Tuesday, September 16, 2008

The Pi-angle

It has been assumed for eons that the universe could be explained as containing dimensions and that these dimensions were sequential. One dimensional space is an indivisible point, two dimensional space is at least two one dimensional points connected by a line and three dimensional space is at least three of these two dimensional lines on at least two planes. There may be other dimensions but they're too hard to explain so I'll just ignore them. There is a problem however: There is no two dimensional space, it's just a convenient abstraction.

The absence of a second dimension is only apparent with an object having some curved component, a circle for instance. We are taught that circles are derived by multiplying the diameter of a circle by pi which will give us that circle's circumference. Thing is, pi is ugly. It's an irrational number not only because the decimal portion of the number continues forever, but also because it makes no sense. The fractional part of pi assumes that there really are two dimensions when it actually comes from trying to render a two dimensional object in three dimensions.

The constant, pi, is just an unnecessary complication. In reality it's a rendering error (RE) of just over 4% (4.7197551% to be fairly precise) that results from trying to render three dimensions as two dimensions. What this means is that the diameter of any circle actually 4% longer because it's really a curve that we insist on seeing as a straight line. What happens is that we look at the diameter of a circle from above so it appears as a line. Rotate it 90 degrees and we can see its curvature. Since we don't think we can rotate a two dimensional circle in three dimensions, we never see the curve.

So why care? Will correcting this error really change anything? Consider that the standard circle using pi doesn't exist in nature, it's wholly artificial, a shortcut. This error is incorporated into everything we build having curved elements. This include machinery, architecture, bubble gum and sport equipment. But there's more.

Since we try to force three dimensional shapes into a fictitious two dimensional space, things never fit together quite right. A "round" shaft, for instance, is made to rotate in a "circular" bearing. Since neither the shaft nor the bearing are fabricated in three dimensions, there is always friction, leading to heat and finally, failure. If these rotating parts had been manufactured without resorting to pi, they would be frictionless and would last forever.

The 4.7197551% rendering error also exactly matches the ratio of Dark Matter and Dark Energy in the universe to that fraction of the universe that can be "observed" by science. The 95.2802449% of the universe we can't observe occupies that part of "space" we think of as empty. All of everything we thought was in between "things" (sub-atomic particles, atoms, elements and molecules, people), is actually filled with dark matter and dark energy. The universe is really a solid mass. The part we see is just a frothy mass bubbling up from the underlying dark matter and dark energy.

What we think of gravity is really the exact opposite of attraction, it is the absence of a force holding things apart. We don't fall because there's a force pulling us down but rather the lack of a force holding us up. The tides we believe are caused by the gravitational pull of the sun and the moon are really the result of the earth's spin. As the earth rotates on its axis, the oceans bulge upward at a right angle to the spin. The land masses move into that bulge to create tides. The whole universe works the same way.

The visible universe "floats" in a sea of dark matter and energy and, since there is no force (gravity) to affect movement, things settle into stable trajectories (orbits) determined by sea of dark matter and dark energy. Is any of this important, are there any practical consequences of this delusion? Not really. All it shows is that the impossible is commonplace and we will never understand it because we think it's impossible. Academics Top Blogs

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