tour of the ten dimensions, a logical presentation of ideas that I believe will one day be embraced by mainstream science. In the meantime, even though this is not what you would currently be taught in a university physics class, the five million unique visitors who've been to the tenth dimension website show me that a great many people see resonances and connections between this approach and their own understanding of how reality works, and for that I'm truly grateful.

Thanks and enjoy the journey!

Rob Bryanton

PS - here's a classic clip from Carl Sagan showing us his introduction to the Edwin Abbott concept of 2D flatlanders.

A direct link to the above video is at http://www.youtube.com/watch?v=Y9KT4M7kiSw

Next: Jumping Jesus



A direct link to the above video is at http://www.youtube.com/watch?v=AjR69ddBK78

A direct link to the above video is at http://www.youtube.com/watch?v=SqVA6uEfR54

Check it out! Famous author, blogger and creative commons enthusiast Cory Doctorow has just posted my original animation at boingboing.net !
http://www.boingboing.net/2009/08/18/visualizing-up-to-te.html

As usual, the comments are a mix, with some people angrily dismissing the whole thing as drivel, and a smaller contingent of people who appear to "get" where I'm going with my project. Here's the comment I posted at Boing Boing:

Hi, Rob Bryanton here, I made this much-discussed video, and as a long time fan of Boing Boing this is quite an honor. Thanks very much to Cory Doctorow and Bowloftoast for their interest, and thanks to those of you in the comments who understand the intent of this animation: as I say at the end, this is not the explanation for string theory, but it does have interesting connections to a lot of different schools of thought for a lot of people, and that's why it continues to be watched, and why it has been translated into so many other languages. Do I hope that this video has started people thinking about big picture ideas, and encouraged some to learn more about cosmology, the multiverse, and quantum mechanics? Of course I do! And every day I hear from people thanking me for waking them up to these possibilities.

When I came up with this way of visualizing spatial dimensions twenty-five years ago, I had not heard of the point-line-plane postulate, but it is very related. That postulate is accepted as a way of conceiving of any number of spatial dimensions, and that is what we are talking about here - spatial dimensions, each one at a new "right angle" to the one before. Trying to view a representation of a 4D hypercube without using "time" to rotate that object is a good way of thinking about how time, for us, is just one of the two possible directions in the fourth spatial dimension.
http://imaginingthetenthdimension.blogspot.com/2008/03/hypercubes-and-platos-cave-full.html
http://imaginingthetenthdimension.blogspot.com/2008/04/time-is-direction.html

I published my book and this animation in 2006. In 2007, physicist David Deutsch supervised a team of scientists at Oxford to publish a proof equating the branching possibilities resulting from chance and choice with the probabilistic outcomes of the quantum world. New Scientist magazine went on to call this one of the most important science news stories of the year.
http://www.newscientist.com/article/mg19526223.700-parallel-universes-make-quantum-sense.html

The Deutsch team's proof and my video both show a way of visualizing Everett's Many Worlds Interpretation of quantum mechanics. Everett proposed that the quantum wave function is not actually collapsed, but merely observed in different states. In that regard, this way of thinking shows how free will can exist and yet all possible outcomes could already exist within a timeless underlying fabric. Physicist Tim Palmer's "Invariant Set" is receiving a lot of attention this year because it also confirms the validity of this approach:
http://imaginingthetenthdimension.blogspot.com/2009/02/invariant-set.html
Physorg.com has just published a very positive story about Palmer's work:
http://www.physorg.com/news169725980.html

This year well-known physicist Brian Greene has come out to say that he now accepts the idea that the other different-initial-conditions universes are not merely theoretical, but just as real as our own. This "multverse" is another idea that is central to my approach to visualizing the dimensions which was much less in vogue back in 2006.
http://imaginingthetenthdimension.blogspot.com/2009/05/does-multiverse-really-exist.html

Another important point to note is that this way of visualizing the dimensions does show a way of visualizing how the fifth dimension and above are "curled up at the planck length" from our perspective - it's because our spacetime reality is not continuous, but rather divided up into quanta. For more about this:
http://imaginingthetenthdimension.blogspot.com/2009/01/slices-of-reality.html
http://imaginingthetenthdimension.blogspot.com/2009/01/holographic-universe.html

There are a few questions that come up again and again with my project:
What would a flatlander really see?
http://imaginingthetenthdimension.blogspot.com/2008/07/what-would-flatlander-really-see.html
Aren't There Really 11 Dimensions?
http://imaginingthetenthdimension.blogspot.com/2008/12/arent-there-really-11-dimensions.html
Why Stop at Ten Dimensions?
http://imaginingthetenthdimension.blogspot.com/2008/11/tenth-dimension-polls-archive-22.html

If you go to my website you will find many more connections.
http://www.tenthdimension.com/flash2.php

And as has already been mentioned in the comments above, I have a youtube channel where I've posted 250 different videos that discuss the huge cloud of ideas that can be connected to this way of visualizing the dimensions:
http://www.youtube.com/10thdim

Since my day job is composing music and designing sound for films and television shows, you will also see that my project has 26 songs attached to it. Here's one of those songs: "The Anthropic Viewpoint".
http://www.youtube.com/watch?v=du86lNCvOdA

For those of you who are angered by a non-physicist trying to get people to think about cosmology and the really big picture, I can only say that the goal of my project is to stimulate people's brains into considering new possibilities. My next book is called "O is for Omniverse", and it boils all these ideas down into what looks like a children's alphabet book, full of brightly colored pictures and bouncy poems. My most popular blog entry of all time is called "Creativity and the Quantum Universe" and that's what this is all about for me: creativity.
http://imaginingthetenthdimension.blogspot.com/2009/02/creativity-and-quantum-universe.html

Sincerely,

Rob Bryanton

According to wikipedia, Cory was the first person to release a novel under the Creative Commons license. I'm sure he had would be happy to see that my books are also being freely distributed on bit torrent:
http://imaginingthetenthdimension.blogspot.com/2009/07/tenth-dimension-books-on-bit-torrent.html

Isn't it amazing how more and more people around the world are coming to this project? As I said last month, by the time I'm being satirized on collegehumor.com it seems that we're crossing some kind of threshold here. Cool!

Enjoy the journey,

Rob Bryanton

Next: Poll 42 - Does Twitter Connect or Distract?