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The Diamond Archetype

"All the most powerful ideas in history go back to archetypes. This is particularly true of religious ideas, but the central concepts of science, philosophy, and ethics are no exception to this rule. In their present form they are variants of archetypal ideas, created by consciously applying and adapting these ideas to reality. For it is the function of consciousness not only to recognize and assimilate the external world through the gateway of the senses, but to translate into visible reality the world within us."
- Carl Gustav Jung, "The Structure of the Psyche" (1927), in Collected Works Vol. 8, The Structure and Dynamics of the Psyche, P. 342
The Diamond as a Symbol of the Self:
"...The Self is symbolized with special frequency in the form of a stone.... The nuclear center, the Self, also appears as a crystal.... The crystal often symbolically stands for the union of extreme opposites - of matter and spirit."
- M.-L. von Franz, "The Process of Individuation," in Man and his Symbols, ed. C. G. Jung
Of Matter:
On the Lapis Philosophorum, the Philosophers' Stone -

"'What is this Stone?' Chloe asked....
'...It is told that, when the Merciful One made the worlds, first of all He created that Stone and gave it to the Divine One whom the Jews call Shekinah, and as she gazed upon it the universes arose and had being.'"
- Pp. 43-44, Many Dimensions, by Charles Williams, Eerdmans paperback, April 1979

"The lapis was thought of as a unity and therefore often stands for the prima materia in general."
- P. 236, Aion, by C. G. Jung, Princeton paperback, 1979

"Its discoverer was of the opinion that he had produced the equivalent of the primordial protomatter which exploded into the Universe."
- P. 216, The Stars My Destination, by Alfred Bester, Vintage hardcover, July 1996

"Take it! Keep it! It's your future.... It's yours. Make them tell you what it is."
- Pp. 252-253, The Stars My Destination

Of Spirit:
"And if the truth about reality is always in our soul, the soul must be immortal...."
- Socrates in Plato's Meno dialogue (86b, tr. by W.K.C. Guthrie)

"This Jack, joke, poor potsherd, patch, matchwood, immortal diamond
Is immortal diamond."
- Gerard Manley Hopkins, 1888

The Self as the Union of Matter and Spirit:
Gerard Manley Hopkins and Carl Jung have, in their own ways, used a diamond to symbolize the self. Hopkins's "immortal diamond" metaphor probably referred to a literal stone, although he may also have been referring to a Platonic concept, or "form." Jung's discussion of the lapis philosophorum, the philosophers' stone, referred to an alchemical concept that is rather poorly defined... although Jung occasionally referred to the chemistry of carbon in discussing the lapis. Jung also wrote of "quaternity," or fourness, in connection with the lapis, and drew, as a symbol of the self, a set of four geometrical diamonds (squares rotated by 45 degrees). This web site discusses neither alchemy nor chemistry, but does deal with what might be termed the "sacred geometry" of the diamond.
The Geometry of the Diamond Archetype:

Plato tells how Socrates helped Meno's slave boy "remember" the geometry of a diamond. Twenty-four centuries later, this geometry has a new theorem.

The Diamond Theorem (S. H. Cullinane):

Inscribe a white diamond in a black square.
Split the resulting figure along its vertical and horizontal midlines into four quadrants so that each quadrant is a square divided by one of its diagonals into a black half and a white half. Call the resulting figure D.



Let G be the group of 24 transformations of D obtained by randomly permuting (without rotating) the four quadrants of D. Let S4 denote the symmetric group acting on four elements. Then

(1) Every G-image of D has some ordinary or color-interchange symmetry (see below),

(2) G is an affine group generated by S4 actions on parts of D, and

(3) Results (1) and (2) generalize, through intermediate stages, to symmetry invariance under a group of approximately 1.3 trillion transformations generated by S4 actions on parts of a 4x4x4 cube.

Links to related pages:

Diamond Theory: Mathematics of Symmetry
The Diamond Theorem
The Diamond 16 Puzzle
A Mathematician's Aesthetics, by S. H. Cullinane
Geometry of the I Ching
Block Designs
Theme and Variations
Solomon's Cube
Geometry of the 4x4 Square

Page last updated May 14, 2004; created July 30, 2000.