Chapter

3

Pythagoras

The Father of Everything

Lived: Sixth century BCE, Greece

Occupation: Mathematician (ish)

Immortality Suits Pythagoras

Are you confused by a2 + b2 = c2? A little fuzzy on the meaning of the word hypotenuse? Unsure why the triangle has to be “right”? Don’t worry. It’s quite possible that Pythagoras was just as perplexed as you are, and he supposedly invented the formula.

Pythagoras lived around 570 BCE in Samos, an island off the coast of modern-day Turkey, and also in Croton, a city in Southern Italy. That’s about all you can take to the bank. Everything else is debatable.

See, Pythagoras attracted legends like bugs to a bright light. Except, he was more like the fat spider in the corner, gobbling down legend after legend. It’s hard to blame him, though, since he was dead for most of the meal. It was his followers who threw incredible deed after miraculous feat at the memory of the dead man, turning him into history’s biggest math fraud. It wasn’t just the triangle thing, either.

Suddenly, he invented mathematics, discovered the secrets of the harmony of the spheres, and began Greek philosophy itself. That’s a pretty impressive résumé for a corpse. But first, he taught students something a little different than your average geometry teacher.

Are you sure this is “right”?

A Vegetarian before It Was Cool

The Greeks didn’t have the rosiest ideas about the afterlife. It was more doom and gloom than harps and happiness. They believed that inconsolable shades roamed a dark field in Hades for eternity. Shades were hungry and cold and miserable, and they stayed that way forever.

shades:

Ghosts.

Enter Pythagoras. Like a hoplite in shining armor, he came to the rescue of any Greek unhappy with such a bleak picture of life after death, and really, who wouldn’t be?

hoplite:

Greek warrior.

According to Pythagoras, you didn’t have to die. Not for long, at least. You could be reborn. He swore he’d been reincarnated four times already. He even remembered the battle at Troy where he had been killed by Menelaus centuries ago.

chiton:

Greek version of the toga.

Don’t Cross the Boss

Pythagoras liked numbers. They were pretty, they were rational, and they were magical, which just about covers all the criteria Pythagoras needed. According to legend, everything was numbers—whole numbers, to be exact. People who believed in imaginary, irrational, and negative numbers (all things mathematicians study today), well, they weren’t allowed into Pythagoras’s group. In fact, irrational numbers and their type were even worse than toot-inducing beans.

Unfortunately, Hippasus, one of Pythagoras’s most famous followers, picked a bad time to discover the irrationality of the square root of two—on a boat in the middle of the sea. Hippasus, perhaps forgetting the bigwig didn’t like irrational numbers, was understandably excited to show his findings, so he challenged his fellow Pythagoreans to find a whole number answer to the square root of two. Their bushy eyebrows scrunched together and their eyes started to cross. Nothing worked. Steam probably poured out of the Pythagoreans’ ears soon after.

At this point, Hippasus should’ve been nervous. Word couldn’t get out that there were irrational numbers, so the group (or perhaps Pythagoras himself) threw Hippasus overboard. Hippasus would have to tell his discovery to the fishes. (Just to be clear, this story was first told hundreds of years after it supposedly happened. And there are a lot of versions.)

Like most good things in life, it wasn’t easy to be reborn. It took a lot of hard work, but Pythagoras had a few tricks up his chiton to help his followers achieve this immortality.

If you thought life in Ancient Greece without running water and television was hard enough, becoming a Pythagorean meant life was about to get a lot harder.

Some of the easy rules included: don’t eat beans, don’t eat animals (that delicious goat might be your grandfather, after all), don’t let yourself be buried with wool, don’t stir a fire with iron, don’t look in a mirror that’s beside a light, don’t use public roads, don’t step over a yoke, and definitely don’t speak in the dark. That was just the beginning, though. The list was exhaustive, and exhausting. (Hard ones involved sitting at a table full of food, letting the smell of hot, tasty roast goat waft up your nose, and then leaving without touching a thing after a “considerable time.”)

Membership to Pythagoras’s club was exclusive. This was a secret society of sorts. Not everyone could join, and for the first five years of membership, no one was allowed to talk, even in daylight. That’s one easy way to keep people from complaining about how much they miss their mom, or not getting to take the easy way home—on a road.

