#CosmicWisdomGr • Pythagoras • Plato's Lambda on Tetraktys

Pythagoras • Plato's Lambda on Tetraktys

The Pythagoreans approached the source of truth through a combination of research, experimentation, and the study of mathematics, music, and astronomy.

They believed that the universe was composed of numbers and that these numbers could be used to understand the underlying structure of reality.

For the Pythagorean model of the Universe and Cosmos, numbers are the symbols of Principles and Divine Energies, and when they use them in their theories they offer a symbolic narrative that is up to the reader to unveil the hidden meaning.

True arithmetic & geometric figuration, with the resultant harmonic (musical) figurations, are the most essential tools that Plato posits the Divine Craftsman uses to adorn the 'likeness' of the perfect cosmos.

ত  When Plato proposed the portioning by number of the Same, Other and Being in the unified mixture (Timaeus 35b-c), he set up what was subsequently been called his Lambda. It is a portioning arranged into two 'arms', each with three intervals.

Starting from the top, the generation from 1 to 2 and 3 gives the eventual seven stages.

The principle of "twice" and "thrice" as well as the 'progression'.
On one arm, we see the progression from 2 into a plane 4 and a cubic 8,
while on the opposite arm we see the progression of 3 into a plane 9 and a cubic 27.

We have seven positions representing two progressions, which leaves us the impression that there could be three more points or positions within the open triangle, so that if filled the model would become lie the Sacred Tetraktys or the triangular "four" representing the full decad.

ত Each dot becomes representative of a position in the process of generation :

• from undifferentiated unity into 'twiceness' and 'thriceness' in the 1st dimension.
   
• 'fourness' and 'nineness' as their respective planar reflection.
  
  
• 'eightness' and 'twenty-seveness' as their projections into the ultimate third dimension or bodily world.

We have two squared and cubed, and three squared & cubed, giving us a dyad of forms of generation passing through the three dimensions on each arm.

The challenge that follows the allocation of three more points within the triangle is to discover what numbers they should be, if they are not part of the existing progressions of 2 or 3.
~ The solution becomes a matter of the logic of the symmetry or 'angles' that the progressions of times2 and times3 follow.

 

If we start from the monad or one at the top and follow down the right-angle, the fourfold progression is 1x3=3, x3=0, x3=27.

If we shift down from 1 to the position 2 and follow a similar angle down through the pattern, we pass through the center point, which becomes 2x3=6, and arrive at the point on the base, which becomes 6x3=18. Doing the same, while starting with the diagonal that moves down from 4, we have 4x3=12.

ত In summary, we might say that

• the point positions, represent the Decad.
  
  
• the sets of points represent the oneness, twoness, threeness and fourness of the constituent horizontal lines which we can call the first symmetry.
  
  
• the allocated number progressions represent "states of being" of the refraction of one, particularly of two and three respectively as they move from plane to cubic form and thereby provide a pattern that has within it the essential numerical harmonies.

On the basis of simultaneous qualities interpenetrating and mutually present, we might take the point model as representative of the background archetypal 'isness' of the 'incomparable' ideal numbers - those complete at ten.

In another sense, we could take the allocated soul-generating numbers to be representative of the number moving into bodiliness or cubic being and ready to facilitate the geometrical basis of materiality. (Timaeus 36e, 53c-e)

 

ত The geometrical basis of materiality consists of

• the tetrahedron or 'fourness' of fire or light
• the octahedrality or 'sixness' of the gaseousness of air
• the icosahedrality or 'twelveness' of the liquidity of water
• and the cubic 'eightness' of the solid earthiness.
  

These numbers are the points in space that define the solidity of the regular figures.

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Tetraktys of Cosmic Cycles

A new set of numbers has an interesting cosmological quality; it includes numbers which were not represented in the previous set, and numbers that appear in the cosmic cycles.

The apex takes up the generating role of the dyad or principle of multiplicity and thereby the created order.

The first pair are the three and the four. Four completes the Decad, yet this pair of 3 & 4 also represents threeness and fourness as 'spirit' and 'matter' or principle and expression - aspects of cosmic duality.

Further the cosmological seven of the planetary systems, is produced by 3+4 and 7 takes up the central position of the 'new' Tetraktys.

Five & Ten, the 'quintessence' and the 'decad', flank the cosmic Seven.

2 - Sun and Moon, day & night.
3 - Geocentric pattern of Mercury loops
4 - four seasons, or quarters of year.
5 - Geocentric pattern of Venus loops.
7 - Cycle of the Moon's quarter, or a week.
9 - The trine conjuctions of Saturn & Jupiter over a 60-year period, or a lifetime.
10 - Tetraktys.
13 - Lunar months of the year.
19 - Metonic cycle of coincidence between Sun & Moon every 19th year.
28 - Full cycle of the Moon.

On the Heptad

• The Pythagoreans say that the heptad is not similar to the other numbers, and that it deserves reverence.

 

• We see seven things ~ body, distance, shape, size, color, movement, and rest.

• There are seven movements ~ up, down, forward, backward, right, left, and circular.

 

• Seven is not born of any mother and is a virgin.

• The sequence from the monad to it, added together totals 28; the 28 days of the moon are fulfilled hebdomad (week) by hebdomad.

 

• The hebdomad consisting of the three dimensions (length, breadth, and depth) and the four limits (point, line, surface, and solid) reveals corporeality.

 

• Seven is said to be the number of the primary concord, the fourth (4:3), and of geometric proportion (1, 2, 4).

• It is also called 'that which brings completion'.

 

• Seven encompasses the sides around the right triangle of the archetypal right-angled triangle.

Seven is the arithmetic mean between the monad and the decad.

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 Wrap-up to farewell...

The Pythagoreans' quest for truth through numerical symbolism unveils a profound perspective on the very fabric of existence. Numbers are not just symbols; they are the keys to unlock the hidden narratives woven into the cosmos.

Plato's Lambda, with its geometric progression from unity to the third dimension, offers a profound meditation on the essence of creation and the symmetries that underlie reality. As we contemplate the additional points within the open triangle, we grapple with the profound logic of symmetry, unveiling a deeper harmony within the universe.

These numbers are not mere abstractions but represent the fundamental aspects of reality. They manifest as the four elements—fire, air, water, and earth—defining the solidity of regular figures.

The new set of numbers reveals a cosmological quality, emphasizing the intricate dance of threeness and fourness, spirit and matter, within the cosmic order. The heptad, as the enigmatic and revered number, completes this cosmic symphony, embodying primary concord and geometric proportion. 

In this contemplation, we find a harmonious convergence of the abstract and the concrete, a glimpse into the very essence of the universe itself, a reflection of the eternal dance of numbers and principles in our cosmos.

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#CosmicWisdomGr • Pythagoras

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Available readings on Bookshelf :

Theology of Arithmetic - Iamblichus

Pythagoras and the Delphic Mysteries - Edouard Schure

Iamblichus' Life of Pythagoras - Thomas Taylor

Secret teachings of All Ages - Manly P. Hall

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