(NOTE: Much of this is made up because the Pythagoreans were largely exterminated. Only traces of their teachings survive and they are summed up at the bottom of the story. This story will seem cryptic for those who know nothing of the Pythagoreans. But if you Google the terms you don’t know and the people, it will all make sense.)
Greece, 565 BC
An Early Summer Day Two Hours After Sunrise.
“You are ready and don’t try and hide it.”
Adelpha sat there on the stone, her squat frame and square face tense and serious.
“No sir, I … believe not.”
“You have purposely delayed becoming mathēmatikoi and that must end now. You are testing. When you pass, you will ascend to the elite. Your skills have impressed our teacher as well as angered him beyond belief.”
“Hippasus and I … we rocked the boat didn’t we?”
“You cast aspersions upon our core beliefs with your joint discovery that not all numbers are either whole numbers or ratios. But … Master Pythagoras knows that your discovery is true. And let’s face the facts here.”
He looked at the wall.
“Hippasus didn’t do the real work on this, and I know who did, and Pythagoras knows it too.”
He walked over to a bowl of almonds. He took a one, looked at it and then popped it in his mouth.
“And yes, the Master IS having a lot of internal conflict because of your discoveries. It has shattered both his and our world collectively.”
She smiled and quickly looked down.
“Sorry for the truth? My dear, why not apologize for not being able to square the circle?”
He grabbed his robe with his hand and took a posture of authority.
“Still, this matter must remain only for the mathēmatikoi. The akousmatikoi cannot confront such a radical notion that every number cannot be presented as either a whole number or a ratio. Theirs is a practice of religion, and the Pythagorean mathēmatikoi is devoted to pure mathematics. Do you understand?”
“You cannot tell ANY member of our akousmatikoi about these numbers that do not repeat in a pattern. To them every number MUST be represented as we have ALWAYS taught, and you must especially not tell an outsider of them. Such an act will result in your swift punishment and perhaps your death. We suspect that these … um … irrational numbers that you discovered are a minority – a mere oddity. Although some of the mathēmatikoi feel differently, but they are fringe thinkers. And if some of akousmatikoi figure out these discoveries on their own, then we will handle it ourselves.”
“And how in the world you figured this out as a mere akousmatikoi is beyond me.”
“Hippasus mentored me, his methods are AMAZING!” she said.
His jaw went firm.
“Now before we begin, have you consumed any beans in the last five years?”
“Have you consumed any meat in the last five years?
“Have you touched a bean in the last year?”
“Why do I ask you this?”
“Because, beans are the souls of future men and women and to consume them is the ultimate crime.”
“Yes. We were all beans once,” he said.
She made sure she looked like she believed him.
He took a rake and smoothed the floor. Taking a pointed stick, he drew triangles and circles and squares on the ground and asked her questions and challenges and demanded proofs from her. Two hours later, he put the stick down.
“You have certainly passed geometry, but now you must show me you have the discipline to address the infinite and impossible. And more than half the day remains for that Herculean task. For now, we break.”
As they left the temple, Pythagoras passed and looked at Pythias. Pythias’ glance told Pythagoras that she was, indeed, exceptional.
The two ate alone and had a lunch of nuts, greens, beets and bread. As religious vegans that refused beans, they got their protein from leafy vegetables and grains which meant that massive amounts of greens were required at each meal. This resulted in a sect that ate more than anybody and weighed less than everyone.
And they were healthy.
After lunch, she was ordered to take the customary nap and rest for her work in the afternoon. While she napped, Pythias met with Pythagoras.
“She’s already beyond the mathēmatikoi because of her mentoring by Hippasus. She also has strange ideas regarding Pi transcending the irrational which is more insanity. It appears Hippasus’ teaching methods are very effective in some ways. I believe that is this reason as to why she has refused to ascend to our highest order.”
Pythagoras clenched his teeth.
