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  1. #11
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    Quote Originally Posted by rdelmonico View Post
    The degrees of a circle may link 137 to the fibonacci sequence, but it is off by 1/2 a degree.
    I posted some articles sighting possible explanations for the discrepancy.
    see: Fine Structure Constant Variation

    There are several articles on the subject including one with a description of 3d time.
    Who cares if there is a "link" based on arbitrary units? Why would anyone think such a "link" would have any significance?
    • Skepticism is the antiseptic of the mind.
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  2. #12
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    Quote Originally Posted by Richard Amiel McGough View Post
    Who cares if there is a "link" based on arbitrary units? Why would anyone think such a "link" would have any significance?
    How are the degrees of a circle arbitrary?
    If we find a correlation that seems to show a pattern like the spiral in the formation of a pine cone.
    There may be a reason why a circle has 360 degrees.
    It may not really be arbitrary.

    I thought this might be something?
    There is a minimal level of dignity that should be afforded to all.
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  3. #13
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    Subatomic Particle Spin

    from: http://www.newton.dep.anl.gov/askasc...0/phy00562.htm

    A curious and very mysterious thing is that the quantum mechanical rules for particles that have integer spin are very different from the rules for particles with half-integer spin. All the half-integer particles (e.g., electron, proton, neutron) must be distinguishable from each other: if they are in the same system, they must differ in at least one quantum number. Not so for the integer-spin particles (e.g., photon, meson, gluon). These are allowed to be indistinguishable, and they can all have the same quantum numbers including position. It so happens that particles with half-integer spin are the particles we think of as making up matter, and the particles with integer spin are those we associate with forces. Why spin should be the thing that distinguishes stuff from the forces between stuff is unfathomable to me, and that spin should do this in such an apparently arbitrary way (half-integer as opposed to integer) suggests to me that our understanding is fundamentally flawed, and that the real answer to your question -- if we ever discover it -- will be part of a deeper understanding of /way/ more than spin.
    There is a minimal level of dignity that should be afforded to all.
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  4. #14
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    Quote Originally Posted by rdelmonico View Post
    How are the degrees of a circle arbitrary?
    If we find a correlation that seems to show a pattern like the spiral in the formation of a pine cone.
    There may be a reason why a circle has 360 degrees.
    It may not really be arbitrary.

    I thought this might be something?
    Someone apparently used the number 360 because they thought that was how many days there are in a year. They were wrong. The number of degrees has nothing to do with the nature of a circle or the length of a year. They are arbitrary, like the number of feet in a mile. There is no reason to think there is any meaning in number patterns based on degrees.

    If you find a "correlation" that fits a pattern you like you need to also have a way to determine if it was just random chance. If you don't do this, you will probably end up deceiving yourself with delusions of patterns that are nothing but random chance. I presume you don't want to delude yourself.
    • Skepticism is the antiseptic of the mind.
    • Remember why we debate. We have nothing to lose but the errors we hold. Who but a stubborn fool would hold to errors once they have been exposed?

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  5. #15
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    ok

    Quote Originally Posted by Richard Amiel McGough View Post
    Someone apparently used the number 360 because they thought that was how many days there are in a year. They were wrong. The number of degrees has nothing to do with the nature of a circle or the length of a year. They are arbitrary, like the number of feet in a mile. There is no reason to think there is any meaning in number patterns based on degrees.

    If you find a "correlation" that fits a pattern you like you need to also have a way to determine if it was just random chance. If you don't do this, you will probably end up deceiving yourself with delusions of patterns that are nothing but random chance. I presume you don't want to delude yourself.
    Trying to think outside of the box has it's down side.
    I appreciate any input that you give me.
    However it is fun to discover something unexpected and so I continue to try at my peril.
    Thanks

    It could have something to do with the Merkaba or the flower of life, which seems to be linked to The Fractal-Holographic Universe.







    just for fun
    This guy be be off a bit, not sure.



    What if 360 was not an arbitrary number?
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    Default February 24th, 2012, 09:16 AM

    I discovered this back in 05 when looking into the two symbols known as the triquetra and the pentagram.

    Reminds me of a quote...""According to Greek mythology, humans were originally created with 4 arms, 4 legs, and a head with 2 faces. Fearing their power, Zues split them into two separate parts, condemning them to spend the rest of their lives searching for their other halves." - plato

    In the religious realms there is usually a heaven and a hell and a spokesperson for each. God, other wise known as the holy trinity, and Lucifer, the angel of light. God is now associated with the symbol the triquetra which is far older then the Catholic church. This symbol has three contact points on it which are connected in a pattern consisting of curved lines. Lucifer is represented with the pentagram. A circle, much like the triquetra, though with five contact points. (The Pentagram appears as a sign (UB) in the earliest form of Sumerian pictographic writing (c. 3000 BCE). Although such pictographs do not have a unique meaning, the general sense seems to be "heavenly body." By the cuneiform period (say, after 2600 BCE) the pentagram means "region," "heavenly quarter" or "direction" (Forward Backward Left Right) and is generally used with the number 4. )

    Back in 05 I was bored and began to ponder why these symbols have so much energy surrounding them. I found that they actually belong side by side as part of a very interesting arrangement.

    The triquetra is much like the mercedes sign as a circle with three distinct points evenly spaced in a circle. If we were to start at any one of these points and continue around the circumference stopping every TWO points we pass, we will touch every line once and in doing so we will go around the circle exactly TWICE.

    So im thinking, ok thats cool does the pentagram do this in any way. Is there any balance to it? I find out it does. If we were to start at any one of these points in the pentagram and continue around the circumference stopping every THREE points we pass, we will touch every line once and in doing so we will go around the circle exactly THRICE.

    A circle with one radi obviously has one point so travelling ONE space at a time we will go exactly ONE revolution. I asked my self how far does this go. then I began to draw a ridiculous amount of circles, would you like to know what I found next?

    These are the circles we have so far

    Lines....... Spaces Traveled.... Rotations...... Position of circle in code
    1......................... 1......................1........................ 1
    3......................... 2...................... 2....................... 2
    5..........................3...................... .3........................3

    Here is a list of the rest in the first cycle. Will get to the holy grail part in a sec.........1,3,5,9,12,13,16,19,20,23,27,29,31



    ‎1(+2=), 3(+2=), 5(+4=),9(+3=),12(+1=),13(+3=),16(+3=),19(+1=),20(+ 3=),23(+4=),27(+2=),29(+2=),31

    What is the symmetry of the lines we need to add to form are first stage of the code?

    .......... 2, 2, 4, 3, 1, 3, .....3, 1, 3, 4, 2, 2

    Chris Seekins This is the beginning of the creation. Two halfs a perfect symmetry. Now math is the universal language and would be the foundation of most anything. Remind me of the double helix way later.



