Dimensions as Force Carriers

Don’t read too far, there aren’t pretty pictures and I’m probably full of shit (or am I?)

What is a dimension?

Like “2D” -or- “2-dimensional space”, or 3-dimensional space; what exactly constitutes delineation of dimensions?

A friend of mine, when posed the question of what “dimensions are”, said he thought of dimensions as “different degrees of freedom”.

I would agree with this statement, but only so long as your “dimensions are all independent planes which happen to intersect centrally.

But, I want to posit this…

What if you define dimensions as mathematical force carriers as you might see in physics.

If we start with a 2-dimensional space, with points and lines and stuff as a an arbitrarily bounded area (even if it’s infinite), in which the points and lines act upon themselves as their own sources of “force” within an arbitrarily bounded space. Whatever might cause a point’s position to change in the space, the change is only caused by either a computation on the point itself (think algebraic operator output moving a point), or a computational modification on other point(s) with a tethered relationship to our originally affected point (think linear transforms).

When we move up to 3-dimensional spaces, we still have 2-dimensional spaces embedded within it which points are still operated on. If we were to isolate each 2-dimensional space embedded within a 3-dimensional space and ask questions about how points/lines “move”, we would eventually encounter forces which are not an intrinsic property of each of the embedded 2-dimensional spaces, but instead contain “hooks” embedded inside each point which only forces external to the 2-dimensional space can affect.

I began to think about “up” and “down” as “gravitation” and “mass” within a 3-dimensional point space. I then started to think about the idea of “mass” existing within each point in a 2-dimensional space which can only be affected by changes “gravitation” in 3-dimensional space, “mass” as an embedded property of each point but inaccessible to the forces which govern effects in 2-dimensional space.

So, in this way, further dimensions can be defined as “‘spaces” where forces exist which can act on properties embedded in the lowest dimensional object within the next lowest dimensional space which the next lowest dimensional space does not have access to.

if 3-dimensional space contains the force of gravitation (up and down let’s say for the sake of illustration), and points being the lowest dimensional object in a 2-dimensional space, they will contain “mass” which the the forces of the 2-dimensional space the points live in cannot affect. “Mass” being the mechanism by which the additional axis of “freedom” is created by.

Whatever “force(s)” exists in a 4-dimensional space, I would probably suggest that the lowest dimensional object in a 3-dimensional space would be a straight line.

Perhaps one of the forces active in a 4-dimensional space is the force which creates the mechanism of curvature perceived in a 3-dimensional space.

Because here’s the thing. “How can a curve be created in a 3-dimensional space without an outside force “bending” the crystallized and uniform structure of a matrix?

Ah! Perhaps 4-dimensional forces are what allow for floating point values, I.E. “1.61815…”