


HyperStates, the working symbol Pythagoreans and their methods for the organization of matter There are many elements in nature that compete with each other. Physical elements, rather than being created in conflict, are formed in balance in one of the hyperstates shown here on left.
By
the numbers. Heavy duty 
In the Pythagorean tradition the universe is running on Natural (whole) numbers and on rationing and on squaring. Numerology, then, was the way of looking at just about everything. We are not staying with or departing from tradition. Yet, the picture of the HyperStates is mostly about integers and nearintegers. One hyperstate is a ratio. One other hyperstate, although it is computable and potentially real, does not seem to actually form. As of now, there are ten realizable and observed topologies in the cosmos 

There is much similarity between the colorful dots of hyperstates and the Tetractys of Pythagoras. Verbal interpretations of the Tetractys from the Pythagorean tradition such as the "universal order" in literal terms and "nature's spring" in the figurative sense are indeed close to hyperstates. A new platform, if true, is not the end but the beginning of the next building phase.
HyperStates start with Tetractys of Pythagoras. Tetractys is a numeral 10 rather than just a count of 10.
One (blue) state is added and all eleven states are placed on one facet of the tetrahedron. We arrive at the triangular pyramid geometry. I named the collection of dots the HyperStates. Each dot is a particular tractable solution (a construct) but each dot can also become a component of another solution with a change in scale and this can (and does) go on without bound. The multiple solutions overlay is what prompted me to call this symbol the HyperStates. There is yet another overlay in that a particular cosmic body may belong to several solutions. Moving throughout the cosmos, one is under several HyperStates at any one place. Very nice. But of course, it's in the book. 


