## Friday, November 20, 2009

### Polls Archive 49 - are we a 3D sphere on a 4D hypersphere?

"Our observable universe is an expanding 3D sphere on the surface of a 4D hypersphere." Poll ended Oct. 3 2009. 74.6% agreed, while 25.4% disagreed.

I'm pleased to see how many visitors to my blog were willing to agree with this idea: I suspect a sampling of the general public would show a much lower acceptance of this mind-boggling concept. Imagining a 2D circle being mapped onto a 3D sphere is easy enough for us to do, but our brains tend to hit a conceptual roadblock when we take that up a dimension and try to imagine a 3D sphere being mapped onto a 4D hypersphere! We've talked about the Poincaré Conjecture a few times now, in entries like When's a Knot Not a Knot?, Why Do We Need More Than 3 Dimensions?, and An Expanding 4D Sphere.

In Aren't There Really 11 Dimensions, I suggested that the slight curvature of our 4D hypersphere is what creates the cosmological horizon, and I've talked many times now about how that relates to the fifth dimension. In my blog entry about Nassim Haramein, we looked at how fractals give us a way to visualize how an infinite number of recursions could be contained within a finite space. This time we're tying those two ideas together.

Extra-dimensional spheres are important to all this because they show how our universe could effectively be infinite, but in reality be finite but unbounded. In other words, with each of the dimensions we've been talking about, there are always certain restrictions to that dimension, and you need to move up to the next dimension to move beyond those restrictions. This idea was discussed most recently in What's South of the South Pole?. Here's the video for that entry.

Let me give you and example of what "finite but unbounded" means. If I were to start moving on the surface of the earth, I could keep moving forever, but every now and then I would end up back where I started again. If I had some kind of magic telescope that followed the curvature of the earth, then with sufficient magnification I should be able to look through that telescope and see the back of my head!

Those examples are from topology, where we are effectively thinking about a 2D surface on a 3D sphere. While we're on that 2D surface it appears that we can keep moving in any particular direction forever, but it's the slight curvature of that surface through the next dimension up that prevents us from being able to see that eventually we're going to end up back where we started. Moving those concepts up to each additional spatial dimension gets harder and harder to visualize, but the Poincaré Conjecture (which should now more correctly be referred to as the Poincaré Theorem since it was proved in 2006 by Grigori Perelman) shows that this logic works for 3D manifolds on 4D hyperspheres as well.

Does that mean that if there were some super-Hubble telescope I should be able to look out into space and see the back of my head? No, because the further we look out into space, the further back in time we're looking: in other words, that's not space we're looking at but space-time. If we really were able to look out into space without time being a factor, then we would be seeing that star that's a thousand light years away as it's going to look to us a thousand years from now! It's so easy to forget this important fact.

Which takes us back to the idea that the cosmological horizon, which prevents us from being able to see any further back into 4D spacetime than the cosmic microwave background, is directly equivalent to the horizon we see when we're in the middle of the ocean. Both are the result of a slight curvature. The ocean is effectively a 2D surface mapped onto a 3D sphere. Our 3D universe at this particular instant is mapped onto a 4D hypersphere which we call spacetime, and cosmologists generally agree that our universe is expanding at an accelerating rate so with each new planck length expression of our 3D universe it is slightly larger than it was one unit of planck time before.

With my project, we take that idea one further. Quantum mechanics and Everett's Many Worlds Interpretation tells us there are multiple "world lines" that could have been traveled to get to this moment, and there are multiple "world lines" that branch out from here. Why can't we see those multiple paths from here? Because our 4D hypersphere is moving on a 5D hypersphere, and just as with those other examples, those other possibilities are "just over the horizon" in the fifth dimension. We know those other world lines exist, and we can move towards the available world lines or recognize that there are multiple previous world lines we could have traveled to get to "now", but we can't see them from our current vantage point. Like the land that is just over the horizon as we're in the middle of the ocean, we know these fifth dimensional branches exist even though we can't see them from here, and it's the slight curvature of our 4D spacetime that gives us our small window into a much larger 5D reality. Why, then, do string theorists say that the fifth dimension is tiny? Because from our 3D/4D perspective it is, just as the ocean appears to be a relatively tiny circle that surrounds us when we're out in the middle of it.

