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möbius

The elements could a priori interface in six ways: emo-ero, emi-eri, emo-emi, ero-eri, emo-eri, emi-ero.

Transitions at the first two interfaces, emo-ero and emi-eri, are clearly possible in both directions, since things start to move and come to rest both outside and inside.

The situation at the remaining four interfaces is more difficult to estimate, because they all cross the boundary between in and out. Since the outside world has an effect on the inner world, and vice-versa, in and out are obviously connected, but a priori not all 8 possible transitions at these 4 interfaces in-out would be necessary.

Let me take a step back and reconsider the interfaces emo-ero and emi-eri. Take emo-ero. The interface between these two elements must be infinitely thin, because otherwise it would be something that is observed in the outside world, hence it would be one of these two elements. The analog argument can be made for the interface emi-eri.

Usually what one perceives is clearly inside or outside, so interfaces that cross in-out would have to be largely unobservable, too, so that one might imagine them as infinitely thin membranes.

Imagine, say, a blob of ero at the boundary to inside permeating inside. A slice of ero would end up inside and, if it remained passive, would start to flow, becoming emi.

Assuming interfaces in-out to preserve activity, there would thus be transitions emi-ero and eri-emo, but no transitions emo-emi or ero-eri, hence again Aristotle's circle.

[image]

Let me explore this approach a bit more concretely.

If you leisurely observe a typical scene outside where most things rest and just a few move and then close your eyes, what you might see first in your mind might often be what has been moving outside, but initially frozen, hence a transition emo→eri, and, if you stay relaxed, the images will quickly start to flow, eri→emi.

If you already focus on something that rests outside, like a tree, after closing your eyes, it will likely also first be at rest in the mind and only stay at rest if you keep and even increase the focus. So, in a way you would have already had eri before closing your eyes, but it had not been so obvious, so maybe no mirroring of the static image of the tree into the mind, no transition ero→eri.

Consciously moving the outside body (emo) normally requires to focus on what you want to do (eri). But this does not always lead to motion outside: If something outside is hard enough (ero), it may resist, or one may stop something that had been moving by, say, catching it.

Being faced with hard resistance outside (ero) can be frustrating, which might create recurring feelings inside (emi). The same could be the result of maybe stubborn immobile views inside (eri). Conversely, observing motion outside and inside allows to learn inside, to derive stable laws (eri) of how things change, which might calm moving feelings inside (emi). And so on, just to make the idea more tangible, without proving anything for sure.

The interfaces between the elements might a priori have an arbitrarily complex nature, so that the above is a priori just likely one of the simplest ways of seeing them.

Let me map the circle of elements and trigrams onto a Möbius Strip as follows (click below to zoom in):

[image]

Inner elements are placed on the inside of the strip, outer elements on the outside. That way, the strip reminds of the supposed permeable membrane between in and out. The symbols for the moving elements fire and water touch on opposite sides of the strip, coinciding perfectly, and the same is true for the resting elements earth and air. All lines of the trigrams on one side of the strip are mirrored by their inverted lines (yin ↔ yang) on the other side, so that yin and yang are different sides of the same on the strip.

[image]

leads

  • Many paths open from here, just a few ideas below.
  • In a harmonic oscillator, two kinds of energies are transformed into each other. For example, for a mass on a spring, it is the energy in the spring versus the kinetic energy when the mass is moving. This gives the motion of the oscillator four special states, when either of the energies is extremal. And the motion between these states is periodic, thus overall reminding of the circle of elements.

    However, the natural pairing of extremal states of a harmonic oscillator is opposite states in the cycle, which naturally fits rest/move in the elemental circle, but makes it hard to relate two pairs of adjacent states to opposites like active/passive or in/out in a natural way.
  • What kind of formal mathematical models could be derived from the definition of elements ? Could this grow into a scientific way of doing metaphysics, as in Kant's Prolegomena to Any Future Metaphysics That Will Be Able to Present Itself as a Science ?
  • Aristotle considers four "causes" in Physics and Metaphysics, which remind of the four elements. Matter reminds of earth, form of air, primary source of fire and final goal of water.
  • Is the female fire trigram a form of inner fire, emo mapped to some form of eri, that is clinging to a dream, an idea, a wish despite all outer hardness ? Is the female earth trigram a form of inner earth, ero mapped to some form of emi, something that can yield devotely to outer hardness ? Is the female lake trigram a form of outer water, emi mapped to some form of ero, which brings calm to the outside world without hardness ? Is the female wind trigram a form of outer air, eri mapped to some form of emo, free flowing mind and communication ?
  • Is the Chinese approach more balanced ? Conversely, is the Greek approach more likely to start new things, exactly because it is maybe initially more imbalanced ? Are both needed for 'full' balance ? Is there more ?
  • Near the end of Apuleius' The Golden Ass (around 150 CE), Apuleius encounters the goddess Isis at full moon at the sea shortly after moonrise:

