johnreed-Math and Universe, Part 5, September 27, 2007

The Universe and the Mathematics:
Why They Are So Well Matched
Take 1A - Modified September 27, 2007
John Lawrence Reed, Jr.

Part 5 of: "Why the Mathematics Works So Well On the Universe"

Fortunately, many, many years ago, during one of my unrelenting,
contemplative sessions on the mathematics and the operation of the
stable systems in the universe, I found and retained, the "precise"
rational intellectual framework I sought. In one illuminating insight,
that accompanied what I remember as a sudden spring like release of
torqued tension on my brain, I had the answer to the dilemma
articulated by Eugene Wigner, and I had the object of my long sought
for "common thread" that runs through all our physical laws. Galileo
may have been the first to formally assert that, "...the laws of
nature are written in the language of mathematics." Today we may
elaborate: stability in the field requires economy in cyclic motion.
It is illuminating to note that the action stable systems must follow
to maintain perpetuity in the field, is precisely an action that the
mathematics represents well.

The relationship between numbers and regular orders of form like
circles, squares, and triangles, etc. and the relationship between
numbers and other numbers always provide a least action solution
provided we have a required number of givens, or initial conditions.
Thus for every given angle two lines describe, given the length of the
two lines, least action defines the triangle. The lengths of the lines
can be in linear units representing static length, or in standard time
lengths at some constant rate of travel, or as vectors, tensors, etc.
All other regular orders of form can be constructed from this triangle
including the circle, as the early derivation of the formula for its
area shows.

To maintain stability in the field a system must be efficient. Least
action is required. The mathematics fits the stable universe because
the mathematics easily represents [13] the efficient, time controlled,
least action [14] properties common to stable physical systems. Least
action lends itself readily to mathematical analysis. As a
consequence, and as Eugene Wigner alluded to, great care must be taken
to insure that in the study of our least action, time controlled
universe, we do not inadvertently allow our least action dependent,
mathematical models, to include the overly generalized a priori
assumptions, that we attach to the locally isolated (surface planet)
quantities that we measure, solely on the basis of a quantified
consistency within specific local (surface planet) cases of least
action events. And we must circumspectly guard against the
indiscriminate inclusion of the essentially mathematical artifacts of
the mathematical models, in our conceptual world view. This includes
the obvious extra-dimensional fantasies, made acceptable by the blind
faith we attach to the near mystical powers we expect from our gifted
crystal ball, and the additional fantasies made possible by the open
window provided by Heisenberg's uncertainty principle, within the
constraints of Planck's constant.

Consider the word "principle". A pivotal word in english that implies
a fundamental point of reference. Consider "The Principle of
Equivalence" and "The Uncertainty Principle". Both principles rest on
the limits of our perception and on an applied mathematics that
functions quantitatively from those limits. The functional mathematics
reflects the least action properties common to the universe and uses
quantities that we perceive that operate within those least action
parameters. Do we elevate the quantities that result from our
perceptive limits to the status of causal truth by applying them to a
least action universe, which they operate within? And thereafter cite
the principles as a basis for quantitative theoretical fantasies?

Endnotes for Part 5
[13] One example of many in the math: When we differentiate the
function that describes the area of a Euclidean circle (pir^2), we get
the function that describes its circumference length (2pir). In other
words, we get a least action (efficient) "boundary condition" for a
given closed area function factored by "pi".This is the simplest
example, but it holds true for the function that describes the volume
of a 3D sphere and every other least action (efficient) closed area or
volume function factored by "pi", that I have investigated.

[14] A simple example of an efficient or least action (when taken over
time) function, in terms of a static form, is a Euclidean circle. The
circumference is the shortest line length to contain the greatest
area.

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