Fundamentally, numbers come first. The Tetractys with 1, 2, 3, and 4 dots also refers to 0, 1, 2, and 3 degrees of independence because 1 is associated with a dot (geometric point), 2 with a line, 3 with an area (plane), and 4 with volume (some say solid). Degrees of independence are, again, numbers. Degrees of independence form the fundamental constructs for geometry. Yes, each degree of independence has its own geometric rules and, for example, you need to understand the squaring of a circle if you want to move between 1D and 2D. Overall, you need to move from 0D to 3D and back  that is, you'll need to know what it takes and how to go about it. Topology is about building things as it is a static subset of geometry, and could be seen as the 'placement' in the ancient Greek tradition or the 'measurer' of the Mayan Hunab Ku – it's about the real numbers in general. In addition to placement there is also movement (and the second book Stars and Rings will get into that ~ mid 2013). Dots of the Tetractys plus one (blue) dot form hyperstates. Hyperstates are about the creation of the real environment that is tractable (nonchaotic) and that has its origin in the virtual domain, which is oftentimes called hyperspace or ether or "fire." Hyperspace is intangible (invisible) and is not explicitly shown in the HyperStates picture because HyperStates is about the one single facet of the triangular pyramid where all real (visible, hard) topologies manifest. We can represent the hyperspace as an eye and put it on top, which results in a triangular pyramid of tetrahedron with the eye at the apex. Presently, the HyperStates picture includes three axes that project the real plane from the hyperspace or from one's eye. The projection from one's eye reveals the individual and the collective way of building the real world on the real plane because it is our cumulative knowledge that continues to compute and create the ever growing and organized universe. Although the solutions for the axial parameters converge toward integers, the integer value is not fully reached – but their sum adds up to three exactly^{*}. The sum being the integer three stems from the fundamental maxim of the real domain, which deals with tractability limits. (Tractability is a subset of computability.) If we define the triangle as the "summing triangle," then the outer hyperstates would be on the triangle's edge. The triangle can also be defined axially as the "bounding triangle," in which case the outer hyperstates would be just inside it. In either case, all hyperstates are in the plane formed by the triangle and that is the reason for calling the triangle the template of the real plane. Technically, each and every point on the real plane is a solution but because the plane is a logical plane, there is no measurement metric associated with it. The creation of realities, then, has no prescribed size. If we apply integers to the real plane, the summing of 3 out of 4 numbers (0, 1, 2, and 3) in a way that results in integer three yields ten integersumming sequences, which correspond to 10 hyperstates. The presentation (orientation, rotation, view) has no overwhelming preference. The spherical galaxy hyperstate is at the top corner as magenta. It may be said that spherical galaxy's organization is closest to the "harmony of spheres." However, bodies have no independent movement in hyperstate 3,0,0 because they all move in synchrony. Orbits also are not purely spherical but have a large degree of symmetry. Hyperstate 0,3,0 could also claim the top and the sun is indeed an awesome sight — yet the sun can also go nova. Hyperstate 0,0,3 is a simple one and, while common and uneventful, there is opportunity there for new growth because the growth is mostly localized. In the alchemical tradition a discourse on orientation would fill many pages. [If your ship is in hyperspace, you do not want to materialize in 0,3,0. But if you are building a centralized organization, that is the place to be..] Hyperstate 3,0,0 has periodicity while 0,3,0 does not. Hyperstate 0,0,3 has translational (linear) repeatability that can be called periodic as well since the velocity there is constant. In summary, Hyperstates' triangular plane has neither the "top" state nor a direction in which it is pointing (up or down or sideways). Separating the micro and macro Macro: Pythagoras' Tetractys guides and even directs the creation topology on the macro scale. Here, the real and irrational numbers are prominent while the virtual numbers deal with the periodic reduction of the gravitational wavefunction. Micro: Organized topologies also hold on the atomic scale and it is likely we will find additional hyperstates on the Tetractys plane in addition or subtraction to those shown here. Dynamic and eventdriven hyperstates define the micro of the atomic scale. On the atomic scale the hyperstate realization hops around because the plurality of electrons can instantly transition into another tractable state on the real plane. (The real and temporary states are at times called eigenstates. In the macro the hyperstate realization stays put  see below.) Squaring of a circle is unique to micro and the transcendentalirrational number interplay is the most prominent. Much promise is in understanding the tractability of the core, for completely new elements could be created. A [easy] case can be made that the core's tractable solution is periodic and that its period is constant. Tetractys is best applied at the macro. (I'd use HunabKu for the micro.) Returning to the cosmic (macro) scale, the manifestation of a particular hyperstate is the solution – that is, a particular hyperstate realization is the last step in itself. Hyperstates do not change or evolve because they are the solutions ("final condensate") resulting from unbounded and concurrent computations of the whole. One can argue that a gradual change from a dualsun system to a sunplanet system can be called evolution but in fact it is a twobody system that is the one and the same hyperstate. New hyperstates, though, are created every day through hyperspace and that is the norm (Pythagorean spring, source) of universe creation and expansion. When a sun parts into a dual sun system a new hyperstate is formed. When a new sun forms from ether (Atum's mound, scarabspin, Mayan Hunab Ku spiderspin), another new hyperstate is formed. Because the macro hyperstate is the final solution, there are no migrations or evolutions. There may be logical similarities such as a discus, ring, or onebody orbit (moon or planet) topology states but there are no inbetweens and this is because the solutions coagulate around integers. We will not find two or more planets in an identical orbit where there would be a gradual migration to a ring of planets. Similarly, we will not find a planetary ring that would gradually become a moon because, again, the ring is a particular hyperstate that is a final solution yielding a ring topology. Finally, we will not find a discus that would reduce into a body. When the hyperstate is not composed of (near) integers, as is the blue dot, we see greater topological similarity as in the bar and spiral galaxies. A good way of looking at hyperstates is that it is a framework for real solutions. A particular hyperstate is a tractable topology and such topology (such solution) is independent of scale. We can find a particular hyperstate manifestation in a planetary system, not in a solar system(s), but then it forms again in a galactic system. Scale independence results from nonlocal computational aspect of quantum mechanical gravitation having, as one of its characteristicts, an instantaneous reduction of its wavefunction. 'Independent of scale' is not the best phrase here. An entire solar system shrinks to a point with distance and despite the scale shift such solar system continues to serve, this time as a point, on the Tetractys template. (In the Quantum Pythagoreans book the independencedependence of relationships is developed in depth, including the reversible and irreversible property of a relatioship.) A nice way to conclude the micromacro section is in discussing just one aspect of the power of numbes. It is a logical process and it centers on the division of the Unit 1 {May 18, 2010}. In the micro the Unit 1 is the orbital circumference (circle/ring) and the consequent geometry that divides a circle exactly. This brings in the circumpositional numbers. The virtual numbers give you the wavefunction for the nonlocal electrons in their orbitals. Somewhat similar situation happens for the core. The squaring of a circle calls for adding irrationals into the mix to reconcile the curving energy of orbitals and 1D energy of photons that affords a measure of stability. All irrationals are via the Pythagorean Theorem. In the macro we divide the Unit 1 as follows: For Unit distance we work the 1D aspect (length, distance) by dividing Unit 1 with any real and everyday number and we also bring in the irrational distances (yes, all irrationals are in 1D). For energy we divide the Unit square (2D) via the geometric mean into as many squares as we want. Okay, you figured out you also need to to divide the Unit cube into at least two cubes and this will make a nice brainwork for some (think Archytas). Yes, you have to do it geometrically because, well, how else would you solve for planetary orbits? (Think Kepler but stay with geometry.) To top off the Tetractys, the 0D (a point) cannot be divided but it makes The One, the most important and universal geometric construct for the creation of the radial symmetry, which is applicable to both the macro and the micro. There is much more to The One and the knowledge about The One serves as the determinant – the universal credentials if you will – for anybody trying to tell us something about the workings of the universe.



