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Historical credits. Individuals: Pythagoras, Musashi, Böhme, Kepler, Galileo, Leibniz, Newton, Jung, de Broglie, von Neumann, Dirac, Rife


For 2,600 years Pythagoras defines Western in the Western civilization. He built mathematical and physical sciences from scratch relying on numbers and adherence to high symmetry. Pythagoras sought fundamentals for music and by playing particular string length ratios on a monochord established the scale of the musical octave. The scale of notes has particular frequency ratios (making do, re, me, ..) that is unique to the West. Some ratios were found pleasant sounding (harmonious) and a claim made that planetary orbits subscribe to harmonious ratios. Some reports speak of Pythagoras applying harmony to healing. Pythagoreans' admiration of rationing resurfaced at the Renaissance as the 'Harmony of the heavenly spheres.' Planetary orbits were measured and orbit ratios found to correspond to the notes on the musical scale.

Through the geometric relationship of numbers Pythagoras (or Pythagoreans) discovered the irrational numbers, which are constructible exactly only through the Pythagorean Theorem. Every irrational number has infinite precision -- that is, the sub-unity portion does not repeat and goes on forever. Being infinite and issuing from geometry, Pythagoreans described irrationals as the "unspeakables," for it is not possible to describe irrationals with words. (A better translation is nonverbal, which, even today, is closer to the original Greek word 'alogon' then the oft-used 'uspeakable.') The five pointed pentagram star became the Pythagorean standard as it embodies preponderance of the golden proportions -- the golden proportion being made with the irrational number of the square root of five. (The root of five, in turn, is obtained geometrically and exactly through the semicircle and the Pythagorean Theorem.) Pythagoreans discovered the first five perfect geometric 3D solids having the highest possible symmetry, which were the starting point for Kepler some 2000 years later. Plato was the first to actually publish these five solids and so they are at times called the Platonic solids. Pythagoras authored the words philosopher (a lover of knowledge) and cosmos (the order one finds in the universe of stars).

The central symbol of Pythagoras is Tetractys, which expresses the discrete steps of dimensions in geometry (0D, 1D, 2D, 3D). Tetractys also embodies the harmonious notes of vibrating musical strings having 2:1, 3:2, and 4:3 ratios -- which are all harmonious. The Pythagorean School he founded in southern Italy taught 'All is number.' While the secrecy of the school's findings makes it difficult to associate Pythagoras with particular innovations, it appears Pythagoras intended the school to operate as one whole: The intellectual property at the times could only be enforced by the school. Scholars directly attribute to Pythagoras the ideas that are "central" to the school's teaching. Pythagoreans classified numbers not only as even and odd, but also as evenly even (binary), incommensurable (irrational), incomposite (prime), and abundant (divisible by many other numbers such is the case with 360 and 24). The application of numbers also includes the idea of priority (as an unchanging characteristic, though, and that is adequate for physics but not for economics). Attributed to Pythagoras is the right angle theorem, which in its geometric form is valid for both the rational and irrational numbers -- and is the only tractable generator of irrational numbers. (Transcendentals are not constructible via the Pythagorean Theorem -- cannot say if circle squaring was resolved by Pythagoras in some fashion. There are hints on squaring by ancient Greeks.) The Pythagorean Theorem spawned the imperative pursuit of geometry lasting over 23 hundred years, until effectively lowered in priority by Kepler's orbit equations. Still, the incommensurability aspect of numbers is understood at but a gut level.

Well understood but not much publicized is the Pythagorean pursuit of salvation; by understanding the numbers and their relations via symmetries, one could earn and gain admittance into the universe. The Pythagorean way to salvation is about the truth of the workings of the universe, both the real and the virtual. (The virtual numbers issue from the square root of minus one.) There is a rediscovery of the Pythagoreans in that the Pythagoreanism was not and is not only about numbers and mysticism but it is an all-encompasing way of life. The Pythagorean way is then also about friendship, for example, which works on resolving guilt, fear, and intolerance -- the three great vices on this planet.

