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.
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 gives an intelligible shape to everything in the natural universe? Should we consider the possibility of Evolutionary Proportion? Is this a Gnostic secret? Earlier I said that Jesus was a teacher of Gnostic secrets. Do you remember what Jesus said about Gnostic secrets? He told his disciples: "Don't hide your light under a bushel."
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, please note, that in terms of HISTORY, this new mathematical information TELLS US THAT THE ANCIENT PYTHAGOREANS UNDERSTOOD pi is equal to 3.141592654. How could they know that?
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