Pythagoras the Mathemagician

by Karim El Koussa

  “All the spheres of our small universe move in a circular path around the Sun, in a west-to-east direction, and at a constant speed. Remember that five other spheres glide in harmony with our Earth, sun, and moon.”

  “What is really interesting is the fact that every sphere that consorts with the Earth around the Sun makes a specific sound, according to the speed of its rotational movement. The sound pitches higher and higher, the farther away any particular sphere stirs from Earth. The musical tones are calculated based on the distance. On that account, the distance from Earth to Moon is one tone (1). From Moon to Mercury, it is one-half tone (½), and from Mercury to Venus, it is one tone (1). The length from Venus to the Sun stretches one and a-half tones (1½), and from the Sun to Mars, one tone (1). Mars extends at one-half tone (½) from Jupiter, which stretches at a distance of half a tone (½) from Saturn. The distance between Saturn and the Zodiac measures one tone (1). Hence, from these seven varying tones, a coalition of sound takes form. It develops into a perfect septenary melody of Nature. It is Harmony – the Music of the Spheres – the music that we cannot discern because we hear it all the time.”

  Theano gasped in amazement, widened her eyes at him then looked up to the sky. Pythagoras, somehow, felt touched by her feminine reaction. His heart smiled, but his appearance remained composed. In a cool voice, he resumed his explanation, where he had left off when interrupted by her.

  “Listen, my friends! If you really aspire to perceive the Music of the Spheres, you should start by listening to the beats of your own hearts, and then to the sound of the rotating Earth. That is actually feasible through meditation and the creation of a perfect void in your inner realm. Why? You would ask. And my answer is: because it will allow you to tune yourselves, and your heart beats, onto the same musical numbers of the heavenly bodies.”

  “Now, look at the Moon. The part we see, at this very moment, increases or diminishes according to its angle, which faces the Earth, and its other half, which is directed towards the Sun. When the Earth, or any other sphere, stands between the moon and the Sun, an eclipse occurs. Think about it! Take your time. The night is young and long,” he recommended with finality.

  At the time, the Moon illuminated the part of the Earth where they stood on the terrace. The tide kept crashing, with some intensity, on the high walls below. The sound of the waves reverberated high. It crossed the long distance of the Mediterranean Sea to finally reach a safe haven, out of the dark void. The resonance ricocheted smoothly on the shore, there, at the foot of the hill of the Majestic White City.

  Then, silence echoed peacefully in the body-temple of every mathematikoi.

  Would they hear the beating of their hearts?

  Would they listen to the cry of their Mother Earth?

  Would they heed the Music of the Spheres?

  * * *

  As if with a sigh, the Moon – the nocturnal Queen of the sky – disappeared completely from its watchtower. Night turned to day. Time came for the Sun – the King of the sky – to rise high above, and give light to the world, and sight to the living.

  At the center of the White City, a delightful melody drifted from a modest house. The tempo accelerated to be heard everywhere. Inside his small residence, the Mathemagician relaxed while he played a mystical melody. The delicious moment shattered unexpectedly. A woman stormed inside his dwellings, yelling in pain. Through her lamentations, he understood that her uncontrollable ache resulted from the affliction of a disease.

  She, a housewife from the Outer Circle, in her mid-age, pleaded for his help. Calm and composed, he invited her to sit at his side, and while performing his music, he addressed her with a soothing voice.

  “Dear lady, you assume that you are sick, but you are not. Other people may have told you so, but I tell you, fear not. Your pain results mainly from some disorder in your system.”

  “I don’t… understand,” her broken voice interrupted him tearfully. “What are you saying, Master? I am really… terribly ill… What do you mean by… a disorder… in my system?” The woman blurted amidst her sobbing, totally confused.

  “Dear Lady, your system is made of vibrations, like the notes I’m playing now. At this very moment, the mystical vibrations of my Lyre communicate intelligently with yours to set them in order. It’s a truly magical process.”

  She was stunned, speechless.

