Welcome back to “Infinity and Beyond,” the *hidden *blog post site from www.papasitaly.com. This is the place where we spill the beans, let the cat out of the bag, give the game away, reveal, disclose and make known for all to see, the symbols, secrets and synchronicities that can be found in the book, *How Do We Love?- *the true-story-Italian-adventures of Aniello Agostino Oliviero, aka, “Papa,” and me, his grateful granddaughter, Danielle. If you have not yet read the book, please take a peek at www.papasitaly.com! Don’t forget that anything you see in ** bold italics** will show up in a future post!

Last month in this blog, we learned about ** Sacred Geometry**, penguins and pinecones. And we promised that, related to at least one of those subjects, we would introduce a mysterious character from the ancient past.

Well, my dear friends, the next month is here and we are ready to reveal our very secret colleague.

In the book, *How Do We Love?, *in the Chapter on Rome, there was a story about our riotous attempt to cross the enormous traffic roundabout in front of the “Wedding Cake.” In the story, I made a reference to a Roman Emperor that never existed:

* **“They must have waved their handkerchiefs for our valiant effort, amusing costumery and entertaining antics, and convinced Emperor Pythagoras to spare us.”*

There was no Emperor Pythagoras in history, however the veiled reference is another cosmic egg in our hunt for the signs, symbols, synchronicities and secrets you can find throughout the book.

Friends, Romans, countrymen and women, ti presento…** Pythagoras** of Samos: the father (or possible uncle, or even great-great-great-grandson*) of the Pythagorean theorum- the right-angled key to the puzzle lock of…

*Geometry*.

* Musei Capitolini, Rome. Copy of Greek Original. **Source:**Wikimedia Commons.*

Whenever you see a mention of Pythagoras in the book, wise friend, it is a symbol of, a reference to, one of Papa’s favorite subjects, Geometry.

“*To traverse Piazza Venezia that day required the opposite of a simple, single line. It demanded a complicated, circuitous multi-cross, and I had no idea in which direction to begin. I scouted out a route with the lowest odds of injury…and could find none. After two minutes that felt like two hours, I gave up trying to figure it out on my own.*

*‘Papa, I give up! Which way?’*

*And then came not the answer, but the bridge to the answer. ‘Geometry, deah.’*

*Of course. Geometry. I climbed the steps of the monument. At the far left I was able to see my beautiful, peaceful, preferred path down the sidewalk, littered with orange barricades (see Figure 2.) Ah, the elusive, unattainable Line C. But, impossible as it was, that impeded route established the base. I then imagined two more lines and created a giant, imaginary triangle which led, hypothetically, to the picture spot. It was a Pythagorean Theorem of pedestrian possibility!”*

* **Figure 2. The Gauntlet*

*Reading Between the Lines*

Now, those of us that have never heard of Pythagoras are probably content with that explanation. “Pythagoras? Father of geometry? Oh! yes, I think I remember that from high school…maybe…sort of, mmmm…baaaarely.” But those of us that know about the mysterious life of this man also know that he is more than just a mathematician with a penchant for solving riddles of lines a, b and c.

*Pythagorean Theorum in Action. **Author: John Blackbourne. Source: Wikipedia Public Domain*

Please allow me to elaborate.

I stumbled upon the teachings of Pythagoras and his colleagues when I was learning about ** sound vibrations**. I had become very interested in the science of

**as the basis of the entire universe- and the belief that the energy of different vibrations and frequencies is responsible for the existence of everything.**

*energy**Everything*.

Every. Thing.

From the tiniest parts of individual atoms in life forms to our increasingly expanding, infinite cosmic space, and *the whole ball of beeswax* between the two (including, but not limited to: bacteria, rocks, Twinkies, mother earth, sister moon, music, society, congress, lemurs, water and war.) Did I mention *everything? *

* *As I learned about energy and its vibrations, I also learned about the power that sound vibrations can have on the human body. And that, dear friends, is where I ran into Pythagoras.