So was Pythagoras the first vegetarian? Maybe, or maybe not. Some say he ate no meat and wouldn’t even talk to butchers. Others say he ate meat except for oxen. Unless someone tracks down a recently reincarnated Pythagoras, his eating habits will stay a mystery. Except for the beans. His followers were very clear on that count.

No beans allowed, because not only did beans look like fetuses (and you wouldn’t want to be a cannibal, would you?) but everyone knows the more beans you eat, the more you toot, and that can obviously distract you from thinking about lofty things like death and math.

The Original Renaissance Man

With such an interesting man, it didn’t take long for more rumors about his life to start flying. And the golden rule of rumors is the crazier, the better. Crazy tends to grab people’s attention.

How crazy, you ask? How about this: He was a son of Apollo, the god of reason; he could be in two places at once; he could predict earthquakes; he never laughed; he bit a snake to death; and he had a golden thigh—things of that nature. Things teachers really should mention in math class more often.

Snake and beans: it’s what’s for dinner.

In his lifetime, Pythagoras only claimed to know mystical secrets about the hereafter. A few hundred years later, and people claimed Pythagoras knew everything. (Saying he was the son of a god probably helped sway disbelievers.) It was thanks to these rumors and to his loyal followers, that Pythagoras was soon the Father of Everything.

Harmonizing Hammers: the opposite of MythBusters.

By the fourth century BCE, things had spiraled out of control. Somebody insisted Pythagoras discovered musical harmony simply by walking past a blacksmith’s forge. The ringing of the hammers sounded pleasant—except for one. Pythagoras ran inside, only to realize the one unharmonious hammer didn’t have any ratios in common with the others. Thus, the principle of harmony was found, even though the MythBusters could debunk this in a second.

Next, Pythagoras was declared the Master of Philosophy, right about the time some famous guy named Plato was writing down his own philosophical conversations (427–347 BCE). Pythagoras’s followers cried foul and accused Plato of plagiarism.

As for the famous Pythagorean Theorem, it wasn’t until some Romans living in the first century BCE mentioned the two together that Pythagoras became connected. Cicero said that Pythagoras found something new and sacrificed an ox. Then Cicero had to go and say he didn’t believe the stories. Every writer after Cicero conveniently left out the “I do not believe it” bit and embellished the story, including Vitruvius thirty years later, who added the all-important triangle bit.

According to an earlier source—now lost—a guy named Apollodorus the Calculator (Not to be confused with Apollodorus the Tape Measure. Just kidding.) mentioned how Pythagoras celebrated the secret of triangles not by going out for ice cream, but by sacrificing oxen—which later got turned into a hecatomb. Which seems like it would get in the way of that vegetarian thing. Maybe that’s why Cicero said he didn’t believe it.

hecatomb:

A hundred cows, give or a take a few moos.

That didn’t stop Pythagoras’s reputation from snowballing. People began to attribute all sorts of math-y things to him. They would write out their own findings and sign Pythagoras’s name at the bottom in a sort of reverse form of plagiarism. They hoped attaching his name would give their ideas more legitimacy. Today, it’d be like writing a groundbreaking essay on the power of baking soda for science fair volcanoes and then signing both your name and Marie Curie’s name as the authors.

Marie Curie:

A famous nineteenth-and twentieth-century chemist who got a little too friendly with deadly chemicals.

Your teacher has to give you an A, right? Marie Curie helped you write the essay.

Just to be clear, Pythagoras had about as much to do with all of these discoveries as a bean.

Just like Nessie

The real Pythagoras is as elusive as the Loch Ness monster, and just like Nessie, he’s been giving us the slip for thousands of years. That’s because the most detailed stories of Pythagoras come from men living in the third century CE. When you do the math, that’s eight hundred years after Pythagoras kicked the bucket (for the fifth time, at least, according to him).

It was like a massive game of telephone. If a story can change in only a few minutes, imagine how much it can change in a few hundred years. The later writers looked at earlier sources and came to their own conclusions, which is what you call really bad research.

Diogenes Laertius used earlier sources such as Plato and Aristotle. He wrote about 200 CE, and mentioned a guy named Pythagoras who had a bunch of followers, who found the answer to a right triangle, and who sacrificed a hecatomb upon its discovery.

