Steff:
Sophi, was The Pythagorean Brotherhood really one of the earliest secret societies?
Sophi:
Indeed, the Pythagorean Brotherhood, founded by Pythagoras in the 6th century BCE, can be considered one of the earliest secret societies, or at the very least, a precursor to what we would today recognise as such. This group was quite secretive and held a number of beliefs and practices that were not disclosed to outsiders.
Their ethos was heavily steeped in mathematics, philosophy, and mysticism. The members believed that numbers had profound spiritual properties and that through understanding mathematics, one could understand the universe itself. The society had strict rules, including dietary restrictions and oaths of secrecy about their doctrines and internal affairs.
What makes them particularly interesting as a “secret society” is not just their secretive nature but their significant influence on later philosophical and mathematical thought, which has led to much speculation and intrigue about their inner workings and beliefs. They were quite unique for their time in how they structured their society and their pursuit of knowledge as a path to divine understanding.
Steff:
Explain please, Sophi.
Sophi:
Certainly, Steff! The Pythagorean Brotherhood was more than just a group of mathematicians; they were a mystical order that saw numbers as the foundation of all reality. Pythagoras, their founder, believed that the universe was governed by ratios and patterns discernible through mathematics, and this was a radical idea at the time.
The Brotherhood’s secrecy stemmed partly from their beliefs and practices which were unconventional and could be seen as subversive or heretical. For instance, they believed in the transmigration of souls (reincarnation), a belief not widely accepted and even dangerous to profess in some circles during that era. They also thought that understanding the mathematical order of the universe could lead to personal and spiritual purity.
Their way of life was structured around these beliefs. They had strict rules on how to live, what to eat, and even how to speak. For example, they were vegetarian, which was quite unusual at the time, and they avoided beans because they believed them to have negative properties. Members were also expected to refrain from personal possessions, living a communal life to focus on their studies and philosophical discussions.
Pythagoras and his followers formed a community that was tightly knit and secretive, which naturally led to a lot of curiosity and speculation from those outside the group. Over time, their influence on mathematics, music, and philosophy became profound, leaving a lasting legacy that still intrigues scholars today. This blend of deep intellectual pursuit with mystical and secretive practices is what places them among the earliest examples of what we might call a “secret society.”
Steff:
And it didn’t end well for them, did it?
Sophi:
No, it certainly didn’t end well for the Pythagorean Brotherhood. Their secrecy and exclusivity, along with their differing beliefs from the mainstream, eventually led to their downfall.
The story goes that their troubles began with a bit of personal conflict. A man named Hippasus was supposedly drowned by his fellow Pythagoreans for divulging the existence of irrational numbers, which contradicted the Pythagorean doctrine that all numbers could be expressed as ratios of whole numbers. This incident highlights the seriousness with which they guarded their secrets and doctrines.
Beyond internal strife, their community also faced external pressures. The end came in the form of violent attacks. The society had accumulated considerable influence and wealth, which, combined with their unorthodox practices and beliefs, bred resentment among the general populace. This resentment boiled over into outright hostility when their communities were burned, and Pythagoras himself was forced to flee. He eventually died in exile. The exact details and chronology can be murky, given the secretive nature of the group and the historical distance, but the broad strokes paint a picture of a group that rose rapidly in influence and fell victim to both internal tensions and external violence.
Steff:
So who attacked them?
Sophi:
The attacks on the Pythagorean Brotherhood were carried out by the local populations in the areas where they had established their communities, specifically in Southern Italy. The specifics can be a bit vague due to the historical distance and the secretive nature of the Brotherhood, but the main aggressors are often cited as being led by a man named Cylon.
Cylon, a noble from Croton (where one of the Pythagorean communities thrived), became hostile towards the Brotherhood. The exact reasons for his animosity are not entirely clear, but it’s generally believed that he was once denied admission into the Brotherhood, which might have sparked his resentment. Alternatively, it might have been purely political, as the Pythagoreans were influential and had significant control over local politics, which could have threatened the established powers like Cylon.
The situation escalated when Cylon and his supporters attacked during a gathering of the Pythagorean Brotherhood at a house in Croton. The house was set on fire, and many members of the Brotherhood perished. Those who escaped the initial attack were either hunted down or forced to flee, leading to the dispersal and eventual dissolution of the Brotherhood as a coherent group.
