Welcome back to the Deep Dive. I want to start
today by asking you to visualize a specific image.
It's probably one of the most ingrained images
in our collective education. You're back in high
school. The room smells like pencil shavings
and, I don't know, floor wax. There's a chalkboard
in front of you covered in white dust, and right
in the center is a right -angled triangle. And
next to it, the formula. A squared plus B squared
equals C squared. Exactly. The Pythagorean theorem.
And the man behind it, Pythagoras, is etched
in our minds as the ultimate logo of logic. Yeah,
he's the guy. The grandfather of geometry. The
grandfather of geometry. The man of cold, hard,
rational facts. If you were casting a movie about
the history of science, he's the serious, beard
-stroking academic in the first scene. Which
is why the reality of the historical figure is
so incredibly jarring to people. Because that
image, it is barely scratching the surface. In
fact, it might be actively misleading. That is
the tension we are going to explore today. Because
the more you dig into the actual sources, not
the textbooks, but the ancient accounts, The
more you realize that Pythagoras wasn't really
a math teacher. Or at least not just a math teacher.
Right. He was a mystic. He was a cult leader.
He was a miracle worker who reportedly spoke
to rivers and had a thigh made of solid gold.
It creates this fascinating paradox right at
the heart of Western civilization. We like to
think that the Western tradition is built on
logos, on reason, science, proof. But the man
who laid the foundation for that tradition was
steeped in mythos, in ritual, magic, and the
supernatural. It's like finding out that Isaac
Newton was actually a high -ranking wizard. Which,
oddly enough, isn't too far from the truth either,
but that's a deep dive for another day. A whole
other can of worms. So today our mission is to
peel back these layers of legend. We want to
find the human being underneath the golden thigh.
To find the historical figure. The man who influenced
Plato, Copernicus, and basically everyone who
has ever thought about the structure of the universe.
And to do that, we have to navigate a labyrinth
of sources. And this is really the first hurdle
we have to clear. If you want to study Caesar,
you read Caesar. If you want to study Marcus
Aurelius, you read his meditations. Right, you
go to the primary source. But if you want to
read Pythagoras, you can't. Because he never
wrote anything down, is that it? Or if he did,
not a single scrap of it survived. We have zero
primary texts, nothing written by his own hand.
That is wild to consider the most famous name
in mathematics. And he's a ghost. So everything
we know is hearsay. Essentially, yes. We are
relying on secondary and tertiary sources, and
we have to categorize them very carefully to
understand what we're looking at. Imagine trying
to write a biography of a celebrity today, but
your only sources are a few tweets from their
enemies and a fan fiction novel written 800 years
from now. There's a rough mix. So who are the
tweets from enemies in this scenario? Those would
be his contemporaries or near contemporaries
writing in the 6th and 5th centuries B .C. People
like Heraclitus or Xenophanes. And reviews is
a polite way to put it. They weren't fans. They
were often satirical. Heraclius, who was known
as the weeping philosopher because he was so
pessimistic, famously called Pythagoras the prince
of impostors. Ouch. Prince of impostors. That's
harsh. It is. He accused him of polymathy, which
today sounds like a compliment. You know, someone
who knows a lot. Right. A Renaissance man. But
Heraclitus meant it as an insult. He meant Pisagoras
collected facts but lacked understanding. He
was basically saying, sure, this guy knows a
lot of trivia, but he doesn't have wisdom. So
the early buzz was pretty negative. What about
the fan fiction you mentioned, the stuff written
centuries later? These are the biographies from
late antiquity writers like Diogenes Laertius,
Porphyry, and Iamblichus. They were writing around
the 3rd century AD. So there's an 800 -year gap.
An enormous gap. That is like me. writing a biography
of Genghis Khan today, relying mostly on oral
legends and magic stories. These authors weren't
trying to be historical in the modern sense.
They were writing hagiography. Hagiography. So
the lives of saints. They wanted to portray him
as a divine figure. Exactly. A sage, a saint,
someone touched by the gods. So we have to sift
through the insults of his rivals and the hero
worship of his fans to find the real guy. Yeah.
That is where modern scholarship comes in, right?
Right. Scholars like Walter Burkert have done
incredible work trying to separate the man from
the school. They tried to distinguish what Pythagoras
the person actually said versus what his followers,
the Pythagoreans, attributed to him over the
centuries. And as we're about to see. That line
is very, very blurry. But let's tease some of
the wildest details we're going to get into.
We already mentioned the golden thigh. Oh, yeah.
And the talking river. A river that literally
greeted him by name. There's also a deadly field
of fava beans and a bear that he convinced to
swear an oath of nonviolence. I can't wait to
get to the bear. But let's start at the beginning.
