The Religion of Mathematicians

(Copyright 2015, John Manimas)

Mathematicians have at least one religious doctrine: "We cannot square the circle." This is an authoritarian doctrine accepted and enforced by mathematicians since 1882. Could it be a false doctrine? All humans are subject to the risk of authoritarian behavior and mathematicians are human. Mathematicians could have engaged in the same pattern of behavior as the authoritarians of major religious institutions.

In 1882, within the golden age of
German self-adoration, the "pi is God" doctrine was articulated in
writing by German mathematician Ferdinand Lindemann. He said that it is a
waste of time for mathematicians to pursue a means to construct squares and
circles exactly equal in area. Lindemann wrote that pi is a "transcendental"
number and therefore pi cannot be constructed as a straight line with a compass
and straightedge. Thus, like the loyal members of a church, mathematicians
believe that Lindemann proved pi exactly cannot be constructed like other
numerical values, such as 1 or 5 or the square root of 5 or the cosine of 36
degrees (0.809016994). Two times the cosine of 36 degrees is equal to Phi, or
the Golden Mean, or 1.618033988, also the sum of the infinite Fibonacci series.
We just did a computation! Uoooooo! Are you scared? Did you run away to get
a snack or visit the bathroom? Or are you brave enough to believe that
mathematicians are not divine and ordinary people can challenge the religious
doctrines of the *Institution of Mathematics*? Our American culture has
challenged, examined, and criticized all other religious beliefs. To be fair, *and
scientific*, we should do the same for the religion of mathematics. Of
course, they do make it difficult, since they conceal most of their beliefs within
a secret code (far more contrived than Latin) to avoid pesky questions from the
skeptical rabble. If Socrates were alive today, he would teach the youth of
New York (or Boston or Stanford) to ask pesky questions about mathematics. For
example: "Why do we worship mathematics and say that a child good at math
is a genius?" But for now let's just ask: "What if it is possible
to construct pi as a straight line?" Would that break the first icon of
mathematical religion?

The ancient civilization of Atlantis knew that the collapse of their society due to both human violence and nature's forces would produce an evolutionary regression. They knew the development of an intelligent human species would have to start over on Earth. So, they sent messages of hope forward to the future generations, and a declaration of fact: "We can construct squares and circles exactly equal in area." Which means: "We can construct pi exactly as a straight line," and which is also an important message that our ancient ancestors were once as technologically advanced as we are today.

The construction of pi as a straight
line has profound meaning for what mathematics is, what a number is and what
proportion is, and how the universe works. Later, over the painful centuries
of physical struggles and historical preservation and manuscript translations,
this message became a riddle: "Can we construct a circle exactly equal in
area to a given square using only the compass and straightedge?" Yes, we
can. The Pythagoreans were too smart (like a lawyer) to ask this question
unless they knew the answer was "Yes." Let's discuss the geometry
and the mathematics, and keep in mind that we are also discussing *HISTORY*,
the real history of life on Earth.

*Proportion is Everything*

The Pythagoreans, who brought the trigonometry
of the right triangle to European culture, also brought the three-word philosophical
comment on the real, physical universe that: "Proportion is
everything." What if this is not just a philosophical comment, but
instead is actually a scientifically accurate statement about how the universe
works? Among the significant students of the Great Pyramid is John Taylor, who
wrote in 1859 that the builders of the Great Pyramid incorporated the value of
pi (*exactly*) into the dimensions of the Great Pyramid. He argued that
the construction of the Great Pyramid was divinely inspired and that a complete
understanding of the Pyramid would reveal the "Secret of Life in the
Universe." My work has been from the start a commitment to find the best
evidence that "Proportion is everything" is in fact "the secret
of life in the universe." And, this same evidence would be the best *historical*
evidence that the Pythagoreans carried forward from our distant past a form of
arcane knowledge, a Gnostic secret that only an advanced civilization could
possess: how pi exactly is constructed as a straight line.

