WHAT CAN A SIMPLE GEOMETRIC PRINCIPLE TELL US that might just shed some light on why the sun shines?

FOR EXAMPLE, IMAGINE A SPHERE. It is well known that a sphere’s circumference is pi times the length of its diameter. This holds true for any size sphere regardless of how big or small. The sphere also has two other important qualities: surface and volume. But unlike the ratio between every sphere’s diameter and circumference, which is fixed, the amount of surface compared to volume varies depending on the size of the sphere.

GEOMETRY GIVES US A SORT OF BENCHMARK in the form of a sphere having a 6-unit diameter. This particular size sphere has exactly 1.0 surface unit for each 1.0 volume unit contained beneath. Its surface and volume are equal; they are in a 1.0 to one 1.0 ratio, a harmony or balance of some kind. A little larger sphere will have a little more volume than surface; and a little smaller sphere will have a little more surface than volume. A sphere having a diameter twice that of the benchmark 6 unit diameter will have 2.0 volume units for every 1.0 surface unit. And a sphere with ½ the benchmark diameter will have 2.0 surface units for every 1.0 volume unit.

THE TREND IS CLEAR. The larger a sphere gets the more dominant its volume quality becomes at the expense of surface. And the smaller a sphere becomes the more surface dominates. Taken to the two extremes we can see that, geometrically speaking, the largest sphere is ALL volume with comparatively negligible surface; and, the smallest sphere is ALL surface with negligible volume. This relationship holds for ALL “things” in general (not just spheres) regardless of their form.

NOW IF WE DREW A PICTURE OF A SMALL SPHERE, and then a picture of a larger sphere, without holding one next to the other for a size comparison both pictures would look the same. But in reality we know that the spheres are very different since they have different surface to volume ratios. How can we illustrate or model this difference?

USING TWO COLORS, and starting with the benchmark six-unit diameter sphere, paint its’ surface dark blue and fill its volume with bright red. Of course all we see is its rich blue surface until we slice the sphere in half revealing the bright red volume within. Remember, this sphere has a one-to-one ratio between surface area and volume. So how does this change when we “paint’ a picture of a larger sphere, a sphere having more volume than surface?

WE CAN ILLUSTRATE THIS DIFFERENCE IN THE FOLLOWING WAY. And, we can see this difference in sphere-size without cutting into the larger spheres. Imagine for example, that as the size of the sphere increases its’ blue surface begins to fissure like fine cracks in an egg’s shell with the red of the volume within leaking visibly through the blue surface. The larger the sphere considered the more units of volume each individual unit of surface must contain. A very large sphere illustrated in this manner would look like a red-ish ball with a fine blue netting stretched over its’ exterior. The “largest’ spheres (or, all large spheres after a certain size) would be literally red balls of volume with imperceptible surface according to the parameters of this particular manner of modeling.

AGAIN STARTING WITH GEOMETRY’S BENCHMARK six-unit diameter sphere, we find that surface area begins to dominate over volume as comparative spheres diminish in size. To see this by the parameters of our present modeling it is necessary to cut into these smaller spheres. For as the size of the considered spheres diminish, a cross-section of the spheres would show a thickening of surface at the expense of its volume core. The dark blue color of the benchmark sphere’s surface would be seen to penetrate deeper and deeper into the red-ish core of volume as “size” diminishes. Finally, after reaching the “smallest” spheres, it practically disappears altogether. Thus in our model, the cross-sections of the smallest spheres are “painted” the same blue as their surfaces.

NOW OUR UNIVERSE IS FILLED WITH SPHERES. How do these spheres appear in nature, in the real world? Does the structuring of the Universe show this design demand of geometry?

OUR EARTH IS A GOOD EXAMPLE OF A REAL SPHERE in a universe filled with many different sized spheres . . . yet still, a universe designed with but one yardstick, one fundamental “unit”. Earth is a large enough sphere to have an “at-most-sphere”. This is simply to say that its surface thins out with distance from the center. The larger planets have thicker and higher atmospheres. Their surfaces seem to be oozing out stuff (volume?) when compared to our much smaller Moon which has a sharp definition between its’ surface and the rest of universe. Jupiter, the largest of our neighboring planet-spheres, has a volume approaching “kindling” size, and an atmosphere that is thick, deep, and turbulent. Its surface boundary is most indefinite. But the sun, the biggest of all nearby spheres, is literally volume uncontained by surface, which leaks though and out into the rest of universe.

GOING IN THE OTHER DIRECTION toward smaller and smaller spheres (or “things”) we find there are asteroids with crisp well-defined surfaces, dust particles, electrons, etc. These, because of their extremely small size, are practically all surface . . . at least according to the dictates of geometry, and they should manifest themselves accordingly.