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the disk it shines strange and eternal
the disk it shines
strange and eternal
but there is one
hidden from its rays
alone in my secret cave
living out my secret days
I dream only one dream
until my final slumber
I would that I might
become a number
There is not a single detail in the life of Pythagoras that stands uncontradicted. But it is possible, from a more or less critical selection of the data, to construct a plausible account.
— Walter Burkert, 1972
For context on the poemand its accompanying work of art, I offer these brief biographical notes on Pythagoras with interspersed commentary (all quotes from wikipedia unless otherwise noted). If even half of this is true then he wins the all-time World’s Most Interesting Man award hands down—I mean the man invented triangles, who can top that? (/s)
Pythagoras of Samos was an ancient Ionian Greek philosopher and the eponymous founder of Pythagoreanism. His political and religious teachings were well known in Magna Graecia and influenced the philosophies of Plato, Aristotle, and, through them, the West in general.
Porphyry repeats an account from Antiphon, who reported that, while he was still on Samos, Pythagoras founded a school known as the "semicircle". Here, Samians debated matters of public concern. Supposedly, the school became so renowned that the brightest minds in all of Greece came to Samos to hear Pythagoras teach. Pythagoras himself dwelled in a secret cave, where he studied in private and occasionally held discourses with a few of his close friends.
This was the kernel of inspiration for this post. Why I was reading Pythagoras’ wikipedia page and why his dwelling and teaching in a secret cave struck a chord with me I do not know. I have a long-running fascination with secrets (hence the name of the blog, latin for “of secrets”) but I hadn’t given much thought to the notion of secret places, perhaps because I live in NYC where there is essentially no such thing (the internet tells me there are at least 17 secret places here but somehow I don’t know if these count). I wonder if there is some connection between living in or having access to a secret place and one’s ability to discover secrets (like a hidden mathematical relationship at the heart of geometry).
Although the exact details of Pythagoras's teachings are uncertain it is possible to reconstruct a general outline of his main ideas. Aristotle writes at length about the teachings of the Pythagoreans, but without mentioning Pythagoras directly. One of Pythagoras's main doctrines appears to have been metempsychosis, the belief that all souls are immortal and that, after death, a soul is transferred into a new body. Nothing whatsoever, however, is known about the nature or mechanism by which Pythagoras believed metempsychosis to occur. Empedocles alludes in one of his poems that Pythagoras may have claimed to possess the ability to recall his former incarnations.
Another belief attributed to Pythagoras was that of the “harmony of the spheres”, which maintained that the planets and stars move according to mathematical equations, which correspond to musical notes and thus produce an inaudible symphony.
The influence of the “harmony of the spheres” on philosophy and science (and western culture writ large), is wildly underappreciated.
“Every planet in his proper sphere in moving harmony and sound…You must conceive yourself looking up at a world lighted, warmed, and resonant with music.”
I wrote about this before in “Research Papers Used to Have Style. What Happened?” while talking about how the (over)emphasis on clarity and concision in modern science writing has harmed our creativity (but of course “Disruptive science has declined — and no one knows why”).
Another way in which the aesthetic deficiency in scientific writing dampens our creativity is that it makes us less likely to use metaphor in our prose. Metaphor is a particularly valuable tool for creativity because it can bridge ideas between the sciences and other domains of culture, allowing virtually any phenomenon to serve as a source of scientific inspiration. Historical examples abound.
In comparing planetary motion to musical harmony, for instance, Johannes Kepler made revolutionary discoveries in astronomy: “Something akin to poetic creativity — the search for hidden likenesses — can be traced to the roots of scientific revolution. Kepler, who believed in the ''music of the spheres'' and tried to work out the notes sounded by each planet, discovered laws that describe how the planets trace elliptical paths about the Sun. (Broad, 1983)”
Harmonices Mundi (Harmony of the Worlds), the book in which Kepler derived his laws of planetary motion, devoted three of its five chapters either wholly or partially to musical themes.
Back to Pythagoras:
According to Aristotle, the Pythagoreans used mathematics for solely mystical reasons, devoid of practical application. They believed that all things were made of numbers. The number one (the monad) represented the origin of all things and the number two (the dyad) represented matter. The number three was an "ideal number" because it had a beginning, middle, and end and was the smallest number of points that could be used to define a plane triangle, which they revered as a symbol of the god Apollo. The number four signified the four seasons and the four elements. The number seven was also sacred because it was the number of planets and the number of strings on a lyre, and because Apollo's birthday was celebrated on the seventh day of each month. They believed that odd numbers were masculine, that even numbers were feminine, and that the number five represented marriage, because it was the sum of two and three.
Ten was regarded as the "perfect number" and the Pythagoreans honored it by never gathering in groups larger than ten. Pythagoras was credited with devising the tetractys, the triangular figure of four rows which add up to the perfect number, ten. The Pythagoreans regarded the tetractys as a symbol of utmost mystical importance
I don’t know if Pythagoras actually sought to “become a number” as I suggested in my poem, but it wouldn’t be all that surprising if he had—who knows what kind of impossible dreams he dreamt in his secret cave? I suppose that he fell short of that aspiration, but perhaps only slightly so—after all, he did succeed in becoming a theorem.
Way of Life
Both Plato and Isocrates state that, above all else, Pythagoras was known as the founder of a new way of life.
I’m reminded of this:
“Peter Thiel’s argument is broader: Not only religious vitality but the entirety of human innovation, he argues, depends on the belief that there are major secrets left to be uncovered, insights that existing institutions have failed to unlock (or perhaps forgotten), better ways of living that a small group might successfully embrace.