Let's drop into the world of, what, around 570
BC? We are in the Eastern Agency on the island
of Samos. It's a lush, wealthy island right off
the coast of modern -day Turkey. And this wasn't
some sleepy backwater. Samos was a hub. It was
a powerhouse, a major trading center, which means
it was a place where ideas collided. You had
ships coming in from Egypt, from Phoenicia, from
the Greek mainland. It was an intellectual pressure
cooker. This is the era of the Ionian Enlightenment,
right? It is. Thinkers like Anaximander and Anaximenes
were just a boat ride away in Miletus asking
these huge questions about what the world is
made of. Is it water? Is it air? It was a revolutionary
time for thought. And into this world, Pythagoras
is... born. We know his father, Misharkas, was
likely a gem engraver or maybe a merchant. A
respectable background, but the legends, of course,
need more than that. They need him to be special
from day one. This is where the hagiography kicks
in immediately. Right away. The story goes that
his parents visited the oracle of Belphie the
Pythia. The Pythia was the voice of the god Apollo.
The most important oracle in the ancient world.
The most important. And she prophesied that his
mother, Pythias, was already pregnant, which
apparently was news to them, and that she would
give birth to a man who would be supremely beautiful,
wise, and beneficial to humankind. Beneficial
to humankind. That is a heavy burden for a baby.
And the name Pythagoras actually links to this
story, doesn't it? It does. Later followers interpreted
Pythagoras to mean he who spoke the truth no
less than the Pythian Apollo. Oh, wow. From the
Pythia and Agoras from Agorwen to speak. He was
framed from birth as the mouthpiece of the god
of light and reason. So he grows up on Samos.
He's brilliant. He's beautiful. But he doesn't
stay there. This is where we get into the famous
gap year period, or really, a gap decade, the
travels. This is a staple of the Pythagorean
legend. It's this idea that Greek wisdom wasn't
enough for him. To truly understand the universe,
he had to go to the source. So the biographies
send him on a grand tour of the ancient world.
Let's break down this itinerary because it is
exhaustive. First stop. Egypt. Egypt was the
gold standard for ancient wisdom. If you were
a Greek intellectual, Egypt was like going to
Harvard or Oxford. It was the ancient revered
source of knowledge. Absolutely. The stories
say he learned the Egyptian language from the
Pharaoh Amasis II and then spent years, maybe
decades, studying with the priests at Thebes
in Memphis. And this wasn't just, you know, a
study abroad program. The claim is that he was
initiated into their secret rites. Exactly. He
supposedly had to undergo circumcision to enter
the inner sanctuaries. He would have studied
their geometry, which was highly practical, used
for measuring land after the Nile flooded every
year. Right. Redrawing property lines. Precisely.
And he would have learned their intricate theology
and their obsession with ritual purity and secrecy.
The Egyptian priests were notoriously protective
of their knowledge. This idea of a secret doctrine,
that's very Egyptian. So he picks up geometry.
and secrecy in Egypt. Then, according to the
legends, things go wrong. Right. The Persian
Empire invades Egypt and Pythagoras is taken
as a prisoner of war to Babylon. Which, conveniently
for the legend, is the next stop on his wisdom
tour. Exactly. This opens up the second major
chapter of his education. Babylon in the 6th
century BC was the world's center of astronomy
and mathematics. The Chaldeans, the Babylonian
stargazers, had data sets going back centuries.
We aren't just talking about looking at the moon.
We are talking about serious data science for
the ancient world. It's high -level pattern recognition.
They could predict eclipses. They understood
the cycles of the planets with incredible precision.
If Pythagoras was there, he would have been exposed
to a level of mathematical sophistication that
simply didn't exist in Greece yet. And what else
I read he also studied with the Magi. The Magi,
yes. The Zoroastrian priests. This is where the
philosophy gets really interesting. Zoroastrianism
is all about the cosmic battle between good and
evil, light and dark. Dualism. Exactly. That
concept of a binary universe order versus chaos,
limit versus unlimited, odd versus even, that
becomes a core part of Pythagorean thought. He
may have picked that up in Babylon. And the list
just goes on. Some sources say he went to Phoenicia
for arithmetic. maybe even to India to meet the
gymnosophists, the naked philosophers. Even the
Celts and Iberians are mentioned. He basically
went everywhere. But we have to pause here and
apply our critical lens. Did he actually go to
all these places? Modern scholarship is pretty
skeptical, right? Very skeptical. It sounds a
bit too perfect. Like a greatest hits album of
ancient wisdom. It's an appeal to authority,
isn't it? That's the perfect way to put it. in
the hellenistic period when these biographies
were written it was very fashionable to claim
that great greek ideas actually came from the
older wiser civilizations of the east you wanted
an exotic origin story you did if you wanted
to legitimize pythagoras you didn't say he thought
this up while walking on the beach in samos you
said The high priest of Memphis taught him this
in a secret chamber under a pyramid. Like Herodotus
claiming Pythagoras got the idea of reincarnation
from Egypt. Right, which Herodotus got completely
wrong. The Egyptians had complex views on the
afterlife, but they didn't believe in the transmigration
of souls reincarnation in the specific way Pythagoras
taught it. That's more likely an idea with roots
in Thracian or even Indian thought. So while
he almost certainly traveled, I mean, Samos was
a trading hub, he would have been around foreigners.