    Grail comes from the latin word "gradual" (ha duel/nevermind) which means in stages, by degree


    I must diverge briefly into the grail legends. Originally from Scotland (http://scottishrite.org/) that was not originally the cup of Christ. Originally it was referred to as a bowl in which the elements were mixed in though we can continue on this later. Two quick notes....31st degree mason (highest masonic level), 33rd degree is the "new birth" or Illuminati (will get to later). (Somalian temple/ Knights Templar coming later/1098/King of Jerusalem) The grail became the cup of Christ with the king Aurthur legends. You know the 12 knights of the round table and the extra chair for the king.Scottish Rite of Freemasonry, S.J., U.S.A.

    scottishrite.orgWelcome to the official web site of the Supreme Council, 33°, Southern Jurisdiction, U.S.A., founded 1801.






    Any how every stage in this code except the first has 12 circles in it. A stage being the circles that complete the 2,2,4,3,1,3,3,1,3,4,2,2, symmetry


    Know to save time lets add up all the lines in the 12 circles of the first cycle starting with the triquetra. 23+5+9+12+13+16+19+20+23+27+29+31 = 207


    ‎13 is also a major masonic number. Our 13th circle has 31 lines in it. If we want to know how many lines in a circle we would need to go exactly 14 spaces at a time, touch each line exactly once and go exactly 14 revolutions we only need to look at the 2,2,4,3,1,3,3,1,3,4,2,2. we add 2 to 31 and get the start of our next stage 33 lines ·


    Now the fun part. I asked recently on numerous physics forums why there are 360 degress in a circle. I was told because there is, dont know and its an arbitrary number.


    Lets add up all the lines in our second stage 33,35,39,42,43,46,49,50,53,57,59,61 = 567


    ‎567 minus all the lines in the first stage equals what? Yes 360



    This code is infinite. and every stages lines in every circle minus the same of the stage before is 360. does not matter if it is the 2nd minus the first stage or the 999 minus the 998. When I say I drew alot of circles I drew alot of circles.


    Getting the degree of the circles with circles? Quackery it was called and I was kicked off the forums in under two minutes for life for posting a picture of this you can find here. I would post a link though do not want to give a reason to kick me off.

    Shall we continue this is only the beginning?
    Last edited by rdelmonico; 02-02-2014 at 10:33 AM.
    There is a minimal level of dignity that should be afforded to all.
    No-one is above anyone else.
    No-one cares what you know unless they know that you care.
    Winning an argument and losing a friend is not (in my humble opinion) winning.

  6. #16
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    Quote Originally Posted by rdelmonico View Post
    Trying to think outside of the box has it's down side.
    I appreciate any input that you give me.
    However it is fun to discover something unexpected and so I continue to try at my peril.
    Thanks
    Well, before you can "think outside the box" you probably should have some concept about what is in the box. You appear to be fishing for random ideas from the fringe of physics. I know that can be fun and exciting, but in truth its pretty silly to be making any kinds of conclusions based on things you don't really understand.

    What are you looking for? What do you imagine you may find?

    Quote Originally Posted by rdelmonico View Post
    What if 360 was not an arbitrary number?
    I don't know. What if Islam is true and the name of Allah is encoded in your DNA?

    What if Mickey Mouse really is the soul of Elvis?

    Quote Originally Posted by rdelmonico View Post
    Lets add up all the lines in our second stage 33,35,39,42,43,46,49,50,53,57,59,61 = 567

    ‎567 minus all the lines in the first stage equals what? Yes 360
    A random number game cherry picked out of the infinite set of possible number games because it yields the number 360 is anything but evidence that 360 is not arbitrary.

    You will never find truth by cherry picking random numbers you happen to like from mathematical systems you don't understand.

    Quote Originally Posted by rdelmonico View Post
    This code is infinite. and every stages lines in every circle minus the same of the stage before is 360. does not matter if it is the 2nd minus the first stage or the 999 minus the 998. When I say I drew alot of circles I drew alot of circles.

    Getting the degree of the circles with circles? Quackery it was called and I was kicked off the forums in under two minutes for life for posting a picture of this you can find here. I would post a link though do not want to give a reason to kick me off.

    Shall we continue this is only the beginning?
    Is this something you put together, or is it just another page you found on the net?
    • Skepticism is the antiseptic of the mind.
    • Remember why we debate. We have nothing to lose but the errors we hold. Who but a stubborn fool would hold to errors once they have been exposed?

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  7. #17
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    Quote Originally Posted by Richard Amiel McGough View Post
    Well, before you can "think outside the box" you probably should have some concept about what is in the box. You appear to be fishing for random ideas from the fringe of physics. I know that can be fun and exciting, but in truth its pretty silly to be making any kinds of conclusions based on things you don't really understand.

    What are you looking for? What do you imagine you may find?
    I am reading every day in my spare time.
    I have not made any conclusions.

    Quote Originally Posted by Richard Amiel McGough View Post
    I don't know. What if Islam is true and the name of Allah is encoded in your DNA?
    DNA could turn out to yield some interesting stuff.

    Quote Originally Posted by Richard Amiel McGough View Post
    What if Mickey Mouse really is the soul of Elvis?
    Leave Micky out of this.

    Quote Originally Posted by Richard Amiel McGough View Post
    A random number game cherry picked out of the infinite set of possible number games because it yields the number 360 is anything but evidence that 360 is not arbitrary.
    Interesting point, but what if there was a good reason for the Babylonians or the Egyptians to pick this number. It could be based on the hexagon, or the geometry of something they knew that we have not discovered yet.
    If I wanted to take a mystical view of things, then I would argue that nothing is random, especially something so common as 360 degrees. (Notice the word "if").

    Quote Originally Posted by Richard Amiel McGough View Post
    You will never find truth by cherry picking random numbers you happen to like from mathematical systems you don't understand.
    Doesn't stop me from looking.


    Quote Originally Posted by Richard Amiel McGough View Post
    Is this something you put together, or is it just another page you found on the net?
    Not mine, I figured you wouldn't like it, notice: the guy who wrote that got suspended from the site.



    from: http://www.icr.org/article/299/

    In the area of very large phenomena when the time period of each planet's revolution around the sun is compared in round numbers to the one adjacent to it, their fractions are Fibonacci numbers! Beginning with Neptune7 and moving inward toward the sun, the ratios are 1/2, 1/3, 2/5, 3/8, 5/13, 8/21, 13/34. These are the same as the spiral arrangement of leaves on plants!


    from: http://www.khouse.org/articles/2003/479/

    Uniformitarianism Fallacy

    Most scientists take for granted that the movements of the planets and other objects in our solar system manifest an unchanging uniformity through time. These movements, however, also manifest minute variations that have, so far, eluded any consistent conjectures.

    Furthermore, careful observations of the objects in our solar system indicate that it has been-at least at times-a rather rough neighborhood. Take a look at the Moon through binoculars and you will see a lot of bruises. Or examine any of the photographs from our space probes. You see craters and other evidences of collisions and catastrophes.

    There is evidence that the present orbits were not always so. And some of the changes appear to have occurred during the memory of mankind.

    The Mysteries of Mars

    Why did so many of the early cultures worship the Planet Mars? They were terrified of this strange planet. It was called the "God of War." Why? (The term "martial arts" is still in our working vocabulary.) And there are other mysteries that seem to be associated with this strange planet.