  A few minutes later, she walked out of the house, relieved from her pain, and cured from her illness. Realigned, so to speak, she became in tune with herself, and thus, healed and healthy again.

  This episode was one of many in which Pythagoras performed his healing powers. Sometimes, he would visit the sick members of his Society to heal them, as he would openly state.

  Down, inside the crypt of the Temple of the Muses, that morning, the Master lectured his disciples on Cosmology.

  “The Kosmos, I tell you, is not continuous and linear like a river. It is instead circular and cyclical like an egg. The same applies for Nature, as we have previously observed. Thus, the Kosmos and Nature are alike. Everything in existence repeats itself. This recurrence of events in the Kosmos occurs because of the spherical form of the stars and planets that revolve in circles around the Sun.”

  “Know also that the sphere is perfect, and so is the circle. They are perfect because all the points that exist on their surfaces, or circumferences, are at the same distance from their centers. Our Earth is then perfect, so are the Heavenly Bodies!”

  “Listen, I assure you, fellow brothers and sisters, that it is only by pure thought that you can logically deduce the laws of Nature and those of the Kosmos. Mathematics will reveal to you a pure Kosmos, accessible to your Intellect in which numbers and shapes are perfectly connected with the natural order of existence.”

  He scrutinized his 10 chosen disciples who appeared motionless as if their minds dwelt in a different orbit, somewhere amidst the stars, the planets, and the sun.

  Moments elapsed…

  “Now!” Pythagoras snapped, interrupting the chain of their thoughts to haul them back to Earth; the sphere where they belonged. “Let’s consider a right triangle. The sum of the squares, of the shorter sides, is equal to the square of the longer side. Hence, a2 + b2 equal c2. Let me show you how by a simple demonstration.”

  He drew its sketch on the wall while explaining again to demonstrate his theory through mathematics. “Here it goes!” He pointed to the completed triangle.

  “There are infinite numbers of regular polygons as in the infinitude of the Kosmos,” he continued his tutorial. “I would, however, focus here on two of the five solids mentioned earlier. The Cube, for example, contains six sides. It represents Earth. Now, when we unfold its sides, we obtain a cross of seven squares; the Symbol of the Initiate!” He asserted while he showed them in a drawing on the wall how the Cube was transformed into a Cross.

  “I told you previously that the Earth is the Sphere of Generation. It is so because souls come down to it continuously through birth, and always ascend out of it at death. Hence, they follow a circular movement in an order of necessity. And thus, to become an Initiate, one must rise up and above this circle, and I, esoterically, mean above the cycle of life and death.”

  “There, above the Cube that symbolizes Earth, which has not yet unfolded, I place the Dodecahedron that represents the Heavens. This important solid contains twelve pentagons as sides. In a mystical mode, I associate it with the Ether of Kosmos which is, in truth, the quintessence of the Heavenly Bodies. It is the fifth element, and the purest form of the Kosmos.”

  “Listen and listen well! The Ether is a very flexible essence that moves through all visible matters. Through it, the Divine Mind exercises its sovereignty upon the world. It is, indeed, the Great Medium between the Invisible and the Visible, between the Spirit and the Matter. Verily, I tell you now, and this is a very crucial issue, no one outside the Inner Circle should ever know the Great Mystery of the Dodecahedron and the secrets within it!” He came to
a halt and observed…

  These Pythagoreans understood well that the deepest Mysteries of Nature and Life, revealed and taught by the Master, should be highly respected at all times. They should be admired wholeheartedly, yet kept well concealed from the ignorant in order to protect them, and save them from the profanation of the outside world.

  Hence, the Master commanded them to pledge total secrecy, which they did in a solemn and unanimous voice. He then proclaimed their silence on the sacred doctrines to be symbolized by a particular clandestine sign that displayed an Ox over a Tongue.

  Ox over the tongue!