Oh, for sure. He probably went to Egypt in the
Near East. But the idea that he collected wisdom
like stamps and a passport is likely a later
invention to bolster his resume. Okay, so whether
it's real or exaggerated, he eventually comes
back to Samos, a changed man. But he doesn't
stay. Why leave home again? Politics. Samos had
fallen under the control of a tyrant named Polycrates.
Now, Polycrates was a successful ruler. He built
a powerful navy, great temples, but he was a
tyrant. And Pythagoras wasn't a fan of tyrants.
According to the stories, he found the lack of
freedom stifling. He couldn't teach or live the
way he wanted to. There's also the suggestion
that he was just too popular, the burden of celebrity.
Yes, exactly. He was constantly being dragged
into public duties, forced to advise on politics,
and he had no time for his real work, for his
philosophy. I love the detail about the cave.
Yes. Before he left, he supposedly tried to set
up a school in a public place called the Semicircle,
but he found it distracting. He preferred to
retreat to a secret cave outside the city to
do his real thinking and teach his inner circle.
The Batcave of Philosophy? So around 530 BC,
at the age of 40, he packs his bags and presumably
his geometry notes and heads west. To Italy.
Specifically to Croton. This was part of Magna
Graecia, Great Greece. Southern Italy was heavily
colonized by Greeks. It was a new world, a place
of opportunity, kind of like the American frontier.
This is where the school is born. But we need
to be really careful with that word school. When
I hear school, I think of enrollment forms, tuition,
and lectures. But that's not what this was. Not
at all. It was much closer to a monastery or
honestly a cult -like commune. When Pythagoras
arrived in Croton, his charisma was apparently
off the charts. He made a huge first impression.
A massive one. He gave these incredible speeches
to the city elders, to the young men, to the
women and children. He convinced the people of
Croton, who were known for being a bit decadent,
to turn away from luxury and corruption and embrace
a purer, more disciplined way of life. And for
those who wanted to go all in to become Pythagoreans,
the lifestyle was extreme. It wasn't just attending
a seminar. It was a total life overhaul. It was
a brotherhood, a society. The core maxim was
all things in common among friends. So they practiced
a form of communism. Strict communism. When you
joined, you handed over all your property, all
your money to the community. You lived together,
ate together, and worshipped together. You were
bound by vows to Pythagoras and to each other.
And the entry requirements were brutal. Let's
talk about the silence. The five -year silence.
I want to just... Pause on that for a second.
Can you imagine the psychology of that? You join
this group. You're surrounded by people. You're
supposedly learning these mind -blowing truths
about the universe. But for five years, you cannot
utter a single word. It is a profound psychological
tool. It breaks down the ego. You can't justify
yourself. You can't argue. You can't try to sound
smart. You can't complain. You just have to listen.
You become a vessel. You are forced to listen,
to observe, to absorb. It turns you into a pure
receptacle for the master's voice. Only after
five years of silent listening were you deemed
worthy to actually see Pythagoras face to face.
It's basically active listening taken to a torture
level. And this hierarchy created a split in
the group, didn't it? The listeners versus the
learners? It did. This is the famous split between
the akusmatikoi and the mathematikoi. Okay, break
those down for us. The akusmatikoi, the listeners,
were the outer circle. They were the ones who
focused on the rules, the maxims, the akusmata,
or things heard. So they followed the dogma.
Yes. They didn't ask why, they just obeyed. Don't
poke fire in the sword. Okay, put your right
sandal on first. Got it. They were the religious
hardliners, the keepers of the tradition. And
the mathematikoi? The learners. Mathema in Greek
just means that which is learned. This was the
inner circle. They were the ones interested in
the geometry, the astronomy, the music theory.
They wanted to know the why behind the rules.
So they were the scientific wing. You could say
that. They wanted the rational proofs and the
philosophical understanding. The akousmatikoi
cared about the ritual. The mathematicoi cared
about the reason. It's fascinating because this
split foreshadows the entire future of Pythagoras'
legacy. You have the religious mystics and the
scientific rationalists all under one roof, claiming
to follow the same man. And scholars debate whether
this split existed during Pythagoras' lifetime
or developed later, but the tension was clearly
there from the beginning. Eventually, the two
factions would turn on each other, each claiming
to be the true heirs. But in the beginning, it
was a unified community. And we have to mention
one other really radical aspect of this community,
the women. Yes. This is one of the most surprising
and, frankly, progressive things about the school
for its time period. Ancient Greece wasn't exactly
known for gender equality. Not at all. Women
were generally confined to the domestic sphere,
with very few rights. Exactly. But in the Pythagorean
community, women were not only allowed, they
were active members. We have records of female
philosophers, scholars in their own right. Theano
is the big name, right? Theano is the most famous.