    The 360-Day Year

    All early calendars appear to be based on a 360-day calendar: the Assyrians, Chaldeans, Egyptians, Hebrews, Persians, Greeks, Phoenicians, Chinese, Mayans, Hindus, Carthaginians, Etruscans, and Teutons all had calendars based on a 360-day year; typically, twelve 30-day months.

    In ancient Chaldea, the calendar was based on a 360-day year. It is from this Babylonian tradition that we have 360 degrees in a circle, 60 minutes to an hour, 60 seconds in each minute, etc.

    The Biblical Year Is 360 Days

    It is also significant that the Biblical year is also based on a 360-day year reckoning.1 This critical insight unlocks several incredible prophecies which the reader is urged to discover-- in particular, the remarkable "70 Weeks" prophecy of Daniel 9, which is undoubtedly the most amazing passage in the Bible.2

    All Calendars Change in 701 B.C.

    In 701 B.C., Numa Pompilius, the second King of Rome, reorganized the original calendar of 360 days per year by adding five days per year. King Hezekiah, Numa's contemporary, reorganized his Jewish calendar by adding a month each Jewish leap year (on a cycle of seven every 19 years). 3

    The Roman year began with March, the month named after Mars. (They later reorganized their calendar in 364 B.C. to begin on January 1st.) Most of the early cultures organized their calendars around either March or October. Why? Why was any change necessary after 701 B.C.? What happened to affect all the calendars after that year?

    Mars Interferes?

    The recent space age discovery of "orbital resonance"-the tendency of orbits to synchronize on a multiple of one another--has led to a fascinating conjecture that the orbits of the Earth and the Planet Mars were once on resonant orbits of 360 days and 720 days, respectively. A computer analysis has suggested that this could yield orbital interactions that would include a near pass-by on a multiple of 54 years, and this would occur on either March 25 or October 25. Such near pass-bys would transfer energy, altering the orbits of each. 4

    In near proximity, such pass-bys would be accompanied by meteors, severe land tides, earthquakes, etc., and this would help explain why all the ancient cultures were so terrified by the Planet Mars5 and why calendars tended to reflect either March or October.6 A series of such pass-bys could also explain a number of the "catastrophes" of ancient history, including the famous "long day of Joshua" and several other Biblical episodes.7

    Stability appears to have been attained during the last near pass-by in 701 B.C., resulting in Earth's and Mars' present orbits of 365 1/4 days and 687 days, respectively. Provocative, but where's the evidence?

    Swift to the Rescue

    This remarkable conjecture, that Mars made pass-bys near the Earth, would seem to be corroborated by Jonathan Swift (1667-1745) in his famous fantasy known as Gulliver's Travels. In his third voyage, Gulliver visits the land of Laputa, where the astronomers brag that they know all about the two moons of Mars.8 Their highly detailed description includes the size, the rotation, the revolutions, etc., of each of the two moons.

    What makes this particular allusion so provocative is that the two moons of Mars were not discovered by astronomers until 151 years after Swift's publication of Gulliver's Travels in 1726. It was in 1877 that Asaph Hall, using a new telescope at the U.S. Naval Observatory, shocked the astronomical world by discovering the two moons of Mars.

    What makes the two moons so difficult to see is that they are only about 8 miles in diameter and have an albedo (reflectivity) of only 3%. They are the darkest objects in the solar system: they are almost black. The two moons are also unique in their rotations and one of them is the only object in the solar system that orbits in reverse.9 For Swift to have "guessed" these correctly is absurd.

    Yet the telescopes of his day were inadequate to have actually seen these objects. But then how could he have known what the astronomers of his day did not? Swift, in order to embroider his satirical fiction, undoubtedly drew upon ancient records he probably assumed were simply legends, not realizing that they were actually eye witness accounts of ancient sightings when Mars was close enough for the two moons of Mars to be viewed with the naked eye!

    Other Implications

    The possibility that the Planet Mars interacted with the Planet Earth may have implications beyond simply ancient perturbations of our calendar and the subsequent veneration of October 31 as Halloween. It has been widely noted that the ancient Stonehenge monument in England and the Great Pyramid at Cairo have astronomical implications.10 The geometric and mathematical mysteries of these fabled monuments have been the subject of much conjecture. Cairo was founded on August 5, A.D. 969 by conquering Fatimid armies and named, "Al Kahira," after Mars. Why?

    And there are other enigmas.

    The Nebular Hypothesis

    Most of us have been taught that the planets of our solar system came out of the sun. It may come as a surprise that there are serious scientific difficulties with this presumption. In fact, a careful analysis of existing evidence suggests some surprising alternative possibilities.

    Immanuel Kant, in his General History of Nature and Theory of the Heavens, in 1755 in Germany, theorized that some four billion years ago, the sun had ejected a tail, or a filament, of material that cooled and collected and thus formed the planets. Kant is generally credited as the originator of what is commonly called the "Nebular Hypothesis," but the originator was actually Emanuel Swedenborg (1688-1772).

    Swedenborg wrote his treatise on cosmology in 1734, in Latin: Prodromus Philosophiae Retiocinantis de Infinito et Cause Creationis. Some 21 years before Kant's publication, Swedenborg proposed that the planets were the result of condensations of a gauze or filament ejected out of the sun. Swedenborg was a mining engineer with a wide range of interests and also claimed to have psychic powers. Historians and biographers seem to take him quite seriously and a number of public incidents caused his fellow Swedes of Stockholm to regard him as irrefutable. He claimed confirmation of his nebular hypothesis from sances with men on Jupiter, Saturn and other places more distant.

    (Some 20 years earlier, in 1712, when Swedenborg was 24 years old, he had the opportunity to visit with Edmund Halley at Cambridge, who described to him the various aspects of comets and their tails. Halley had made a study of the reports of various medieval comets, their orbital trajectories, dates, and descriptions, and, of course, is famous for his predictions regarding the comet that still bears his name.)

    The famous mathematician Pierre Simon Laplace (1749-1827) lent his endorsement to Kant's theory, but without checking the mathematical validations he was capable of providing. Thus, the nebular hypothesis gained widespread respectability despite serious mathematical flaws. Subsequent writers have continued to develop variations of this view even though increasing difficulties render it increasingly doubtful.

    Enigmas Increase

    The sun contains 99.86% of all the mass of the solar system. Yet the sun contains only 1.9% of the angular momentum. The nine planets contain 98.1%. There is no plausible explanation that would support a solar origin of the planets.

    James Jeans (1877-1946) pointed out that the outer planets are far larger than the inner ones. (Jupiter is 5,750 times as massive as mercury, 2,958 times as massive as Mars, etc.)

    Other observations seem to raise even more provocative enigmas concerning our planetary history:



    There are three pairs of rapid-spin rates among our planets: Mars and Earth, Jupiter and Saturn, and Neptune and Uranus, are each within 3% of each other. Why?


    Earth and Mars have virtually identical spin axis tilts (about 23.5). Why?