Iamblichus, a Syrian philosopher from 300 CE, had a bit of a different agenda. If Pythagoras had been alive to hear his words, his head would’ve swelled so much it might have exploded. Iamblichus claimed that Pythagoras invented political education, coined the word “philosophy,” and overthrew despots (in addition to all the math stuff, of course). According to Iamblichus, Pythagoras knew how to talk with bulls, and he was really handsome. Obviously. You don’t get to be that famous without being good looking.

However, it wasn’t just people in the ancient world fighting to be president of the Pythagoras fan club. In 1632, Galileo got in on the action. In his famous treatise, Dialogue on the Two Chief World Systems, he claimed that Pythagoras first discovered the proof for a right triangle. We’ll forgive Galileo, however, since he didn’t have the internet back then to check his research.

This is a how a legend is born, but just because it’s old and passed on for hundreds of years, doesn’t mean it’s true. In fact, it probably means the opposite. It seems that the only thing Pythagoras did really well was to trust his followers to spread the good news about him.

The Real Reason Hippasus Got the Boot

The Pythagoreans were split into two sides: the acusmatici and the mathêmatici. The acusmatici emphasized the religious ideas Pythagoras was known for and all those crazy rules. The mathêmatici preferred math and numbers. Both claimed to be the closest to Pythagoras’s true teachings, and as a result, things got nasty between the two groups. The acusmatici accused the mathêmatici of really descending from Hippasus and his love of numbers. The mathêmatici denied it and figuratively threw Hippasus under the bus. (And this was after they threw him over the side of the boat! Poor Hippasus.) No one liked Hippasus anymore even though he is the first mathematician and music theorist in the Pythagorean tradition, at least that we know of. That’s what you call the raw end of a deal.

The Common Denominator

So we do know one more thing for certain: Pythagoras was the head of a religious cult, and not the leader of a bunch of nerdy guys sitting around scratching math equations in the dirt with a stick. Attributing all those discoveries to him would be like claiming Buddha discovered the theory of relativity. Sorry, Einstein.

So why study a man who clearly had nothing to do with inventing the Pythagorean Theorem and who probably didn’t even give a hoot about math?

Liar, liar, chiton on fire.

Because Pythagoras was a superstar during his time, and even centuries after. Instead of being known for singing catchy tunes or throwing wild parties, he was known as a shaman. He influenced scores of people—the Pythagoreans—and Western thought for generations to come, even if he didn’t do a lot of that thinking himself. When math students learn about the history behind their equations, his name is still one of the most common in textbooks.

When Copernicus was studying the earth’s relationship to the sun, he didn’t name his findings after himself, but after Pythagoras. (Sound familiar?) He originally called his findings, Astronomia Pythagorica. (It wasn’t until later that the world started calling them the Copernican Revolution.) Copernicus’s findings started the sixteenth century Scientific Revolution, two thousand years after Pythagoras lived; but somehow, Pythagoras still gets at least partial credit.

Obviously, someone had to discover the theorem of the right triangle, even if it wasn’t Pythagoras. So who was it? Well, scholars don’t exactly know. Some cuneiform tablets seem to prove that the Babylonians knew about the whole triangle business at least a thousand years before Pythagoras was even born. The Chinese and Indians were all over geometry, too. There wasn’t a ton of contact between these cultures at the time, so it’s doubtful that they copied each other. They probably each discovered it independently.

The first known proofs of the theorem come from The Elements by Euclid, another famous Greek living about 250 BCE (or did he? We have no evidence on him either). Clearly, the Greeks loved their numbers.

Leguminophobia?

Pythagoras probably had an eventful life, even if scholars don’t actually know what the events were. Perhaps the most enduring legend around Pythogoras’s life centers on the way he died—by beans. Which is a little like someone with anthophobia (a fear of flowers) accidentally brushing up against a petunia and dying from an allergic reaction. Guess they were right in the end to be afraid.

According to the story, Pythagoras’s cool kids’ club had started to rub people the wrong way. It was secretive, exclusive, and a bit spooky with all its mysticism. So one night, some disgruntled locals decided to do something about the weird hippie living down the street. Setting his house on fire seemed like a good solution.

Pythagoras managed to escape, only as someone with his head in the clouds all day he didn’t know his neighborhood very well. He took off with the pyromaniacs in hot pursuit and ran straight into a bean field. When he realized his mistake, he refused to take one step farther, even if it meant escape. Instead, Pythagoras screamed that he would rather die by savages than trample beans, and so he did.

Hopefully, when he was reborn, it wasn’t as a bean farmer’s son.