Pythagoreans do not dwell on and do not fancy descriptions of reality because the Pythagorean way is about the creation of reality. The making of reality is not about pretensions but it is about the understanding of pretensions. Pythagoreans do not claim that some parts of the universe are delusions, either. The creation of real and stable and objective systems, then, requires a thorough understanding of the virtual domain that deals with the infinite superposition and relation of virtual energies, each of which brings in a measure of relevance. Conflicts resolution such as those stemming from a war, global warming, or financial markets instability call for stable solutions that  short of outright destruction (usually possible)  are not obvious or straightforward. From among the myriads of plausible answers Pythagoreans find the ones that are executable and, in the end, tractable. 

^{*} If you are familiar with incommensurable/irrational numbers and how their discovery created consternation among some nonPythagoreans, consider that it is the sum that yields the hyperstate solution. The individual components (addends) are integers, nearintegers, rational numbers, and reduced (truncated, rounded, fractioned) irrational numbers – that is, the individual components of the hyperstates are real numbers. (Quantum mechanical aspects in the Quantum Pythagoreans book deal with yet another mechanism besides truncation and rounding – that of the ancient Egyptian fractions.) Perhaps the best way of starting on irrational numbers is by taking a look at the golden ratio with one original application, or It cannot be exact from March, 2005, DSSP topic [advanced]. 

What is behind The Numbers 

Hyperstates framework is difficult, though not impossible, to figure out. The thing about hyperstates is that in the process of figuring it out you will find the answer to something that is important to you. Your solution may be personal or it may have wide applications. While it is possible to teach "everything" about hyperstates, the idea is that your solution is the most important solution. 

If you look at the missing axial parameters as a mystery, you may be able to figure out the parameters and thus the maxim. The secret behind the secret is not the lock that would be in front of the secret, for once you figure it out you will know there is no better lock than the engagement of the mystery. In fact, there is no lock but an interlock that creates order out of the competition of the triad. The Hyperstates interlock is so robust it cannot be stolen or given away, so extensive it cannot be memorized, so unique you will know right away, so practical it can be applied every day, and so logical that even a wrong answer bespeaks of a correct concept. Should you come upon a person who claims the earth is flat and square while showing you a triangle, you can laugh and enjoy the conversation while, maybe, you will be able to appreciate there is more than one way to the center of the maze. You may want to move from things and into relationships. There are benefits in a discourse on square portholes when it comes to building ships and transforming new energy sources. Overall, Pythagoreans may find HyperStates a significant yet natural extension of Tetractys. Perhaps you can wear it as an amulet if you feel the organizing power of Tetractys. 


One App: The Barbury Castle Tetrahedron {July 17, 2011} 

This 1991 crop circle has thrilled many people, myself included. In it I saw the triangle of the Pythagorean Tetractys but at that time it was not extended into the 3rd dimension. The Secret Teachings of All Ages by Manly P. Hall has sections on the Pythagorean math and that helped a lot. I am returning to this topic {on July 17, 2011, 20 yr anniversary} as I am working on my second book. I am not soliciting input  it is a bit late for that. I'll be commenting on what's on the Internet about the The Barbury Castle Tetrahedron because some people are close. 

