De Alchemia Cybernetica

[…] there exists in Nature a force which is immeasurably more powerful than steam, and a single man, who is able to adapt and direct it, might change thereby the face of the whole world. This force was known to the ancients; it consists in a Universal Agent having equilibrium for its supreme law […] — Eliphas Lévi, Dogme et Rituel de la Haute Magie (Transcendental Magic, its Doctrine and Ritual)

[…] one thing is abundantly clear; all serious writers, though they seem to speak of an infinity of different subjects, so much so that it has proved impossible for modern analytic research to ascertain the true nature of any single process, were agreed on the fundamental theory on which they based their practices. […] Yet beneath this diversity, we may perceive an obscure identity. They all begin with a substance in nature which is described as existing almost everywhere, and as universally esteemed of no value. The alchemist is in all cases to take this substance, and subject it to a series of operations. By so doing, he obtains his product. This product, however named or described, is always a substance which represents the truth or perfection of the original "First Matter"; and its qualities are invariably such as pertain to a living being, not to an inanimate mass. In a word, the alchemist is to take a dead thing, impure, valueless, and powerless, and transform it into a live thing, active, invaluable and thaumaturgic. — Aleister Crowley, "Chapter 20. Of the Eucharist and of the Art of Alchemy", Magick in Theory and Practice

Every process produces a product. Every product is produced by a process. — Gordon Pask

One interpretation of the mass of circles and lines at the center of the above mandala is an alchemical symbol for the Philosopher's Stone , the finding of which is the penultimate task in the alchemist's Great Work (Magnum opus). It unites (certain qualities of) salt , sulfur , and mercury under time . As you study the symbol, you may re/cognize how your re/cognition of its components (sub-symbols) competes or cooperates with your re/cognition of the symbol as a unity having its own definition that exceeds the sum of its sub-symbols' definitions (cf. the state space of the Philosopher's Stone, which is greater than the sum of state spaces of sulfur, salt, and mercury).

The symbol that may appear as a crowned lizard eating its tail ("Now the serpent was more subtil than any beast of the field which the LORD God had made" — Genesis 3:1, King James Bible), is the ouroboros ("tail-devourer"), and may re/present circularity (cf. enso) and the union of opposites (as the tail is consumed by the head, making one indistinguishable from the other—"a circle begins where it ends"). For the alchemist, it may re/present the cycle of birth-and-death she seeks liberation from (cf. samsara), the conjunction of solution and coagulation (i.e., the et of solve et coagula), and the "All Is One" (hen to pan, lit. "the one, the all"). For the cyberneticist:

Should one name one central concept, a first principle of cybernetics, it would be circularity. Circularity as it appears in the circular flow of signals in organizationally closed systems, or in "circular causality," that is, in processes in which ultimately a state reproduces itself. — Heinz von Foerster, [source?]

The realization that the observer, the observed phenomenon, and the process of observation itself form a totality [cf. the inside, outside, and boundary itself, of a circle /jam], which can be decomposed into its elements [cf. nigredo and solve /jam] only on pain of absurd reifications, has far-reaching implications for our understanding of man and his problems—especially of the ways in which he literally "constructs" his reality, then reacts to it as if it existed independently of him "out there," and eventually may arrive at the startling awareness that his reactions are both the effect and the cause of his reality construction. This "curved space" of human experience of the world and of himself, this closure—as Heinz von Foerster calls it—finds its symbolic expression in the Ouroboros, the snake that bites its own tail, or its poetic expression in the words of T. S. Eliot, for whom "The end of all our exploring will be to arrive where we started and know the place for the first time." — Paul Watzlawick, foreword to Lynn Segal's The Dream of Reality: Heinz von Foerster's Constructivism (emphasis in original)

Compare Eliot's line in the above quote to the Buddhist Nirvana, which is by some accounts a heavenly palace, and by others the ordinary world where-when-in the observer, having realized her Buddha-nature, operates free of karmaic bondage (cf. King James Bible, Luke 17:21: "Neither shall they say, Lo here! or, lo there! for, behold, the kingdom of God is within you"). Compare also the two suns in alchemy: one black (Sol niger) and material, re/presenting the beginning (nigredo) of the Great Work; the other white or golden, and ethereal, re/presenting culmination of the Work.

Ouroboros may re/present a feedback loop, where-when part of the output (tail) of a process is returned to the process' input (mouth). Negative and positive feedback correspond to the attenuation and amplification of knowledge and variety, which conserve a system's autopoiesis.

