Provisional metaphysical reflections
Energy, time, space and matter as a fourness, assigned to the four start figures. A provisional look beyond physics.
One idea runs through all the chapters: the four start figures of the tetractys can be read as four fundamental quantities of the world.
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
Triangle, hexagram, pentagram and double pentagram.
| Start figure | Number | Fundamental quantity |
|---|---|---|
| Triangle | 3 | energy, cause, spirit |
| Pentagram | 5 | time |
| Hexagram | 6 | space |
| Double pentagram | 10 | matter |
The reasons:
- The triangle is the first figure and the cause of all others. In Hermeticism it stands for the creative spirit.
- The hexagram, two interlocking triangles, is the order of the rhythm of six and of the crystal lattices, and so of space. For Kant, space is the condition of outer perception. Paracelsus spoke of the macrocosm.
- The pentagram breaks the order of space and stands for life and the human being. It corresponds to time, for Kant the condition of inner perception, the microcosm.
- The double pentagram, the ten, unites all four figures. It stands for matter, in which everything is realised.
The same fourness appears in harmonics: wavelength and frequency, which correspond inversely in the lambdoma and on the monochord, are space and time. Energy and matter complete them into a tetractys. These assignments are speculative, but worth pursuing as a line of thought. The full comparison with other fournesses is in the tetractys analogy table.