Pythagorean even-odd transformation and invariance rules among numbers led to the 19th Century mathematical group theory and the discovery of symmetry invariance of the atomic even and odd functions. (This may seem a stretch but the similarities are there as Pythagoreans were the only ones working the even and the odd aspects of numbers. Pythagorean classification of some numbers as evenly-odd has tantalizing links for even-odd symmetry in matter [advanced].) Johann Balmer's integer based formula governing discrete -- that is quantized, wavelengths of light issuing from hydrogen opened atom's orbitals and the whole of quantum mechanics to the Pythagorean tradition. In the future, Pythagorean concepts will also become applicable to the pyramid geometry and to the creation/realization of the unique group of incommensurable numbers -- the transcendentals. (Also see Leibniz, below.) The Pythagorean School admitted women -- something Plato and Aristotle would not follow. Pythagoras considered Tetractys the symbol of the universal order and, based on his comprehension of dimensions of independence, he likely understood more about the universe than is known today. The meaning of Tetractys, as applicable to dimensional independence, was not picked up by Euclid and is still not generally understood (the book Quantum Pythagoreans derives all known cosmic topologies from the Tetractys).

Pythagoras fame is with us as each generation rediscoveres Pythagoras through direct and indirect sources. Pythagoras not only worked the numbers as the constructs of creation, but his ideas and teaching encompasses a way of living and a way to salvation. Perhaps you will connect with Pythagoras and HIS School, which exists in written and unwritten forms on this planet.


This site's Pyhagoreans page also extends Tetractys through HyperStates. One Pythagorean application is on the golden proportion page while in the free energy article we comment on the Pythagorean discovery and the excitement over the irrational numbers. Some Pythagorean and geometric concepts are also applied at the stump-your-teacher page.

 Picture credit: The Web Gallery of Art,

        Picture credit: The Web Gallery of Art,

            The School of Athens painting above is by Raphael, which could also be called "Who is Who in Magna Graecia." As you might expect the painting has much symbolism such as the statues of Apollo and Minerva (Athena) and, of course, the semicircle. Yet, the overall feel of the painting is very human. This fresco is in Vatican (Stanza della Segnatura, Palazzi Pontifici), and it is a mystery the sponsors in 1511 would allow Raphael to forgo biblical motives. One commentary would have Vatican graciously integrating the pre-Christian accomplishments (Aristotle liked, Plato not) while another commentary sees it as a cold-and-calculating usurpation and control of Pagan knowledge. As it oftentime happens the real challenge came from within and after Martin Luther (1483-1546) the battlelines were drawn in the Counter-Reformation -- Paganism having no place in the back-to-orthodoxy fight (Galileo labeled a Pythagorean and sentenced). In retrospect the School of Athens is no victory dance for the Vatican even if it was intended that way.


            In the detail above, Pythagoras is shown reading from a book on music. A student holds a tablet in front, which shows (in another detail on right) the harmonic proportions as well as Tetractys. Pythagoras is reported to wear trousers, an unusual attire for his times.



Samurai of feudal Japan of the late 16th century, Musashi maps military strategy into the five ancient elements of Ground (earth), Water, Fire, Wind (air, culture), and Void (aether or quantum vacuum). Balancing his desires of independence and loyalty, Musashi was feared and admired. He speaks of spirit as encompassing all that can be learned and put to – in his case military, art, and agriculture – practice. Some credit Musashi with the expulsion of Christianity from Japan by fighting against the "Christian Lords."


In his drawings around 1620, Böhme shows, via back-to-back semicircles, the separation and a point contact between the real and the virtual domains, as well as some primary charkas and a dantien. Being a pious man, he fits it in a context of the church


The original SOW (son-of-a-witch), Johan (or Johannes) Kepler takes time from making a decent living doing horoscopes to successfully defend his 70 year old mother on charges of witchcraft. From the field data of (de) Brahe, Kepler derives two-body gravitational orbit equations that have general solutions. The mathematical solution of planetary orbits allows the application of the parameter of time to make orbit predictions. His use of a mathematical equation is the first departure from the 'angelical knowledge and power keeping planets going,' which, presumably, was out of man's purview. His equation was first applied by Newton who calculated the orbit of a certain comet, which allowed Halley to make a successful prediction of this comet's return. [Kepler's calculation of the volume of a beer barrel should be the textbook example on science-industry cooperation!] Even small satellites being launched into the Earth's orbit comply with Kepler's equation. He was the first to propose that the gravitational force is a mutual force between material bodies, including bodies of water, which led to his action-at-distance moon-causes-tides proposition. Kepler describes obtaining the orbit equation as his "War on Mars." As a mathematician, Kepler first noticed that the ratio of consequent Fibonacci numbers converge toward the golden ratio. Following the appearance of a telescope, Kepler places optics in the geometric-mathematical context. Kepler is the author of the words satellite and focus, and his optical tracing method continues to be in use.