The elemental associations chosen for the above diagram are not arbitrary, but neither are they absolute. There are multiple re/configurations of the elemental model, even with-in the Hermetic tradition. One interpretation of the above is that skillful solution and coagulation of microcosmos and macrocosmos, produces the Philosopher's Stone and Elixir of Life. I.e., applying a logical calculus of the ideas immanent in distinction-making activity, to the domain of (self-)regulatory systems, may yield wisdom-cum-immortality. That is explained in more detail, below. I encourage you to seek your own interpretations and re/configurations, borrowing what you will from what I have given here.

Solve et coagula

Combinations, wholes and not-wholes, conjunction and separation, harmony and discord—out of all things comes One, and out of One all things. — Heraclitus

The outer and the inner are one thing, one constellation, one influence, one concordance, one duration, one fruit. — Paracelsus, "Concerning the Art of Transformation"

Solution and coagulation, what Jack Courtis called "the alchemical koan" ("Commentaries on the Secret Symbols of the Rosicrucians of the 16th and 17th Centuries").

[…] the [Zen Buddhist] koan, like the alchemical expression or riddle, by virtue of its initial incomprehensibility, forces one to wrestle with it alone, to work it through, to come to terms with it not just by rational explication, but through meditative concentration and inspiration. — Arthur Versluis, Restoring Paradise: Western Esotericism, Literature, Art, and Consciousness

Before Zen, mountains are mountains and rivers are rivers. During Zen, mountains are not mountains and rivers are not rivers. After Zen, mountains are again mountains and rivers are again rivers. — variation of a popular Zen aphorism

The work of alchemy, whether material or spiritual, is concerned with trans-forming things in-to other things: lead in-to gold, ignorance in-to knowledge, sickness in-to health, mortality in-to immortality, etc. Operations similar to solution and coagulation—analysis and synthesis, dissociation and association, separation and mixture, simplicity and complexity, etc.—are boundary phenomena, e.g., where-when we make a distinction from-with-in a unity—distinguishing two or more items, and dissolving the unity—or we combine two or more items in-to a unity, and dissolve the items, or we change our operation from or (each) to both (and) (cf. quantum superposition), etc. They emerge out-of the connections and distinctions we make and break between things (cf. magical link). Distinction-making is afforded a logical calculus (means of calculation) in George Spencer-Brown's Laws of Form (cf. George Boole's Laws of Thought and set theory) (the Laws of Form apropos of analysis and synthesis, evocation and invocation, and magical links, are given more treatment in [offline]Cybermagical Models[/offline]). The ability to make correct (i.e., viable) distinctions is the measure of wisdom (cf. divination), and is amplified by the Philosopher's Stone, which transmutes all things (cf. enchantment).

The most fundamental concept in cybernetics is that of "difference", either that two things are recognisably different or that one thing has changed with time. […] All the changes that may occur with time are naturally included, for when plants grow and planets age and machines move some change from one state to another is implicit. — W. Ross Ashby, An Introduction to Cybernetics

The process of drawing out and congealing may describe the externalization of an idea from conception to manifestation. Also, in addition to breaking down and (re-)joining (cf. re-pairing, healing, spagyric, panacea), solution may refer to a homogeneous mixture in which the identity of the dis-solved substance is lost (cf. untying knots, solving puzzles), and coagulation may refer to re-inforcing (thickening) a substance (as when blood coagulates).

Lapis philosophorum

The Philosopher's Stone, a.k.a. the Stone of Wisdom, "was believed to mystically amplify the user's knowledge of alchemy so much that anything was attainable" (Wikipedia). Cf:

[…] 'problem solving' is largely, perhaps entirely, a matter of appropriate selection. Take, for instance, any popular book of problems and puzzles. Almost every one can be reduced to the form: out of a certain set, indicate one element. […] It is, in fact, difficult to think of a problem, either playful or serious, that does not ultimately require an appropriate selection as necessary and sufficient for its solution. It is also clear that many of the tests used for measuring 'intelligence' are scored essentially according to the candidate's power of appropriate selection. […] Thus it is not impossible that what is commonly referred to as 'intellectual power' may be equivalent to 'power of appropriate selection'. […] If this is so, and as we know that power of selection can be amplified, it seems to follow that intellectual power, like physical power, can be amplified. Let no one say that it cannot be done, for the gene-patterns do it every time they form a brain that grows up to be something better than the gene-pattern could have specified in detail. What is new is that we can now do it synthetically, consciously, deliberately. — Ashby, An Introduction to Cybernetics