If we don't count generalizations ("great shift," "warning," "new age") or simplifications ("tree of life" made of a bunch of triangles), there isn't much remaining on the Internet about this great event. Are there no Pythagoreans on this planet who'd care to comment? (Pythagoreans who didn't work for the govt in a similar area and can talk?) There was a couple of people who seemed to have stopped communicating about their experiment (Chris and Jean) after they built the tetrahedron and got some lift out of it  and so there is an aura of mystery here as well. On this web page the Hyperstates illustration (on left) is also a tetrahedron and it is not difficult to see that one facet of it makes the wonderful Tetractys. This tetrahedron symbol is explained in the Quantum Pythagoreans book in all dimensions including 0D. The axes are identified in the book and metrics included as well, even though the metrics are bit different than what you might be used to, for they are the degrees of independence. The Barbury Castle Tetrahedron has a circle at each of its four corners (vertices) and no English to describe the axial parameters. Here is the first and easy hurdle. The symbol inside the circle at each of the corners describes the qualitative state (or qualitative function) of that point. The whole thing is a logical drawing and it doesn't have to be drawn exact (and it isn't). Well, I shouldn't have said this is easy because the interpretations I read speak of circles as physical spheres and axes as physical tubes. Suddenly the situation seems to have gotten complicated because the two guys (who are quiet) have built the tetrahedron from tubes and spheres, pumped microwave energy into it at one end point  and got a lift out of it, too. So there is no way I could talk you out of the impression that they are onto something real and really interesting. But this site is more into true knowledge integration (using your right brain) rather than proving or disproving something. The important part is that but one corner of the physically built tetrahedron got the lift. That also tells me these two guys really built it and the picture I saw is not just a mockup. In fact, the corner that got the lift is the one that is on top of the tetrahedron in the picture on right (it's a sixray swirl, which is really the ± 3D Cartesian coordinates under rotation at the origin). I found but a couple of people who were or are working the Tetrahedron on the Internet. Here are my comments:
Quote
by Harold Stryderight:
Quotes
by Jeremy Stride: " .. the watersphere goes at the center of the large tetrahedron structure!" Neeh. It's right at the top at the fourth point of the tetrahedron. It's infinite and 0D at the same time. Regardless, I like what I read. Think about the degrees of independence. In summary so far, the Tetrahedron geometry (based on the number 3) deals the our world's reality. This includes gravitation, atomic construction, and "takeoffs and landings" of interstellar travel. The four sided pyramid geometry (based on the number 4) deals mostly with interstellar travel and the balance between 3 and 4, which is the balance between the real and virtual domains. It's the same thing as talking about YangYin balance but I prefer English. The way the balancing act works is suggested by our pentagonal pyramid. 

Living with Numbers 

Pythagoras and the Pythagorean tradition puts numbers first. This may seem difficult to some and indeed Aristotle had a field day poking fun at Pythagoreans. The basic aspect to 'All is number' is that each number can be constructed  that is, each number can become. Each number, then, can be actualized. A number is not at the core, it is the core. A number can be written on a piece of paper and then the number is a representation of something real, irrational, or transcendental. (Irrationals and transcendentals enable the formation of virtual variables.) Yet numbers can be applied to actually come alive and that is the meaning of 'All is number.' Pythagoreans not only use numbers to measure somebody else's creation  they create new stable and alive entities with numbers. A good question is: What is the number or numbers the human is made of? [Actually, it is a root of a number.] 

1)
Real numbers Real numbers also spawn the degrees of independence (some say degrees of freedom). Pythagoras' Tetractys also includes the representation of the degrees of independence as four levels: Top dot is 0D (a geometric point), two dots on the next level is 1D (a line), three dots on yet another level is 2D (a plane), and four dots on the last level is 3D (a volume). Pythagoras' Tetractys also creates geometry through geometric constructs of degrees of independence. The most powerful finding here is that each level of increasing freedom provides a different context within geometry. This aspect is not presently understood, as all mathematicians try to treat geometry uniformly and "as a whole" where dimensions are "just trivial extensions." They are not. For example, squaring of a circle is a quandary that's right between 1D and 2D – and is still waiting integration into mainstream. Pythagorean geometric concepts provide powerfully simple answers to very complex problems. The question "What is and where is the difference between a point and a line?" seems almost impossible to answer objectively. This is the same question as "what is the minimum separation between two points so that we can connect them and call it a line?" Yet there exists a real answer that also yields insight on the smallest possible separation between atoms. Yes, infinitesimals had to wait until the 17th Century to bridge the 0D to 1D. 