Pythagoras took his love of mathematics and Geometry, and applied it to sound vibrations- especially, ** music**. In our sister blog at www.papasitaly.wordpress.com, I explained a fraction of it in the January story, “

*Aniello Agostino Oliviero’s Infinity Symphony in G Major*.” (If you haven’t read the story recently, quite a few new links and videos have been added.) But for those of us that did not have a chance to dance along, or forgot the steps, here is a reminder:

“Math and music may seem disparate, a paradox- however, ancient cultures discovered that there really are patterns, hidden structures and relationships between numbers and musical scales. ** Pythagoras**, an ancient Greek philosopher, mystic, mathematician and the father of Geometry, was one of the most famous to recognize such a mathematical pattern in music. The legend goes that he heard the sound of several blacksmiths hammering and decided there must be a mathematical answer to the beautiful sounds. Further curiosity led him to discover the musical scale of tones, called Octaves.

^{1}

* Source: Theorica Musicae, Francino Gaffurio, 1942. **Public Domain*

Since Pythagoras laid a heavy blanket of mathematics over everything, he of course also applied mathematics to explain the stars and planets. He believed that the cosmos moved in very predictable mathematical patterns and equations, that these equations, ‘corresponded to musical notes, and with each movement of the universe, they collectively produced a symphony.’^{2} Pythagoras and subsequent philosophers called this cosmic symphony, ‘** The Music of the Spheres**.’

Pythagoras also believed that ‘musical instruments, when tuned to the mathematical Pythagorean Harmonics, were capable of *tuning the human soul to sing the rhythms of the universe*.’^{3} In short, Pythagoras asserted that if music is math, and the entire universe is math, then, by Pythagorean inference, the entire universe… is music.

These beliefs led to his theory that the human soul can be tuned to the music of the universe- a theory that our native ancestors already knew, and that philosophers, scientists and healers have been pursuing ever since.”

Aha! So, when we mention Pythagoras in the book we are not just doing it with a knowing side-glance to our friend Geometry, it’s also because we are huge fans of Pythagoras’s philosophies, beliefs and teachings related to sound, sound vibrations, music, and the *rhythms of the entire universe*.

*Time-Traveling International Man of Mystery*

Hopefully by now, you are realizing that when I mention something like a cigar in the book that it is not *necessarily* just a cigar. And that, similarly, just because it walks like a duck and quacks like a duck does not *necessarily* mean that it’s just a duck. As I’ve mentioned previously, anything and everything in the book is fair game to serve as a nesting toy, a Russian Matryoshka, appearing simple and whimsical on the outside, but containing many meanings and secrets within. Pythagoras is definitely one of the more elaborate playthings I have hidden in the book, and, believe it or not, there is more to him than “just” Geometry and the Music of the Spheres.

Pythagoras, like Papa, was a man of many interests and avocations. Born in 570 BC Greece, on the island of Samos, he was known in the roles of mathematician and philosopher, but also mystic, scientist, musician, religious leader, legend, explorer, traveler, student, light-emanating golden-thighed deity, and possible time and space traveler.* In their online entry on Pythagoras, the Stanford Encyclopedia of Philosophy advises that many people thought Pythagoras was superhuman, a “Wonder-Maker,” and provides Aristotle’s “evidence” of that:

*“Aristotle emphasized [Pythagoras’s] superhuman nature in the following ways: there was a story that Pythagoras had a golden thigh (a sign of divinity); the people of Croton called him the Hyperborean Apollo (one of the god Apollo’s manifestations); the Pythagoreans taught that “of rational beings, one sort is divine, one is human, and another such as Pythagoras” (Iamblichus, VP 31); Pythagoras was seen on the same day at the same time in both Metapontum and Croton; he killed a deadly snake by biting it; as he was crossing a river it spoke to him (all citations are from Aristotle, Fr. 191, unless otherwise noted).”*

*(Sidenote for the Skeptics: It is important to pause and mention here that many people think Pythagoras was none of those things. There exist very few physical records of his writings, findings and teachings [the Stanford Encyclopedia of Philosophy has a list of them: www.plato.stanford.edu/entries/pythagoras/.] And so, some people believe that while Pythagoras may have set out the punch bowl, it was his colleagues and followers over the centuries that actually filled it up with and drank the Kool-Aid.)

*The Secretest of Secret Societies*

Regardless of this academic area of disagreement as to what the man did himself or lead others to do, Pythagoras and his philosophies developed a huge group of very dedicated followers. Open lectures on some topics were provided to the general community, but the most secretive of information and knowledge was saved for a clandestine group called the “Pythagorean Brotherhood.”