    "Her many-coloured robe was of finest linen; part was glistening white, part crocus-yellow, part glowing red and along the entire hem a woven bordure of flowers and fruit clung swaying in the breeze. But what caught and held my eye more than anything else was the deep black lustre of her mantle. She wore it slung across her body from the right hip to the left shoulder, where it was caught in a knot resembling the boss of a shield; but part of it hung in innumerable folds, the tasseled fringe quivering. It was embroidered with glittering stars on the hem and everywhere else, and in the middle beamed a full and fiery moon." (Chapter 17, translated by Robert Graves)

    Astrologer Antiochus of Athens and physician Galenus of Pergamon attributed colors resp. body fluids (humors) to elements around the time Apuleius lived, based on older roots going back at least partially to Hippocrates: white to water (phlegm, phlegmatic), black to earth (black bile, melancholic), yellow to fire (yellow bile, choleric) and red to air (blood, sanguine), the colors of Isis' dress above, plus stars and moon for the round fifth element in the sky.
  • In alchemy, also since about at least the same time, the transition of materials toward what is now called the philosopher's stone was believed to be from black via white (moon) and yellow (sun) to red, i.e. earth-water-fire-air, which is roughly in order of lightness of the elements and their relatively layered appearance on earth. It is apparently also the order of elements in the four tasks that Venus gives Psyche in an inner story in The Golden Ass, as I explore elsewhere, see artemis. All of this has ancient Egyptian roots, with Osiris (and his brother Seth), Isis and their son Horus, as well as with ancient crafts of creating fake noble metals and gems.
  • One of the oldest ancient Indian Upanishads, the Chandogya Upanishad (ca. 1000 BCE), speaks of three elements, fire (red), water (white) and earth (black):

    "The red colour of gross fire is the colour of the original fire; the white colour of gross fire is the colour of the original water; the black colour of gross fire is the colour of the original earth. Thus vanishes from fire what is commonly called fire, the modification being only a name, arising from speech, while the three colours (forms) alone are true." (Part 6, Chapter 4, translated by Swami Nikhilananda)

    Why do these the three colors red-white-black appear in so many cultures as primary colors? Robert Graves links them to the moon and I guess he is right, but why stereotypically the colors of the moon at night instead of green, brown, blue, etc. of nature at daylight where there is so much more color?

    Maybe because these are the colors that remain when light gets dimmer: red embers turning to black and white ashes; red of a blood moon during a total lunar eclipse, white of stars and moon, black of night sky and moon?
  • Plato talks about colors in the Timaeus, Aristotle in On Sense and the Sensible. Both start with black and white as basic colors, which is scientifically correct in the sense that by selectively taking frequencies out of the full spectrum of white, you get all colors, including black and white.
  • In August 2015, I playfully assigned Greek goddesses to elements: Artemis/Hecate to birth/death at new moon as fire around water, Hera (and Clotho) to a young woman or girl at the first quarter as air around earth, Aphrodite (and Lachesis) to a mature woman at full moon (like Isis above) as water around fire, and Athena (and Atropos) to an old woman at the last quarter as earth around air. Artemis/Hecate would thus contain the first and fifth element and elements would touch, as on the Möbius Strip.
  • Zhuangzi's famous butterfly dream:

    "Once Chuang Tzu dreamt that he was a butterfly, a fluttering butterfly who felt at ease and happy and knew nothing of Chuang Tzu. Suddenly he woke up: Then he was again really and truly Chuang Tzu. Now I do not know whether Chuang Tzu dreamt that he was a butterfly or whether the butterfly dreamt that it was Chuang Tzu, even though there is certainly a difference between Chuang Tzu and the butterfly. This is how the change of things is." (translated by me from the Wilhelm translation to German)

    The same day I had first quoted the dream here, on the streets of Zürich, two butterflies on a truck, 21 Sep 2016 at 13:34. White, red, black, a little yellow, even a little circle and her.

    (In Apuleius' encounter with Isis, it is left open whether he was "just dreaming" or "it really happened".)

    [image]

    The image is by Elena Vizerskaya (Getty Images 108350631); I bought the rights to use it, too, just to be safe.
  • See Billy Culver's Energy Language website, which inspired me in summer 2016 to reconsider old attempts to arrange elements and trigrams on a Möbius Strip or an infinity symbol ∞ and whose style influenced the graphics above, but in my feeling his images carry more potential than that.
© 2002-now Alain Stalder