Why the Cartesian Coordinate System

One of the main factors I believe is holding back some advances in physics is the inability of the human race to accept the possibility that space is not what it appears to be. We are all stuck on a 3D universe. When we talk about hyper dimensionality, dimensions above 3 are seen as being bound up so that we can’t see them but are still extensions of the 3D space. This belief is entrenched in the Cartesian coordinate system. What’s wrong with the Cartesian coordinate system? My feeling is that it’s unnatural and clumsy. Here’s an example.

Let’s say we want to plot a tetrahedron on a 3D plane. We need 4 points, therefore we need 12 coordinates to plot these points. These are pure independent points with no relationship to one another. In order to relate them we apply various formulas to calculate the distances between them. In certain cases the relationships are not seen as important and the points are used in isolation. The question is, does nature work things out this way? Is there a more natural way?

Consider this option. We take the four points without defining a position for them, and then apply the distance relationship directly between them. This time we achieve the same shape while retaining the relationships and without being constrained by the dimensional limits or orientation of the plane.

We would not be able to draw shapes beyond 3D but using this system I believe that it would be much simpler to represent them. Consider again the tetrahedron. What would one look like in 4 spatial dimensions? If we consider the rules for a tetrahedron we have 4 equidistant points. I’m not sure what a 4D hyper tetrahedron is but lets assume 5 points at equal distances. Much more easily represented, at least verbally, using a relational coordinate system. Relativity itself is based on these relationships. That’s where the word comes from, this thing relative to that thing.

The concept of a relational coordinate system will become relevant later on in the piece. For now I’ll let you ponder the logic of it and go onto the next section.

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