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Karin Di Giacomo

The Tetractys of Pythagoras

By | Cosmology

Unparalleled is the wisdom contained in the Tetractys as an illustration of the forces and energies that constellate the origin, evolution and destiny of the Cosmos.
Tetra in Greek means “four”. The Tetractys is a geometric figure consisting of the first four integers (numbers 1,2,3,4) arranged in a triangle of ten points. Examining the meaning of each number of the Tetractys, allows us a deeper insight into the peculiar synergy of geometry, number and philosophical meaning that is characteristic for Hellenistic cosmology henceforth.
Pythagoras gave us this most succinct tool for understanding the cosmos, its qualities, structure and function in a unique teaching device: the Tetractys. Iamblichus, (c.AD 250-325), one of the most prominent Neo-Platonist philosophers, writes in his famous compendium on Pythagorean Philosophy:
“The Tetractys is an equilateral triangle formed from the sequence of the first ten numbers aligned in four rows. It is both a mathematical idea and a me6aphysical symbol that embraces within itself – in seed-like form – the principles of the natural world, the harmony of the cosmos, the ascent to the divine, and the mysteries of the divine realm. “ Iamblichus
In contrast to its complex and profound significance, the visual appearance of this symbol is utterly simple; indeed, it can easily be traced with a stick or by arranging stones in the sand. Yet this simplicity is pregnant with meaning and insight:
“Bless us, divine number, thou who generated gods and men! O holy, holy Tetractys, thou that containest the root and source of the eternally flowing cosmos! For the divine number begins with the profound, pure unity until it comes to the holy four; then it begets the mother of all, the all-comprising, all-bounding, the first-born, the never-swerving, the never-tiring holy ten, the keyholder of all”
For the Pythagoreans, number is a living, metaphysical presence, a reality to be experienced, not a tool to be used. For Pythagoras, numbers represent universal principles as real as e.g. light or sound, they are divine beings, the source and the root of all things, a viewpoint that is substantiated by modern physics that expresses energy through numerically defined frequency and amplitude.
The Tetractys represents the organization of space and time
1. The first row represented zero-dimension, eternity (no time) and omnipresence – no space.
2. the second row represents time which begets space
3. the third row represents time/space interaction i.e. creation
4. The fourth row represents the qualities of creation in form of the elements.
The Tetractys symbolizes the harmony of the Cosmos. It symbolizes the four elements, fire, water, air and earth. The points of the four rows add up to ten, which is unity of a higher order.
Exploration of the Pythagorean Numbers as expression of the cosmic order.