We have a book review of Kepler's Witch. In the book, the intricacies of the Rudolf II Court include the year long negotiations between Kepler, the Court, and Brahe's family for the Kepler's use of Brahe's field data. Similar protracted negotiations dealt with Kepler's royalties when publishing his findings. A particular letter Kepler wrote shows him in a unique light. At the times, the Counter-Reformation executives were actually billing Kepler for his mother's jail expenses. In the letter to the jailers of his mother Kepler points out that because his seventy year old mother was held in chains it would not be reasonable to pay for two guards keeping an eye on her.

(1564 – 1642)

There are two aspects that in retrospect are the most relevant, particularly as his work happened during the Counter-Reformation and contributed to the end of the Dark Ages. Galileo Galilei is, first and foremost, the prototype entrepreneur who applied discoveries in his own business. He improved and promoted the telescope to the "civilian" authorities and, while cognizant of the need for a sponsorship he leveraged the technology of the press to publish his findings. Secondly, Galileo directly challenged -- consciously or subconsciously -- the Aristotelian credo 'Nature abhors a vacuum.' Galileo worked with a vacuum in the derivation of the (cannonball's) parabolic -- that is suborbital, trajectory, and also postulated the conservation of momentum. (It was then 100 years after the fall of Constantinople where Islamic gunnery were the principal breach weapon.) Accused of heresy at seventy by the Church and unable to squash the subpoena, Galileo travels to Rome. Because the accusation at the times is equivalent to a conviction -- the "suspicion of heresy" was really the finding -- Galileo repents and draws the minimum sentence: Galileo spends the rest of his days under house arrest.


It seems there exists no complexity Gottfried Leibniz (or Leibnitz) could not structure. Leibniz did not mind trying to make sense of the most abstract ideas one finds in metaphysics such as the monad. His discovery of the integral calculus was deeply connected to his love for a continuum, which he continued to hold on to as he delved into the ever smaller world of the infinitesimal. His clarity of presentation served him well as a diplomat-for-hire and as the inventor of the integral-differential math notation that became preferable to "Newton's own." Leibniz can well be a model of an ideal professional who continued furious and prolific career of discovery in face of much criticism while managing to acquire a considerable fortune. He also stayed close to physics applications by formulating and differentiating the scientific unit of 'momentum' and 'energy' of moving bodies. Leibniz was first to realize that the direction, in addition to energy, is being conserved -- today summarily referred to as the 'vector' law. There is one unique and very cool word Leibniz coined: the Transcendental number. He defined the Transcendental number and also came up with a numerical series (Pi/4 = 1/1 - 1/3 + 1/5 - 1/7 + 1/9 . .) that converges to the most famous of all Transcendentals, the Pi.


As much as one could make him a "mad hatter" or "The Moon is falling!" kind of guy, Isaac Newton is the archetypical alchemist, identifying with the volatility of new issues he pursued. Being a man of science, Newton fits gravity and light in the real, scientific context. He formulates the gravitational force equation -- and confirms Kepler's orbit equations -- when he places force vs. distance in the inverse square relationship. Newton's physics includes the existence of absolute spatial distance and absolute time. (An object performing discontinuous movement does not violate absolute space and time. The 'absolute' variable refers to the multitude of independent observers obtaining the same value when measuring such variable.) Considering the absolute speed light has in a vacuum (in ether), as well as the latest discoveries in electron's dual slit (self)superposition that requires the absolute reference if math is to match reality, Newton is due for another outstanding insight. Through his review of fringe (superposition) rings, Newton was first to measure the wavelength of light (1/80047 of an inch for the blue light; the node -- that is, the absence, of the blue light makes yellow). Newton calculated the air gap and determined the wavelength based on the light's standing wave -- that is, he calculated the wavelength without needing to know lightspeed. Newton is the author of the concept of mass inertia (vis inertiae) as a dynamic characteristic of mass, and his particular design of a reflecting telescope is scalable so well many models continue to be built.


From archetypes to synchronicity to introvert/extravert, Jung practices balancing of mental objects' associations as a way to mental health. Visualize. His description of inferior systems can be worked – in the context of this web site – as 'dependent variables capable of becoming independent.' This meshes with the Pythagorean notion of priority.

de Broglie

'If wave has particle properties, then particle has wave properties.' Simple. The hyperbolic reversal holds. This guy is not done yet, for he needs to generalize his wavelength equation to include virtual (complex) numbers and angular momentum in addition to his linear momentum formulation that lacks the i (the SQRT(-1)). The mechanism of momentum conservation and the non-linear inertia at high speed are to be found in de Broglie's generalized momentum-to-wave (frequency) equation. Still vaguely recognized is the advantage of reversibility that is inherent in his equation. De Broglie wave-momentum relationship (not wave-particle -- see primer on QM) is also the foundation of the proof that absolute spatial distance and absolute frame of reference can be derived and applied -- if math is to describe the reality of the experimental observation (dual slit).