This project has been completed
successfully and the results are shared publicly on the worldwide web at
"thepilinesite.com." The story of that mathematical fact is shared
here in summary. A mathematical fact is not subject to copyright or trademark
and it cannot be patented. It belongs to everyone because it is our human heritage
and because no monetary value can be assigned to it. If this mathematical fact
is the secret of life in the universe, then it is probably also knowledge of "the
kingdom of heaven" and the *pearl of great price* referenced by
Jesus, who was also a teacher of Gnostic secrets.

To see the evidence that I searched
for over a period of 44 years, one has to make use of TWO NEW STRATEGIES. The
first is to treat the quadratic equation as the quadratic *construction*.
This means that the quadratic equation which we treat as an important element
of modern *algebra* was originally not algebra but rather *geometry*.
This viewpoint is consistent with two mathematical facts: one, our "al-gebra"
is dependent on the use of the modern Arabic *zero*; two, the modern quadratic
equation or formula is used to find pairs of solutions to problems where *one
of those two algebraic solutions is a negative value and is discarded because
it is obviously not a meaningful solution*. Why is one of the two
"solutions" junk and the other is perfectly correct? Because the
"equation" was originally a geometric construction and not
"algebra." When we see the quadratic equation with new eyes, making
it a guide for geometric constructions, then we see that BOTH solutions are
correct because both solutions are line lengths where the plus and minus signs are
irrelevant and both lines are two correct results of a geometric construction.

The second new strategy is to construct
"pi-lines," which means to explore proportional values that are
"almost pi" meaning close to pi exactly in value but either slightly
lesser or slightly greater. The two strategies taken together carry one
forward through the world of proportion, which I prefer to name
"Evolutionary Proportion," until one finds, partly by accident and
partly by instinct, the *Unification Construction*. That means using only
the compass and straightedge to construct a straight line equal in length to pi
exactly. The desired "perfect precision" of the result is difficult
to verify, because such verification is not within the reach of ordinary modern
electronic technology, impressive as it may be. Our electronic calculators are
not perfect. They are more sophisticated than older forms of mechanical calculating
devices but our electronic calculators still have limitations. The digital result
of a complex calculation can lose precision in terms of the
"mantissa" or digital decimal fraction. That means an ordinary electronic
calculator is reliably precise only to a specific digital decimal place, such
as to the ninth decimal place (1.000 000 001). In terms of the significance of
this precision issue, it is realistic to note that if a calculation is reliably
precise to the twelfth decimal place, such as 1.000 000 000 001 of a meter, we have
reached the natural limit of the smallest possible particle of discrete matter
(the atom). At that limit of measurement, we can no longer increase the actual
precision of the real measurement by fractional parts because we cannot add a
fraction of an atom to any dimension of a real object.

My theory of *Evolutionary
Proportion* is that the *Unification Construction* is the "Secret
of Life in the Universe" because construction of pi exactly as a straight
line is the best evidence in support of the concept that "Proportion is
everything." This concept means evolutionary proportion is the
fundamental force of nature that enables molecules to measure themselves and
then assemble themselves into living organic structures. This is consistent
with the mainstream biological viewpoint that living organic molecules are
"self-organizing." Self-organizing means the same thing as
self-assembling, and the first step before self-assembly is self-measurement.

*The Successful Constructions in the
Form of Calculations*

To see with one's own eyes and appreciate the reality of this evidence, one needs to be able to operate a common hand-held scientific calculator, and understand -- or accept on trust -- that we can verify a specific series of geometric constructions by means of ordinary numerical calculations. In other words, the operations we can perform as mathematical calculations are actually the same as common geometric constructions. These include adding and subtracting lines, multiplication and division (by means of similar right triangles), taking the square root of a number (or line), squaring a number (or line), and converting a rectangle to a square. This is all spelled out in the long version at "thepilinesite." The fact that we can "calculate" our way to pi exactly as well as construct the line is further evidence that this is a truth of proportional reality and not just a "geometric trick." No new construction or geometric discovery is needed. We can construct pi exactly as a straight line using only the common construction tools that are known to geometers throughout the world. Any reader who has "I am not good at math" engraved on their brain can call upon a mathematical friend for help.

