#pythagorean

[artthatgivesmefeelings]

Fyodor Andreyevich Bronnikov (Russian, 1827-1902) Pythagorean hymn to the rising sun, 1869 State Tretyakov Gallery, Moscow

[didanawisgi]

[porphurios]

The verses and the image of the Pythagorean Y (Upsilon) contain a challenge to students of classical and esoteric philosophy, as well as to mystics of every religion.

Of uncertain authorship, ascribed in a vague way to “Maximinus”, the verses have also been falsely ascribed to Virgil. Yet they are certainly ancient, and the main idea in them belongs to universal wisdom and literature.

They say:

“The Pythagoric Letter two ways spread,

Shows the two paths in which Man’s life is led.

The right hand track to sacred Virtue tends,

Though steep and rough at first, in rest it ends;

The other broad and smooth, but from its Crown

On rocks the Traveller is tumbled down.

He who to Virtue by harsh toils aspires,

Subduing pains, worth and renown acquires;

But who seeks slothful luxury, and flies,

The labor of great acts, dishonored dies.”

[33-108]

“That the monad was the beginning of everything. From the monad proceeds an indefinite duad, which is subordinate to the monad as to its cause. That from the monad and the indefinite duad proceed numbers. And from numbers signs. And from these last, lines of which from figures consist. And from plane figures are derived solid bodies. And from solid bodies sensible bodies, of which last there are four elements; fire, water, earth, and air. And that the world, which is endued with life, and intellect, and which is of a spherical figure, having the earth, which is also spherical, and inhabited all over in its centre, results from a combination of these elements, and derives its motion from them; and also that there are antipodes, and that what is below, as respects us, is above in respect of them.”

- Diogenes Laërtius - The Lives And Opinions Of Eminent Philosophers

[semi-deuses]

Teorema de Pitágoras.

Pythagorean theorem.

"Eduque as crianças e você não precisará punir os homens" - Pitágoras.

"Educate children and you will not need to punish men" - Pythagoras

[jayjuno]

If Socrates had reddit, he'd be at -60 karma on the first day...

[h0bg0blin-meat]

Here's the link to the video

👏 SAY 👏 IT 👏 LOUDER 👏

[wordsmithic]

Ancient Greek Women Mathematicians you didn't know about

Αίθρα - Aethra (10th - 9th century BC), daughter of the king of Troizina Pitthea and mother of Theseus, knew mathematics in another capacity unknown to many. So sacred to the beginnings of the most cerebral science, Aethra taught arithmetic to the children of Troizina, with that complex awe-inspiring method, since there was no zero… and the numbers were symbolically complex, as their symbols required many repetitions.

Πολυγνώτη - Polygnoti (7th - 6th century BC) The historian Lovon Argeios mentions Polygnotis as a companion and student of Thalis. A scholar of many geometric theorems, it is said in Vitruvius' testimony, that she contributed to the simplification of arithmetic symbols by introducing the principle of acrophony. She managed this by introducing alphabetic letters that corresponded to each in the initial letter of the name of the number. Thus, Δ, the initial of Δέκα (ΤΕΝ), represents the number 10. X, the initial of Χίλια (Thousand), represents the number 1000 etc. According to Vitruvius, Polygnoti formulated and first proved the proposition "Εν κύκλω η εν τω ημικυκλίω γωνία ορθή εστίν" - "In the circle the angle in the hemi-circle is right angle."

Θεμιστόκλεια - Themistoklia (6th century BC). Diogenes the Laertius scholar-writer mentions it as Αριστόκλεια - Aristoclia or Θεόκλεια - Theoclia. Pythagoras took most of his moral principles from the Delphic priestess Themistoclia, who at the same time introduced him to the principles of arithmetic and geometry. According to the philosopher Aristoxenos (4th century BC), Themistoclia taught mathematics to those of the visitors of Delphi who had the relevant appeal. Legend has it that Themistoclia decorated the altar of Apollo with geometric shapes. According to Aristoxenos, Pythagoras admired the knowledge and wisdom of Themistoclia, a fact that prompted him to accept women later in his School.