2) Incommensurable numbers Mainstream math guys got it mixed up and to them the transcendentals and irrationals are the same. However, transcendentals are incommensurables that exist on a curve or, by the same token, they exist in 2D or 3D. Pi is the prime example of a transcendental number. Irrationals are incommensurables that are straight – that is, they exist in 1D. Constructionwise, transcendentals need a pyramid for their actualization while all irrationals are constructible through the Pythagorean Theorem.
3)
Virtual numbers The group theory can be applied to establish transition operations between real and virtual numbers because the operation of transformation deals with both the variance and invariance of number's properties. (Pythagorean evenodd grouping of numbers was a good start.) Virtual numbers' positive and negative values are generally (but not always) subjective. Virtual variables "fold in about zero" when these transform (reduce) into real numbers. This is analogous to foldingin of a hand held fan while the pivot (zero) becomes excluded. A scientist has difficulty understanding the virtual variables because the QM wavefunction is treated mathematically as but a technical parameter while its actual (though virtual) existence is denied. In the Pythagorean tradition via Aetius, the virtual number is most likely the 'undefined dyad' and I interpret the characterization "undefined" as 'nonlocal' or 'spread out' in the present day quantum mechanical context of a wavefunction having even symmetry  such as a photon. The 'dyad' is the even wavefunction based on the number 2 of the even (axial) symmetry.
4) Circumpositional numbers
Applicationswise, The Western preoccupation with reality handicaps incommensurables' applications. The free energy (zeropoint energy) effort, however, got a good start in the US and may yet rebound. In the East, incommensurables are used mostly for personal empowerment and healing. Incommensurables can be actualized (come alive) only through its construction. So, the square root of two is an irrational number that is, however, not actualized per se. Moreover, some people think 1.41421356 is the same thing as, or close enough to, the square root of two, but such number is a real number and cannot be actualized as an irrational number as it no longer carries the infinite mantissa. Incommensurables are in the virtual domain but their means of construction can be real, as Pythagoras discovered. There are other aspects to the actualization and this introduces yet another subset of irrationals. Overall, a very intriguing number group. The squaring of the circle attempts to resolve the differences between curving and straight geometries  that is transcendentals and reals  think atomic construction with adaptive orbitals. 


Relating Numbers Numerology is not strict and, for example, two entities produce one relationship. Numerology can be contextdependent when, for example, the interaction among three variables results in tractable matter while three bodies are in general chaotic  the number three can stand for both stability and chaos.* Numbers, then, do not exist only in standalone fashion because numbers also spawn the operators (relationships) and degrees of independence. Perhaps the best example of the operator is in the definition of Pi. Once a group of numbers reaches a stable system, Pythagoras calls it the Monad. Monad is 'onesum', a unique summing sequence or grouping of numbers that relate through the operators. The simplest monad is a triad  that is, you need at least three numbers or three variables to make something lasting out of it. Indeed, three parameters build the whole real universe. The mystical aspects are treated in alchemy, which deals with transformations and invariance  that is, a transforming or "becoming" monad has some of its numbers variant and some invariant (see group theory). Monad is synonymous with 'object,' 'entity,' or 'conglomerate.' A Monad is always a real entity that is commensurable with any other monad. (SelfTest:) If your ears perked up on this paragraph, you are doing well. Monad is also the first counting real number one issuing from the first real thing. The numerology (coming up) has a qualitative division on the interpretation of numbers as these apply to the real and the virtual domain. You may note that letters issue from numbers in that the vowels have even symmetry**. In all Latin vowels the even symmetry survives, although in the letter 'E' the even symmetry survives via the horizontal axis. 