This group engaged in number worship- a belief that mathematics and its related music was the key to the universe. They also believed in the transmigration of souls (** reincarnation**), treating all living creatures as one, restrictions on consumption of animal flesh and possibly full vegetarianism, and an event relationship between the cosmos, the planet and humans. Their motto was “God is number,” and they formed a secret society that turned into more of a religion– complete with symbols, rituals, rules and a very select congregation. Members were not allowed to speak of what took place within the brotherhood, and the one that did was possibly murdered.**

*Pythagoreans Celebrate Sunrise (1869), Fyodor Bronnikov. **Wikipedia Commons*

* **The Pythagorean’s Secret Symbols*

There were at least two well-known symbols sacred and secret to the Pythagoreans: The Pentagram and the Tetractys.

The Pentagram (The 5-pointed star)

Members needed to show the pentagram to gain admittance to the Pythagorean gatherings:

*Image Courtesy of John Baez at the **Mathematics Department at University of California Riverside. **http://math.ucr.edu/home/baez/week265.html*

There was never anything written about why the Pythagorean’s chose the pentagram as their sacred symbol, however future followers speculated it was for the mathematical potential represented by the pentagram. One being the pentagram’s capacity of division into an infinite** number of pentagrams (as seen above in John Baez’s drawing), and another being its representation of the mystical “Golden Ratio.” (For more explanation on the Golden Ratio, you can look back on February’s “Sacred Geometry” post.)

**(Dangers of Discovering ** Infinity** Sidenote: Pythagoras and his immediate contemporaries “discovered” the mathematical concept of infinity when they discovered irrational numbers. Discovered is in quotes because initially they did not accept the idea of infinity. You see, their “religion” was based on simple “whole” numbers, like 1, 2, 3, etc., and not “irrational” numbers and their infinite integers, like 3.1415… and so the discovery of the Golden Section (whose ratio is 1.618033988…to infinity), and other concepts with irrational numbers attached was a colossal awakening for the group (to say the least, it completely freaked them out by shattering the foundation upon which all of their beliefs had been based.) Because irrational numbers countered their previous dogma, the subject of mathematical infinity was not shared with the public- until, allegedly, one of the members of the Pythagorean brotherhood, named Hippasus, revealed the secret to non-members. Author Amir Aczel tells us that a “number of legends record the aftermath of the affair. Some claim that Hippasus was expelled from the society. Others tell how he died. One story describes how Pythagoras himself strangled or drowned the “traitor,” while another describes how the Pythagoreans dug a grave for Hippasus while he was still alive and then mysteriously caused him to die. Yet another legend has it that Hippasus was set afloat on a boat that was then sunk by members of the society.”

^{4 }Regardless of whether Hipassus spilled the magic beans or not, infinity was tinkered with but not widely entertained again until the philosopher Zeno expounded upon it a century after Pythagoras. )

*The Tetractys*

The Tetractys most likely came not from Pythagoras, but from a subsequent Pythagorean Brotherhood member, Philalaos.

*Source: **Hemenway, Priya – Divine Proportion pp.63, Sterling Publishing, **Wikimedia Commons, Public Domain*

The Pythagoreans of Philalaos’s time expanded the practice of number worship, delving into number mysticism. These Pythagoreans believed that numbers were symbols of cosmology. For example, the number 3 represented harmony and the “noble number,” the number 6 was creation, and the number 7 was an awe-inspiring number as it represented the number of the 7 planets. But the most divine number of them all was the number 10*, *which represented the number of the entire universe. The image of a Tetractys is a triangular figure with four rows adding up to that perfect number 10. It was a symbol of worship to the Pythagoreans who would swear oaths by it:

“*Bless us, divine number, thou who generated gods and men! O holy, holy Tetractys, thou that containest the root and source of the eternally flowing creation! For the divine number begins with the profound, pure unity until it comes to the holy four; then it begets the mother of all, the all-comprising, all-bounding, the first-born, the never-swerving, the never-tiring holy ten, the keyholder of all.”*^{5}

The Tetractys is very mysterious and complex indeed. It has been related to many other symbols, including the symbols of the early ** Kabbalists**, such as the Hebrew Tetractys,*** which contains the letters of the Hebrew “Tetragrammaton” (the four-lettered name of God in Hebrew scripture, also seen as the Latin letters YHWH.)