Μελίσσα - Melissa (6th century BC). Pupil of Pythagoras. She was involved in the construction of regular polygons. Lovon Argeios writes about an unknown work of hers: "Ο Κύκλος Φυσίν - η Μελίσσα - Των Εγγραφομένων Πολυγώνων Απάντων Εστί". (The title translates to "The circle is always the basis of the written polygons" or so.)

Τυμίχα - Tymicha (6th century BC). Thymiha, wife of Crotonian Millios, was (according to Diogenes Laertius) a Spartan, born in Croton. From a very early age, she became a member of the Pythagorean community. Iamblichus mentions a book about "friend numbers". After the destruction of the school by the Democrats of Croton, Tymicha took refuge in Syracuse. The tyrant of Syracuse, Dionysios, demanded that Tymicha reveal to him the secrets of the Pythagorean teaching for a great reward. She flatly refused and even cut her own tongue with her teeth and spat in Dionysius' face. This fact is reported by Hippobotus and Neanthis.

Βιτάλη - Vitali or Vistala (6th – 5th century BC). Vitali was the daughter of Damos and granddaughter of Pythagoras, and an expert in Pythagorean mathematics. Before Pythagoras died, he entrusted her with the "memoirs", that is, the philosophical texts of her father.

Πανδροσίων ή Πάνδροσος - Pandrosion or Pandrossos (4th century AD). Alexandrian geometer, probably a student of Pappos, who dedicates to her the third book of the "Synagogue". Pandrosion divides geometric problems into three categories:" Three genera are of the problems in Geometry and these, levels are called, and the other linear ones."

Πυθαΐς - Pythais (2nd century BC). Geometer, daughter of the mathematician Zenodoros.

Αξιόθεα - Axiothea (4th century BC). She is also a student, like Lasthenia, of Plato's academy. She came to Athens from the Peloponnesian city of Fliounda. She showed a special interest in mathematics and natural philosophy, and later taught these sciences in Corinth and Athens.

Περικτιόνη - Periktioni (5th century BC). Pythagorean philosopher, writer, and mathematician. Various sources identify her with Perictioni, Plato's mother and Critius' daughter. Plato owes his first acquaintance with mathematics and philosophy to Perictioni.

Διοτίμα - Diotima from Mantineia (6th-5th century BC). In Plato's "Symposium", Socrates refers to the Teacher of Diotima, a priestess in Mantineia, who was a Pythagorean and a connoisseur of Pythagorean numerology. According to Xenophon, Diotima had no difficulty in understanding the most complex geometric theorems.

Iamblichos, in his work "On Pythagorean Life", saved the names of Pythagorean women who were connoisseurs of Pythagorean philosophy and Pythagorean mathematics. We have already mentioned some of them. The rest:

Ρυνδακώ - Rynthako

Οκκελώ - Okkelo

Χειλωνίς - Chilonis

Κρατησίκλεια - Kratisiklia

Λασθένια - Lasthenia

Αβροτέλεια - Avrotelia

Εχεκράτεια - Ehekratia

Θεανώ - Theano

Τυρσηνίς - Tyrsinis

Πεισιρρόδη - Pisirrodi

Θεαδούσα - Theathousa

Βοιώ - Voio

Βαβέλυκα - Vavelyka

Κλεαίχμα - Cleaihma

Νισθαιαδούσα - Nistheathousa

Νικαρέτη - Nikareti from Corinth

There are so many women whose contribution to science remains hidden. We should strive to find out about more of them! For more information, check out the books of the Greek philologist, lecturer, and professor of ancient Greek history and language, Anna Tziropoulou-Eustathiou.

