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möbius

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

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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, but with different elements touching: 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.

So, even though fire and water would touch, and maybe mirror each other between in and out, they could not transform directly into each other, only indirectly by going along the single surface of the strip via air or earth.

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leads

  • In a harmonic oscillator, two kinds of energies are transformed into each other. For example, for a mass on a spring, the energy in the spring transforms into the kinetic energy of the moving mass and vice-versa. 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.
  • Could a mathematical model of the elements as defined here 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?

    rest/move in/out passive/active
    bind/release wet/dry cold/hot
    soft/hard heavy/light
    malleable/brittle dark/light
    mixed/isolated female/male
    collective/individual moon/sun
    night/day
    un-/conscious
    Such a mathematical model, as useful as it could be, would be essentially air, something that rests inside the mind.
  • 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 thus 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?
  • In Psychologische Typen (1921), C.G. Jung combines extra- and introversion with implicitly the four elements, which he terms thinking (air), feeling (water), intuition (fire) and sensation (earth), into 8 psychological types, almost certainly already implicitly inspired by the I Ching.

    Memories, Dreams, Reflections (1961): "I first met Richard Wilhelm [...] in the early twenties. In 1923 we invited him to Zürich [...]. Even before meeting him I had been interested in Oriental philosophy, and around 1920 had begun experimenting with the I Ching." (Appendix IV, recorded and edited by A. Jaffé, translated by R. and C. Winston)

    Also in Psychologische Typen, Jung additionally categorizes thinking and feeling as "rational" or "judging", because they would judge the world based on their inside, and conversely intuition and sensation as "irrational", but even writes:

    "But I am prepared to grant that we may equally well entertain a precisely opposite conception of such a psychology, and present it accordingly. I am also convinced that, had I myself chanced to possess a different individual psychology, I should have described the rational types in the reversed way, from the standpoint of the unconscious-as irrational, therefore." (A III 5, translated by H.G. Baynes)

    In that sense, what Jung calls "irrational" could also be considered "realistic", as judging the world rather based on measurement outside than on inner conceptions, just like in science, as opposed to e.g. medieval Christian views, where looking at Jupiter's moons through Galileo's telescope could apparently not have convinced people that not everything revolves around earth. In astrology, rationality is typically air, reality typically earth, but both air and water (which is usually considered rather irrational and related to the unconscious) have to do with judgment, which is maybe not so astonishing, considering that eri and emi would be inner elements. In my definition of the elements, the world consists a priori symmetrically of both in and out, except that the observing self is arguably observing rather from the inside out, and perceives and judges the world based on all four elements.

    So Jung would have been quite close in a way, with the first text I know of to bring "in/out" near "elements", with extra-/introverted and judging from within or without.

    His definition of rational/irrational seems also to reflect the difference between medieval world views, where inner worlds had quite some weight, and newer ones, from the Renaissance on, where the outer world generally gained precedence.
  • 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. [..] 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 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 when there is so much more color?

    Maybe because the colors that remain when light gets dimmer would be more fundamental? Moon, stars and sky at night? And also the colors of a fire, humanity's own light source at night, independent of a full moon: Colors that reflect light for the passive elements earth (black coal) and water (white ashes), colors that create light for the active elements air (red embers) and fire (yellow flames)?

    Did ancient cultures maybe often not distinguish red and yellow as separate colors? Only three elements first?
  • 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.

    There are three kinds of color sensors in the human eye, for red, green and blue, sorted from low to high frequency. None triggered (no light) is black, plus red gives red, plus also green gives yellow, plus also blue gives white, hence a sequence black-red-yellow-white or earth-air-fire-water.
  • Is the Lakota "Medicine Wheel" so old that it already came to America with immigrants walking across the Bering Sea at least 10'000 years ago? The Yangshao culture "Xishuipo M45 Tomb" in China, which dates back to the 4th millenium BCE, features the mosaic of a tiger opposite the mosaic of a dragon, as constellations in the sky, exactly the animals that are traditionally assigned to West and East in China.

    My impression is that the more you go back in time, the more likely "knowledge about elements" was something that only "shamans" had and only secretly passed on to their pupils.
  • In August 2015, I assigned Greek goddesses to pairs of elements and moon phases, and tentatively flipped Athena and Hera in May 2018: Artemis/Hecate to birth/death at new moon as fire around water, Hera (and Clotho) to growth as a young woman or girl at the first quarter as earth around air, Aphrodite (and Lachesis) to bloom as a mature woman at full moon as water around fire, and Athena (and Atropos) to withering as an old woman at the last quarter as air around earth. Artemis/Hecate would thus contain both 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".)

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    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.
  • (The walking cat of the metamorphosis section came to me at Delphi in Greece on Tuesday, 4 September 2018 at about 13:09, ate some of my food, a dry pretzel and salmon jerky, then, after a few burps (still a kid) and playing a little, took a nap of about 20 minutes on my lap, then left roughly in the direction of the Athena Pronoia temple, where I had been a bit earlier. During these few minutes there were no doubts what to do and felt so good, like having a child to care for. Was the AC maybe even an oracle for the AC of π, with the moon maybe late at glowing quincunxes, or early spring?)

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© 2002-now Alain Stalder