Calling All Math Majors

I've been thinking about the flash video below that explains the ten dimensions. The way the dimensions are defined, there can be no more than ten dimensions, because the 10th dimension is the infinity of all the infinite universes. But I remember reading of some string theories that propose the existence of more than 10 dimensions, most notably 11 or 26. Are these other definitions just different ways of categorizing the same thing, like instead of "5, 6, 7" it's "5a, 5b, 5c, 6a, 6b, 7a..."

Do I even want to know? Sometimes I like asking questions more than the answers. Questions are easy. Answers are hard. When I think about researching my own questions, part of my brain goes, "Woah, hold on there, Einstein. We haven't had our second nap yet Why don't you go grab that duck feather pillow there, and we'll think about this in an hour."