    (From angular momentum and orbital calculations, it would seem that these three pairs of planets may have been brought here from elsewhere.)
    Why does Mars have 93% of its craters in one hemisphere and only 7% in the other? It would appear that over 80% occurred within a single half-hour!



    There are other mysteries and we certainly must take most of the conjectures in the field of cosmology as simply what they are: conjectures. But the more we learn, the more we have come to take the Word of God more seriously. After all, He made them all and ought to know! But He has left the thrill of discovery to us all if we will but trust Him:

    It is the glory of God to conceal a thing: but the honor of kings is to search out a matter. - Proverbs 25:2

    The secret things belong unto the LORD our God: but those things which are revealed belong unto us and to our children for ever, that we may do all the words of this law. -Deuteronomy 29:29

    We hope that this brief article will provide some conversation for a warm summer evening.

    * * *
    Last edited by rdelmonico; 02-02-2014 at 02:38 PM.
    There is a minimal level of dignity that should be afforded to all.
    No-one is above anyone else.
    No-one cares what you know unless they know that you care.
    Winning an argument and losing a friend is not (in my humble opinion) winning.

  8. #18
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    Quote Originally Posted by rdelmonico View Post
    What makes the two moons so difficult to see is that they are only about 8 miles in diameter and have an albedo (reflectivity) of only 3%. They are the darkest objects in the solar system: they are almost black. The two moons are also unique in their rotations and one of them is the only object in the solar system that orbits in reverse.9 For Swift to have "guessed" these correctly is absurd.
    Hello Rick
    Besides this interesting point of the two moons and the one with a reverse orbit, it is also a mystery why Venus is the only planet spinning in our solar system with a spin in the opposite direction to all the other planets.


    David

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    Wolfgang Pauli and the Fine-Structure Constant

    from: http://worldsciencepublisher.org/jou...e/view/887/821



    Journal of Science (JOS) 148
    Vol. 2, No. 3, 2012, ISSN 2324-9854
    Copyright © World Science Publisher, United States
    www.worldsciencepublisher.org




