In 1884, an English schoolmaster named Edwin Abbott wrote a rather curious story. It is a science fiction novella that is a blend of satirical commentary on Victorian culture and the dynamics of dimensionality. I’ve only just started reading it, but any way you slice it, that’s my kinda story. 
Speaking of dimensionality, I’ve just realized a rather interesting point. I previously described an object as an n dimensional surface distributed through n+1 dimensional space. For example, a circle is a 1D surface distributed through 2D space.
However, it just occurred to me that to fully observe a circle in its 2D space, it must be viewed from a 3D perspective. In other words, if you draw a circle on a piece of paper (the 2D space) and then actually want to see the circle, you must look at it from above (the 3D space). If you could somehow inhabit the paper with the circle, all you would see of it would be a line that was closest to you in the middle and curved away from you towards either end.
You can see how this extrapolates upwards by looking at a ball. We never actually see the entire ball. We only see a circle that is closest to us in the middle and curves away around the edges. We can deduce a sphere by turning the ball around and seeing the other side, but we never observe the whole thing at once.
This brings up an intersting notion of a 4D perspective. From this hypothetical vantage, one would actually be able to observe the entirety of the sphere simultaneously. This would be due to the fact that this point of view would be able to see it upon a 3D surface distributed through 4D space.
This whole thing creates a description of dimension as a channel for the transmission of information. But is it the only medium? Perhaps these are channels that we can see and understand because they are within our field of dimensional perspective. Would other channels from higher dimensions be essentially invisible to us and the information from them appear to simply pop in from nowhere? Perhaps something akin to this could be used to build a model for experiences such as intuition, ghosts, or channeling.
In my recent alchemical explorations, I’ve kept getting hung up on not being able to specify exactly what it was I was looking at. For example, for the basic diagram of process of X → Y, what exactly are X and Y, and what exactly is the → process between them? After crunching that for a while, I finally realized that they weren’t anything by themselves. To be meaningful, they had to be placed in context. Specifically, they have to be placed in dimensional context.
X and Y are objects of some variety, but to be meaningful an object must be described by its dimensions. For example, a sphere is a two-dimensional surface evenly curved through a three-dimensional space. But the ideas of surface and space are entirely relative to the current point of reference. If we draw a circle on our sphere, we have then created a new object which is a 1-D surface (a line) evenly curved through a 2-D space (the surface of the sphere). Similarly, we could extrapolate that the 3-D space the sphere lives in is also a 3-D surface within a 4-D space, and so on.
So to make X → Y meaningful, we would have to describe the dimensionality of X and Y. Then the specifics of what processes could possibly be occurring to those objects would also be defined by the dimensions in which they exist. For example, we could speculate that one thing that could happen to two spheres is that they could intersect. This process would create a quasi-shared expanding circle on their respective surfaces and a shared expanding interior space which is distinct from their respective interiors and their shared exterior.
The circle created upon their surfaces by this intersection would have an interesting quality. Remember, here a circle is a 1-D surface in a 2-D space. But it would only be the circle’s 1-D surface aspect that was shared between the spheres. It would then have unique 2-D interiors and exteriors upon the surfaces of each sphere. So the product of the process would be a curious new sort of object, which I’m not immediately sure how to describe.
All of this feels very much to me like it will have great application to the consideration of alchemical objects and their processes. If we could describe the dimensionality of people, for example, we would have a model to describe what happens with the various surfaces and spaces involved in their interactions (or whatever terms will turn out to be appropriate for those dimensions).
I think maybe it’s time to read up on some non-Euclidean geometry.
I just lost my main hard drive. 