* Religion and mythology deals with this through the multiple talent of the Personalities, or Aspects, of gods. Shiva can be creator at times and destroyer at times. ** Odd symmetry is a symmetry about a point (origin) while even symmetry is a symmetry about a line (axis). Symmetry contains reflected duplication about axis or rotated duplication about a point. All Latin vowels preferentially carry even symmetry. Pythagoreans call even numbers feminine and "inclusive" while odd numbers are masculine and "exclusive." The Tibetan alphabet is highly developed along both symmetries. We apply incommensurables/irrationals in an article on free energy because geometries have a pivotal role there. When you hear 'pivotal,' think spin. We also have a page on ether. 

Pythagorean College Numerology 



Universal Harmony
While many authors speak of the harmony of the universe or about the universal balance, the basic idea behind harmony is that it takes two sounds before these can be called harmonious or disharmonious. Any two notes of the Pythagorean (Western) octave are for the most part harmonious. The difficult part is that  while we can agree on harmonious or disharmonious sounds  there is no written procedure or mathematical logic that would allow us to determine ahead of time if the tones will be one way or the other. However, in the article on the five pointed star orbit, which is made from two orbits (Venus and Earth), there is enough disclosure to begin to appreciate what it takes to be in harmony. To build the universe, harmony is a requirement in that it makes lasting planetary orbits or galactic structures  and atomic orbitals as well. You do not have to make it harmonious but then the system will be rudimentary, degenerates, or comes apart. The book Quantum Pythagoreans explains what makes two numbers  or two orbits or two frequencies  harmonious or disharmonious via a formula. You will then be able to predict which notes are harmonious before you play them. Harmony is then also expressed geometrically for the reader as the stars. For hamony in the musical context, the note you (wish to) play can now be instanly associated with the harmonious or disharmonious notes. Ditto for chords. This relates not only to pleasing sounds but to your health as well. As always, harmonious and disharmonious sounds are about dual use  supportive/creative or detractive/destructive  and so you may want to know what makes the diff. The golden proportion is a unique pair of two numbers  one incommensurable (irrational) and one rational. Because the ratio and other relations of these two numbers also have interesting arithmetic and geometric properties, they should be included in the Pythagorean style harmony analysis. We have a page on the golden proportion with new application and (of course) a relationship to the Great Pyramid. The unreduced real number of the golden proportion is 2, and it is likely the number 2 (or ½) is representative of the octave, for octave doubles the parameters such as frequency or spatial distances and deals with (relates to) square numbers. 

The Pythagorean Y
Pythagoreans were engaged in proper living and proper conduct. Today we could call it character building but an additional objective is the salvation of the soul. Pythagoreans were following a path, the Way, in which mathematics is applied to cosmology and harmony, which in turn is about music in general and health in particular and friendship all around. It is likely the geometric shape of the letter Y was used symbolically for a person to choose a particular path for its soul. You come to a "fork in the road" and you want to make the decision that is right for you.
There exists the duality of the real and the virtual – the visible real universe and the spirit – that are intertwined yet separate. The Pythagorean Y could be about this very duality particularly as these are qualitatively different. Here is a sentence from Aetius regarding Pythagoras:
Aetius, Placita, 1st Century CE The real (material) and the virtual (godly, spiritual) components of duality, being not only intertwined but actually interacting while remaining separate, also suggest the letter Y. Moreover  and even if you choose one over the other  the components of the duality will always engage each other. The bottom line on this is that one cannot be both, for the duality cannot be merged. Another Y I'd love to have this Y associated with Pythagoras:
Instead of looking at the black ink outline, as we do with all letters, look at the white wedge gap inside the letter and imagine the narrowing end spiraling toward a point at the bottom. Yes, it is about the magic of waves and there is a bit more on this in one of our DSSP topics. 

The Pythagorean Theorem The Theorem relates the squares made from the sides of any rightangle triangle. The Theorem is very old and it is then easy to speculate about what really happened back then. Regardless, it is not difficult to show the Theorem originated with Pythagoras or Pythagoreans, for the discovery of the irrational numbers is linked to Pythagoras without much disputation. But first we look at one conclusion in this excerpt from John Burnet's book Early Greek Philosophy:
The previous paragraph is a scholarly method for researching the past. But there is another and a simple way to link the Pythagorean Theorem to Pythagoreans.
Also, because one cannot get to irrationals directly via rationing, one must first engage the square numbers (today's area or 2D). Pythagoreans were [and are] very much into square numbers and that opened the path toward the Theorem. In other words, one starts in 1D, moves to 2D, and returns to 1D via the root before being able to get to the irrationals. There is no other way to get to irrationals exactly and in finite time (tractably). 

