A line is made of infinite points next to each other. A plane is made of infinite lines next to each other. A universe is made of infinite planes next to each other. Why wouldn't it just keep going like that?
In abstract math, you can define a space with as many (or as few) dimensions as you need -- e.g., an n-dimensional vector is basically just a list of n real numbers. The tricky part is figuring out which abstract mathematical models represent accurate descriptions of the reality that we inhabit.
For example, Special and General Relativity both push for using a mathematical that uses 4-dimensional vectors containing a "time-like" entry (e.g., time, or energy) and three "space-like" entries (e.g., three spatial coordinates, or the magnitude of momentum in three different directions). Thus, we describe reality with models using 4-dimensional vectors because those models produce predictions that are a better match for our observations than any of the competing models.
With the holographic principle, the conjecture is that one of the spatial coordinates (radius in
polar coordinates?) is somehow fundamentally different from the others -- e.g., that it represents a change in scale factor, rather than a change in "position." The holographic principle is motivated by the observation that the entropy of a black hole (and thus the maximum entropy of a region of space) is determined by its surface area, rather than its volume.
Conversely, although we can create models that use 4+ spatial dimensions (infinitely many 3-d spaces stacked together, or infinitely many 4-d hyperspaces stacked together, etc.), I'm not sure that there's any particular motivation to think that those models describe the reality that we inhabit.
Why wouldn't it just keep going like that?
Narrowing in on this point -- we know that
something changes when you try to go past three dimensions. If you have, say, four pencils, you can arrange three of them so that each is perpendicular to the other. If you try to add the fourth pencil so that it is also perpendicular to all three other pencils, you run into a problem.
With Relativity, the resolution this issue that what you see of each of the pencils is a 3-d slice of an extremely long 4-d thread. Arranging the fourth pencil to point time-wards
at all requires twisting the thread in such a way that means that the 3-d slice is moving through 3-d space. Arranging the fourth pencil to be perpendicular to the other three is equivalent to teleporting it.
Doesn't really affect my theory as I have no reason to think gravity would propagate along the 'flatness' spectrum.
Well, the effects of gravity aren't confined to a narrow beam emanating from its source, nor does it propagate out in a plane. Rather, it spreads out in every observable direction. If there were additional spatial dimensions, "Why
wouldn't it just keep going like that?"