“It matters not,” said Pythagoras, “Hippasus is a traitor to sacred number itself. He revealed this abomination to outsiders and must be put to an end. In fact, if he sees tomorrow, he will be lucky. And the woman here is almost right behind him.”
Pythias calmed his face so it would not show concern.
“Master, be kind to her. She is gifted indeed. I know there is more she is not telling. I suspect she knows more about Pi, the golden mean and the ultimate abomination – the numberless number.”
Pythagoras glared at him and said, “She’s too good to banish, but dangerous. Keep her mind seeing and her lips still. Also, I want every one of Hippasus’ methods out of her for he won’t be around long enough to tell us.”
An hour later, Pythias and Adelpha were back in the temple to finish the exam.
“Sit straight with perfect posture and ponder the following until the shadow on the wall moves over the mark that indicates our time is done.”
He placed a square and a straight edge in front of her.
“In your mind’s eye take this square and straight edge and square the circle. Nobody has ever done it. So far, it appears impossible. Work it from every angle in your mind until you transcend the problem. I’ll behold your presence and discipline because it is your concentration I am testing.”
He watched her eye lids drop to cover most of her eye as she look beyond everything. Her face smoothed out and her breathing turn shallow. A small but slight smile appeared as every bit of her energy railed upon the challenge.
He saw her body shift into a deeper discipline.
There was almost a light around her countenance he could feel. The room appeared softer and lighter at the same time. He knew that she was transcending and her presence was so clean and perfect that anyone beholding her visage would know with one look that such concentration cannot be faked.
As the hours passed, sweat from the day’s heat tickled her skin, but she took no notice and used the discomfort to concentrate more. Numbers and images flew before her in a collage of clarity. Infinity and nothing shown forth from her face like a full moon.
Time flew and the hours passed with barely a flinch.
“The shadow has crossed the mark,” he said. “Your discipline is superior in how you face the impossible.”
She stood in great calm.
“You are now mathēmatikoi. And this cannot be taken from you.”
“What did you discover?” he asked.
“I proved the challenge is impossible.”
He tried to look unimpressed and asked with a faux disinterest, “Show me the proof.”
“I demand it!”
“I’ll show you when my teacher Hippasus is an old man.”
“Then … I’m afraid I’ll never see it. You are dismissed. Move your belongings to your new home.”
It was getting dark as she went to gather her things. A few miles away Hippasus, her beloved teacher, was already dying from the direct order of Master Pythagoras for teaching outsiders the mystery of irrational numbers.
She never got over it and kept all her discoveries to herself as well as Hippasus’ methods of instruction.
Five years later, almost all the Pythagoreans were killed mysteriously by a rival religious faction. Pythagoras himself was murdered and Adelpha fled to become a maid for a political leader. And the remaining Pythagoreans went into hiding.
She survived. She was too unimportant to notice.
And when she was alone and her duties done, Adelpha would take a pointed stick and sketch out diagrams in the sand. She would sit and see the circles, angles and numbers dance in her mind as she continued to make discoveries. She meditated upon her beliefs that god is number and that her soul itself was a mathematic that transcended reality. She meditated upon the golden mean, the pentacle, the tetractys and looked forward to the day that her religion would return to the world and thrive once again.
But it never did.
And she vanished into history working as a maid – her triumphs forgotten.
The Basic Doctrine of the Pythagoreans:
Basic Pythagorean Numerology:
The Monad (union) – 1. The maker of numbers. The founder of reason.
The Diad (opinion and diversity) – 2. The first female number.
The Triad (union + diversity) -3. The first male number
The Square (Integrity) – 4. The number of honesty and fairness.
Marriage – 5. The combining of male (3) and female (2).
Creation – 6. The combining of marriage (5) plus the maker (1).
The Universe – 10. The Tetratys – the most sacred number: (union + female + male + integrity)
Transmigration of Souls
God is Number
Symbol of the Order
Divisions of the Order
mathēmatikoi – Followers of Pythagoras who were true mathematicians.
akousmatikoi – Followers of Pythagoras who were mystics.