    Wolfgang Pauli and the Fine-Structure Constant
    Michael A. Sherbon
    Independent Researcher
    Email: michael.sherbon@case.edu
    Abstract – Wolfgang Pauli was influenced by Carl Jung and the Platonism of Arnold Sommerfeld, who introduced the fine-structure constant. Pauli’s vision of a World Clock is related to the symbolic form of the Emerald Tablet of Hermes and Plato’s geometric allegory otherwise known as the Cosmological Circle attributed to ancient tradition. With this vision Pauli revealed geometric clues to the mystery of the fine-structure constant that determines the strength of the electromagnetic interaction. A Platonic interpretation of the World Clock and the Cosmological Circle provides an explanation that includes the geometric structure of the pineal gland described by the golden ratio. In his experience of archetypal images Pauli encounters the synchronicity of events that contribute to his quest for physical symmetry relevant to the development of quantum electrodynamics.
    Keywords – Wolfgang Pauli; Fine-Structure Constant; Pauli's World Clock; Cosmological Circle; Platonism
    1. Introduction
    Wolfgang Pauli (1900-1958) was an Austrian-Swiss theoretical physicist noted for his work on the discovery of the exclusion principle, the fourth quantum number in the theory of spin, prediction of the neutrino, and calculation of the hydrogen spectrum [1-5]. While under the direction of Arnold Sommerfeld at the university, Pauli was influenced by Sommerfeld’s search for a Platonic understanding of physics and connections implied by the mystery of the fine-structure constant. Pauli’s interest in the philosophy of science was applied to the interpretation of quantum physics and magnified with the analysis of his dreams early in his career by Carl Jung [5]. This work then deepened his attraction toward the relationship between his dream images and the abstract concepts he encountered in physics. Richard Feynman proclaimed the fine-structure constant as one of the greatest mysteries of physics [2]. The physicist Max Born declared, “... the explanation of this number must be the central problem of natural philosophy.” [2]. As the fine-structure constant determines the electromagnetic strength its theoretical origin was for Pauli “... the most important of the unsolved problems of ... physics.” [3, 6].
    2. Wolfgang Pauli’s World Clock
    Both Pauli’s waking vision of the World Clock and the Cosmological Circle embrace the archetypal images of space with the circle, square, triangle, and the cycles of time. In an allegorical study Plato described the geometric proportions of the Cosmological Circle [7, 8], the ground plan for many ancient monuments and temples. The Pythagorean geometry of the 3, 4, 5 right triangle and the “squared circle” form the basis of the Cosmological Circle. The heptagon is an additional feature of the Cosmological Circle, and its relation to the cycloid curve connect it to the foundation of calculus and the history of the least action principle. Pauli’s world clock has three rhythms with two orthogonal central discs, encircled by a gold colored band divided into 32 parts, and supported by a blackbird (the bird of Hermes [9]). The outer gold colored band represents 32 cubed or 32,768 total pulses of the three rhythms, which is the harmonic of Walter Russell’s carbon pressure point of the carbon octave and significant to William Conner’s harmonic system [10] related to the energy of the World Grid [11]. According to Pauli a feeling of “most sublime harmony” was produced by this abstract structure [2]. “According to Jung, Pauli’s vision of the World Clock represents the essence of space-time ...” [1, 12], and was likened to Kepler’s first geometrical ordering of the solar system, similar to the construction from the ancient canon that involves the geometry of the polygon circumscribing constant; to which Pauli adds his interpretation of time in his “Great Vision.”
    Another interpretation of Pauli’s World Clock could be made comparing it to a basic yin-yang space-time model of brain-mind function describing hemispheric interactions [13]. Pauli associated the rhythms of the World Clock with biological processes (in particular the four chambers of the heart and its average rhythm of 72 beats per minute) as well as with psychic processes [14]. In Wolfgang Pauli’s visionary World Clock geometry the blackbird is a symbol for the “turning inward” at the beginning stage of alchemy and the
    M. Sherbon, JOS, Vol. 2, No. 3, pp. 148-154, 2012 149
    messenger for the creative solar principle. Corresponding to this inward turnabout is the angle of 180º = 32º + (4 × 37º) ≃ 32º + 4 tan−1(3/4). From the Beyers-Brown drawing of Pauli’s dream, half of a golden rectangle encloses the blackbird. A line extended from the left side of the golden circle through the beak to the back foot, then a right angle up to the right side of the gold circle forms a triangle of approximately 32º, 90º, and 58º respectively. The cot32º ≃ sec(2π/7) ≃ 16/π² ≃ φ, the golden ratio. The csc² 32º ≈ 1 + φ² = φ√5, square of the diagonal of a golden rectangle, and 360º/φ² ≃ 137.5º the golden angle. 7φ divides the circle into approximately 32º segments, 360º/7φ ≃ 32º (φ = 2 cos 36º ≃ 1.618 033 988 749, (see Eq. (6)), 32º + 45º = 77º ≃ 3π/7 radians, apex angle of the large triangle in the heptagon. One radian, 360º/2π ≃ 32º + 180º/7.
    The World Clock has three rhythms or pulses and 32 partitions dividing the circle, 360º/32º = 45º/4 = π/16 radians and cos(π/16) ≈ R cos32º where R is the outer radius of the heptagon with side equal to one, R sin32º ≃ 3/5. On the top of this “Pauli triangle” are two smaller back-to-back triangles with approximately the same angles. The apex at the top of the vertical disk is 58º + 58º ≃ 116º approximately the regular dodecahedron dihedral angle. The dihedral angle is the internal face angle where the two adjacent faces of the polyhedron meet.
    3. Space, time, and synchronicity
    The subject of synchronicity was investigated at length by Pauli and Jung in their essay on The Interpretation of Nature and the Psyche [15] and the geometry of this artwork could be an example of a synchronistic “meaningful coincidence” as well as intuitive clues toward something more than “numerical coincidence” for calculations that follow [16]. The “Pauli triangle” is also found in the symbolic form of the Emerald Tablet of Hermes, appearing at the very end of the same chapter of Jung’s description of Pauli’s World Clock and having a vertex on the Philosopher’s Stone [12]. The “Golden Chains of Homer extending from the Central Ring of Plato” in the tablet divides the mandala into the golden angle and forms a triangle that also intersects the Philosopher’s Stone [17, 18]. The location of the Philosopher’s Stone is the same area as the zero-point crossover of the infinity symbol (called the Singularity or the Primal Point of Unity) in the Rodin Coil schematic, based on the nonagon and modular arithmetic [19], with parallels to Walter Russell’s cosmogony [20]. The pentagon angle of 72º minus 32º is equal to the nonagon angle of 40º. The vertex angle of the nonagon, 140º, when considered as the central angle of a triangle in a circle forms the Egyptian hieroglyph for neb or gold [21] related to quintessence, or the “unified field” of physics.
    The symbolic form of the Emerald Tablet is also described by Sir Laurence Gardner as the “Alchemical Medallion of the Hidden Stone” and he reports that
    Newton and Boyle’s discoveries were attributed to help from the archive of the Hermetic Table [17, 18]. Also stated by John Michell, “Newton, who laid the foundations of modern cosmology, was also one of the last of the scholars of the old tradition who accepted that the standards of ancient science were higher than the nobler, and sought, like Pythagoras, to rediscover the ancient knowledge.” [11]. From the symbolism of Pauli’s World Clock 9 × 9 × 32 = 2,592, compared to the archetypal 144 × 180 = 25,920 of the Platonic Year completing a 360º precessional cycle [7]. Also, 25,920/504 = 360/7 ≃ 85/√e, see Eq. (1), and e is Euler’s number, base of the natural logarithm. The proportion for the classical “squared circle” construction is 8/9 = 320/360 and 8 × 9 = 72 = 32 + 40.
