3D vs. 4D

As the 21st century dawns, we find ourselves on the brink of what may be mankind’s greatest challenge. Can we, as a species, use the tools we have at our disposal to continue to survive, if not thrive?
3D vs. 4D
We have come to accept the concept of a 3-dimensional space as such a given that it is hard to imagine any alternative, and yet it is a totally arbitrary, even erroneous assumption. Just to put this in perspective; Rene Decartes, for whom the Cartesian coordinate system is named, expressed surprise that the Royal Society chose a 90 degree system, thinking that they would have chosen a “more obtuse” system. Interestingly, Stephen W. Hawking, holder of the Sir Isaac Newton Chair in Physics at Cambridge University, at the end of his book, A Brief History of Time states that it is “impossible to imagine a 4-dimensional” universe. Ironically, several pages later, he states; “When we combine Quantum Mechanics with General Relativity there seems to be a new possibility…that space and time together form a finite, four dimensional space without singularities or boundries, like the surface of the earth with more dimensions.”
As confusing as this may sound I am going to show several models which should clarify exactly what a 4-dimensional system looks and acts like. Nothing changes but our point-of-view.
First we’ll look at several models of the 3-dimensional system and their 4 dimensional counterparts.

Linear :

On the left we have the familiar 3 dimensional cubical system with the x,y and z coordinates shown as green, blue and red lines. On the right we are showing a 4 dimensional tetrahedral system with a,b,c and d coordinates shown. Due to the inherent differences in these systems there are some noticeable anomalies. Notice, first, that the Synergetic dimensions, on the right, go through the vertices and opposing faces of the tetrahedron rather than opposing faces. Also noticeable is the fact that the tetrahedron appears significantly smaller even though the edge length of it and the cube are equal (for the moment we will call this one unit), the tetrahedron being the structure with the smallest surface area per unit volume. It is also the minimum structure; being the simplest, point-to-able structure with an inside and outside. Not so obvious is the fact that the cube in not stable without the addition of diagonals, something the Greeks overlooked; probably because they were so used to building with stone. We will go into more detail on the importance of these differences at a later time.


Planar:


In this pair of models we are looking at the planes which comprise these two systems. Again, on the left, we see the 3 planes which make up the 3 dimensional x,y,z system. On the right we have the 4 planes of the Synergetic system. While the Synergetic system appears to be far more complicated, you may may remember from your math studies that a more complicated system enables us to more easily model complex ideas. This will become readily apparent later.
Another notable difference is that while the 3 dimensional system only requires 3 coordinates to locate a “point” it requires 6 planes to define a cube, the minimum structure, whereas the 4 dimensional Synergetic system only requires 4 planes to model the minimum structure, the tetrahedron.
Finally, we note that the Synergetic system is based on the closest packing of spheres, a phenomenon very common in nature; atoms, molecules, microbes, cells, planets, stars, star clusters, galaxies and nebulae, everywhere we look we see examples of closest packing of spheres. Very rarely, outside of manmade structures do we see any form of cubic structure. Even in those cases, most indigenous peoples opt for triangular structures; igloos, yurts, tepees.
So again, nothing changes. The Universe still works the same way but we now have a different point-of-view, one which I, and others, believe gives us a new perspective, a new way of looking at our surroundings and perhaps a means to make more sense of a Universe which has become ever more difficult to understand. Or, as Richard Feynman, one of the preeminent physicists of our time stated, “Anyone who tells you they understand modern physics is lying.”


Well, maybe they just haven’t looked at it in the right way, with the right models.

2 comments on “3D vs. 4D

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