Wednesday, March 30, 2016

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 physics1996.


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 symbol I've constructed below, however, is composed of the glyph (shown above) transposed with its mirrored equivalent. That is to say, it's been flipped and superimposed over itself to reveal its innate reflective symmetry... the first operation in restoring its full - or unbroken - rotational expression.** It has, in fact, become a "star." And, not just any star; a highly significant star. It is, in fact. the first of the triangulations described here, that is, the hexagram, which, symbolically, carries a lot of weight across a wide spectrum of theologies and philosophies.

The same glyph with its symmetry restored, that is, its reflective symmetry.

It is known best as the Star of David, the symbol of Judaism, but was pre-figured by the Kabbalist's talismanic Seal of Solomon which was primarily a magical symbol. This, in turn, was described by medieval Arabic writers as a signet ring belonging to Solomon which was engraved with the name of God. As it was, the hexagram had formerly decorated Christian churches, and was known as the "Star of Creation." In the Hindu and Buddhist Tantric traditions it is the symbol of the 4th chakra, Anhata, the heart chakra. In Tibetan Tantric philosophy it is at the center of the mandala belonging to Vajrayoginī - the female Buddha - and represents "chos-kyi 'byung-gnas", the origin of phenomena. (see inset image below)

So, we begin to see that the hexagram, although emerging from different cultures and different locations of the world, has a similarly rich significance wherever it is found. Moreover, especially in Indic Tantric tradition, we find it is, in fact, the symbol of the hieros gamos, the Mysterium Congunctivus, mentioned in my previous post (see Alchemy of Love). In this case, it is the sacred marriage of the male and female principles, Shiva and Shakti, represented by the two intercepting triangles. Tantric traditions themselves center upon the idea of Maithuna, the consecrated union between a man and a woman. This union isn't always in the material realm, however, and may be experienced by a transference of energies. From the Wiki entry: "It is when this transfer of energy occurs that the couple, incarnated as goddess and god via diminished egos, confronts ultimate reality and experiences bliss through union of the subtle bodies."

The hieros gamos is also alluded to by Maier himself in the text which follows his emblem:
"Make of the man and woman a Circle... but this again must be changed into a Circle... by which operation the woman is converted into the man and made one with him, and six (my emphasis) the first of the perfect numbers is absolved by one, two having returned again to a unity in which there is Rest and eternall peace."

Maeir's Stone, then, appears to align with hermetical alchemical philosophies and the idea I put forward in my previous post: that is, the Philosopher's Stone is, metaphorically, the force of Love. (Keep in mind, however, that Meyer's statement : "by which operation the woman is converted into the man and made one with him" might also be inverted to read: by which operation the man is converted into the woman and made one with her.) In this capacity, the force of Love is essentially the Law of Creation... wherein the amalgamation of opposites becomes a metaphor and a reflection of creational forces on a cosmic scale.

But, there's more. Because, when Maeir's Philosopher's Stone is transformed into a hexagram - its restored symmetrical expression - it has disclosed another secret as well. At its center two circles have intercepted, and from this interception the Vesica Piscis has emerged; a Sacred Geometrical figure which has appeared often on this blog.  And, so it should. It is the diagram of the Great Mother and the masonic template for the Gothic arch. It is also the center of the Flower of Life: the Sacred Geometrical symbol for Creation, because it can demonstratively generate every geometrical figure and form.

The Vesica very often appears on amulets.

Moreover, it, too, is an expression of the hieros gamos, as described on Randall Carlson's  Sacred Geometry International page***:

“Geometrically, the Vesica is constructed from two intersecting circles, so that it may be taken as having a double significance. Edward Clarkson says that it ‘means astronomically at the present day a starry conjunction; and by a very intelligent transfer of typical ideas a divine marriage,’ or the two-fold essence of life, which the ancients supposed to be male and female."