    Pauli’s interpretation of the World Clock as the “three permeating the four” is essential to the polemic between Fludd and Kepler that Pauli tried to resolve within himself and related to his presentation in “The Influence of Archetypal Ideas on the Scientific Theories of Kepler” of the hieroglyphic monad in Fludd’s excerpt describing the quaternary [3, 22]. Pauli’s interpretation also relates to the Pythagorean-Egyptian tradition regarding the 3, 4, 5 right triangle that is the basis for the construction of the Cosmological Circle. The various interpretations of the Cosmological Circle include the maze of nested polyhedra within the dodecahedron and their transformations. David Lindorff comments, “Pauli’s sense that number in itself had a deep psychological significance is striking; it would later become of singular importance to him. ... He wrote, ‘Here new Pythagorean elements are at play, which can perhaps be still further researched.’” [23]. Harald Atmanspacher and Hans Primas explain, “Pauli understood that physics necessarily gives an incomplete view of nature, and he was looking for an extended scientific framework.” [24]. Pauli also worked with Marie-Louise von Franz, who wrote in Number and Time, “Numbers, furthermore, as archetypal structural constants of the collective unconscious, possess a dynamic, active aspect which is especially important to keep in mind. It is not what we can do with numbers but what they do to our consciousness that is essential.” [25]. With this numerical analogy and parallels to neuroscience, Mark Morrison states in his overview, Modern Alchemy: “At this border of science and our deepest sense of our mental and even spiritual selves, alchemy is again demonstrating its relevance and durability.” [26]. Other examples of solving the Kepler-Fludd problem that Pauli symbolized by the numbers three and four are found in the philosophy of Joseph Whiteman [27] and Franklin Merrell-Wolff [28].
    4. The fine-structure constant calculation
    The fine-structure constant has a dimensionless value determined by the most recent experimental-QED calculations: α−1 = 137.035 999 173 (35) (T. Aoyama, et al [29]) and α−1 = 137.035 999 173 3 (344) (T. Kinoshita [30]). Approximating α−1 ≃ 137.035 999 168:
    sin α−1 ≃ 504/85κ. (1)
    The quantitative and qualitative reasoning for the approximation is significant to Plato’s geometry, 7 × 72 = 111 + 393 = 504, proportional to the large radius of the Cosmological Circle [31], and Plato’s favorite 5040 = 7!, of the larger harmonic proportion [8]. cos(π/16) cot(π/16) ≃ 504/85 and 6 × 85 = 6 + 504. 2 × 54 = 108 and 108 + 144
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    = 252. 2 × 252 = 504. The polygon circumscribing constant [32], κ ≃ 8.700 036 625 208 ≃ e² sec32º and cot32º ≃ φ. Another calculation involves Pythagorean triangles related to the Cosmological Circle and the prime constant [33], ρ ≃ 0.414 682 509 851 111 ≃ φ√5/κ, which has a binary expansion corresponding to an indicator function for the set of prime numbers. The inverse alpha again:
    α−1 ≃ 157 − 337ρ/7 (2)
    where α−1 ≃ 137.035 999 168, approximately the same value as determined in Eq. (1) from above. The square of the diagonal of a “prime constant rectangle” is 1 + ρ² ≃ κ/e² ≃ 5/3√2 ≃ sec32º, with the angle from “Pauli’s triangle” found above. 180 − 23 = 157, and 360 − 23 = 337. 23 + 37 = 60, 60/φ ≃ 37, and φ ≡ (1 + √5)/2 see [34]. 37 + 120 = 157. 23 + 85 = 108, proportional to the Moon radius of the Cosmological Circle. 7² + 108 = 157. Related to this is the main Pythagorean triangle 108, 144, 180. The triangles 85, 132, 157, and 175, 288, 337 are primitive Pythagorean triples. 60 + 72 = 132 and 72 + 85 = 157. 85 + 90 = 175, 4 × 72 = 288, and 85 + 504/2 = 157 + 180 = 337. 6² + 7² = 85 and another triangle is 36, 77, 85. 36 is the basic multiplier for the 3, 4, 5 right triangle geometry, while 72 is the next. With the two basic radii 7 and 11, 7 × 11 = 77, and 5 × 36 = 180.
    Other related approximations include 1 + ρ ≃ √2, cos32º ≃ 2ρ, 5ρ ≃ φf /φ where φf is the reciprocal Fibonacci constant [34], and 360/φ³ ≃ 85. Also, α ≃ ρ/32√π. The outer radius of the regular dodecahedron (√3 + √15)/4 ≃ γ/ρ where γ is the Euler-Mascheroni constant, see Eqs. (4) and (6).
    An “infinitely nested set of circumscribed polygons and circles” [32] gives the polygon circumscribing constant κ  sec(π/3) sec(π/4) sec(π/5) ..., which is also formulated as a converging series involving the Riemann zeta function ζ(s) that is found in determining alpha, the fine-structure constant. The Riemann zeta function is involved in the perturbative determination of the fine-structure constant from quantum electrodynamic theory and the experimentally measured value of the electron’s gyromagnetic ratio [35].
    In 1949 Wolfgang Pauli and Felix Villars published a paper together on Pauli–Villars regularization for the problem of infinities in quantum electrodynamics [36]. Pauli also corresponded with Julian Schwinger, noted here for his introduction of α/2π in the corrective calculation for the anomalous magnetic moment of the electron and his zeta function regularization for the renormalization effort.
    Accurate to seven places, sinα−1 ≃ 8δ/7, where δ is the Gompertz constant (or the Euler-Gompertz constant, which can also be expressed in relation to Euler’s number [37]), δ  −e Ei(−1) ≃ φ/e, where Ei is the exponential integral. Returning to the polygon circumscribing constant, κ² ≃ 76, κ² + π² ≃ 85, sinα−1 ≈ 32φ/κ², and sinα−1 is the approximate ratio of the 32º × φ ≃ 51.8º base angle of the Great Pyramid of Giza to the apex angle of approximately 76º. Vertex angle of the pentagon 108º − 32º = 76º and cscα−1 ≃ R√φ, see Eq. (4) discussion, with Ras the radius of the regular heptagon with side equal to one. α−1 ≃ 16π²/R. With prime constant ρ and γ, the Euler-Mascheroni constant; R ≃ 2γ ≃ − ln(ρ √γ) and γ ≈ 5/κ. Also, κ + D ≃ 11, the basic diameter of the Cosmological Circle, where D is the diameter of the regular heptagon with side equal to one [8]. The PDG [38] value for the strong coupling constant αs ≃ 0.1184 (7) is proportional: αs/α ≃ κ/πρ². αs ≃ 1 − κ/π² ≃ sec32º/π². κρφ² ≃ φρ² is the diagonal of a 5 by 8 approximate golden rectangle.
    Brown Landone writes that long before the Egyptians the Teleois were used by the ancient masters of Tiajura, then the Tiahuanacans and Incas of South America. “Teleois numbers form the long lost canon of Polykleitos, since they were used to determine the structures of all great temples of Greece and Egypt where Pythagoras lived ...” [39]. “The Teleois proportions are used by the creative force because they best fit the electromagnetic energy fields of the atom.” [40]. As part of a series based on modulo 3 arithmetic, the Teleois proportions are easily noticeable in the Queen’s Chamber of the Great Pyramid of Giza, designed with seven Teleois spheres that also correspond to the geometry included in the Cosmological Circle. “Within the great sphere of 31 – represented by a circle – six other Teleois circles exactly contact or intersect each other in perfect Teleois proportions.” [39]. The diameters are 1, 4, 7, 10, 13, 19, and 31. The sum of these seven diameters is 85, harmonic of the √α. The sum of the first six diameters is 54.
    William Conner also referenced the Teleois as a “cosmic formula behind form in the physical world” and modifies this series with a 144 multiplier beginning with 4 as 144, giving a culminating Teleois diameter of 11,664 or 108² (“a number of extraordinary interlocking potential” determining the root tone generators of his Fibonacci-harmonic Quadrispiral and also found in the Great Pyramid proportions) [10]. 11,664 is also the proportional harmonic of α/2π, equal to the classical electron radius divided by its Compton wavelength.
    Julian Schwinger introduced α/2π to the quantum electrodynamic problem of the anomalous magnetic moment of the electron, see Eq. (6) [41]. The harmonic of α/2π is also the value of Coral Castle builder Ed Leedskalnin’s proportion, proclaimed by some of his followers as the “secret of the universe” [42]. On the Teleois again, “Understand the proportions of the atom and its electromagnetic frequencies and you can understand why the proportions of the Teleois were used.” [40]. α−1 ≃ 85φ and cscα−1 ≃ √85/2π . More exactly, α−1 ≃ 137 tan (tanh(302/285)) where 302/285 = 1 + 17/285 ≃ √(2/eγ) ≃ δ√π see Eq. (4) discussion. From the harmonic braiding shown by William Conner [10], 370 − 285 = 85, 5 × 17 = 85, 360 − 58 = 302, and 32 + 58 = 90.
