The Restoration of Symmetry: The Philosopher's Stone

The illustration for Michael Maier's 21st alchemical Emblem
from Atalanta Fugiens, by Swiss engraver, Matthäus Merian, 1617.
(All images in this post can be clicked for their original, larger size.)

The Philosopher's Stone

"Make of the man and woman a Circle, of that a Quadrangle, of this a Triangle, of the same a Circle and you will have the Stone of the Philosophers.

...In like manner the Philosophers would have the Quadrangle reduced into a Triangle, that is, into a Body, Spirit and Soul, which three appear in the three previous colours before Rednesse: that is, the Body or earth in the Blacknesse of Saturn, the Spirit in the Lunar whitenesse as water, and the Soul or air in the Solar Citrinity. Then the Triangle will be perfect, but this again must be changed into a Circle; that is, into an invariable rednesse, by which operation the woman is converted into the man and made one with him, and six the first of the perfect numbers is absolved by one, two having returned again to an unity in which there is Rest and eternall peace."

- From Emblem 21 of Michael Maier's alchemical test, Atalanta fugiens, 1617.

"The theoretical roots outlining the stone’s creation can be traced to Greek philosophy. Alchemists later used the classical elements, the concept of anima mundi, and Creation stories presented in texts like Plato's Timaeus as analogies for their process. According to Plato, the four elements are derived from a common source or prima materia (first matter), associated with chaos. Prima materia is also the name alchemists assign to the starting ingredient for the creation of the philosopher's stone. The importance of this philosophical first matter persisted throughout the history of alchemy. In the seventeenth century, Thomas Vaughan writes, "the first matter of the stone is the very same with the first matter of all things".

- From the Wiki entry for Philosopher's Stone.

"Dr. Sigismund Bacstrom believed that if a physician could establish harmony among the elements of earth, fire, air, and water, and unite them into a stone (the Philosopher's Stone) symbolized by the six-pointed star or two interlaced triangles, he would possess the means of healing all disease. Dr. Bacstrom further stated that there was no doubt in his mind that the universal, omnipresent fire (spirit) of Nature: "does all and is all in all." By attraction, repulsion, motion, heat, sublimation, evaporation, exsiccation, inspissation, coagulation, and fixation, the Universal Fire (Spirit) manipulates matter, and manifests throughout creation. Any individual who can understand these principles and adapt them to the three departments of Nature becomes a true philosopher."

- From the The Secret Teachings of all Ages by Manly P. Hall, 1929.

"Associated with spontaneous symmetry breaking is the phenomenon of symmetry restoration. If one heats a system that possesses a broken symmetry it tends to be restored at high temperature. ... Above the critical temperature the system exhibits rotational symmetry. Such a transition from a state of broken symmetry to one where the symmetry is restored is a phase transition. We believe that the same phenomenon occurs in the case of the symmetries of the fundamental forces of nature. Many of these are broken at low temperatures. Very early in the history of the universe, when the temperature was very high, all of these symmetries of nature were presumably restored. The resulting phase transitions, as the universe expanded and cooled, from symmetric states to those of broken symmetry have important cosmological implications."

- An excerpt from David J. Gross's The role of symmetry in fundamental physics, 1996.

***

I suppose the "Restoration of Symmetry" seems like a rather coldly analytical approach to Love, but, for a "geometer moth"  - that is, those of us for whom connecting-the-dots, so to speak, is an integral part of our nature - finding the hidden codes which help describe the world in which we live is not so much what we do, but what we are. And, like the geometrid, we do not tenaciously hide this information from view - as if it were knowledge we, alone, had access to - but, instead, wear the information on our metaphorical wings... or the skin of our backs. That is to say, we display information; we are unable to secret it away.

A contemporary glyph for Maier's diagram shown in his 21st emblem (above).*

Symmetry is a word that has tremendous importance in the world of science - in physics, chemistry, mathematics, biology, and, yes, even philosophy - in which its definition varies somewhat, but, ultimately, refers to the similar phenomenon one finds in art and geometrical figures. Basically, it refers to physical parts, properties, or processes which are equivalent in two or more directions. The circle is a figure which, for instance, is geometrically equivalent in all directions, and is thereby described as having rotational symmetry. The Philosopher Stone glyph shown above - a modern interpretation of German alchemist (and counsellor to Emperor Rudolf II) Michael Maier's emblem (circa 1617) (artist unknown) - has bilateral symmetry, in that if a line is down its center, each side is exactly equivalent to the other, although seen in reverse. This can also be referred to as reflective symmetry as one side effectively mirrors the other.

