Hey, thanks for this. You have helped me, a lot, by chance, or not. I will try to, briefly, sum up what is with all of these dimensions.
The first thing that is agreed on, with some theorems or whatever, is that the basic, working dimensions of things - the day-to-day operations - involve a multiple of four dimensions. What can't be explained in four dimensions of space (three), and time (one), is taken as, say, a curled-up dimension within the four. Curled-up means just that these additional dimensions, often taken as one for each new phenomenon of whatever, are not something we, normally, experience. I think a way to try to "cheat" with theorizing about things that can't, or don't seem to fit what we already know.
Now scientists eschew too many dimensions, as much as mathematicians, the notion of infinity. It's not just that infinity is, well, infinite, something still, in some ways, as undefinable as zero. Maybe, by "definition", it's not supposed to be (fully) definable. It's that, apparently, there are only so many physical phenomena, so, the need for only so many dimensions. Just as four dimensions make sense for explaining what we, normally, see, etc, different (finite) particular numbers of total dimensions make sense for different models of the universe. Some mathematicians tried to do away with infinite set-theory simply because of the paradoxes involved. As far as I know, everybody, both physicists and mathematicians, tries to cancel out the remaining infinities, of calculations, etc, by one on the other. There are, I guess, an infinity of levels of infinity. Simply put, in string theory, there are ten spatial dimensions, and, one temporal dimension. In M-theory, which is used to combine various versions of string-theory, there are twenty spatial dimensions, and, one temporal dimension. Just as, seemingly, in the normal sense of things, two spatial dimensions is unworkable, well, more than one temporal dimension is unworkable. There has to be some sense of the basic multiple of the four dimensions that we experience. The added dimensions are the makeshift, curled-up ones.
Somewhere along the line, I gave up on the above restrictions. Early on, I guess. However, there are ways to retain the gist of these, and other, restrictions. So, part of what I do is to try to smooth out the (four, eight, twelve or whichever) working dimensions into the abstract or curled-up ones, and, as an infinity of both. But, again, to retain a sense of the finite. Early on, I focused on a five-fold symmetry to things. Then, on to a six-fold symmetry. At this point was, eventually, when the various physical quantities, of mass, energy, motion, etc, were more able to fall directly into place. Don't get me wrong, I still had to have a lot of observations under my "belt" to begin to feel comfortable to make the shift. Talking a process, over many, many years. As I more refined the periodic table approach to things - I went back to it, for some more attempted calibration, every few years or so - a basic four-fold (to eight-fold) symmetry emerged to things. I tried to rework this, but, had to give in to it. Then, soon, I was able to "generalize" the six-fold symmetry to the eight. It's funny-odd, but the more I worked with the six-fold approach, the more I felt that it was a bit cramped, but, this feeling was never enough to cause me to try to thusly "generalize" it. The feeling alone wasn't enough. It took the logical confirmation of this "generalized", from six to eight-fold, symmetry to things. The "locked-in" bit from the six basic themes/dimensions. By locked-in, I mean something that, finally, I knew I had to go with, never discard as with so many attempts that didn't pan out all the way.
Well, along the way, going from the six and eight-fold, I ended up with reworking the "virtues" of the five-fold symmetry through the ten. It's hard to explain, suffice for saying that just have to try things, in every way imaginable, until blue in the face, day after day, in the stretches it's worked on. I mean, a true theory of everything has to work in every way, from every perspective, right or wrong, yet, how to get on such a path, in the first, second, third, and, so on, place? Truly weird stuff. How to hide a universe, if not in plain sight? Which leads one on to trying to work also the asymmetry of things.
Anyway, I think that the number, 62, has as much to do with stuff as the number, 42, but, the former is in the realm of the divine, so, we don't notice it in the same way. The same as the number, 43, is less conspicuous (to us) than its counterpart, 41. Each of these latter realms is more mortal, but, our (mortal) universe more involves the dimension-41, this mix of the three spatial dimensions, and, the one temporal one. On some ultimately deep level, we are more about time than space. If you want to look at this last bit philosophically, it has to do with space being more about the nature of paradox. Our universe is more about moving ahead than about some paradoxical bind (of thinking things through more carefully, empathetically, etc.)
Look, it's actually quite intuitive not to be comfortable with "higher" dimensions. Once one realizes that what we don't know about the "higher" dimensions, well, we still don't know about the lower ones, and, of course, versa. In the end, each dimension has to be of the same defined "stuff", something average out, in some weird way. The physical side to things.