Of course, I'm a stickler for precision, so I was not yet sold on the glyph I've just analyzed... because its triangle is interpreted as equilateral - meaning all of its sides are the same length - whereas, in Maier's original illustration**** the triangle is an isosceles triangle, in that only two sides are equal in length.  As you can see in my diagrams below, this changes the playing field. When this glyph's reflective symmetry is restored, the central circles have formed, instead, the figure 8, the lemniscate and/or the symbol of infinity. That being said, does this mean that everything I've just described is wrong?

Another interpretation of Michael Maier's description of the Philosopher's Stone.

No, not really. In the end, if we place Maeir's second (and last) circle in the center of the figure, as opposed to the outside of the diagram (see figure above, right), we are presented with what is, in fact, a double Vesica! Moreover, we have reason to believe that, although Maier illustrated his figure with an iscoceles triangle, he may have been deliberately misleading the viewer. After all, he was an alchemist. He wasn't going to spell it out for us, so, his actual diagram may be somewhat innacurate. In fact, although our second operation isn't shabby, our first operation may have been the correct one, after all.

The hexagram in Maeir's 21st emblem.

I say this because, ultimately, he gave us a clue. If you look closely at the object in the foreground (bottom. left-hand corner) (detail shown above), there is a slip of paper lying at the geometer's feet, and, drawn there, very clearly is a geometrical figure: the hexagram!

* In the Wiki article, this glyph is also referred to as "Squaring the Circle," a reference I fail to see. Certainly, the circle is contained within a square in Maeir's diagram, but it doesn't describe the actual operation referred to as squaring the circle. In the past, I have seen one example of this operation which actually does seem to successfully create a square with the area of its corresponding circle - generally described as being mathematically impossible - but, believe it or not, it was actually a diagram of a crop circle. If I can find it in my files I'll upload it here.

** Throughout this post, the "restoration of symmetry" refers to translating any given object, symbol, diagram, concept, etc. into the least "unbroken" aspect of its reality, which can often be represented by it's reflective or rotational aspects, and, in the case of graphic images, quite literally. 

*** Sadly, this "international" page appears to have no translatable text apart from its English form. I do my best to link to translatable pages - the lack of them across the board is, in my opinion, a grievous oversight - but this is, unfortunately, not always possible.

**** In this article I refer to the illustrations found in Atalanta Fugiens as Michael Maier's but, in fact, the emblems were engraved by Matthäus Merian, also known for his Topographia Galliae.


The Philosopher's Heart

The Vesica Piscis and Lozenge shown here as a kind of "infinite" spiral fractal - 2016, DS

"The form of geometry I increasingly favored is the oldest, most concrete, and most inclusive, specifically empowered by the eye and helped by the hand and, today, also by the computer … bringing an element of unity to the worlds of knowing and feeling … and, unwittingly, as a bonus, for the purpose of creating beauty."

"The rhombus (or lozenge, diamond, kite) shape consists of two triangles, one downward (Yin) and one upward pointed (Yang), joined together. It is found within the subsequent cultures and communities of our global world, often together with other geometrical depictions and it refers to the same notion everywhere. This geometric symbol represents the inner focus that a human being needs to hold onto his life task during his life time on Earth. That task was and remains to this very day  to reinstall balance within self between the Yin and Yang energy aspects that make up every human being and to reflect that inner balance into the outer world. When the geometric shape of the rhombus appears a significant change is installed within the consciousness of a human being; one that supersedes the limited ego-self of the human personality and that acts for the benefit of all people."
- Excerpt via this Eternal Symbols page.

"... regarding the Southern Lozenge stone, a talisman type identified by its lozenge shape (plan view) and lenticular cross section, this study documents 29 such specimens recovered from the Cogged Stone site at upper Bolsa Chica Mesa, Huntington Beach. Distinctions are drawn between lozenges and locally recovered elongate, plummet-like charmstones whose cultural floruit also occurred within the middle Holocene of south central coastal California.