    From William Eisen’s [43] construction of the “All-Seeing Eye” 60º + 77º = 137º and sin137º = cos47º. 47º/2 = 23.5º, the approximate tilt of the Earth axis, considered by Scott Creighton and Gary Osborn in The Giza Prophecy as “the most important of the precessional angles encoded in the Giza pyramids ...” [44]. With tetrahedral angle, 19.5º + 23.5º + 47º = 90º. Additionally, the northern shaft in the King’s Chamber pointed to Alpha Draconis, circa 2450 B.C. at an angle of approximately 32º. Corresponding to the construction of the Great Pyramid layering of
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    stones and Pauli’s World Clock symbolism is the connection between paramagnetism (including Pauli-paramagnetism) and the diamagnetism found in the golden ratio geometry of organic growth [45].
    5. Quintessential questions of the golden ratio
    A golden rectangle of whirling squares constructed by Bonnie Gaunt, based on the sacred geometry of the solar system, has the side of a square proportional to 504 [31]. 504/85 ≃ √2φ³ ≈ 2√κ . Dan Winter puts two of these golden rectangles together in opposite directions, constructs a Vesica Piscis, and draws two intersecting golden ratio spirals. This forms a main Pythagorean triangle φ, φ + 1, φ √(φ+2) with side ratios φ √(φ+2)/φ = √(φ+2) ≈ csc32º which is also the approximate cube-sphere ratio of 6/π = π/ζ(2), a significant ratio in ancient Egyptian geometry [34]. Also shown above, cot32º ≃ φ.
    Continuing with Winter’s geometric construction, the golden ratio spirals are then shown dynamically forming a toroidal vortex that fits in a dodecahedron. Winter suggests this action is the source of gravity and the formation of mass, by “fractal charge compression” (charge is interpreted broadly here as a form of the ether, or the alchemical quintessence, in which Winter and others report an interesting relationship with the dodecahedral structure of the noble elements). The dodecahedron has been considered a three-dimensional version of the Cosmological Circle and was associated with the alchemical quintessence [8, 34]. Also suggestive, the expression for Newton’s gravitational constant G in terms related to Planck momentum is G = ħc/mP2 and from the relation for the fine-structure constant ħc = e²/α therefore, αG = e²/mP2, the electric charge to Planck mass ratio [34, 46].
    In William Eisen’s Cabala the number 137 is interpreted as the MG or “image” and 37 is the CG or “center of gravity” [43]. According to Marcus Chown [47], “Perhaps the most surprising place the golden ratio crops up is in the physics of black holes, a discovery made by Paul Davies,” [48, 49] (for other examples see [50-53]). This brings up one of the most fundamental concepts of alchemy, the prima materia, or “first matter” symbolized by the color black (Pauli’s blackbird) and related to the aethereal quintessence of the Philosopher’s Stone.
    The angular momenta found in massive particles are related to quintessence, the Pythagorean harmonic of Planck momentum as described by Malcolm Macleod, Q² ≃ mP c/2π [46]; with the fundamental geometry related to the regular heptagon (which is related to the origin of calculus and the least action principle [8, 34]). The quintessence Q has a Pythagorean relationship with C:
    C² = Q² + Q² ≃ cot (π /7), (3)
    where C² is the approximate inner diameter of the regular heptagon with side equal to one. Quintessence also has other simple relations with the pentagon geometry, tan72º ≃ 1 + 2Q², and Q ≃ √3 cos54° ≃ 2 tan27° (54° is half the vertex angle of the pentagon and also noted ln32 ≃ 2√3). C is also a fundamental harmonic of the “grid speed of light” found in the World Grid [11, 34], the fundamental tone of William Conner’s version of the Pythagorean Table [10], and proportional to the decagon vertex angle. Also, 2C² ≃ √(e2+ π 2) and C² ≃ 5ρ ≃ φf /φ where φf is the reciprocal Fibonacci constant [34]. Q² ≃ 25/24 canonical ratio of ancient metrology related to the precessional cycle calculation [11]. Next the fine-structure constant is shown related to the angular momentum property characteristic of massive particles, which again is related to “Pauli’s triangle.” The quintessence harmonic related to the golden ratio and inverse fine-structure constant:
    csc α−1 ≃ CQ = √2Q2 ≃ 2γ√φ. (4)
    cos32º ≃ γCQ and γ ≃ 2/R with R as the outer radius of the regular heptagon with side equal to one. Other approximations of quintessence: Q ≃ 1 + αφ² ≃ √2ρ/γ, where γ is the Euler-Mascheroni constant again. Also, Q ≃ ln(κ/π) ≃ ln(R/ρ) and Q/3 ≃ √γ/5 ≃ e/8. Q³ ≃ √2/eγ ≃ √φ /C. With the inverse of α/2π from Schwinger, in radians sin (2π/α) ≃ Q/φ.
    Another geometric relationship, recalling Euler’s formula shows a connection between the golden ratio, the dodecahedron, and quintessence: eiQ ≃ (φ²/5) + (√5 i /φ²) ≃ cosQ + i sinQ, thus Q ≃ 1.019 radians. The cos−1(φ²/5) ≃ 58º, sin−1(√5/φ²) ≃ 59º which shows angles close to the complementary angle in “Pauli’s triangle” and the sum of both is approximately the regular dodecahedron dihedral angle.
    The proton/electron mass ratio mp /me ≃ 1836.125 672 47 [38] and with nine place accuracy csc(mp/me) ≃ √3 − π/85. Other important mass ratios also have simple approximations involving quintessence and “Pauli’s triangle.” The W boson from electroweak theory and the Higgs boson, mw/mHo ≃ Q tan32º. The Z boson from electroweak theory and the Higgs boson:
    mz/mHo ≃ cos² 32º ≃ Q/√2. (5)
    Also, Higgs boson and top quark from quantum chromodynamics, mHo/mt ≃ Q cos² 32º [38]. In later graphical representations Winter shows how racheting a cube five times by 32º forms the dodecahedron and explains how this is related to the opening of the pineal gland. The main supporting reference is the 32º head tilt of the Great Sphinx of Giza noted by John Anthony West.
    The aspect of the dodecahedron in question here is related to Krsanna Duran’s Timestar, where Winter finds the square root of phi to be significant in the proportional relation between the dodecahedron and the rotation of the enclosed tetrahedra (recall the discussion above, cos23.5º ≃ √φ tan36º showing the decagon angle and φ = 2 cos36º) [54]. The action has parallels to Pauli’s vision of a World Clock described by Jung as a mandala.
    The configuration of polygons determining the polygon circumscribing constant κ was also described as a mandala, notable in the ancient canon according to Marie Franz and Elson Haas [25]. The harmonic of the polygon circumscribing constant is also found in the
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    diameter of Stonehenge (with an architectural design also based on the Cosmological Circle) and 87/54 ≃ φ. Also from the Cosmological Circle, the Earth-Moon radius divided by the Earth radius, 504/396 ≃ √φ ≃ 108/85, with the proportional Moon radius of 108 [31, 34].
    A more precise approximation for quintessence reveals a factor of 7 and 85 again, Q ≃ exp (42/(56P + 85e))² [8, 34]. P ≃ 1.324 795 724 47 ≃ 5Q3/4, the silver number P [8] is the root of x³ − x − 1 = 0, also the limiting ratio of successive terms in the Padovan sequence and Perrin sequence. The silver number has a property similar to the golden ratio, P + 1 = P³.
    6. Electron magnetic moment anomaly
    In modern quantum electrodynamics the g-factor of the electron is represented as a series expansion in powers of α/2π yielding the value g/2 = 1.001 159 652 180 73 (28) [35], also one of the most precise experimental measurements [35]. A general approximation of the anomalous magnetic moment of the electron ae  (g − 2)/2 can be made from explanations of spin-orbit coupling and reasoning from alternative theory [45, 55-58]:
    g/2 ≃ 1 + (α/2π) − (φα/2π√2)2 + (α/2π γ)3 − (α/2π φ)4. (6)
    g/2 ≃ 1.001 159 652 180 75 with the value of alpha from Eqs. (1) and (2). The harmonic formula above involves a convergence of Julian Schwinger’s work with Green’s functions [41], the classical geometry behind Pauli’s World Clock vision, and the corresponding golden ratio φ aspect of the Cosmological Circle (from the center to the mid-edge of the dodecahedron equals φ²/2 = π/golden angle in radians and the chord of the pentagon face is φ).
    From the regular heptagon, the radius with side equal to one, R ≃ 2γ. The Euler-Mascheroni constant is the finite part of the harmonic series in the Riemann zeta function of ζ(1) [59], used in quantum electrodynamic calculations [60, 61]. Euler’s constant γ ≃ 0.577 215 664 901 32 [62], for γ and the Riemann zeta function ζ(s) see Julian Havil’s Gamma [62]. The heptagon of the Cosmological Circle is related to the torus. With the volume of a torus, or the hypersphere surface area: 2π²R³ ≃ 32R³/φ and R = φ sec32º, α−1 ≃ 2π²(φ sec32º)³. R³ ≃ 360º/tan−1(√φ), with an approximate heptagon angle. The cube/sphere ratio, 6/π ≃ φ sec32º.