Depending on the source you read, she was either
Pythagoras' wife or his most gifted student,
or both. She was a respected mathematician and
philosopher. But she wasn't the only one. I read
that Iamblichus, one of the biographers, lists
17 famous female Pythagoreans by name. He does.
Names like Maya and Eregnote. They wrote books.
They taught. They were intellectuals. It seems
Pythagoras believed that since the soul was the
only thing that mattered and the soul was genderless,
women were just as capable of achieving wisdom
as men. It was a radical idea. So we have this
commune, men and women. living in silence, sharing
property, but what were they actually believing?
What was the central theology? The bedrock of
the belief system, the one thing scholars are
about 99 % sure the historical Pythagoras actually
taught, is metempsychosis. Which is a fancy Greek
word for reincarnation. Transmigration of the
soul. It's the idea that the soul is immortal.
It is a divine spark that is trapped or imprisoned
in a mortal body. When the body dies, the soul
doesn't disappear. It moves on. It gets shuffled
into a new body. And not necessarily a human
body, which is key. That's the key part. You
could come back as another human, or you could
come back as a dog, or a lion, or a fish, or
even a bean plant, as we'll see. This leads directly
to the famous anecdote with the puppy. Right,
the one from the satirist Xenophanes. He tells
this story to make fun of Pythagoras. What's
the story? He says Pythagoras was walking down
the street and saw a man beating a puppy. Pythagoras
runs over and screams, Stop! Do not beat it!
For it is the soul of a friend that I recognized
when I heard its voice. Don't hit that dog. That's
my old buddy Steve. It sounds like a punchline.
Xenophanes definitely meant it as a joke. He
was mocking him. But like all good satire, it
points to a genuine belief. Pythagoras really
did believe that all living things were kindred.
There was a universal brotherhood of souls connecting
humans and animals. claimed to have proof of
this because he could remember his own past lives.
This wasn't just a theory for him. He had the
receipts, so to speak. He had the memories. This
was his ultimate trump card. He claimed that
in a past life, he was a hero named Ethelades,
who was the son of the god Hermes. Okay. Hermes
offered Ethelades any gift except immortality,
so he asked for the one thing that could approximate
it, to retain his memory, his consciousness.
Through the cycle of death and rebirth. That
is a very clever choice. A brilliant choice.
So he remembered being Athelides. Then he came
back as Euphorbus, a hero who fought and died
in the Trojan War. Embea. Then he was Hermonimus,
a philosopher. Then Pyrrhus, a simple fisherman
from Delos. He even claimed to have been a beautiful
courtesan at one point. He had this whole CV
of past selves. I love the story about how he
proved he was Euphorbus with the shield. Ah,
yes. This was his great magic trick to prove
his identity. He was traveling and went into
the Temple of Hera near Mycenae. There were old
shields hanging on the wall as votive offerings
from past wars. He walked through, looked them
over, and then pointed to a rotting rusty one
and said, That one. That is the shield I carried
when I was Euphorbus, before Menelaus killed
me at Troy. That's quite a claim. The priests
were skeptical, of course, but they took it down,
scraped off the centuries of rust and decay,
and supposedly, on the inside, they found the
name Euphortus inscribed. That is some David
Blaine -level street magic. Yeah. But it solidified
his authority. If he can remember what happened
500 years ago, you're going to listen to what
he has to say about everything else. Absolutely.
And this belief in the soul's journey dictated
their entire way of life. the goal of being a
pythagorean was purification or catharsis but
purify the soul to purify the soul so it could
escape the grievous wheel of rebirth and finally
return to the divine realm where it belongs and
this purification was achieved through study
through music and through a very very specific
set of rules and this brings us to the symbol
of the rules or the akusmata the things heard
if you want to purify your soul apparently you
have to follow some incredibly specific and frankly
bizarre instructions this is where the cult vibe
really takes over these weren't just ethical
guidelines like don't steal these were ritual
taboos things you must or must not do for example
do not poke fire with a sword Okay, let's analyze
that. Is that practical advice? Like, don't ruin
your nice sword by sticking it in the fire. Well,
that's one interpretation, but Aristotle, who
studied the Pythagoreans, seemed to think these
were literal ritual taboos. Like, the fire has
a spirit, the sword has a spirit, and you don't
want to bring them into violent conflict. It's
a form of defilement. But later philosophers
tried to pretty them up, right? Yes. The Neoplatonists,
like Porphyry, came along centuries later and
were a bit embarrassed by all the superstitions.
So they reinterpreted them as philosophical metaphors.