Since everything that grows comes from a seed, the fruit must be contained in its seed. Mark this well, for here lies the secret of creation. The raising of specimen, as said before, is the raising of vibrations. Herbs, animals, as well as minerals and metals, grow from seed. To understand this secret of nature, which is only partly revealed to mankind generally, constitutes the main theoretical subject in Alchemy. Once this is known, then only the proper understanding is necessary in order to obtain results in the raising or elevating of specimen, which is nothing else but transmutation. If we can help nature in her ultimate goal, that of bringing her products to perfection, then we are in harmony with her laws. Nature does not resent an artificial effort, or a shortcut, to bring about perfection. — Frater Albertus, The Alchemist's Handbook

The Great Work of alchemy is the transmutation of base metals into gold, i.e., changing corruptible entities into incorruptible ones (cf. the incorruptibility of some Catholic saints), and the Stone is the mechanism which accomplishes that. Stone implies substance; it is not the Philosopher's Word or Idea. The Stone is an embodied phenomenon. Many spiritual systems, including alchemy, agree that it is not enough to study their teachings intellectually; we must practice i.e. embody them. Wisdom is applied knowledge. The wisdom of living—the selection of states that conserve an organism's autopoiesis—is embodied in the biology of cognition (cf. instinct and reflex). So why have I associated the Philosopher's Stone with fire instead of earth? "To recapitulate: the individuality of the body is that of a flame rather than that of a stone, of a form rather than that of a bit of substance" (Norbert Wiener, The Human Use of Human Beings: Cybernetics and Society). And, "The properties commonly ascribed to any object [entity] are, in the last analysis, names for its behavior [event]" (Charles J. Herrick, Introduction to Neurology, my emphasis).

It is the essence of fire, manifested as the human organism, which provides us with the instrument for the Great Work. — Paul Foster Case, Esoteric Keys of Alchemy

Compare the Philosopher's Stone to the Elixir of Life (below), and re/call that "all knowing is doing" (Humberto Maturana). The Stone is able to change all things, without being changed, which is a mystery of structural coupling (cf. Tao Te Ching 37: " The Way [Tao] takes no action, but leaves nothing undone"). Solve et coagula.

Separabis terram ab igne, subtile ab spisso, suaviter, magno cum ingenio. (You shall separate the earth from the fire, the subtle from the gross, suavely, and with great ingenuity.) — Tabula Smaragina Hermetis (Emerald Tablet of Hermes)

Elixir vitae

The Elixir of Life is sometimes equated with the Philosopher's Stone, which is also supposed to grant immortality. One of the Arabic names for it (elixir derives from the Arabic for "miraculous substance," al-iksir) is Dancing Water. The famous martial artist and founder of Jeet Kune Do, Bruce Lee, favored water as a metaphor for fluid response:

I said, empty your mind; be formless, shapeless, like water. Now you put water into a cup, it becomes the cup. You put water into a bottle, it becomes the bottle. You put it in a teapot, it becomes the teapot. Now water can flow, or it can crash. Be water, my friend. — Bruce Lee, "The 'Lost' Inteview" (from The Pierre Berton Show)

We may re/cognize similarity between Bruce's water and Maturana's structural coupling and determination. Re/call that the more variety is available to an organism, the more perturbations it is able to compensate. If an organism could trans-form to (cor)respond favorably to-with any and all potentially destructive perturbations, then it could indefinitely conserve its autopoiesis, as the perturbations would never become destructive (re/call that conservation or destruction happens between the organism and its environment: a bullet is a destructive perturbation to an ordinary person, but only a perturbation to a werewolf—unless it is silver!). In that sense, Herbert Spencer's "survival of the fittest" refers to the organism which is fluid enough to best fit (adapt to) the structural changes of its environment.

When someone attacks you it is not technique number one (or is it technique number two, stance two, section four?) that you are doing, but the moment you become "aware" of his attack you simply move in like sound and echo without deliberation. It is as though when I call you, you answer me or when I throw something to you, you catch it. That's all. — Bruce Lee, "My View of Gung Fu" (from John Little's Bruce Lee: Artist of Life)

Consider how water responds to vibrations (waves; cf. the Hermetic Principle of Vibration), by "permitting" them to pass through, and returning to a state of calm (cf. homeostasis; cf. meditation; cf. the Bene Gesserit Litany Against Fear; cf. von Foerster's Hermeneutic Principle—"The hearer, not the speaker, determines the meaning of an utterance"—and your mother telling you that your peers cannot make you do things you do not want to do, or feel things you do not want to feel [cf. operational closure]).

Water is called the universal solvent (cf. alkahest), due to its chemical polarity (cf. the Hermetic Principle of Polarity). "Haec est totius fortitudinis fortitudo fortis, quia vincet omnem rem subtilem, omnemque solidam penetrabit (This is the strong force of all forces, overcoming every subtle and penetrating every solid thing)" (Emerald Tablet).

