Cosmopoeia
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Philosophy

The tetractys analogy table

The four start figures alongside the fournesses of physics, philosophy, Hermeticism, Kabbalah, Freemasonry and religion. A comparison, partly explicitly speculative.

A number of other fournesses can be set against the four start figures of the tetractys. The assignments in number theory and geometry follow directly from the mathematics. The rest are interpretations, some explicitly speculative. The idea of looking for such correspondences is old. According to Aristotle the Pythagoreans already saw resemblances to things in numbers, and Hermeticism later put it into the sentence: as above, so below.

Polygon3the number itself, no divisor
Compound polygon6 : 2 = 3n is divisible by k
Star polygon5 : 2 = 2.5n and k are coprime
Compound star10 : 4 = 2.5n is not divisible by k, but they share a factor > 1

The four start figures: triangle, hexagram, pentagram and double pentagram. In the table below the pentagram stands in the second column, the hexagram in the third.

Number and form

1 2 3 4
Tetractys 1 1 + 2 = 3 1 + 2 + 3 = 6 1 + 2 + 3 + 4 = 10
Dimension 1 point: 0 2 points: 1 3 points: 2 4 points: 3
Divisibility all natural numbers, the number itself coprime divisible not divisible, common factor > 1
Example point, line, triangle 5 : 2, a pentagram 6 : 2, two triangles 10 : 4, two pentagrams
Figure polygon star polygon compound polygon compound star
Angle sum of the start figure ½ full circle ½ full circle 1 full circle 1 full circle

The line stars that pass through the centre for even numbers have an angle sum of zero.

Physics and metaphysics (speculative)

1 2 3 4
Fundamental forces strong interaction weak interaction electromagnetism gravity
Metaphysics spirit, energy time space spacetime, matter
After Kant inner intuition (microcosm) outer intuition (macrocosm)
Philolaus, interpreted unlimited: fills the plane limited: fills neither plane nor space unlimited: fills plane and space limited: fills neither plane nor space
Philosophy axiom thesis antithesis synthesis

Traditions

1 2 3 4
Four elements fire (active) air (active) water (passive) earth (passive)
State of matter plasma gas liquid solid
Psyche after Bardon and Stejnar will thought feeling consciousness
The four worlds of the Kabbalah Atziluth, pure spirit Beriah, spiritual form Yetzirah, formation Assiah, material realisation
Kabbalah, practical the idea the plan the execution the result
Name of God Y H W H
Sephirot Kether (1), Crown Geburah (5), Strength Tiphareth (6), Beauty Malkuth (10), Kingdom
The three lesser lights of Freemasonry wisdom strength beauty the building of Solomon’s temple
The three lesser lights, other order wisdom beauty strength Great Architect of the Universe
Religion idea of God human spirit human soul human body
Kabbalah idea of God Adam Kadmon creation the fall
Anthroposophy idea of God Lucifer Christ principle Ahriman
Hinduism Brahma Shiva Vishnu Maya

The row on Philolaus is an interpretation of this website. Philolaus himself speaks of the limiting and the unlimited and of the harmony that joins them, but not of figures that fill a plane. In the Pythagorean table of opposites, moreover, the odd counts as limited and the even as unlimited.

Note the sephirot: Kether bears the number 1, Geburah 5, Tiphareth 6 and Malkuth 10, exactly the numbers of the start figures 5 : 2, 6 : 2 and 10 : 4 and of the one from which everything proceeds.

In German lodges the three lesser lights, wisdom, strength and beauty, stand for the Master and the two Wardens. They are not to be confused with the three great lights, the Bible, the square and the compasses. In English rituals, by contrast, the lesser lights are the Sun, the Moon and the Master of the Lodge.

Individual rows are developed in the chapters Herder’s Metacritique, The Kabbalah and Metaphysical reflections.

Sources and further reading

Sources

  • Philolaus, fragments B 6 and B 11 (B 11 is considered spurious)
  • Immanuel Kant, Critique of Pure Reason, Riga 1781
  • Sefer Yetzirah (Book of Creation), composed between the 3rd and 6th century AD

Further reading