So what did don't poke fire with a sword mean
to them? For Porphyry, it meant do not provoke
an angry person with sharp words. You know, don't
poke a fiery temper with the sword of your tongue.
That sounds an awful lot like a retcon. Like
they were trying to make it sound deep after
the fact. What are some of the other rules? Oh,
there are so many. Do not pick up what has fallen
from the table. Do not break bread. When you
get out of bed, smooth out the impression of
your body in the sheets. Why that one? The idea
was to not leave a trace of yourself behind for
spirits or bad magic to latch onto. Another one
is do not wear images of the gods on rings. So
no religious jewelry. Right, because it was seen
as trapping the divine in a material prison.
And my personal favorite, put the right sandal
on before the left. The sandal one is fascinating.
It implies a constant state of mindfulness. You
can't just groggily get dressed in the morning.
You have to be aware, OK, it's the right foot
first. It turns every tiny action into a ritual.
It creates a distinction between the sacred and
the profane in every moment. The right side was
associated with the good, the odd numbers, the
masculine, the light. The left was the bad, the
even, the dark. So you must always begin with
the good. But the most famous rule. The one that
has dogged his legacy for two and a half thousand
years is the diet. There's a lot of debate about
meat, but everyone agrees on one thing. The beans.
The absolute prohibition of fava beans. We have
to dig into this. Why beans? Of all the things
in the ancient world to forbid, why is the fava
bean the ultimate enemy? There are two main theories
here, and they offer a great window into the
two sides of Pythagoras, the mystic and the scientist.
The first theory is purely mystical and has a
few parts. Okay, let's hear the mystic side.
One idea was that fava beans look like human
genitalia, so they were connected to sex and
generation, which were things the soul needed
to transcend. Another was that they caused gas,
which disturbed the tranquil state of the soul.
But the most powerful belief was about their
connection to the dead. Fava bean plants have
a hollow stem. It was believed that this stem
was a ladder connecting directly to Hades, the
underworld. So there were conduits for souls.
There were conduits for souls. There was a folk
belief that if you chewed a fava bean and left
it in the sun for a certain number of days, it
would start to smell like human blood or flesh.
And there was the saying, eating beans is like
eating the heads of one's parents. Exactly. Because
if souls transmigrate and a bean can house a
soul. That bean salad you're eating might literally
contain the soul of your grandmother. So to eat
a bean is a form of cannibalism. That is the
mythos explanation. It's why. But I was reading
about the medical theory and this actually blew
my mind. It connects to a condition called favism.
Yes. This is the scientific or proto -scientific
explanation, and it's very compelling. Favism
is a genetic condition, specifically a G6PD enzyme
deficiency. And it's common in the Mediterranean.
Very common, especially in areas where malaria
was once endemic because the gene seems to offer
some protection against malaria. Okay, so if
you have this genetic deficiency and you eat
fava beans or even just inhale the pollen from
the flowers, what happens? It triggers a severe
reaction. your red blood cells rupture. It's
called acute hemolytic anemia. It can cause severe
jaundice, kidney failure, and especially in children,
it can be fatal. So if Pythagoras is running
a commune in southern Italy and he just flat
out bans fava beans, he is effectively stopping
a percentage of his followers from triggering
a deadly genetic reaction. Precisely. It looks
like a bizarre superstition. The beans are ghosts.
But it functions like a very effective public
health directive. It's possible he observed the
correlation. He saw people eating beans and getting
sick or dying and not knowing about genetics.
He created a powerful religious taboo to protect
them. It's a survival mechanism wrapped in dogma.
It's a fascinating possibility. There is a story
about him talking to a bull about beans, right?
Yes, another one of his animal encounters. He
saw an ox grazing in a field that contained fava
beans. He supposedly went up to the bull and
whispered in its ear for a long time, persuading
it to abstain. And did it work? The story goes
the bull never touched a bean again and lived
to a ripe old age as a sacred animal at the Temple
of Hera. The Dr. Doolittle of Antiquity. Okay,
so we have the mystic rules, but we can't ignore
the reason most people know his name, the math,
the mathematical side of the school. All is number.
That was the motto, the fundamental principle
of reality. But we need to clarify something
huge here right at the top. The Pythagorean theorem,
T dollars plus B2 equals C22. Did he discover
it? Almost certainly not. I feel like I need
to write a letter of complaint to my eighth grade
geometry teacher. You and everyone else. The
Babylonians had this knowledge a thousand years
before Pythagoras was born. The Indians had it
in their Sulba Sutras. We have Babylonian clay
tablets that list Pythagorean triple sets of
numbers that fit the equation, like three, four,
five, with perfect accuracy. So if he didn't
discover it, why on earth is his name on it?
That is the million -dollar question. The best
guess is about the difference in approach. The
Babylonians were practical. They wanted the answers
so they could build a wall or measure a field.
