Saturday, August 09, 2008

The Problem of Roundness

Modern geographers proclaim that all the great mysteries in this world have been discovered and explained, all that’s left is some fine tuning here and there. But one of the most mysterious of these mysteries is also assumed to be one of the most obvious. While it’s assumed that the roundness of objects is well understood, our current knowledge barely scratches the surface.

Why is it that writing that originated near the equator is written from right to left while writing originating at higher latitudes goes from left to right? Why is it that a door with the knob on the right on one side has the knob on the left on the other side? How come stars appear so small? Can a person who is a straight shooter also talk in circles?

Spherical Relativity
It is generally believed that spherical objects are well understood and conceptually simple. We've been taught that a sphere can be fully described as "the set of all points in three-dimensional space (R3) which are at distance r from a fixed point of that space, where r is a positive real number called the radius of the sphere. Thus, in three dimensions, a mathematical sphere is considered to be a two-dimensional spherical surface embedded in three-dimensional space, rather than the volume contained within it (which mathematicians would instead describe as a ball). The fixed point is called the center and is not part of the sphere itself. (Wikipedia)" This, however, only describes a sphere at rest.

When a sphere (see more detail, Here) is not moving then all points are exactly equal and there is nothing to distinguish any one point on the surface of the sphere from any other. While this is the normal state of spheres we generally encounter on earth, there's more to the story. If a sphere acquires spin it simultaneously acquires an axis which will include poles. Every point on the surface of a spinning sphere can be plotted by its angle from the nearest pole (the latitude of that point). Any point at an angle of 90 degrees from either pole will lie on the sphere's equator. On earth latitude is calculated from the equator since the axis is tilted 23.5 degrees from the plane of its orbit. Pretty boring stuff.

Ethelburt Maloderus Discoverer of Spherical Displacement

Notice though that just adding spin to a sphere changes everything. A sphere at rest has no reference points; every place is just like every other. A sphere with spin now has poles, an equator and latitudes. This spin also introduces the phenomenon of a period of rotation (time) so that one complete rotation can be determined by observing a point in relation to some other point beyond the sphere. We now have both location and time to specify any point of the surface of a sphere. It's at this point that an especially strange phenomenon becomes apparent.

This phenomenon has been aggressively ignored over the centuries since it introduces all manner of bizarre and unwelcome paradoxes. If this phenomenon were to be taught in public schools the social and political upheaval certain to follow would surely render civilization impossible. Being indifferent to the confusion of future generations, I will explain this phenomenon here. If you are secure in your knowledge of the nature of Nature, read no further, Leave Now!

The Law of Smallness

On earth latitude is measured from the equator. As one moves away from the equator toward either pole, the angle from the equator is the latitude. Notice in the drawing (from the writings of the Medieval Astrologer, Ethelburt Maloderus in his Fragnopolitic Exegesis, Volume 6) that a right triangle drawn from the equator to the point where the latitude intersects the circumference of the sphere yields a circle of less circumference than that at the equator.

As the angle of the latitude increases, the circumference of the circle at that latitude decreases. This smaller circle describes a proportionally smaller area at that latitude. The second part of the Maloderus drawing shows that the time for a complete rotation is likewise truncated with increasing latitude. This is beyond merely interesting.

Since units of measurements of length remain the same at all latitudes, it follows that they must also get smaller. A mile at the equator is 5280 feet and is 1/24000 of the circumference at the equator. That same mile at any other latitude will be less yet will still be 5280 feet which means the a mile is actually shorter. An inch, a foot, a yard and a mile shrink as one moves away from the equator.

A mile at 22.5 degrees from the equator will actually be 25% shorter than at the equator. At 45 degrees, 50% shorter, at 67.5 degrees it will be 75% shorter and at the pole it will shrink to a one dimensional point. A person who is six feet tall at the equator will be less than three feet tall in Paris France. Since everything shrinks at the same rate and to the same degree, there is no way to detect the change by any comparison to anything else at that latitude. A person walking either toward or away from the equator will gain or lose height at the at the same rate as his (or her) surroundings so the change is never noticed.

Before the advent of fast transport, this phenomenon had no noticeable effects since people would grow or shrink at a rate too slow to be noticed. When travel began to exceed 60 miles per hour (a mile a minute) those traveling due north or south began to discern unpleasant side effects. Those going toward the equator began to feel lightheaded and confused as their bodies expanded, those going way from the equator felt the compression caused by shrinkage and became irritable. With air travel these effects became even more pronounced.

