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 four start figures, in the order of the table.
Number and form
| 1 | 2 | 3 | 4 | |
|---|---|---|---|---|
| Tetractys | 1 | 1 + 2 = 3 | 1 + 2 + 3 = 6 | 1 + 2 + 3 + 4 = 10 |
| 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 | matter |
| After Kant | inner intuition (microcosm) | outer intuition (macrocosm) | ||
| Philosophy | axiom | thesis | antithesis | synthesis |
Traditions
| 1 | 2 | 3 | 4 | |
|---|---|---|---|---|
| Four elements | fire (active) | air (active) | water (passive) | earth (passive) |
| The four worlds of the Kabbalah | Atziluth, pure spirit | Beriah, spiritual form | Yetzirah, formation | Assiah, material realisation |
| 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 |
| Religion | idea of God | human spirit | human soul | human body |
| Kabbalah | idea of God | Adam Kadmon | creation | the fall |
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.
Individual rows are developed in the chapters Herder’s Metacritique, The Kabbalah and Metaphysical reflections.