[389]

Scientific future by Valentino Bellucci

[cosmicportal]

“There is geometry in the humming of the strings, there is music in the spacing of the spheres”

-Pythagoras

[porphurios]

Tetractys-Decad and diagram of the harmonic scale intervals from the tablet beside Pythagoras in The School of Athens by Raphael

[33-108]

Throughout the progression of my spritual endeavors, I have always intuitively connected numbers to the subtle order of creation - believing in the role as a bridge between the tangible and intangible. I have felt compelled to bridge aspects of science and mathematics with the metaphysical frameworks and philosophy of mind in which I aligned with over time.

While I tend to be critical of unnecessarily and hastily merging the disparate ideas of respective cultures and I do my best take note of how each of their systems emerged within its own cultural context.. numbers/mathematics; most notably, for me, numbers like 36, 666, and 108 and their relationships reveal how mystical traditions across cultures do share numerical significance.

Whether through the Sun’s journey, cosmic/planetary distances, certain numbers demonstrated a "holographic" nature of creation.

In other words, they implied that the universe is a coherent whole, where the microcosm reflects the macrocosm and where numbers guide us toward understanding the unity of all things.

Numbers have long been considered a subtle blueprint for the material realm, serving as a universal language that bridges spiritual and physical realities.

Throughout history, mystical traditions like Pythagoreanism, Kabbalah, and Eastern philosophies have recognized the significance of numbers, seeing them as more than abstract symbols..viewing numbers as archetypal forces, cosmic codes that shape the material universe and connect humanity to divine principles.

Among some of the most intriguing of these numbers are 36, 666, and 108, which reveal a deep interplay between geometry, cosmic harmony, and mystical insight.

These numbers, often associated with the Sun and the masculine principle, underscore the shared foundations of mystical traditions and their perception of the universe as an interconnected whole.

The number 36, holds a special relevance in numerology and astrology, especially in its relationship with the Sun.

In ancient astrology, the heavens were divided into 36 decans, each representing a 10-degree segment of the zodiac.

These decans symbolized the Sun’s journey through the year, dividing time into distinct periods governed by specific energies.

The eighth triangular number, 36 encapsulates harmony and balance, reflecting the structure of creation itself.. triangular numbers, which represent sums of consecutive integers, evoke the triangular form, a symbol of stability and creativity.

The triangle, often associated with the masculine principle, signifies upward movement, dynamic energy, and the generative force of the Sun.

The number 666, the sum of all integers from 1 to 36, deepens the mystical significance of 36.

In numerology, 666 is intimately tied to the Sun through the magic square of the Sun. This 6×6 grid of numbers, where each row, column, and diagonal sums to 111, totals 666 in its entirety.

This mathematical symmetry reflects the Sun’s role as the center of vitality, illumination, and order. Just as the Sun sustains life and governs time, 666 symbolizes the culmination of solar energy and its pervasive influence on existence on multiple planes.

Its triangular nature further highlights the interconnectedness of numbers, geometry, and cosmic principles, demonstrating how the gross material realm has its relationships arising from subtle numerical blueprints.

The triangle itself, which underpins both 36 and 666, serves as a symbol of the masculine principle - in both hermeticism/alchemy, the triangle is a symbol of masculine fire, and represents siva tattva in Hinduism..the upward-pointing triangle represents, the Sun, and active energy.

It can convey the creative impulse that arises from and compliments the suns manifestation, mirroring the Sun’s dynamic power.

The connection of 36 and 666 as triangular numbers illustrates the harmonious unfolding of multiplicity from unity, a process that aligns with the metaphysical view that the material world is a holographic projection of deeper, subtler realities.

The number 108, perhaps the most significant number in all of hinduism/buddhism/jainism - is closely related to 36 through multiplication, extends this cosmic harmony into the realm of celestial relationships.

Multiplying 36 by 3, another triangular number, yields 108, a number revered across spiritual traditions.

In Hinduism and Buddhism, 108 is considered sacred, symbolizing the completeness of existence.

Prayer beads often consist of 108 beads, reflecting the unity of the macrocosm and microcosm.

