NINETH BRIEF: The Nonlinear Universe and the Nonterminating Decimal
If the Universe is nonlinear,
why do linear equations work properly in our solar system? For example, the fundamental motion laws, that define orbital motion, are “linear equations.” Thus, they will only work if the coordinate system is linear (see 4th Brief). That
means the coordinate axes must be perfect straight lines, and the units must be constants throughout the coordinate system. Therefore, since these linear equations work properly in defining orbital motion, the solar system must be linear.
Wrong again. The reason the fundamental motion laws work is the same reason the surface of the earth “appears” to be flat. It pertains to the size relationship to a curvature, as
described in the 8th Brief. Linear equations work within our solar system not because the solar system is linear, but because our solar system is extremely small relative to the curvature of the Universe. The curvature of the Universe is so large
relative to our miniscule little solar system that the solar system exists as an approached state of linearity. Just like the surface of the earth, the solar system isn’t linear but is so close to linear that linear equations are accurate within extremely
small error. The error is so slight that we can’t detect it.
This brings us to another most interesting concept that is related to asymptotic variance: a phenomenon
known as a nonterminating decimal. This to me is one of the most amazing yet least understood concepts of mathematics. Although the nonterminating decimal has been known for hundreds of years, as far as I can tell the following concepts seem to be
unknown to the scientific community.
The variance of the nonterminating decimal is similar to asymptotic variance. The difference is in the “limit of variance.”
That is, the linear asymptote approaches linearity relative to a theoretical infinite linear axis, whereas the nonterminating decimal approaches linearity with respect to unity.
For example, π is a nonterminating decimal. The decimal points go on forever (are thus “nonterminating”). This is because π is the ratio of a circle’s circumference to its diameter. In essence,
if we use the linear diameter of a circle as a measuring rod and measure the nonlinear circumference, we get π diameters. By “unity” I mean that if the diameter is equal to “one” then the circumference is equal to π (3.1415926...),
and conversely, if the circumference is equal to “one” the diameter is equal to the inverse of π (which is also a nonterminating decimal).
So therefore, the
reason π is a nonterminating decimal is because the diameter is linear and the circumference is nonlinear. Evidently, if we measure a nonlinear locus of points with a linear measuring rod we get a nonterminating decimal (that has no ending). This leads to the Fifth Theorem in my primary reference book: Premise Theories of the Micro Macro Correlation:
The nonlinear system does not transform to a linear state. The result of such transformation is a nonterminating decimal.
In other words, we have either a linear system or a nonlinear system. We can’t have both. In the nonlinear system we can only approach linearity, but we cannot actually attain it, because
linearity is defined by a nonterminating decimal. We can get close, but we can never actually reach a true state of linearity, because the Universe as a whole (and everything within it) is nonlinear. When we try to impose linearity we end up
with a nonterminating decimal, and the decimal points go on forever. By this hypothesis, the linear coordinate system simply doesn’t exist. Nonlinearity is a conservation law of physics.