Spheres within spheres, wheels within wheels. Branching possibilities that allow us to see the way out of loops that we want to change. Enjoy the journey!

Rob Bryanton

Next: Poll 50 - Ancient Yeast and Extra Dimensions

FRED said...

Hello Rob, My name is Fred Caldwell. Stumbled upon your 10th Dimension video recently and found it very thought provoking. Days later it dawned on me how much like my study of number values mirrors (at least) the first 3 dimensions, but now I believe they have much in common, if not inseperable. I'll try to explain.

It all started on evening in the 1970's I was messing around with an old Texas Instruments calculator with the green numerals that lit up. I think I pressed one, then the plus sign. The next number that lit up was 2. Then next 3 and so on. But if I started with 2, the next number was 4, then 6, then 8, then 10, and so on.
Now why I did the next thing I'll never know, but I thought of writing down the sequence for each number on a piece of paper in rows.
The first row was simply 1 through 9. The seccond row after the number 8 became two digits, so for my purposes I thought I'd just write down what appeared in the ones columns. So the second layer below 1 through 9 became this:
2,4,6,8,0,2,4,6,8. the next row became 3,6,9,2,5,8,1,4,7 and so on until the 9th row became 9,8,7,6,5,4,3,2,1. Hmmmmm!!

A most interesting pattern jumped out at me. The square of numbers I jotted down actually mirrored itself from top to bottom, and from left to right.

It seemed every time I looked at the square I'd discover something different. For example, the only places 5's and 0's occur are in the center making an cross or X.

Quite a while later I continued the sequence beyond the 9 numbers and to my surprise the entire square is bordered with nothing but zeros!

Years later I had a weird idea. MAYBE the plane of values I discovered that are tightly woven perfectly together have another dimension. So I started thinking of the numbers in a cube, and using the same method of adding each number to itself, I peered into what I found to be an entire cube that not only mirrors itself, but is completely encased in zeros!

Including the zeros, the entire cube contains 1215 numbers that perfectly mirror each other. And by that I mean, no matter where you might slice open the cube and spread it apart to look inside, the numbers on both walls of the insides (although always different in configuration) mirror themselves perfectly: top to bottom and left to right - just like the first plane I found.

There's only one thing odd about the cube (I took the liberty of naming after myself, ha.) On the first plane version, there are NO CORNERS. Just an area where there is room for a value, but doesn't necessarliy follow a sequence.
When observing the cube version, these corners become channels that (if the cube sequence is continued outside the cube, the cube mirrors itself again on all six sides) but the channels in between the cubes that contain no value (and not necessarily "zeros") become a square structure that seems to be a skeleton holding all the values in place.

Not a mathemetician here, and barely can express myself properly sometimes, but I thought you should take a look at this cube.

Just yesterday I saw how it relates to the first 3 dimensions of your black and white video.

The first dimension is linear, being a straight line, 1 through 9.
The second dimension is branches off of the linear numbers to make the first square plane.
The third dimension carries the sequence again at a 90 degree angle creating a cube.
Only you know what's next!

Thanks for listening. Think about this for a while. Someone like you just might unlock some cool stuff with it.

I've only seen two of your videos so far but like your approach, and think you've got a great voice too!

Here are the two video links that visualize my discovery. Enjoy.

Mariana Soffer said...

Rob: love to read you again.
Well first of all the issue of the multiple dimensions is really complicated I can understand it in a mathematical way but not in an intuitive one, anyway it still fascinates me.
Just as a world play let me guess what is south of the south pole:
Polar mesospheric cloud, and crepuscular rays and clouds. Just being poetic.