The "tenth dimension"

Imagining the tenth dimension, by Rob Braynton. The place where I originally read about this link thought it was kind of cringeworthy, but I didn't agree at first; it's not a bad popular explanation at the beginning...

But at one point the voice claims that quantum wavefunctions exist in five dimensions, invoking some. This isn't reasonable; the space of wavefunctions is a hell of a lot larger than one-dimensional. Sometime around here I stopped paying too much attention. And all dimensions above four, in this explanation, seem to arise in the same way. Why stop at ten? (In the video, somehow seven-dimensional space gets collapsed to a single point. I won't pretend to explain it. Then ten is seven plus three.)

While I'm on the subject, it's kind of annoying that the narrator says "the tenth dimension" as if you can put "the dimensions" in order. Space may be ten dimensional, but there's no canonical ordering of the elements. "Because we live from moment to moment in the third dimension" -- no! We live in three dimensions. Insofar as the third dimension is anything, it's a single dimension, so this nomenclature seems to insist we live in one-dimensional space. Dimension is a number (usually an integer) which is an invariant of a space; there's not some canonical set of three things associated with our three-dimensional space. (Yes, a basis for our space has three dimensions, but there's no canonical choice of basis.)

And don't even get me started about science fiction that talks about "creatures from the fourth dimension". "Four-dimensional creatures" are at least mathematically acceptable.

In the end he's trying to sell a book, and there's a blog; in one post there's a list of where the ten dimensions arise from but it feels like the methodology (if one could call it that) could justify any particular number of dimensions.