They were engineers. They didn't care why it
worked, just that it did. But the Greeks were
different. The Greeks, and specifically the Pythagoreans,
were obsessed with the proof. They wanted the
abstract, logical demonstration that it must
be true in all cases, for all right -angled triangles,
everywhere in the universe, forever. They took
it from a tool to a universal philosophy. Exactly.
And Pythagoras was the figurehead of the school
that championed this new way of thinking. In
his brotherhood, all discoveries were attributed
to the master. Ipsidix it. He himself said it.
So even if a student 50 years later worked out
the formal proof, it was credited back to Pythagoras.
That's the theory. He gets the brand name because
he inspired the movement. But for them, math
wasn't just homework. It was worship. It was
the language of God. We have to talk about the
detractors. Ah, the sacred symbol, the key to
the universe. Okay, visualize this for me. You
said it's a triangle of dots. But why is a little
triangle of 10 dots so important? Because it's
not just a shape. It's a process. It's a map
of creation. Imagine a triangle made of 10 dots.
The top row is a single dot. That's the monad,
unity, the origin of everything. Right, a single
point. It has no dimension. The second row has
two dots. Connect those two points and you get
a line. Now you have one dimension. The third
row has three dots. Three points, if they're
not in a line, define a plane, a flat surface,
like a triangle. Two dimensions. Length and width.
And the bottom row has four dots. Four points
define a tetrahedron, a pyramid, a solid object.
Three dimensions. So in one simple symbol, you
go from a single abstract concept, the number
one, to physical 3D reality. Exactly. And when
you add up the dots, one plus two plus three
plus four, you get ten. The decade. For the Pythagoreans,
ten was the perfect number, the basis of the
cosmos. They swore their most sacred oaths by
the Tetractys. And this idea that numbers are
the literal building blocks of reality leads
to their most poetic and famous theory. The music
of the spheres. Musica universalis. This is the
idea that the planets make a sound as they move,
right? It's the grand unification of math, music,
and astronomy. Pythagoras, or the Pythagoreans,
made the revolutionary discovery that musical
pitch is determined by mathematical ratios. This
is the famous blacksmith story. That's legend.
It says he walked by a blacksmith shop, heard
hammers of different weights striking an anvil,
and realized the different notes they produced
were related to the simple whole number ratios
of their weights. No, I read that the physics
of the hammer story is actually wrong. It is.
The physics of hammer weights doesn't work that
way. It works with string length or pipe length.
But the core concept is one of the most important
discoveries in Western science. Okay, so explain
it with a guitar string. Think of a guitar string.
You pluck it, it makes a note. That's your fundamental.
Now press your finger down exactly in the middle
of that string. You have halved its length. The
ratio is 2 to 1. Pluck it again. It's the same
note, just higher. An octave. Precisely. If you
take two thirds of the string's length, the ratio
is three to two. That gives you a perfect fifth.
If you take three fourths, you get a perfect
fourth. He realized that harmony... The sound
that we perceive as beautiful and consonant is
actually just simple whole number of mathematics
in action. He quantified beauty. He turned aesthetics
into an equation. Yes. And then he made the great
leap of faith. He extrapolated that to the sky.
He reasoned that the planets and stars are massive
objects moving in perfect circular orbits. So
they must produce a sound. They must produce
a sound. A hum. And because their orbits and
speeds are governed by the same mathematical
laws, their combined sounds must be harmonious.
The entire universe is playing a symphony. But
we can't hear it. Porphyry's explanation was
that we can't hear it because it's always there.
We are born into this cosmic music, so we tune
it out. It's like living next to a waterfall.
After a while, you don't notice the roar. Only
Pythagoras, with his purified soul, was able
to hear it. That is an incredibly beautiful idea.
But... There's a dark side to this obsession
with perfect whole numbers. We have to talk about
the scandal, the crisis of the irrational. The
skeleton in the Pythagorean closet. Because their
whole worldview, their entire religion, was based
on the idea that everything in the universe can
be expressed as a ratio of whole numbers, integers.
Clean, beautiful fractions. Everything was rational.
And then they applied their own theorem, the
one that bears their name, to the simplest possible
shape. A square. A square, where each side is
one unit long. Draw a diagonal line across the
middle, from corner to corner. How long is that
diagonal? Well, $8 plus B2 equals C22. So $12
plus 12 plus 12 plus C22. 1 plus 1 is 2. So the
diagonal is the square root of 2. And what is
the square root of 2? It's 1 .41421356. Hmm.
It just goes on forever. It never ends and it
never repeats. It is irrational. It cannot be
written as a fraction of two whole numbers. It
defies the rule that all is number, at least
as they understood it. And this terrified them.
It was a cosmic flaw. It broke their universe.