The Monad , the number One, (from Greek μονάς monas, “unit”; monos, “alone”), according to the Pythagoreans, was a term for the first being or God, or the totality of all beings, Monad being the source or the One meaning without division. The Gnostics saw in the number One the Supreme Being, Aiōn teleos, Bythos (Depth or Profundity, Βυθός), Proarchē (Before the Beginning, προαρχή), and Hē Archē (The Beginning, ἡ ἀρχή) and the ineffable parent. The One is the high source of all divine emanation, the region of light. All numbers of the Tetractys are primordial emanations of the One.
In Neoplatonic thought, the primeval Source of Being is the One and the Infinite, as opposed to the many and the finite. It is the source of all life, and therefore absolute causality and the only ultimately real existence. It is beyond all created things, albeit their source. Therefore, the Monad cannot be known through reasoning or understanding, since only what is part of Creation or Being can be thus known according to Plato. Being beyond existence, it is the most real reality, source of less real things. It is, moreover, the Good, insofar as all finite things have their purpose in it, and are designed to flow back to it.
The One has no attributes of any kind; it is being without magnitude, without thought; in strict propriety, indeed, we ought not to speak of it as existing; it is “above existence,” “above goodness.” It is also active force as the primeval Source of Being is perpetually producing something else, without alteration, or motion, or diminution of itself. This production is not a physical process, but an emission of force. Directly or indirectly, everything is brought forth by the “One.”
In it all things, so far as they have being, are divine, and God is all in all. Derived existence, however, is not like the original Source of Being itself, but is subject to a law of diminishing completeness. It is indeed an image and reflection of the first Source of Being; but the further the line of successive projections is prolonged the smaller is its share in the true existence. Each lower stage of being is united with the “One” by all the higher stages, and receives its share of reality only by transmission through them. All derived existence, however, has a longing for the higher, and bends towards it so far as its nature will permit.
The Dyad or the number two represents the principle of “double-ness” or “otherness” or polarity. Neoplatonic philosophers like Plotinus treated the dyad as a second cause (demiurge), which was the divine mind (nous) that by its reflective nature causes matter to appear or become perceivable. The potential emanating in form of the dyad is expressed in the figure of the vesica piscis and is the power of all duality, contrast, and sameness for example, male/female, heaven/earth, left/right. It also contains the idea of the twin (didymos) and the mirror image. It is the generative matrix when seen in conjunction with the Monad, the One, with which the Dyad forms the supernal Triad.
The Triad, the number three, was considered ‘the most beautiful number’, as it is the first number to equal the sum of all the terms above it. The three is the child of the two, the product and emanation of the Divine Duality Matrix. With the triad, space is introduced, plane geometry becomes possible and opens the realms of proportion and of harmony. The Three was considered the first true“number” by the Pythagoreans. As the mother of time and space in its generative powers, it becomes manifest in the Triad. It introduces a mean between the polarity of the Two and it wields the power to bring order and harmony to diverse and polarized positions. In the Pythagorean tradition, the soul is the mean that unites the mortal and immortal and binds them into a whole.
The Tetrad, the number 4, represents the final stage of completion because the first four numbers make a sum of ten (1+2+3+4=10) which is the completion of one cycle of manifestation and the beginning of a new one. That means, that with the base line of the tetractys, which completes the figure. With this line, the sum of all the rows (levels) now is the number ten, which repeats the number one, yet on another level. The evolutionary aspect of the cosmos is hidden in the perfection of maniferstation.
Geometrically, the tetrad is expressed by the square or cube, as well as the four sides of a tetrahedron (pyramid). Metaphysically, the Tetrad represents matter and the four primary essences or elements, air, earth, fire and water, which are the essential building blocks’ of the manifest world. In the tetrad time and space are linked, harmonized in the three and brought into manifest reality in the four.
The Tetractys, the Cosmos and Hermetic Medicine
The numerical intelligence of the Universe is represented by the Tetractys. It illustrates the descent of spirit into matter. Its arrangement guides us to contemplate the Divine Source and its emanating polarity or trinity of Spirit and its extension via the soul to its descent into matter. Upon further contemplation we realize that this symbol also illustrates the ascent towards the One Source upwards from the manifest realm of material phenomena (Body) through an understanding of its guiding creative principles in the Triad (Soul). From there we learn to recognize the primordial dyadic forces of polarity which in turn reveal a glimpse of the divine principle, the Monad, the ‘source and root’ of all Creation.
In summary, the tetractys is an illustration of the origin, structure and evolution of the cosmos, integrating the meta-physical and the physical, material paradigms insofar as the latter is contained in and governed by the cosmic source.