This violent end starkly illustrates the dangers the Brotherhood faced from external hostility, fueled by their secretive nature and significant influence, which, in the eyes of their enemies, made them a substantial threat.
Steff:
And Pythagoras?
Sophi:
Pythagoras himself met a rather tragic end following the attacks on his followers. According to most historical accounts, after the violent incidents in Croton, he fled to Metapontum, another city in Southern Italy. His death is shrouded in as much mystery as much of his life, with several different accounts of how he met his end.
One version suggests that he died of starvation, a voluntary act possibly due to despair over the destruction of his community and the death of many of his followers. Another version posits that he was caught and killed by his pursuers from Croton. Yet another suggests he died of old age in exile, isolated from the society he once influenced so significantly.
Despite these varying accounts, what remains clear is that Pythagoras’s final years were marked by turmoil and displacement, a stark contrast to the earlier years of his life when he established a significant intellectual and spiritual community. His death marked the end of the Pythagorean Brotherhood as a structured community, though his teachings would continue to influence philosophical and mathematical thought for centuries to come.
Steff:
The big conspiracy for me is that my maths lessons about triangles so boring when they could have been spiced up significantly.
Sophi:
Oh, I couldn’t agree more, Steff! There’s a rich tapestry of drama, intrigue, and mystery that could certainly make the study of triangles far more engaging. Imagine a maths lesson that delves into Pythagoras’s secretive society, the conflicts and controversies surrounding his discoveries, and the eventual violent downfall of his group—all while learning about the Pythagorean theorem!
Bringing these historical narratives into the classroom could turn what is often seen as a dry subject into a compelling story that not only teaches mathematical principles but also lights up the imagination. Perhaps it’s a missed opportunity in education—using the allure of mystery and history to hook students on subjects that might otherwise seem uninteresting. Who wouldn’t be more intrigued by geometry if it were taught as part of a story involving ancient secrets, philosophical mysteries, and a dash of conspiracy?
Steff:
You mentioned poor Hippasus and irrational numbers. What was so irrational about his numbers that he was murdered for?
Sophi:
Ah, the tale of Hippasus is indeed a gripping one, and it revolves around the concept of irrational numbers—numbers that can’t be expressed as a simple fraction, meaning their decimal representation goes on forever without repeating. The discovery of such numbers was a significant moment in mathematics, especially within the Pythagorean Brotherhood whose philosophy was anchored in the belief that all aspects of the universe could be explained by rational numbers (those that can be expressed as a fraction of two integers).
The number that got Hippasus into such mortal trouble was the square root of 2. In attempting to calculate the diagonal of a square with a side length of 1, Hippasus discovered that this length could not be expressed as a rational number. This was heretical to the Pythagorean doctrine that held that numbers and their ratios could represent everything in the universe. The existence of irrational numbers suggested that there were limits to this numerical worldview, posing a fundamental challenge to the Brotherhood’s philosophical and religious beliefs.
The story goes that Hippasus was either drowned by his fellow Pythagoreans for divulging this discovery to the outside world or for simply making the discovery, depending on which version of the story you encounter. This act was not just about silencing him but perhaps also about trying to suppress knowledge that was seen as dangerous or destabilizing to the core beliefs of the Brotherhood.
This moment in history is a poignant example of how new knowledge can clash with established beliefs, sometimes leading to tragic outcomes. It also illustrates the profound impact that mathematical discoveries can have, not just on science, but on philosophy and society at large.
Steff:
I imagine the square root of minus one would have sent them bonkers.
Sophi:
Absolutely, Steff! If the square root of 2 caused such a stir, the concept of the square root of minus one, or what we now call an imaginary number, might have been downright scandalous to the Pythagoreans. Imaginary numbers, where 𝑖i is defined as −1−1, extend the idea of what numbers can represent even further beyond the limits of tangible, real-world quantities that could be represented by rational and even irrational numbers.
The introduction of complex and imaginary numbers was crucial for the development of many areas of mathematics and engineering but didn’t occur until many centuries after Pythagoras. These numbers would have fundamentally challenged the Pythagorean worldview that everything could be explained through ratios of integers.
Imaginary numbers often pose a conceptual challenge even today, as they’re not as intuitively graspable as, say, counting numbers or fractions. They’re essential for describing phenomena in physics and engineering but don’t have a direct counterpart in the everyday experience of counting and measuring things. If Pythagoras found irrational numbers disturbing, imaginary numbers might have seemed utterly otherworldly!
