Recapitulation of Motion as the Fourth Spatial Dimension

The premise of my idea is that motion (and the measurement of an object’s pathway or history of motion) is the fourth step in the order of spatial dimensions. Some have said that the fourth dimension is time, but time is simply one of the measurements of motion. Motion utilises space and is therefore spatial. I have explained it in my “A Response to the Poincare Conjecture” as follows:

The point is where we start.

The line is the measurement between two points, or we may say it is the point “stretched” into the next dimension.

The square is the line “stretched” into the next dimension. It doesn’t have to be a square to be two-dimensional, but just needs to have a secondary property (width and length) that is measured spatially.

Again, the cube is the square “stretched” into the next dimension.

How, then, is the cube “stretched” into the next dimension? In all other cases we see the point, the line and the square retaining their properties, yet being “pulled” or “stretched” into a direction that its current form has no existence of.

How do we do that with a cube?

Imagine, if like the point, the line and the square, we “stretch” the cube in some way, retaining its current properties but copying its form over and over like we did with the point, line and square. We would see something like a trail of cubes all following each other, leaving infinite copies wherever the original cube goes.

What do we commonly associate with that sort of image? Movement.

In “Motion: The Fourth Spatial Dimension” I go on to describe the motion of a cube that can be represented by the common “shadow” of the fourth dimension known as the tesseract.

Previously we expanded each dimension by the same size as the original line. In the fourth-dimension of motion, we moved it in a direction at a distance of the same size. What would it look like to instead expand and contract by the same size?

A cube contracting its own size would progressively get smaller toward zero. Expanding, it would grow to double its size.

This is what the “shadow of a hypercube” looks like — the tesseract. Only it is a collection of “shadows” of its path of movement.

What I mean by “shadow” is a concept commonly used when referring to higher and lower dimensions, describing how a higher dimensional object would look on a lower dimensional plane. For instance, a sphere passing through a two-dimensional plane would look like a circle growing bigger, then smaller. Some call that the “shadow” of the three dimensional sphere on the two-dimensional plane.

Interestingly, the transforming edge of that circle growing bigger then smaller on the two-dimensional plane describe the sphere’s surface in the third dimension.

If we consider the fourth spatial dimension as motion, then in a world of static three-dimensional objects, how would an object in motion look? Well, in a way the original idea of the sphere passing through the two-dimensional plane has been complicated by adding the element of motion, so I will have to reform the analogy.

What I submit is that each conceptual “snapshot” in time of a three dimensional object in motion is a purely three-dimensional thing and a “shadow”, or “partial surface”, of its dimensional completeness that includes its history of motion.

We can use all the math in the world to describe every three-dimensional formation, from cubes, to spheres to irregularly shaped objects. The next step in spatial analysis is to bring in motion, and describe how objects move, be it directionally, rotationally or by transformation.