…it is probably not exactly true to say that the female genitals are “seldom represented artistically” because “artistically” means something very different to us from what it could have meant to the people who might have wanted to epitomize the kteis [vulva] by drawing an almond shape (i.e., an eye), or a triangle on its point, a fig shape, an apricot, a comb, a lotus petal, the leaves of certain trees, a grain of wheat, rice or rye, a cowrie or a scallop shell, all of which symbolize the female genitals because of their perfunctory resemblance to the vulva. It may be that female symbolism, in fact, occurs more frequently (not less) than male precisely because of the “amorphous” nature of the female external genitals. Anything that resembles the soft curves of the mons veneris becomes a kteis, whereas a phallos is a phallos and is generally depicted as such because it is more easily identifiable. The question of “art” is a convention just as writing is a convention."
- Excerpt from the .pdf file "More on Lozenge Stones: A Record from the Cogged Stone Site" by  Henry C. Koerper and Nancy Anastasia Desautels-Wiley.

"Yet the cross itself is the oldest of phallic emblems, and the lozenge-shaped windows of cathedrals are proof that yonic symbols have survived the destruction of the pagan Mysteries. The very structure of the church itself is permeated with phallicism. Remove from the Christian Church all emblems of Priapic origin and nothing is left, for even the earth upon which it stands was, because of its fertility, the first yonic symbol. As the presence of these emblems of the generative processes is either unknown or unheeded by the majority, the irony of the situation is not generally appreciated. Only those conversant with the secret language of antiquity are capable of understanding the divine significance of these emblems."
- Excerpt from Manly P. Hall's massive tome: The Secret Teachings of All Ages, 1926. (Note: "yonic" here refers to the yoni - a Sanskrit term for feminine genitalia.)

"The alchemists, in their quest for philosophical gold, considered the world to be influenced and manipulated by a multitude of paired forces: wet and dry, cold and hot, sun and moon, male and female, proton and neutron, etc. When these opposing forces are harmonized and balanced through synthesis, creation is commenced. The Great Hermaphrodite is an amalgam of this union.

However, the historical precedent reaches farther back than the European alchemists. In ancient Mesopotamia, the source of so much of the west’s occult theory, we see the first glimpses of the Great Hermaphrodite. One union not mentioned above was the joining of the divine with the earthly. The Mesopotamian king, considered the divine representative, would join with a hierodule (‘sacred prostitute’). The sexual union was seen as the mediator between the godly and the human. It was believed that this sexual encounter ensured that the wheels of creation kept spinning, and liberated the world from the cold and motionless grasp of matter. It is worth noting that Christians borrowed this belief; Christ being born from the union of Jehovah with the very human Mary."
- Via artist Aaron Stewart Lewis Knapp's The Great Hermaphrodite


Well, if you've managed to get through the previous (dry & daunting) section, congratulations! It will all get much easier now. After all, it's far, far less complicated - and far more gratifying - performing a geometrical act than it is discussing it...  kind of like the sexual act, which geometrical figures are often metaphors for. And, for a Geometrid, sex and the drawing of diagrams stimulates similar portions of the brain. Well, okay, I made that up, but it's true that the execution of geometrical figures is an almost orgasmic experience for the Geometrid - and a cerebral high -  but try talking about it when your little grey cells start buzzing!

So, in this section, we'll tend to the prettier (and sexier) pictures regarding the glyph of the Philosopher's Stone, specifically mine (of course). In fact, as is shown in the diagrams below, the "Stone" is no longer a bloodless diagram, it has begun to transform into something more vibrant and organic. Not content with Michael Maier's vague allusion to color - a confusing array of white, black, yellow and "Rednesse" - I chose the more subtle combination of red, blue and violet; colors which occupy the lover's side of the color spectrum.

Because, yes, we are still discussing the alchemy of love, and, as you can see in the third diagram in the revised group above, something new has been added. Ultimately, a new symbolic element has emerged: that is, the lozenge - a diamond-shaped parallelogram, or rhombus, in which the Vesica is both contained and, alternately, created by. (See the first diagram of this section; which describes the simple way this is accomplished... as a sort of simple spiral fractal.)

