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.
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.
What physics says about it
The four quantities are not chosen arbitrarily, and the physics of the twentieth century has joined them in pairs in a remarkable way.
Energy and matter. In 1905 Albert Einstein showed that mass and energy belong together, and in the following years he put it generally in the formula E = mc²: mass and energy are two forms of the same thing. A body that gives off energy becomes lighter. In the sun, matter is turned into light every second.
Space and time. Three years later the mathematician Hermann Minkowski joined space and time into a single entity, spacetime. In his lecture in Cologne in 1908 he said: “Henceforth space by itself, and time by itself, are doomed to fade away into mere shadows, and only a kind of union of the two will preserve an independent reality.”
Both pairs together. In 1915, in the general theory of relativity, Einstein joined the two pairs to each other. Matter and energy curve spacetime, and curved spacetime steers the motion of matter. The physicist John Wheeler put it in one sentence: “Spacetime tells matter how to move, matter tells spacetime how to curve.”
Seen this way the fourness is a twoness of pairs acting on each other. That is the same shape Herder gave his tetractys, an origin, two opposites and their union (see Herder), and the same described by the axiom of Maria.
What of this is interpretation
Proven and measured are the equations of Einstein and Minkowski. That the triangle belongs to energy, the hexagram to space and the pentagram to time cannot be derived from them. It is an assignment of images to concepts, and one could make it differently. It predicts nothing one could measure, and so it does not pass the fourth question from Chance and pattern.
This is no objection to reflection, only a statement of where it stands. The assignment is a tool for asking questions: why are there exactly four fundamental quantities? Why do they appear in pairs? Is there something that joins both pairs, as the one of the tetractys precedes all the rows? Physics is searching for this under the name of a theory of quantum gravity, and it has not yet found it (see What remains open).
Sources and further reading
Sources
- Immanuel Kant, Critique of Pure Reason, Riga 1781, Transcendental Aesthetic
- Albert Einstein, Does the inertia of a body depend upon its energy content?, Annalen der Physik 18, 1905, pp. 639 to 641
- Hermann Minkowski, Space and Time, lecture in Cologne 1908, Physikalische Zeitschrift 10, 1909, pp. 104 to 111
- John A. Wheeler with Kenneth Ford, Geons, Black Holes, and Quantum Foam. A Life in Physics, New York 1998