The Pythagorean Theorem works with addition or subtraction (superposition) of curved areas, areas also known as lunes. The Theorem relates the squares among the sides of any right angle triangle and it is then easy to erect a square on the triangle sides. A circle's area is also proportional to its diameter squared and so the Theorem works with circle areas erected on the sides as well. This particular rendering of the Pythagorean Theorem may reveal powerful properties (read energy) when dealing with 2D geometry. The illustration is from the back cover of the Quantum Pythagoreans book. 

The Pythagorean School Historically, writings about Pythagoras appear to emphasize authenticity by fully capitalizing the reference – such as when saying "It belonged to HIM." But I think the full capitalization references The Pythagorean School, and when saying " .. it is HIS .. " means it belongs to The School. In addition to authenticity and ownership, the oral tradition of Pythagoras teaching is expressed with the usual preamble: HE himself said it .. . The oral tradition is not inconsequential and does not get weaker with time. The present day scholars sometimes muse at the absence of Pythagoras' own writing. They do agree, however, that such writings do not exist – rather than being physically lost through the ages, say. This is an advanced topic that calls for understanding of ether's properties. A good start on etheric knowledge is through a passage in the Pythagorean Oath: " .. who transmitted to our soul the tetractys .. " We would be hard pressed to find the equivalent of the Pythagorean School today. The School did not seek funding from outside, although it is likely the School accepted donations. However, all knowledge such as proofs and breakthroughs belonged to the School. The School enforced its own secrecy provisions (of trade secrets of today), but with methods one would call magical. It is likely some Martial arts schools operate on such basis today. 

You, A Pythagorean If you think you are a Pythagorean, chances are you are. It is not easy to arrive at such designation without joining a real organization. But you know that by truth you know conceit and that is how the truth prevails. The Pythagorean way of learning, teaching, and building does not deal with suffering, for conflicts exist as the imbalance that leads to the next level of the truth. The building part, moreover, establishes the truth in the objective realm. Enjoy. You might not think yourself a Pythagorean but others may think you are. Galileo would not think of being a Pythagorean but his discoveries and his mathematical  as well as apolitical  thinking earned him a Pythagorean label from no other than the members of the Inquisition. Enjoy. Finally, if you could think of a person who started wearing a new piece of clothing that would catch on as a fashion statement for over two thousand years, would you think of Pythagoras? Yes, Pythagoras wore trousers and most of the world today wears trousers. Being a Pythagorean today is about the truth and you can pursue it looking good, too. 

Mother Goose of Tetractys Presently, the Pythagorean Theorem mnemonic exists as "Pythagoras' Trousers," which is a tiein, or perhaps a pun, between Pythagoras' attire (unusual at the time) and his theorem in its geometric form. It is quite likely the Pythagorean numerology of small numbers (110, say) was designed to introduce Pythagorean concepts to larger audiences  not unlike the verses of Mother Goose that combine the poetic and magical qualities of English: "..and the cow jumped over the moon." In the next step the numerical compositions are put together to make stable creations (monads). 

While the 'tetractys' is a
particular method of composing a poem, it is not taken that way here.
Rather, when you are engaged in a particular and difficult pursuit,
which is usually full of conflicts, you just might come upon a
solution or a resolution. The elation and euphoria then results in
composing a short and personal poem as a sort of a whoopee icing on
the cake.


QUANTUM
PYTHAGOREANS
Tetractys of Pythagoras organizes the universe at all scales. Degrees of independence play the role that up to now has not been disclosed. Quantum Pythagoreans book describes numbers, their properties, and their ability to make reality through geometric constructs such as the pyramid. The Pythagorean way is the road to reality, for the creation of reality in the form of a new atom is the only proof you need. Continue .. 


Added paragraphs on Irrationals and Becoming July 2005. 