*Here are the five pi lines that led
to the solution:*

(pi*D) = 3.1416407864998738178455042012388 = 1.8, square root, + 1.8 (9/5)

It is easy. This means take the square root of (9/5) and add that to (9/5). This pi-line is the same as [(cosine 36) * 2]^2 * 1.2, or (2.618033988) * (6/5).

(pi*F) = 3.1446055110296931442782343433718 = [(sine 18), *2, sqrt] * 4

(pi*E) = 3.1418181818181818181818181818181 = (1/0.55) * 1.728, or * (6/5)^3

(pi*V) = 3.1426968052735445528926416093549 = (40/9) * sqrt(0.5)

(pi*Q) = 3.1399111679090046934014154186896 = [(pi*E)*(pi*V)] / (pi*F)

This form of new pi-line is readily constructible.

Then, construct the inverse of 1.118, which = 8.944543828647 / 10

0.9 * 0.8 = 0.72, + 4 = 4.72

/ 5 = 0.944, + 8 = 8.944

/ 8 = 1.118, inverse = (1/1.118) = 0.89445438282647

Then, Line A = [ (pi*V)^2 / (pi*E) ] / sqrt(cos 36)

= 3.49498323774898999309129431119694 __(Line A)__

And Line B: = [ (pi*V)^2 / (pi*D) ] = 3.14375317901321112588817420275095

This form of new pi-line is readily constructible.

Then, Line A minus Line B = Line C = 0.351230058735778867203120108445054

Then Line C * 5 = 1.75615029367889433601560054222527

and that times 0.8944543828647 = 1.57079632708308974598890925064872

and that times 2 = 3.141592654 = pi exactly, a straight line.

Summary: Line A minus Line B = Line C = pi exactly times 0.1118.

So that's it. That is the best
evidence that "Proportion is everything" is an accurate scientific
statement. Evolutionary Proportion is not the *outcome* of a complex
universe. It is the *origin* of a complex universe. How can that be?
What in Heaven's name is the significance of the number 0.1118 ? Where does it
come from? The square root of five is 2.236067977, and one half is 1.118033988
and that is the square root of 1.25 or (5/4) and that plus 0.5 = 1.618033988
which equals Phi or 2 times the cosine of 36 degrees, also the Golden Mean, the
proportion visible in all living things. Visible in *all* things, including
stars spinning in galaxies and hurricanes. But Phi and the spiral form is not
the whole picture. There is more. Did you see the 0.1118 ? It is in the 1.118033988
and 0.1118033988, the square root of (1/80) and that is equal to 0.1118 times
10.000304. But the important part is that Line A minus Line B = 0.1118 times
pi exactly, and from that Line C we can construct a straight line equal to pi
exactly.

** Gnostic secrets**:

This is not a complete proof but it
is the beginning of a proof that *Evolutionary Proportion* is the most
fundamental force of Nature that determines the shapes of everything in the
universe, both living and non-living. Did I say that? Who said that?
Aristotle said: "Everything in the natural universe is composed of matter
and form --- primary, inchoate material given an intelligible shape and
purpose." Ah! Inchoate material (loose particles) ** given**
intelligible shape. Question here: What is it that

What is mathematics then?
Mathematics is *our perception* of proportion. Nature produces
electromagnetic radiation, we see colors. Nature produces vibrations, we hear
music. Nature is shaped by proportions. We measure them. We see numbers and
computations, multiplications and divisions and calculus and probabilities and
equalities and inequalities and the entire haunted castle of contrived and
secretive, encrypted mathematical language that ** hides** the light
under a bushel. That is the religion of mathematicians. And that mathematical
authority is questioned at "thepilinesite," which is not encrypted,
not hidden, not a secret. Some college professor put "Question
Authority" on the bumper of his Saab and it got stuck in my mind. Whether
you verify the math yourself, or have it verified by a trusted mathematical
friend,

-- End --

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