Moreover, this site makes a case that a wave can have particle-like properties only at the wave's transformation, for only at transformation (at absorption) can the photon's energy manifest as real energy.

von Neumann

Works the quantum mechanical concepts to the conclusion that the collapse of the wavefunction is instantaneous. What appears to be a curiosity of the atomic environment, the instantaneous nature of the wavefunction reduction will turn out to be the most radical and the farthest reaching milestone of quantum mechanics -- once the quantum mechanical concepts are generally recognized as operating on any scale.

Von Neumann also contributed to computer development via the implementation of the 'program-store' where the program shares memory with data. While his support for Turing that the 'Turing machine is a universal machine' is freely quoted, such claim is based on intractability because it calls for unlimited time. (Scientists like to hop on intractability in cases where they do not have workable solutions of their own.) In time, von Neumann should be untangled from intractability, for his instant quantum reduction idea is just the answer for many intractable problems.


One of the quantum mechanical guys, Dirac quietly postulates the existence of the matter-antimatter pair. Duality of the real (formal) and the virtual (informal) begins to get mathematical shape. He is the first to introduce transformation operation into the behavior of the electron and kicks off the electron's dual nature.


 Ray Rife with UV microscope In the most remarkable confluence of five disciplines, Royal Raymond Rife engages optics, physics, mechanical engineering, microbiology, and electronics to attack degenerative diseases. He was the first to observe live viruses, their vulnerability, and their ability to change their benign-cancerous modality. Because governments and Nobel prize committees cannot recognize discoveries that empower individuals, Rife's recognition will come only if an infrastructure is put in place that would capitalize on his accomplishments — an unlikely event because his results are complete and the delivery inexpensive. Rife had much difficulty raising funds and Timken Bearings company stands out as the most remarkable benefactor as well. Presently one must seek this technology to avail its powerful benefits and perhaps that is how it should be. A case can be made that Rife's discovery of UV resonance (point source resonance in the ultra violet range) lives on in a much more expensive nuclear magnetic resonance (NMR) imaging -- but with Rife's cure component missing.

Rife's accomplisments include the character dimension. Raymond would not back down to or join the self-serving interests of the AMA -- and fought to the end.

In an interesting 2007 development, a vaccine is being marketed against a cancer-causing virus of the cervix. The vaccine emulates the virus only geometrically and no actual virus components are present. While no credit or a reference is given to Rife, if you become familiar with Raymond's work you will recognize that his cancer cure includes -- in addition to actually destroying the virus -- the effort of keeping the virus in its benign state. Flipping the virus into its benign state or keeping the virus from morphing could well be the mechanism behind the new vaccine (presently not claimed as a cure). [To some it is apparent that a vaccine brings in more money than a cure.] We give Raymond credit inside our article on the squaring of a circle. An engaging writeup on Rife is by Tommy Cichanowski. Comprehensive descriptions with a lot of professional investigative reporting is on RIFE.ORG

The cancer cure is missing from the mainstream (AMA) medicine but the cure is not lost. Toward the end of his life Raymond worked with John Crane, who published a list of frequencies that kill specific viruses and bacteria, including sarcoma and carcinoma. There is even a circuit diagram for building a version of the frequency amplifier similar to Rife's -- done by a person who used it on himself. If you build it and use it, share it with your family and friends [going public entails different risks for different people]. If you get into the actual mechanism you might get confused with low (audio range) frequencies being routed to a coil as a square wave (which has a fast rise time and thus contains many frequencies). You are getting close to Tesla and free energy, and you will need to appreciate that ether not only exists but that it can be energized as well. All debunkers from academia, self-interest promoters, and power seekers rely, at a minimum, on the absence of ether if they attempt to discredit your activities.


And the guys who get furiously busy when there is time to move to a new level. And the guys who almost die getting there.

Book by Mike Ivsin
 To Publisher...

In Quantum Pythagoreans the separation is followed by joining. The separation enables all individual elements to showcase their strengths while the joining creates systems -- or monads -- that continue to improve you and your universe.

The power of the Pythagorean foundation highlights the opportunities of applying new energy sources and building atomic structures from scratch. Some applications are presented in considerable detail while others are ideas waiting to happen.

Much work is in the area of the couplex, for this point has been misunderstood in the West in the past. The book explains why it is a point -- that is, why couplex must have the geometric construct of a point. Couplex can also be found in the Great Pyramid.

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Last updated February 18, 2013

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