The Language of Form - Part 2

Fractal, Form and Field - the Inevitable Symmetries

The interesting thing about fractals (example shown above) is that they illustrate more than just pretty patterns. They, too, employ the same language of form we're discussing, as well as mathematical equations and/or sequences. A new science - the Science of Chaos - is gradually emerging. and fractal theories have been absorbed within that paradigm. But don't be deceived. "Chaos" in this sense, is really the intimations of a higher order, specifically the orders of symmetry, and the fractal nature of the physical world at large. Fractals, in other words, bridge the micro to the macro, and do so by the marriage of mathematics to the language of form. Symmetry, on the other hand, has become the catch-word across the board; in all areas of science, as well as art, music, history and societal analysis. Symmetry, in other words, is a very transdimensional term. It describes both the singular entity and the encompassing field. It can take us from a simple geometric figure to a parallel universe. We can follow it from the atomic to the galactic, from the child's "cat's cradle" to the Super-string universe and beyond.

Artists, of course, generally take both the fractals, the strange geometry, and the form language for granted in their work - for them it is an instinct - and this has been the case since pre-history. Whether it was a lattice or spiral drawn on a cave wall or the crystalline structures tiled onto the walls of the great mosques, artists, intuitively, have generally "been there first" on an unconscious level.

For another intimation of the modern "fractal" for instance, we need only look at some of the illustrations of German naturalist, Ernst Haeckel, (1834-1919). Consciously, he was "drawing from life"... but, observing his work (an example is shown above), I can't help but feel that, once again, on a more unconscious and metaphysical level he was trying to intuitively connect the dots, so to speak, to a larger, more profound picture... the organization of the organism, if you will, its inherent symmetry, and its relation to all phenomenal form.

When it comes to attempting to define a form language, however, it is a mistake to take any form too literally and so superficially that one overlooks the primary source - and/or the larger picture. I'm afraid that those in scientific fields and mathematical fields often have a habit of doing just this. For example, take the Sierpinski "gasket" (my version) shown above. It needs no explanation for the mathematician, but for an artist, myself in particular, the complexity in which it's presented and the way in which it's developed and described is rather daunting and off-putting. In actuality, this triangle describes a portion of a very simple grid, the very same grid from which the Platonic solids emerge. This grid, in turn, is created from a very simple field of inter-penetrating circles, the very same field from which my geometrical figures - the "Platonic" cyclohedra - arose and/or emerged (in 1984). (A graphic of these figures is shown below. Sorry, I no longer have my documentation of these figures online, as there was a decided lack of interest previously shown; in the U.S.A., that is. Interestingly, some of my related diagrams were published in China in 2007, with my permission.) 

The Cyclohedra

The point I'm trying to make, using simple geometrical observations, is that the language of form is inherently transdimensional. Both figuratively and demonstratively it is an emergent - and yes, I am referring to the theories of David Bohm - and, as such, describe form as both a singular entity and the component of a field. In other words, there is symmetry, and then again there is field symmetry. There is the stratum of one dimension as the component of higher dimensions, and what we "see" and cannot "see" is relative to our placement in that stratum... a sort of "Flatland" fable.


Fractals, and geometric observations aside, the interesting thing about more transfigurative forms in artwork - Dali and H. R. Giger come to mind - alchemical symbols and drawings, even the illustrative work (like Haeckel's) often have a "dirtiness" about them. This type of "dirtiness", I think, is the type of "dirtiness" Matta refers to when he speaks of "hallucinations" - that is, inspired images which are inseparable from the unconscious repertoire from which they arise. That symbols from unconscious and imaginal origins ultimately obey the same "laws", the same unwritten code that is used to represent the actual, phenomenal world, is our "cause for pause", so to speak. In my opinion, it intimates one way in which we might someday come to understand the Transdimensional quality of the form language, whereby shapes, patterns, fractals, and "diagrams of forces" become the keys to unlock perceptional doors to a more profound concept of space - and its hidden symmetries - that is, as a tissue, a fabric, a synchronistic and living connective.


Credits:


Fractal form: found here.
Mosque photo: found here.
Ernst Haeckel illustration: found here.


Also: another Fractal link.


"Language of Form" post links: Part I, Part 3