## Sunday, October 18, 2009

### What's Around the Corner?

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.

0
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?

1
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.

2
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.

3
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.

4
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".

5
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).

6
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.

7
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".

8
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.
9
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.

10
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.

Next: Jumping Jesus

#### 1 comment:

meatstack said...

Can I throw a thought experiment by you to see what you think?

I found it hard to imagine the idea of not being able to see around something in 3d until I came up with this idea.

let's say you wanted to watch the superbowl. But some trickster from a higher dimension decided to mess with you and drop a solid, non-destructible sphere around you for the duration of the game. You are trapped! The way to still watch the game is to pop over to the forth dimension and come out either at a time before the sphere existed or at a time afterward. Once you come back into 3D land you can move in your third dimension space to a area outside of the space the sphere took up. If you went back in time, you'll see the sphere pop up beside you, but you won't be in it. Game on! If however that trickster put a 4th dimensional hyper cube around you, well, you are SOL, since no point beginning or ending would be sufficient to get out from the trap. You would have to go to another timeline where the cube never existed.

After that my mind turns to glue, but am I on the right track?