About the Cosmos

By | Uncategorized

A review of the significance and meaning of the Elements without a consideration of the Cosmological matrix within which they are presented, is like surveying building materials without blueprints for the temple they are meant to construct.
– The Cosmos of Antiquity
“What is that which is existent always and has no becoming? And what is that which is becoming always and never is existent?” With this passage in Timaeus, Plato begins his discourse on the creation of the universe. The divine intelligence, the Source of the universe follows a blueprint for his creation, a paradigm that includes both the meta-physical (eternal) and the physical (becoming) dimensions of the cosmos.
Cosmos (κόσμος) is a Greek word meaning order, an apt or harmonious arrangement and also adornment, ornament. The verb kosmein means generally ‘to dispose, prepare’, but especially ‘to order and arrange (troops for battle), to set (an army) in array;’ also ‘to establish (a government or regime)’ and ‘to deck, adorn, equip, dress’ (especially of women). As we can see, cosmos had a secondary sense of ‘ornaments of a woman’s dress, decoration. We still retain this second meaning in our word ‘cosmetics’.
The opposite of Cosmos is Chaos. The Ancient Greek word χάος, kháos means “vast chasm, void” and it denotes a state of disorder, as well as any confused or amorphous mixture or conglomeration and states of existence. The unifying, ordered, relational, harmonious quality of the cosmic order is absent when chaos reigns.
Pythagoras, the eminent Greek Philosopher and Mathematician of the 6th century B.C. is one of the earliest sources of antiquity to present the Cosmos as a harmoniously ordered systemic whole, imbued with meaning and an evolutionary purpose. For Pythagoras, the cosmos is governed by natural laws and on the level of manifestation it is composed of four essential principles, the Elements, expressed through the aspects of matter, form and universal life energy (body, soul and spirit).
– Hermeticism
Hermeticism is a body of philosophical and religious ideas and writings that links back to antiquity, to the teachings of the Pythagorean and Platonian schools, attributed to the legendary figure of the Egyptian teacher, magician and healer, Hermes Trismegistus (the ‘Thrice Great’). As a philosophy, Hermeticism draws on a syncretistic school of Graeco-Egyptian thought, blending Hellenistic philosophy and Egyptian occultism.
“The resulting composite proved to be endurable and persuasive – it was based on the tenet that the universe operated based on orderly principles…Hermeticism was instrumental not only to the development of western philosophy, but also to the emergence of the modern science. This connection can be seen most clearly in the hermetical and alchemical treatises written by some of the most influential thinkers of their respective eras, including Giordano Bruno, John Dee, Francis Bacon and Isaac Newton.”
The writings of the Neoplatonist such as Plotinus or after him Iamblichus and Porphyry of Tyre have cast a long ray of illumination down to the Renaissance and into our times. Hermetic Philosophy presented an integration of the metaphysical and physical paradigms. Meta-physical inquiry and research were as intrinsic to Hermetic thought as physical science.
In particular, Hermetic Philosophy highlights inductive, analogical reasoning through the use of correspondences as a way to gain insight and arrive at truth and “expand knowledge in the face of uncertainty” One of the most famous Hermetic texts ‘The Emerald Tablet of Hermes Trismegistus’ accordingly states …’that which is above is as that which is below…” and “as within so without”, providing landmarks of hermetic thought . Seven axiomatic principles that govern the hermetic world view are summarized in the text “Kybalion”, a 1908 synopsis of hermetic wisdom: the principles of Mentalism, Correspondence, Vibration, Polarity, Rhythm, Cause and Effect and Gender.
In the Dark and Middle Ages, the wholeness of the hellenistic Cosmos was broken apart under the dogma of Catholic religion and the inquisition. The meta-physical Paradigm was replaced by church dogma. Research within the physical paradigm was forbidden in many fields. Research in most areas was limited to bolstering religious beliefs. Scientists who inquired outside of these confines such as Galileo Galilei or Giordano Bruno were burnt or like Kopernicus severely hampered in their freedom of expression. With the Christian view of the body as sinful, Middle age medicine in Europe was “purged” from heathen thought and finally consisted of little more than a jumble of superstitions, taboos, and barely was able to hold on to the remnants of Hellenistic medical arts. The system of elemental composition was lost in a largely simplistic identification of the four humours and the four temperaments, which proved to be of minimal value to the art of healing. Herb lore and folk medicine as practiced by wise women and peasant healers was eradicated by witch hunts and accusations of sorcery, in either case punishable with death by torture. Yet a clear stream of Hermeticism re-surfaced during the Renaissance. The teachings of Pythagoras and Socrates were re-discovered and newly translated, the writings of Plato, Dioscorides, Aristotle and the Neoplatonists appeared, often via Arabic copies of their works. By the end of the fifteenth century a renaissance of classical Hellenistic, Egyptian and roman philosophy swept like a liberating wildfire through Europe.