NASA discovered the only way to launch people into space at escape velocity (24000 miles an hour) was to launch the spacecraft either east or west, never north or south. At the speed necessary to attain escape velocity any trajectory away from an east-west line would either crush astronauts going away from the equator or cause them to expand until they exploded if heading toward the equator.

The Russians, being at higher latitudes, had smaller brains and were therefore unable to figure this out. They would launch their spacecraft due south (there's not much room in Russia to go north). When the spacecraft was recovered they discovered that the cosmonauts had turned into raspberry jam. They blamed the CIA for years until they finally discovered their error by listening to Sesame Street on Radio Free Europe.

Symposium of the Learned Deniers Asembled in 1223 in Tours France to suppress the discoveries of Ethelburt Maloderus as anathema to correct misunderstanding.

Even now aircraft do not fly directly north or south since people going away from the equator get progressively dumber while those flying toward the equator get lazier. Only those flights to places that no one cares about will risk a rapid change of latitude. People flying to either pole are the most severely affected since they will shrink to a singularity once reaching the pole. Most of these people will simply implode which is why the last 40 miles or so before reaching the pole, they will switch to dogsleds for the final approach.

Notice also in the Maloderus map that the length of an hour at the equator is greater than at the higher latitudes. A 24 hour day at the equator is only 12 hours in Hrvaska Croatia which means the Hrvaskanians only work a 4 hour day. This may explain why nothing much gets done there. It's even worse in Moscow where the day is only about 8 hours long and probably explains why the Soviet system never worked very well. At the poles there's no time to get anything done so everything is just frozen in both time and place.

The latitude where these affects of latitudinal discontinuity are least disruptive is within a few degrees of 35°. At this latitude the adverse intellectual displacments are at the minimum possible value. It is no accident that the Institute for Creative Cosmology and Hair Design is located at precisely 35° North and 97° West in the Acme Generic Research Mall (Where the best ideas are always on sale).

The problem of intellectual disparity between the people living near the equator and those at latitudes above about 40° means that those at higher latitudes have to think twice as hard to get half as much done while those nearest the equator are too smart to care that much (See Rasta Canticle 26, Vol. 23, Bob Marley, "Don't worry, bout a ting, cause every little ting, gonna be alright"). This disparity generally balances out since people at higher latitudes try really really hard to figure things out and people in the tropical latitudes don't think too hard about much of anything. Ironically, folks at the higher latitudes think they're more intelligent than those living in the lower latitudes. The exact opposite is true obviously so any differences can be attributed to the variation in attitudes, and probably ganga of course.

The time differential is also something of a paradox since a year in, say, London Engand is only about six months long in the standard equatoral time base. Oddly the little town of Greenwich, near London, is where scholars decided to put the prime meridian from which world time is measured. This is further evidence that the brain at that latitude is quite small since it was the scholars at this latitude who thought the whole thing up in the first place. Everyone at a latitude other than Greenwich (51.29°) has to adapt to a clock that's only accurate about half the time.

One of the most deceptive affects of Spherical Relatvity is the disparity in aging at different latitudes. People at lower latitudes (nearest the equator) age slower that those at higher latitudes since time is distorted by latitudinal displacement. Some guy in Sweden who thinks he's 40 years old would really be 80 at the equator since a day for him is so much shorter than at the equator. Shorter days means there more of them so 365 days in a year comes much sooner.

What is even less obvious is that the time it takes for news to travel from Sweden to, say, Quito Equador slows down. An event at the Arctic Circle cannot be known at the equator until much later. This implies that the speed of light (the time it takes information to get from one place to another), is variable. If the speed of light varies then there is no such thing as absolute time, no stable reference for determining when something actually happens. The speed of light changes so all measurement of time likewise changes.

This means that cosmology and astronomy, even space travel are only valid at one latitude. At some other latitude the observations won't work. Thing is, since everything varies at the same rate, there's no way to know; the observational errors are distributed to every measurement so all the relationships appear valid. Spherical Relativity doesn't apply only to the earth but to the entire universe and that must mean that every point in the universe is on the surface of a spinning sphere (something really hard to think about for very long). Most mysterious.

It should be obvious by now that all of this is far too difficult to imagine so it's better to just ignore it. It's better to think about stuff wrongly than think about things impossible to comprehend. Even so, I feel it's my duty to provide this insight into the absurdity of reality before we humans get too arrogant about the usefulness of human intelligence.

Should we care? Everything seems to work pretty well doesn't it? Well, maybe not. See This


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