    As Malcolm Mac Gregor explains in The Power of Alpha, the essence of the fine-structure constant is the ratio of “... the ‘spherical geometry’ of the electrostatic energy E = e2/r = mc2 to the ‘spherical geometry’ of mechanical energy, ħc/r = mc2, which is defined by the Compton radius of a relativistically spinning sphere.” [63]. Then re/rm = e2/ħc = α.
    Another interpretation of alpha, the fine-structure constant, related to Pauli’s World Clock geometry is the standard perspective of action, the product of energy and time. Consider two elementary particles separated by a distance r that have an electrostatic energy of e2/r and the time for light to travel a distance r is r/c, so the action is (e2/r) × (r /c) = e2/c. Since the unit of quantum action for light is ħ (from E = ħω), the ratio of the electrical action to the quantum action is e2/ħc = α.
    7. Conclusions
    Since Arnold Sommerfeld’s introduction of the fine-structure constant and the discovery of Planck’s constant by blackbody radiation, attempts were made to find relationships between them. They were found connected by prime numbers, particular values of the Riemann zeta function, the Boltzmann constant, and even a dimensionless blackbody radiation constant [64]. Pauli displayed elegance in his own mathematical techniques for calculating the hydrogen spectrum [65].
    From an overview by Domenico Giulini, “In his last paper on the subject of discrete symmetries ... Pauli comes back to the question which bothered him most: how is the strength of an interaction related to its symmetry properties?” [66]. This question is associated with the manifestation of charge from alchemical quintessence, the rotations associated with the symmetry groups of Platonic solids, and part of the archetypal process behind Pauli’s World Clock.
    In “Science and Western Thought” from Wolfgang Pauli: Writings on Philosophy and Physics Pauli asks the question, “Shall we be able to realize, on a higher plane, alchemy’s old dream of psychophysical unity, by the creation of a unified conceptual foundation for the scientific comprehension of the physical as well as the psychical?” [67]. Kalervo Laurikainen responds in The Message of the Atoms, “If we are not bound to materialistic presuppositions, the psycho-physical unus mundus of Pauli and Jung appears, in fact, to be the natural ontology of quantum mechanics.” [68]. This leads to a complementary representation of reality similar to Bohr’s philosophy, rather than that of Cartesian dualism.
    Thus Wolfgang Pauli considered, “Concepts created by mathematics, such as Riemann’s surfaces, lend themselves very well to a symbolic representation of the relativization of the concept of time ....” and concluded that “... most modern physics lends itself to the symbolic representation of psychic processes.” [16]. Pauli’s World Clock vision involves the symbolic images and archetypal stages of alchemical transformation at the root of both mental and physical worlds [69].
    From Pauli’s imaginal geometry the unit circle on the complex plane was his i ring, represented by eiθ and yielding the “Pauli triangle” for θ ≃ Q, quintessence in radians. For Pauli the ring embraced both intellect and intuition symbolic of the unus mundus.
    The World Clock geometry combined with the self-recursive property enabled by the golden ratio and an alchemical interpretation of its symbolism is also descriptive of the pine cone shaped energy field of an activated pineal gland, often depicted in ancient Egyptian art along with the legendary bennu bird that is known for its association with the cycles of time and the final phase of the alchemical process (an awakening of the “golden” crown chakra in the aetheric field of mfkzt [17]). The pineal gland biology is an active area of research in modern biophysics and pineal activation might explain the “Pauli effect” reported by experimental physicists. Pauli knew of Descartes ideas about the pineal gland and Plato suggested that mathematical discipline such as Pauli engaged in could
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    help awaken this special gland. Wolfgang Pauli wrote several unpublished papers considering the symbolic representation of mental process from the mathematics of the electromagnetic field. From the geometry of neb, the hieroglyph for gold [21], Q ≃ 140α. From the previous force field analogy with the four basic constants of “recovered science,” Q ≃ πe²/κφ² [34]. From the torus, tan−1(√φ) is the approximate heptagon angle, with √φ ≃ 4/π.
    Beyond the alchemical interpretations of Carl Jung, the torus topology that relates the dynamics of Einstein’s relativity with classical mechanics and its geometry is found in Egyptian art, especially their representation of anatomical proportions. Some depictions of Tehuti-Thoth from ancient Egyptian art are similar to Pauli’s World Clock having the bird space-form of the alchemical tradition with the archetypal signs and symbols of time- cycles [70-72].
    In The Sphinx and the Rainbow David Loye states, “Wolfgang Pauli felt there could be a correspondence between the wave-particle mystery in physics and the mind-body problem in philosophy ...” [73]. F. David Peat also writes in Synchronicity, “Pauli, as a physicist, was also seeking to discover an inner unity between the elementary particles and their abstract symmetries.” [74].
    Beverley Zabriskie writes in her introduction to Atom and Archetype, the Pauli/Jung letters edited by C.A. Meier, “For Pauli, symmetry was the archetypal structure of matter. Just as the alchemists looked for the substratum of reality beneath matter, he came to the view that the elementary particles were not themselves the ultimate level of realty.” Then she explains, “As he became more familiar with alchemy as a psycho-physical unity, Pauli saw the same lumen naturae, the light of nature, or the ‘spirit in matter,’ glimpsed by Paracelsus and Jung.” [75].
    Writing on “Wolfgang Pauli’s Philosophical Outlook” in Across the Frontiers, Werner Heisenberg says; “Among the studies to which Pauli was prompted by the philosophical labors just referred to, it was those on the symbolism of the alchemists which left particularly lasting traces behind ...” [76]. Many of Pauli’s ancestors were from Prague, a traditional center for alchemical activity [6].
    In an article about Pauli by his former assistants Marcus Fierz and Victor Weisskopf, “If we ask ourselves what above all was Pauli’s calling the answer would be: he was a natural philosopher in the classical sense of the phrase – as it applies to Kepler, Galileo, and Newton.” [77]. A later retrospective by Victor Weisskopf shows Pauli “... developed a deep friendship with Gershon Scholem, the great scholar and world authority on Jewish mysticism, the Kabalah. (The Kabalah ascribes a number to each word of the Hebrew language, a number that has a deep symbolic significance. The number corresponding to the word Kabalah happens to be 137.)” [78].
    In his essay, “Pauli (Wolfgang) 1900-1958,” Charles Enz (Pauli’s last assistant) writes; “This number 137 symbolized for Pauli the link with the magic world of the alchemists which has so much fascinated him.” [79]. Recalling his preoccupation with the fine-structure constant and research on synchronicity with Carl Jung, Pauli was moved upon finding his room number was 137 at the Red Cross hospital during his last days; when pineal activation can happen in transition [16, 79].
    Acknowledgements
    Special thanks to Case Western Reserve University, Franklin Merrell-Wolff Fellowship, Social Science Research Network, Pauli Archives, MathWorld, and WolframAlpha.
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    There is a minimal level of dignity that should be afforded to all.
    No-one is above anyone else.
    No-one cares what you know unless they know that you care.
    Winning an argument and losing a friend is not (in my humble opinion) winning.

  10. #20
    Join Date
    Dec 2013
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    To Richard

    Hi Richard
    Please read my previous post about Wolfgang Pauli.
    It should tie up some loose ends in our discussion.
    thanks
    Rick

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