  Only when reassured that the Mysteries would be well kept, did he resume his extremely informative lecture. “In the Kosmos, there exists a series of opposites developed from the eternal conflict between the finite and infinite principles. There are, actually, ten opposing principles of being, at the very heart of existence. However, since Ten is a perfect number, as discussed earlier, these ten opposites fit, accordingly, within the Kosmic existential harmony. For that reason, I assert that Harmonia is Balance! It displays the unification of the compounds and the multiples, and the agreement of the opposites. Just like music!”

  “De facto, music, my friends, bears a dual value. It is, in reality, one of the greatest, if not – I confidently stress – the greatest expression of Harmony! The truth I tell you, my dear mathematikoi, Harmony is nothing less than a clever, manifested impulse of the Divine Law that brings order to chaos and agreement to conflict,” he explained then added, “Here! I will draw for you a comprehensive table that describes best these ten opposing principles.”

  Having said that, he grabbed a papyrus, and sketched, bringing the table to their attention. Exhibited in such a way, the opposing effects of the principles appeared clear to them. The explanatory table read:

  Achieved

  Not Achieved

  Limited

  Unlimited

  Odd

  Even

  One

  Plurality

  Right

  Left

  Male

  Female

  At rest

  In motion

  Straight

  Crooked

  Light

  Darkness

  Good

  Evil

  Square

  Oblong

  Master Pythagoras explained further, “Once combined, these pairs of opposites, called duals, produce a material third that is obviously their synthesis. Everything in Nature is dual. Nothing is complete without its opposite. Only together could they form a perfect balance, a stability, and a natural physical union. However, they can never generate a supernatural, a spiritual, or even a mental union with the Great Monad!”

  With this revelation, he concluded his tutoring of the day. He grabbed his Lyre and played a brisk melody. From their places, his disciples studied the table and shared their thoughts in quiet voices. They then made their own individual drawing of the table on a piece of papyrus to keep. They also drew from the wall the right triangle and the Cube that transformed into a Cross.

  At the time, around two hundred mathematikoi had been enrolled in a succession of 10 disciples each period, under his direct apprenticeship of the sacred Hieros Logos. On the other hand, the akousmatikoi, who learned in parables and allegories, numbered a thousand members.

  Led by his wisdom, these two groups, along with the Sebastikoi before them, formed the perfect society – the Pythagorean Society. Whether they gathered in the Assembly Hall, on the terraces of the Temples, down by the crypts, or in the Sacred Garden of his cave, they would eagerly congregate to heed his profound doctrine.

  To their attentive gazes, he disserted about Life, and all its related matters. His vast knowledge educated them on most life Mysteries and Divine meanings.

  Days and nights together constituted a perfect balance of earthly luminosity – earthly, for their time duration differed from Eternity. His teachings abided by the same order of division, in the sense that he conferred them in two timely and opposite parts: some in the mornings and some at nights. As a result, he complied with a balance of earthly opposites at all times.

  And yet, Eternity prevailed in waiting…

  * * *

  The night carried the beauty of the spring, along with the breeze that caressed the faces of the students and their Master on the sandy beach. Seated in the middle, a young musician played the Lyre, the way Pythagoras had taught him for so long. The melody drifted, enchanting the mood, the way the aroma of the nearby fields wafted, blending with the smell of the sea. The stars grinned at them in millions of tiny lights. The aura of the Master appeared to match the regnant one of the Moon. However, like all great Masters, he fared, in that confident modesty of his, unconcerned by his radiant strength. His aim totally converged on the youth and his guidance to their enlightenment. His lecture that night broached a particular question raised by Opsimus of Rhegium, one of his mathematikoi.

  “Why, Master? Why bother seeking the secrets of the stars and the planets, say the Kosmos, if it is to have death continually lurking ahead?”

  The Master nodded with a smile, for he understood the quandary of his young student.

  “Verily I say unto you, brother Opsimus, the physical world of the Kosmos that displays all the stars and planets in such a wonderful manner for us to admire, is not at all a real matter! It is but a passing form of things and shapes that are in eternal transformation. In fact, what your eyes perceive is just a phantom existence of the hidden Truth; Maia, the Universal Soul which disperses matter in the infinite space, and then changes it into Kosmic Fluid, or what I call: the Ether.”

