Source: http://imaginingthetenthdimension.blogspot.com/

According to string theory, our observable universe is a small part of a larger space having more dimensions than the three we directly see. The other dimensions may be microscopic in size (or otherwise difficult to penetrate) and crumpled up in a funky shape known as a Calabi-Yau space. The observable universe may be on a membrane, or simply a "brane," sitting at the tip of a spike (what physicists call a "throat") or composing part of a membrane wrapped around teacuplike handles.

When I published my book in 2006 did I know that string theory proposes that our universe is constrained at the third dimension and the seventh dimension by "branes" in those dimensions? I did not. Still, there seems to be another very interesting parallel here between my proposal that our universe is "locked in" at the seventh dimension, and the string theory idea that our universe is constrained by a seven-dimensional brane. My goal, since the day I launched this project back in 2006, has been to continue to document interesting connections between leading edge science and my approach to visualizing the dimensions, and I believe we're looking at a particularly useful one here.

The word "multiverse" has a number of different meanings for different people, so there are some possibilities for confusion. As you'll see in the wikipedia article on this topic, physicist Max Tegmark has proposed that there are four different levels of Multiverse (some of the following is paraphrased and some is quoted from the wikipedia article):
Level I: Beyond our cosmological horizon

Remember the cosmological horizon? It gives us a way of seeing that each of us is at the center of our own version of the observable universe, and that if we were on a planet billions of light years from here, we would still see ourselves to be at the very center of a different but essentially similar cosmological horizon. Those two would overlap much like a space-time Venn Diagram. But what if an observer were so far away that their cosmological horizon didn't overlap with ours at all? In a Level I multiverse, space-time is perfectly flat. On that flat "sheet" of space-time there are an infinite number of self-contained universes, all with the same physical laws and constants. Almost all will differ from our own universe. However, because there are infinitely many, there will eventually be similar, and even identical, configurations.

Even though this version of this multiverse has many supporters, particularly since it doesn't require the existence of any extra dimensions, this one feels extremely unlikely to me.

Max Tegmark estimates that within a Level I multiverse, an identical volume to ours should be about 1010115 meters away from us (a number larger than a googolplex).

If that's the case, then how far away is the one where I got up five minutes earlier this morning? And how far away from that one is the one where I got up four minutes and fifty-nine seconds earlier? It's easy to see why some people who are taught this version of the multiverse dismiss it as being ridiculously extravagant.

With my project, I've proposed that the cosmological horizon is the space-time equivalent of the 3D horizon we see around us when we're in the middle of the ocean - it's the same in every direction because of an underlying curvature. Topologically speaking, if we think of our 4D space-time as a flat plane, or the surface of the ocean as a flat plane, where is the curvature? In either case, I would say it's in the next dimension up. So our observable 4D universe is really on the surface of a 5D hypersphere! Which means that if Tegmark's calculation is correct we have a measurement of the circumference of that hypersphere. Just as we could travel east on the surface of the earth and eventually end up back where we started, this would indicate that if we traveled 1010115 meters