When very cold, water becomes hard but also brittle; when very hot, it evaporates. The freezing, melting, evaporating, and condensing transitions of water may metaphorically describe other transformative phenomena.

Compare the "quickness" of water to that of mercury.

Mercury is liquid and flowing, and the surface of each globule of this metal is a mirror reflecting its environment. Its rapid movement, like that of a living creature, accounts for the name quicksilver, in which "quick" means both living and rapid, as we may see from the French argent vive, literally, "living silver." — Paul Foster Case, Esoteric Keys of Alchemy

A gung fu man employs his mind as a mirror—it grasps nothing and it refuses nothing; it receives but does not keep. — Bruce Lee, "The Tao of Gung Fu: A Study on the Way of the Chinese Martial Art"

Quod est superius est sicut quod est inferius

"That which is above is as that which is below (and that which is below is as that which is above, for the performance of the miracles of the one thing)" (Emerald Tablet).

The Law of Regulatory Models, developed by Roger C. Conant and W. Ross Ashby as the Good Regulator theorem, states that, "every good regulator of a system must be a model of that system" (Conant and Ashby, International Journal of Systems Science, Vol. 1, No. 2, October 1970). Klaus Krippendorff restated it as the Law of Required Model-Regulatory Identity:

This is a stronger version of the law of requisite variety and posits that any regulator able to confine the fluctuations in the system to be regulated must not only have adequate amounts of variety available to control that system but also be or have a homomorphic representation of that system. — Web Dictionary of Cybernetics and Systems

There are at least two types of models described by those laws. One is more obvious, and is the sort of thing humans do when we "mentally" construct (through languaging) a re/presentation of a system we wish to predict and control, such as weather (controlling the weather can be as simple as opening an umbrella in the rain, which creates more-or-less local conditions as-if the rain had ceased falling; cf. rain dancing, an especially non-local means of controlling weather). A more subtle model is the one that is embodied. When an engineer engineers a climate control system, she makes use of the aforementioned sort of model, to design, say, a thermostat (cf. homeostat). But the thermostat itself must embody a set of states that correspond to the variety of temperatures it is expected to regulate (since it cannot embody all variety without being equally complex as the domain of regulation, the thermostat must "anticipate" or "know" the range of perturbations to operate with-in—cf. the law of requisite knowledge). This is the sort of modeling that an organism embodies when it co-regulates (maintains homeostasis, conserves autopoiesis) itself-with-in-its-environment. "Survival of the fittest is a special case of survival of the stable" (Richard Dawkins, The Selfish Gene; cf. ultrastability).

Similar to the idea that there must be homomorphism between a good i.e. viable regulator and the domain regulated, are the macrocosm and microcosm, which again applies to maps in the ordinary sense (as a miniature model of a territory—cf. Borge's map), and in the alchemical sense to correspondences between all things and especially between humans/observers (Microcosm) and the universe/world (Macrocosm) (cf. anthropomorphism and the anthropic principle)—"There is nothing in heaven or earth that is not also in man (Paracelsus, "Concerning the Art of Transformation"). E.g., how the four elements correspond to the four humors, or the aspects of heavenly bodies correspond to human personalities and other terrestrial affairs, in astrology. "As above, so below." Cf. a theory of everything.

Cybernetics is similar [to geometry vis-à-vis ordinary space] in its relation to the actual machine. It takes as its subject-matter the domain of "all possible machines", and is only secondarily interested if informed that some of them have not yet been made, either by Man or by Nature. What cybernetics offers is the framework on which all individual machines may be ordered, related and understood. — Ashby, An Introduction to Cybernetics

In a piece of wood there lie concealed the forms of all animals, the forms of plants of every description, the forms of all instruments; and he who can carve them finds them. — Paracelsus, "Concerning the Art of Transformation"

A related idea (and model) is the meta-system transition, the emergence of multilevel control structures. Cf. "Ascendit a terra in coelum, iterumque descendit in terram, et recipit vim superiorum et inferiorum (It ascends from earth to heaven and descends again to earth, and receives the power of the superiors and of the inferiors)" (Emerald Tablet). I.e. control arises from a system to a meta-system, which controls "down" to the original (now sub-)system, real-izing the combined power of both. "Sic habebis Gloriam totius mundi (So you have the glory of the whole world)."

[…] the universe of the alchemists is organized in a series of concentric spheres, the outermost of which is the macrocosm of the planets and the stars. The macrocosm's pattern rules the microcosms, each of which is a replica of it in small, reproducing its structure. — Andrea Aromatico, Alchemy: The Great Secret