*Symbol of the 17 ^{th} century Kabbalist Mystic Jacob Boehme, *

*from 1730 Libri Apologetici. Wikimedia Commons*

***(Hebrew Tetractys Sighting Sidenote: I think it’s worth noting here, that the Hebrew Tetractys has been spotted in the most interesting of places: )

*5 ^{th} Chapel of the Palace of Versailles. *

*Wikimedia Commons*

*St. Charles Church, Vienna Austria. **Wikimedia Commons*

*Basilica of St. Louis, King of France, St. Louis, Missouri. **Wikimedia Commons*

The Tetractys’s influence can also be seen in other forms, such as the Roman Catholic Archbishops Coat of Arms:

The Baryon Decuplet:

(Subatomic Sidenote: The Baryon Decuplet is a physics term for a form that results from the movement of ** subatomic particles**. It is interesting to note that this form is part of a theory by American physicist Murray Gellman, called the “Eightfold Way”- a title which is Gellman’s intentional allusion to the Noble Eightfold Path of

**.)**

*Buddhism*And see if you can spot the two Tetractys’s, one upright and one inverted in the U.S. Dollar bill:

*Source: Carnaval.com*

(Dan Brown Was Right Sidenote: In his book, *The Power of Myth, *noted American mythologist and writer, Joseph Campbell, said this about this symbol on the dollar: “In the Great Seal of the U.S. there are two of these interlocking triangles. Above (the eagle’s) head are thirteen stars in the form of ** Solomon’s Seal**. Each triangle is a Pythagorean Tetractys where the apex represents the creative center out of which energy the universe and everything comes…Two of these symbolic triangles are interlocked on the Great Seal creating thirteen points with six apexes – one above, one below and four in the four quarters. The sense of this is that

**or from any point of the compass the creative**

*from above or below***might be heard so that anyone from any quarter might speak the truth because no one is cut off from it. This is the great thesis of democracy.”)**

*Word*Finally, we also find the Tetractys in ten pin bowling, Chinese checkers (which, by the way, was developed in Germany and not China), and, I would like to offer my own discovery, the Tetractys in Billiards. Although the standard Billiards triangle rack holds 5 rows of billiard balls, for a total of 15, it is interesting that the first four rows form a perfect Tetractys, with 1,2,3 and 4 billiard balls in each row, for a total of 10. I know that, because, when I was a small child Papa only ever racked up the first 4 rows for us grand-kids. (I never questioned why at the time. We must have either misplaced 5 billiard balls from Papa’s beloved “pool table,” or he had learned from experience that he had a 10-ball-patience-limit for our version of pool, with its requisite accompanying green felt shredding, blue chalk flying, pool cue weaponizing, high-pitched shrieking, and whining accusations of cheating.)

*Pythagorean Fan Following*

Other mathematicians, scientists, philosophers, musicians and teachers were also members of and contributors to the Pythagorean think tank (always secretly), including famous Greek thinkers such as Plato, Socrates, Parmenides, and Philolaus (a contemporary of Socrates and the man reported to be most responsible for historical evidence of Pythagoras’s ideas and teachings). Over time, many an ancient sage subscribed to Pythagorean influences. Even the famed Italian painter Raphael showed his respect for Pythagoras when he included the likeness of Pythagoras in his famous painting, “The School of Athens,” which represented the most brilliant minds of ancient Greece.

*School of Athens–Raphael (Rafaello Sanzio da Urbino) Wikimedia Commons. *

*School of Athens (detail, Pythagoras)– Raphael. **Wikimedia Commons.*

*It’s Only Platonic*

As mentioned, Plato was also reported to be an ardent, yet covert, follower of Pythagoras’s teachings, especially those related to Geometry. Plato had the phrase, “Let no one ignorant of Geometry enter here,” inscribed above the gates of his academy.^{4} But before and during Plato’s time and for some time after, Pythagoreans and other scientists, mathematicians and philosophers were often persecuted as a threat to the church and religion. (See our previous post on Italian philosopher Giordano Bruno.) For that reason alone, being secretive was an important part of being a Pythagorean.