  His words echoed in the night.

  Stunned by this new revelation, Opsimus gawked at him then at the sky above then back to him.

  With a kind smile, void of any hint of admonishment, the Master enjoined, “Have you forgotten your oath, brother?”

  Ashamed, Opsimus lowered his eyes. He muttered under his breath the most solemn oath of all times:

  “I swear by him who has transmitted to our minds the Sacred Four, the Tetraktys, High and Pure, the Root and Source of ever flowing Nature, The Model of the gods.”

  The student at his side tapped him on the shoulder in a friendly gesture of sympathy and smiled at him.

  “The truth I tell you,” the Master prompted in a firm inflection of warning. “Fear not death for it is an illusion, an ever changing state of existence!”

  A general nod of consent ensued in unanimous response.

  “Master, if I may,” Alcmaeon of Crotona requested to speak. “I would appreciate your opinion on a very strange incident that happened to me, almost a year ago.”

  “Go ahead, Alcmaeon, ask!” Pythagoras goaded him with an encouraging grin.

  “In fact, Master, I meant to consult with you, about it, for a while now,” he revealed then halted in hesitation. “But, the opportunity never arose, really,” he said, as in apology, to which those friends at his sides nudged him teasingly.

  Someone gushed out from behind him with exasperation, “Say it, Alcmaeon. Say it!”

  Alcmaeon shrugged his shoulders as if to tell them to leave him alone. He waved his hand in a gesture of annoyance to which a general chuckle sprung out. The smile of the Master widened in amusement.

  “Yes, Alcmaeon, say it, I’m listening,” he invited him gently.

  “Yes, Master. See, one night, I don’t quite remember which night, I sat alone on a rock in the fields, like I do sometimes, under the moonlight. Out of nowhere really, a man came by and took a seat at my side without a word. His profile appeared familiar to me. He remained silent for a long while, until… well, until he turned to look at me, and…,” he halted, uneasy.

  “Yes, Alcmaeon?” The Master pressed on in a tone of encouragement.

  “He looked exactly like my late father!” He spurted out and prompted a glance of dread at his fellow mathematikoi. No mockery ensued as he had expected. Instead, the general
stance became serious and attentive.

  Encouraged, he pursued, “We spoke for some time before he disappeared. I don’t quite remember the topics of our conversation. I frankly don’t remember even how he disappeared. He vanished… just like that! What could that possibly mean?”

  “My dear Alcmaeon,” Pythagoras addressed him with affection. “It only means one thing. You have, indeed, communed with your father. That’s the reality.”

  Several students gasped at the answer, and some, very few nodded pensively as if such a weird experience was not new to them. Silence prevailed among them, leaving the ground to the sounds of nature, and to their inner thoughts to reflect on that statement. Even the Lyre player stopped the game of his fingers on the cords of his instrument.

  The Master let it be. A sense of peace engulfed him as it always did when he revealed a truth. For a moment, his eyes met the adoration in those of Theano; bright green that bespoke of her hidden love for him. It was a swift instant, but enough to warm his heart for her.

  He cleared his throat and broke the silence to give voice to his wisdom, “The truth I tell you, brothers and sisters, the Kosmos is but an imperfect reflection of the realm of the gods. It falls short of the Divine Archetypes – the Numbers – that perfect reality that conveys to us a glimpse of the Truth through Mathematics. The Absolute reality, therefore, is not material but rather spiritual, and it emanates from the ideas within the Numbers. Hence, these ideas, you should understand, are sacred and higher than all forms and shapes.”

  “Every small universe, or Kosmos, contains a partial element of the Universal Soul. Small, incomplete, yet essential, such an element evolved in the central Sun of a Kosmos. Driven by an impulsive power, and a special measure of the Divine Mind, its evolution took millions of years.” He paused for a thought, but before he could continue, he was interrupted by a new question.