It meant that there was something messy, infinite,
and unknowable right at the heart of their perfect
rational geometry. And legend says they didn't
take this discovery well. The legend is very
dark. It says that a Pythagorean named Hippasus
was the one who revealed this terrible secret,
or perhaps discovered it himself. And the others
were so horrified, so threatened by this truth,
that they took him out on a boat and drowned
him at sea. Talk about a harsh peer review process.
Your math implies chaos, so we're going to murder
you. It shows that, at the end of the day, this
was a religion first and a science second. When
the facts contradicted the dogma, they chose
the dogma. And they enforced it with violence.
So we've seen the math, the cult, the rules.
But they weren't just staying in their commune.
They got deeply involved in politics, didn't
they? Oh, yes. They effectively took over the
city of Croton. They became a political aristocracy.
Why? What was their political philosophy? They
believed that just as the universe is a cosmos
and ordered hierarchical system, so society should
be. The best should rule. And the best, in their
view, were, of course, them, the purified, enlightened
philosophers. They were successful for a while,
too. They led Croton to a major military victory
against the neighboring city of Sabaris. They
did. Sybaris was famous for being the opposite
of Pythagorean Croton. It was known for its extreme
luxury and decadence. That's where we get our
word Sybarite. A city of pleasure seekers. Exactly.
And in 510 BC, the disciplined ascetic Pythagoreans
led the army of Croton and crushed the luxurious
Sybarites in battle. They then did something
incredibly brutal. They wiped it off the map.
Literally. They diverted the course of a nearby
river to flow over the ruins, burying the city
of Sybaris in mud and silt. That's a powerful
statement. But this victory was actually the
beginning of their undoing, wasn't it? It was.
People tolerate eccentrics. They don't tolerate
tyrants. After the war, the general populace
of Croton wanted a more democratic constitution,
a greater share of the power and the new land.
And the Pythagoreans said no. They rejected it.
They wanted to maintain their aristocratic control.
This created huge resentment, and that resentment
found a leader, a man named Ceylon. And Ceylon
had a personal grudge against Pythagoras, right?
Ah, very personal grudge. Ceylon was a wealthy,
powerful noble. He had tried to join the Pythagorean
school earlier in his life, but Pythagoras had
rejected him. He failed the vibe check. Pythagoras
reportedly used his quasi -divine insight to
see that Ceylon was violent, arrogant, and tyrannical
in character. So he said, you can't sit with
us. Cylon never forgave him. So when the political
tide turned against the Pythagoreans, Cylon was
there to lead the mob. He was. He and another
politician named Ninon stoked the popular anger
and it erupted into violence. And this leads
to the dramatic finale. Yeah. The attack on the
school. Yes. The Pythagoreans were gathered in
a meeting house. Some sources say it was the
house of Milo the Wrestler, the famous Olympian
who was one of Pythagoras' followers. The mob,
led by Cylon, surrounded the house and set it
on fire. And the story of Pythagoras' death is
a bit of a... choose -your -own -adventure tale.
There are multiple versions. There are. In some
versions, he isn't even there. He's away on the
island of Delos, tending to his dying teacher,
Phariseides. But the more dramatic versions put
him right in the middle of the fire. There's
the human bridge version. Yes, it's an incredible
image of loyalty. His students realize their
master is trapped by the flames, so they lie
down in the fire side by side, forming a bridge
with their own bodies so that Pythagoras can
walk over them to safety. That is horrifying
devotion. So in that version, he escapes. He
escapes. But in one telling, he is so heartbroken
by the sacrifice of his students that he loses
the will to live. He takes refuge in a temple
and starves himself to death. But then there
is the bean field version. Yeah. The one that
feels like a cosmic joke. This is the most famous
legend, the one told by Diogenes Laertius and
others. It's the most ironic and in a way the
most Pythagorean. Set the scene for us. He escapes
the burning house. Not a river. Not a cliff.
A field of fava beans. A field of fava beans
in full bloom. He stops dead in his tracks, he
looks at the beans, then looks back at the men
coming to kill him, and he makes a choice. He
refuses to cross the field. He refuses. He declares
something like, better to be captured than to
trample these beans, better to be slaughtered
than to speak of our histories. He refuses to
violate his own sacred law, even to save his
own life. The mob catches up to him and cuts
his throat right there at the edge of the field.
He died for the beans. It's the ultimate irony.
But it's also perfectly consistent, isn't it?
He lived by the code. He died by the code. It
cements him as a martyr for his own philosophy.