Pythagoras definitely believed in secrets, and as you’ll see, he definitely created something that was not a new religion or philosophical system or socio-economic arrangement but all of them and moreso.
Questions to ponder as you read on: Could there be a new Pythagoras (or a reincarnation of the old)? Can we conceive of such a figure arising in today’s world—something like a mystic and religious leader who also makes foundational discoveries in mathematics and science? What would be the new way of life that this new Pythagoras develops?
The organization Pythagoras founded at Croton was called a “school”, but, in many ways, resembled a monastery. The adherents were bound by a vow to Pythagoras and each other, for the purpose of pursuing the religious and ascetic observances, and of studying his religious and philosophical theories. The members of the sect shared all their possessions in common and were devoted to each other to the exclusion of outsiders. Ancient sources record that the Pythagoreans ate meals in common after the manner of the Spartans. One Pythagorean maxim was "koinà tà phílōn" ("All things in common among friends").
Both Iamblichus and Porphyry provide detailed accounts of the organization of the school, although the primary interest of both writers is not historical accuracy, but rather to present Pythagoras as a divine figure, sent by the gods to benefit humankind.
Are we sure that he wasn’t?
Two groups existed within early Pythagoreanism: the mathematikoi ("learners") and the akousmatikoi ("listeners"). The akousmatikoi are traditionally identified by scholars as "old believers" in mysticism, numerology, and religious teachings; whereas the mathematikoi are traditionally identified as a more intellectual, modernist faction who were more rationalist and scientific. Gregory cautions that there was probably not a sharp distinction between them and that many Pythagoreans probably believed the two approaches were compatible.
The Pythagoreans believed that music was a purification for the soul, just as medicine was a purification for the body. One anecdote of Pythagoras reports that when he encountered some drunken youths trying to break into the home of a virtuous woman, he sang a solemn tune with long spondees and the boys' "raging willfulness" was quelled. The Pythagoreans also placed particular emphasis on the importance of physical exercise; therapeutic dancing, daily morning walks along scenic routes, and athletics were major components of the Pythagorean lifestyle. Moments of contemplation at the beginning and end of each day were also advised.
So I guess we are basically just re-discovering everything that Pythagoras already knew??? Music, dancing, exercise, long walks, beautiful scenery, and contemplation as food for the mind, body, and soul. Needless to say, I’m 100% in on Pythagoreanism—all of the aforementioned activities + hanging with my bros in caves + the mystical pursuit of knowledge—where do I sign up?
Pythagorean teachings were known as "symbols" (symbola) and members took a vow of silence that they would not reveal these symbols to non-members. Those who did not obey the laws of the community were expelled and the remaining members would erect tombstones for them as though they had died. New initiates were allegedly not permitted to meet Pythagoras until after they had completed a five-year initiation period, during which they were required to remain silent.
Ehhh I might be out on the 5 years of silence thing.
Sources indicate that Pythagoras himself was unusually progressive in his attitudes towards women and female members of Pythagoras's school appear to have played an active role in its operations.
Pythagoreanism also entailed a number of dietary prohibitions. It is more or less agreed that Pythagoras issued a prohibition against the consumption of fava beans and the meat of non-sacrificial animals such as fish and poultry.
It turns out that Pythagoras’ disdain of fava beans wasn’t just a random superstition; from “Fava, the Magic Bean”:
Favism is a hereditary disease found worldwide but it is most prevalent in the Mediterranean. The red blood cells of individuals with favism lack G6PD, an enzyme needed to break down peptide glutathione. Since this substance is present in fava beans, the exposure to fava beans or even their pollen can trigger fevers, jaundice, hemolytic anemia and death.
Fashion sense and demeanor:
Pythagoras was said to have dressed all in white. He is also said to have borne a golden wreath atop his head and to have worn trousers after the fashion of the Thracians. Diogenes Laërtius presents Pythagoras as having exercised remarkable self-control; he was always cheerful, but “abstained wholly from laughter, and from all such indulgences as jests and idle stories”.
He must have been great at parties…
Pythagoras was said to have had extraordinary success in dealing with animals. A fragment from Aristotle records that, when a deadly snake bit Pythagoras, he bit it back and killed it. Both Porphyry and Iamblichus report that Pythagoras once persuaded a bull not to eat fava beans and that he once convinced a notoriously destructive bear to swear that it would never harm a living thing again, and that the bear kept its word.
Anti-Pythagorean legends were also circulated. Diogenes Laërtes retells a story told by Hermippus of Samos, which states that Pythagoras had once gone into an underground room, telling everyone that he was descending to the underworld. He stayed in this room for months, while his mother secretly recorded everything that happened during his absence. After he returned from this room, Pythagoras recounted everything that had happened while he was gone, convincing everyone that he had really been in the underworld and leading them to trust him with their wives.
I love how he supposedly got his mother in on this, “Okay mom, so I’m going to need your help with something, I got this plan that is going to get me so much pussy but it might take a few months…”
The second to last line was an homage to Sonnet VII by George Santayana
I would I might forget that I am I,
And break the heavy chain that binds me fast,
Whose links about myself my deeds have cast.
What in the body’s tomb doth buried lie
Is boundless; ’tis the spirit of the sky,
Lord of the future, guardian of the past,
And soon must forth, to know his own at last.
In his large life to live, I fain would die.
Happy the dumb beast, hungering for food,
But calling not his suffering his own;
Blessèd the angel, gazing on all good,
But knowing not he sits upon a throne;
Wretched the mortal, pondering his mood,
And doomed to know his aching heart alone.