Jay Kennedy, a Plato scholar, told National Public Radio that although Plato did not outwardly declare his dedication to the Pythagorean school of thought, Kennedy thinks he has found secret messages in Plato’s writings– secret messages embedded within every 12 lines of Plato’s *The Republic-* that refer to music. (Ancient music was based on a 12-note scale.) Kennedy believes this is no coincidence and the evidence reflects Plato’s show of solidarity with the Pythagoreans. “Plato was a closet follower of Pythagoras, who believed mathematics and music were the key to the order underlying the world,” Kennedy says, and has suggested that “Perhaps some scholar will find that— in *The Republic*, at least— that there is something like a melody or a score embedded in the text.”^{6}

*Papyrus Page from Plato’s Original Text of The Republic*

The Pythagoreans and Pythagoras himself eventually grew very powerful, and, consequently, as is so often the case in all things new and mysterious and counter to long-held beliefs, were perceived as a threat to society. The primary meeting place of the fraternity was eventually stormed and burned, with many of the members (including possibly Pythagoras) perishing in the blaze. Some say Pythagoras could travel through space and time, and so his remains were never found. Others say he escaped to nearby Metapontum and starved himself to death. No matter what the method of his mortem, Pythagoras’s physical self was eventually gone, but his ideas, teachings and spirit would clearly carry on.

I recently found evidence of this enduring spirit in a most unusual place- embedded in the work of one of Pythagoras’s more modern fans, and a beautifully creative mind of our time, Walter Elias Disney. Mr. Disney had an animated short created, called, “Mathemagic.” The cartoon, starring Donald Duck, includes an introduction to Pythagoras (2:45-4:55); a discussion of the “mathemagic” of the pentagram (7:00); a demonstration of Sacred Geometry (8:28); examples of Sacred Geometry in nature (11:10-13:45); and even a nod to * Lewis Carroll *for the geometric references in

*.*

**Alice in Wonderland**

*(Thanks to our friends at True Disney for the video.)** *

*Po-TĀ-to, Po-TÂ-to, Pythagoras, Pythagorean*

Whether the teachings are *from* Pythagoras or *of* Pythagoras, we will probably never know, and it doesn’t matter to me. Like many extraordinary minds from the past, Pythagoras’s discoveries and teachings are far-reaching and have impacted us in ways we are not aware of and can’t even fathom. Pythagorean thought even influenced aspects of ** Hermeticism**,

**and**

*Gnosticism***, the powerful and influential religious and philosophical traditions (which are also threads of themes in**

*Alchemy**How Do We Love?)*. To this day, a rainbow of realms of science, mathematics, music, mysticism, cosmology, art, literature and written thought can be attributed to the foundations of ideas brought about by the earliest Pythagoreans.

I don’t know if Papa had ever studied Pythagoras or the Pythagoreans– Papa never spoke the name, and did not attribute any of his learning to Pythagoras, other than the famed namesake Geometric theorem. But, then again…maybe Papa did know of Pythagoras– maybe in a former “transmigration of the soul” he was a Pythagorean mathematician, or musician, or both! It *is* quite curious that Papa singlehandedly came to the same conclusions about Geometry’s mystical and sacred nature permeating all things…And, now that I really think about it, if he did know Pythagoras, Papa too was sworn to secrecy. It does make perfect sense. Papa did teach me everything I know about the spiritual pursuit of Geometry, after all– and I still don’t know why he filled that billiards rack up with only 4 rows.

Thank you for taking the time to travel back through history and meet Pythagoras! If you are still hungry for more on Pythagoras and his world of Geometry (as well as some additional theories on the murder of Hippasus) go to Vihart’s funny, smart, notebook animation video at http://www.youtube.com/watch?feature=player_detailpage&v=X1E7I7_r3Cw

That is it for this month! Be well, dear friend, and may you seek out and discover your own synchronicities, symbols and signs in the world around you. They are everywhere, all the time, and can guide us to where the universe needs us to be – if we just pay a little bit of attention.

Ce Vediamo al Prossimo Mese! See you next month!

References:

- http://en.wikipedia.org/wiki/Pythagoras
- Christoph Riedweg, Pythagoras: His Life, Teaching and Influence, Cornell: Cornell University Press, 2005
- John Beaulieu, “Human Tuning”, Biosonic Enterprises, 2010
- Aczel, Amir D., (2000)
*The Mystery of the Aleph: Mathematics, the Kabbalah, and the Search for Infinity.*Four Walls Eight Windows Press, NY., New York. - Dantzig, Tobias ([1930], 2005) Number. The Language of Science. p.42
- http://www.npr.org/templates/story/story.php?storyId=128288987

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