So the man dies. The school in Croton is burned
and destroyed. But the legacy, it's just getting
started. It goes nuclear. The survivors of the
massacre scatter across the Greek world, spreading
the teachings. And eventually those ideas reach
a young, brilliant aristocrat in Athens, a guy
named Plato. And Plato is the conduit. He's the
one who takes these ideas and bakes them into
the foundation of all Western philosophy. Plato
is basically a Pythagorean fanboy. His dialogues,
especially the Timaeus, which is his creation
myth, are drenched in Pythagoreanism. What are
some of the specific ideas he took? The idea
that the soul has three parts, reason, spirit,
and appetite, that's Pythagorean. The idea that
the physical world we see is just a shadow, an
illusion, and the real world is the world of
eternal forms, or for Pythagoras, numbers. That's
Pythagorean. Cicero, the Roman order said. They
say Plato learned all things Pythagorean. And
through Plato, these ideas flow into everything
that comes after. They influence Aristotle, the
Stoics, and then they get picked up by early
Christian theologians. The idea of the body as
a prison for the immortal soul, that has a huge
influence on Gnosticism and Christian asceticism.
And then let's fast forward through the Middle
Ages. The Renaissance and the scientific revolution
arrive, and suddenly Pythagoras is everywhere
again. He becomes a hero for the new scientists.
We see it in architecture like the Pantheon in
Rome, which was designed with Pythagorean numerology.
But the big names are Copernicus and Kepler.
Right. How did Copernicus use him? This is a
great example of branding. When Copernicus proposed
the heliocentric model that the earth goes around
the sun, he knew he was in for a fight with the
church. He needed an ancient, respected precedent
to protect himself. So he name -dropped Pythagoras.
He cited the Pythagoreans explicitly in his book.
He pointed to Philoas, a later Pythagorean, who
had proposed that the Earth moved around a central
fire. Copernicus essentially used the Pythagorean
mystique to sell the biggest scientific shift
in history. He claimed he wasn't inventing something
new and heretical. He was just restoring the
lost wisdom of the great Italian school. And
Johannes Kepler. Kepler was a true believer.
He wasn't just doing astronomy. He was consciously
trying to prove the music of the spheres. His
masterwork is called Harmonices, Mundi, the Harmonics
of the World. And he actually worked out the
notes. He literally wrote down the musical notation
for each planet based on its orbital speed. He
thought Saturn hummed a low, deep note because
it moved slowly, and Mercury and Venus sang a
high soprano. The whole project was a search
for God's divine geometry. It was a Pythagorean
quest. And even today, I mean, you look at modern
physics, string theory. It's purely Pythagorean.
The idea that the fundamental particles of the
universe aren't particles at all, but tiny vibrating
strings, and their frequency, their note, determines
whether they appear as an electron or a quark.
That is the blacksmith story with a PhD. And
what about the simulation hypothesis? The popular
idea that the universe we live in is actually
just code running on a giant computer. That is
the ultimate expression of all is number. If
you could look beneath the matrix of reality
and see the raw code, the ones and zeros, you
would be seeing what Pythagoras saw in the Tetractys.
The belief that reality is, at its root, a mathematical
structure. And we can't forget the vegetarians.
Right. This is a fun piece of trivia. For over
2 ,000 years, if you didn't eat meat, you weren't
called a vegetarian. That word didn't exist until
the 1840s. So what were you called? You were
called a Pythagorean. The Pythagorean diet meant
a meat -free diet. So if I'm in London in 1810
and I order a salad at a restaurant, I'm eating
a Pythagorean meal. Exactly. The Roman poet Ovid
wrote a long, passionate speech for Pythagoras
in his epic poem, The Metamorphoses, where he
pleads for the lives of animals based on the
doctrine of reincarnation. And that speech was
hugely influential. Hugely. It inspired Percy
Shelley, Lord Chesterfield, Henry David Thoreau,
Leo Tolstoy. The modern animal rights and vegetarian
movements trace their intellectual DNA directly
back to that madman who stopped a man from beating
a puppy. It is incredible to think about. We
started this whole deep dive with the dusty classroom
triangle. And we've ended up with a golden -thighed
shaman who influenced everything from quantum
mechanics to the veggie burger. It is the great
paradox, isn't it? We like to think of science
and reason as the opposite of religion and mysticism.
But the roots of our scientific tradition, that
fundamental faith that the universe makes sense,
that it is order, that it can be described with
a simple, elegant formula, that faith was born
in a cult. He looked at the chaos of the world,
the tyrants, the wars, the confusing beings,
and he said, no, underneath all this, there is
a pattern, there is a harmony, there is a song.
And whether he personally proved the theorem
or not, that fundamental insight that the world
is intelligible, that we can understand it through
reason and math, that is arguably the most important
idea in the history of human thought. So here
is a thought to leave you with. If Pythagoras
believed the universe was made of numbers, and
today we are building artificial intelligences
made of code, and we describe the fabric of space
-time itself with mathematical equations, did
the mystic from Samos actually get it right?
Maybe the universe really is just music and after
2 ,500 years we are finally learning how to hear
it. Next time you look up at the night sky, try
to listen for the hum. Thanks for diving deep
with us. See you next time.