so, although i of course may be wrong, i don't think that i didn't understand the video but that i understood why it was incorrect
i'm not going to watch it again because i was enough convinced last time not to spend time on it again
Yeah... it's sort of crazy. Everything up through 4-d was fine, though they neglect to mention that time is weird -- it's not quite like the spatial dimensions.
This business of the "5th dimension" being "alternate futures" or "alternate timelines" is total nonsense, though. You can certainly talk about alternate universes/timelines, if you want; there's even a certain amount of physical plausibility in it thanks to the apparent randomness of QM. But it has nothing to do with extra spatial dimensions! It makes no sense to talk about "alternate timelines" being an extra fifth dimension. To even say that and have it be a meaningful statement, you need to assume that, first, all possible timelines can be labeled by a single number (that's to have
one dimension -- if you needed two numbers to label timelines, you'd be talking two dimensions). For example, if you assume that the total mass of the Big Bang could have been anything, but everything else was fixed, then you could speak of a one-dimensional space of possible 4-d universes. It still is rather silly to stick this possibility dimension on to the spacetime dimensions -- it's something totally different.
Similarly, if you want to imagine a big higher-dimensional space where various 4-d worldlines of the universe branch out into possible universes, you can. But that's what you're doing -- imagining a space where you could visualize that. The extra dimensions of this imaginary space are not going to have anything to do with the physical dimensions of the universe; they're another thing entirely. It's like drawing a family tree on a sheet of paper: when you arrange things horizontally, you're not drawing another dimension of space, you're just the direction to organize information.
I don't even know what happened to the "6th" dimension in his talk; he seems to have more or less jumped over it entirely. And from there it just sort of loses its connection with real dimensions entirely; he's just talking about stuff and counting up to ten while he does it.
The 10 dimensions of many string theories are
completely unrelated to this stuff. Those 10 dimensions are ordinary, normal dimensions -- 9 spatial ones and 1 time one. The spatial dimensions include our usual 3 ones plus 6 "extra" ones. The only difference between those 6 and the normal 3 is in the overall shape of space. The 3 dimensions of our universe are either infinite, or at least really, really big. If they aren't infinite, we could travel straight in some direction and end up back to where we started, and we could see ourselves (our backs) if we looked far away enough. The extra 6 dimensions, in string theories, are not only finite and wrapped up like this, but they're also so small we "take up" the entire way around the dimension. (Alternatively, we're stuck on a 3-space-dimensional brane inside the 10 dimensions.) But they're still just space dimensions, like the 3 ordinary ones. Nothing to do with alternate realities, timelines, etc., and all that.
(It's actually surprisingly easy to do physics in a world with more than 3 dimensions. Much easier than trying to visualize living in it. The # of dimensions shows up in the math as how you label points -- (time,x,y,z) for 3 space+1 time dimension just becomes (time,x,y,z,w) with 4 space dimensions+1 time. You just make that change and that's about it. In string theory, it turns out you have big problems if the number of dimensions is most anything other than 10 or 26, and the 26-dim theories have their own issues. Hence the assumption that you have 10 dimensions; it's the only way string theories work. The extra dimensions are also convenient for other reasons: first, it's long been known that you can re-phrase gauge theories of particle physics in terms of gravity acting in extra spatial dimensions. Second, the hope was that the different ways strings could "wrap around" the extra dimensions could explain the different types of observed fundamental particles.)
The video Trish posted --
http://www.youtube.com/watch?v=uDaKzQNlMFw -- is much better. It's basically correct in talking about the geometry of 4-d space -- how it relates to 3-d space, ways to visualize how 4-d entities would appear, etc.