And, its emergence is important to us, because the lozenge is another mystical figure pregnant with meaning, and I'm not using the term loosely. As we've seen in the cases of the hexagram and the Vesica, although both are often representative of the Divine Feminine their larger importance is that all are representative of the sacred marriage or chemical wedding, that is to say, union, or reunion of polar opposites. And, this is true whether we're referring to primal forces, principles, genders or mind-sets. But, also importantly, all three are symbols of creation on a cosmic scale. Once again, these symbols were found by restoring a symmetry, and they also represent the concept of a restored symmetry (i.e., the underlying purpose of this post).

As to the antiquity of the lozenge-shape, we can see by the second quote in this section, that a number of stones carved and polished into this shape were discovered in an archeological dig in southern California (see inset, right). So, it becomes apparent that the lozenge is not merely an ancient symbol, but a truly prehistoric one. They're referred to in the text as "talismans" and possibly symbolic of the female genitalia,  But, what did it really mean to the prehistoric people and what was it used for? Was it a fertility talisman... or was it possibly used in love spells or some variety of sympathetic magic? Had it proto-pagan religious significance?

As it so happens, along with the Lozenge stones were found what are intriguingly referred to as "hook/bird" effigies (see inset image, left). Yeah, well, we can probably conjure up a use for this little item (actually 23 cm in length)... had it not been made of stone!

But, this isn't an exposé about prehistoric sex-toys, so, allow me to get to the point, specifically the diagrams below. Because, when we begin really digging around in the symbolic realm we needn't stop at merely the esoteric or arcane; even the most prosaic, mundane, every-day sort of symbol - and beware of the advertising/corporate logo sort* - arrives to us from geometrical sources. One such popular symbol - referred to as the heart symbol -  which, as I've shown below (right) is simply created by the (rotated) Vesica and it's diamond shape enclosure.

As for the diagram on the left: interestingly enough, when the symmetry of the lozenge, itself, is broken, and the diamond is sliced in half (and repositioned apex to apex), we find another playing card symbol - and Tarot symbol - a glyph for the suit of Cups. So, we find three playing card symbols - the heart, diamond,  and cup - can all be generated by and/or within the Philosopher's Stone symbol. And, interesting, all three symbols have been interpreted as symbols of Love... which will be explored in a future supplement: Love and a Deck of Cards - The History of Romance.

The Philosopher's Stone as an "infinite" embedded fractal.

* This is kind of off-topic, but I'm guessing that there should be an entire branch of psychology devoted to graphic symbols & images and their subliminal prompts and effects on the human mind. See: Subliminal advertising leaves its mark on the brain, and 15 Corporate Logos That Contain Subliminal Messaging.


Note: This post is now complete. Originally, it was also (partially) comprised of the material which will eventually appearing in the following three posts: The Restoration of Symmetry - b) Love and a Deck of Cards,  The Restoration of Symmetry - c) The Symmetries of the Music Box, and, lastly: The Music Box: Supplement 2: Music, A Transcendent Function.*

After a period of nine days "under construction," it finally became apparent that my initial plans for the "Restoration of Symmetry" had to be revamped!

I realize the titles of these posts are unwieldy... it's beginning to look like a thesis! Hopefully, in time, I can sort this out.

*There are, however, three more additions to the series: The Music Box: Supplement 3: The Swan People, The Language of Birds & the Alchemy of Love II: The Beloved, and, lastly,The Language of Birds & the Alchemy of Love III: Dark Eros (or, Eros Underground)

Updated Note: I've posted a tentative menu here, but this is also subject to change.


  1. Great article!! Came here looking for philosofers stone fractals and found so much more.

    1. Thanks so much! When it comes to geometry and symbolism the comparisons and correlations are stunningly complex... and endless!