What makes 108 particularly fascinating is its alignment with the Sun, Moon, and Earth. The average distance from the Earth to the Sun is approximately 108 times the Sun’s diameter, and the distance from the Earth to the Moon is similarly 108 times the Moon’s diameter.

This geometric coincidence creates the unique phenomenon of total solar eclipses, where the apparent sizes of the Sun and Moon align perfectly in the sky. These relationships reveal a profound synchronicity, suggesting that the cosmos itself is structured according to numerical harmony.

The interconnectedness of 36, 666, and 108 demonstrates how numbers transcend individual traditions, serving as a bridge between mystical frameworks and the subtle and gross realms.

In traditions such as Pythagoreanism, numbers are seen as the essence of reality, with each number embodying archetypal qualities. The Pythagorean view of the universe as a harmonious structure, governed by mathematical ratios, aligns with the Eastern perception of cosmic cycles governed by numbers like 108.

Similarly, Kabbalah’s Tree of Life and its ten sefirot express the descent of divine energy into the material world through numerical relationships. The interplay of numbers in gematria, Kabbalistic numerology, mirrors the vibrational patterns that underlie creation in Hinduism and Tantric cosmology.

These insights highlight how numbers act as a unifying force across spiritual traditions. They offer a subtle blueprint for the material realm, encoding the principles by which the universe unfolds. From the triangular unity of 36 and 666 to the cosmic resonance of 108, numbers reveal the hidden order of existence, connecting the physical and the metaphysical.

In Kashmir Shaivism, the 36 tattvas represent a comprehensive framework for understanding the process of manifestation - from pure consciousness to the physical world. While many Indian philosophical systems, like Samkhya, recognize 25 tattvas, Kashmir Shaivism expands this number to 36 by including higher spiritual principles and subtle realms that bridge the gap between the absolute (Shiva) and the individual experience.

The 36 tattvas are categorized into three main groups, each representing different aspects of reality:

Shuddha Tattvas (Pure Principles): The first 5 tattvas relate to pure consciousness and divine energy. These include:

Shiva (Pure Consciousness)

Shakti (Divine Energy)

Iccha (Will)

Jnana (Knowledge)

Kriya (Action)

Shuddhashuddha Tattvas (Mixed Principles): The next 7 tattvas deal with the interface between the absolute and the manifest, incorporating the role of Maya (illusion) and the limitations it imposes.

Ashuddha Tattvas (Impure Principles): The remaining 24 tattvas correspond to the physical and mental aspects of existence, akin to the 25 tattvas in Samkhya (e.g., the five elements, five senses, and mind).

Why 36 Instead of 25?

The Inclusion of Higher Principles: Kashmir Shaivism incorporates the five pure tattvas, which represent the divine reality of Shiva-Shakti that transcends duality. These principles are absent in Samkhya, which focuses on dualistic concepts (Purusha and Prakriti).

Acknowledgment of Maya: While Samkhya emphasizes the physical and mental realms, Kashmir Shaivism includes the tattvas that describe the workings of Maya, which creates the appearance of separation and multiplicity.

Focus on Unity: The system of 36 tattvas emphasizes the non-dual nature of reality, showing how the pure, subtle, and gross realms are interconnected and emanate from the same divine source.

I have a connection to the 36 tattvas and the nondual metaphysics of Kashmir Shaivism.. for its detail of unity within multiplicity and integration of the subtle and gross realms into a cohesive spiritual worldview.

The expansion beyond duality offered by Kashmir Shaivism aligns with a holistic perspective that transcends rigid categories. I resonate with its acknowledgment of Shiva as Atman (Self) and the dynamic interplay of Shiva and Shakti.

The symbolic significance of the number 36 has been very beautifully explained by Yogacharya Sri Somananda 1 in the following lines:

"Does it matter whether there are twenty-five or thirty-six Tattvas? The answer is that it does matter. Lord Shiva is the Lord of Yoga and His tradition teaches that the Tattvas are 36 in number. For the sake of harmony and unity, all Yogic traditions must agree with this.

