Dimensionality
Saturday, February 14th, 2009In 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.