However, there is another important reason. The number "36" is a sacred number which has a special meaning in Yoga. Indeed, it has many different meanings or one meaning with many different facets, like a diamond. Strictly speaking, this must be revealed by the Teacher to the disciple. We may nevertheless disclose some of it so that the seeker may acquire a taste of the infinitely profound, unsurpassed and incomparable Wisdom of Yoga Dharma.

1) "30" represents the Moon (the thirty-day lunar month of the Indian calendar is called "Maasa" or "Moon", in Sanskrit) which is the symbol of Lord Shiva; and "6" represents the Six Disciplines of Yoga (physical postures, breath-control, detachment, concentration, meditation, union with Shiva); the Six Paths (Shadadhvaa: mantra, varna, pada, kalaa, tattva, bhuvana); and the Six Chakras or Sthalas; which are the Path that leads to Shiva.

2) By further applying the Yogic method of numerological interpretation, "36" will be explained as follows. "3" signifies that Shiva is Three-times the Greatest: He is the Greatest on Earth (the Terrestrial Plane); the Greatest in the Air (the Astral Plane); and the Greatest in Heaven (the Celestial Plane).

"6" is made up of "5" and "1" . "5" signifies that Shiva is the Lord of the Five Divine Powers (Intelligence, Bliss, Will, Knowledge and Action) and the Performer of the Five Divine Acts (Creation, Preservation, Dissolution, Obscuration and Illumination or Salvation).

"1" (One) signifies that the Supreme Lord is the All-Powerful, Unique, Ever Existing One Who alone exists and Who holds the totality of all things within Himself. Therefore, "5" and "1", being inseparable, are taken together as "6". Thus by writing "3" and "6" we arrive at the sacred number "36". This is the innermost, secret meaning.

3) In terms of external reality which is the domain of multiplicity, when multiplied by the base "10", it yields "360" which is the number of days in a year; the number of degrees in a circle, etc. It stands for the Totality of Being or All-Encompassing Supreme Reality Itself.

In brief, it represents a symbol of completeness. In practice, therefore, the number "36" (or 360) symbolises man's (and the World's) Revolution or Completion of the Circle of Life and return to the original Point of departure.

This Spiritual Revolution is not a return to the past but a return to the Ever Present, Ever-Living Truth that nourishes all life. It is a return that must be urgently effectuated by the modern World for the Salvation of all Souls and the Establishment of Divine Life on Earth.

Finally, if we add "3" and "6", we obtain the number "9". "Nine" ("Nava") in the Sanskrit Language, also means "New", thus indicating the advent of a New World Order based upon the Eternal Principle of All-Encompassing Unity and Harmony, that is to say, the Supreme Eternal Law of Heaven (Sanatana Dharma) which must prevail over all other laws as Shiva (the Supreme Intelligence) Himself decreed at the beginning of time. "

[beaft]

listening to a podcast about troy and losing my mind over how fucking scary helen of troy is. her skin is pure white. she hatched out of an egg. she can perfectly mimic other people's voices. she's the most beautiful woman in the world but she is also completely faceless. she's a ghost. she's an eidolon. people keep trying to kill her but they fail every time because she's so beautiful that it hypnotises them and they are physically unable to hurt her. she's a central figure in the trojan war but her ultimate fate is almost never described because if she aged or died she'd stop being beautiful

[mathhombre]

The Pythagorean Theorem

Honor Pythagoras, Per I--Per VI

Great section on Jensen at Wikiart. I've got to dig in at some point.

Alfred Jensen, In-text plate (folio 3) from A Pythagorean Notebook, (one from an illustrated book with twenty lithographs), Tamarind Lithography Workshop, Los Angeles, CA, 1965, Edition of 20 plus 9 Tamarind Impressions [MoMA, New York, NY. © Estate of Alfred Jensen / ARS, New York]

[chthonic-sorcery]