A is to B as B is to C. See? But, seeing is not always believing.How does one mediate opposites which appear contradictory and hostile to one another? Jung suggested a transcendent function which is a combination of conscious and unconscious elements, real and imaginary that produces something new, a third way: the symbol. Power and eros in proportional balance led to a moment, a place that can be thought of as a moment where the golden Mean is constellated and we could glimpse the “eye of God.” But, this would imply not forgetting the past, and precludes a meaningful reinvention of the individual.
So, for Jung the wise man may be one who is serene and tired, and predictable, after a hard day of work. But, ideally the wise is one who can no more be captured than the wind and who strikes like lightning when necessary. Wisdom is connected with intuition, and with seeing things whole, and so it links up with the transpersonal perspective. It is the power to play with opposites and to establish a synthesis;
the perspective to create harmony among the apparent contradictions. Unfortunately, we are conditioned by the past but we have the
power to disown it, to walk away, to change ourselves, which a psychology of the golden mean mean be a hindrance as prisoner these so-called immutable laws of the universe
One of several instructive descriptions Jung employed for mediating opposites is the transcendent function, a combination of conscious and unconscious elements, real and imaginary that produces something new, the symbol. But can a symbol be new? Does its existence deny a link with higher unconsciousness; that state where language is inadequate? …: We would like to suggest the optimal combination of opposites occurs when the forces in the field are in a proportional relationship reflective of the individuation process….
…There is one particular type of proportion that permeates western history both in the arts and sciences, and which can be directly linked to Jung’s archetypal theory, i.e., the golden section, ratio or mean. Put simply, this section is formed by dividing a line unevenly such that the ratio of the whole line to the longer segment is the same as the ratio of the longer segment to the shorter one . Similar to the ratio of the diameter of a circle to its circumference, π, the gold mean, phi Φ is an irrational number, approximately 1.618033988… and an asymmetric cut, the parts are not equal. Read More:http://www.institutcgjungbcn.cat/joecambray.htm
Ultimately,Aristotle’s golden mean may produce a mellow life but it makes for undramatic living. Comforting and satisfyingly numb. The vision of a comprehensive and harmonious development of the human personality and an elimination of all conflicts and obstacles that might block this development seems a bit trite and simplistic. Something the Gilmore Girls might yakety-yak in their hyper-articulation of their feelings as synthetic, pseudo wise children.It seems optimistic at best and quite naieve at worse. Should not psychotherapy be more modest avoid grand visions, utopian ideals, and just content itself with the minor glory inherent in coping, jst a bit of peace between the dialogue and the gesture.
Yet, in terms of psychology, the directed movement of the spiral, the golden mean, within a structured field of specific proportions opens some imaginative comparisons to analysis and the individuation process. The the specific asymmetric proportions of phi evident in nature, art, architecture and music create a felt experience of harmony, beauty, wholeness.Although social psychology, group pressure and the tyranny of the majority may play a factor. There appears to be an inherent human attraction to things with proportions approximating the golden mean. Or, its one of the great ruses of history and the basis of the commercial and aesthetic “values” we have acculturated. Against the weight and marketing prowess of the divine ratio are other aesthetics such as the purity of iconoclasm. It was known, according to David Pimm, to have permeated and become ritual in the reformed English church and the Bourbaki movement. He asserted that notions of “purity”, in the religious and also in the pure math sense, led to the same sense of iconoclasm: rejection of figures, geometric or human, and an attempt to get at Truth directly, without any mediating interference. The quantum leap that our collective conscious seems reluctant to accept. The ultimate revolution from within that could topple the entire cultural industry.
After the iconoclast view, Jungian notion of the Golden mean seems like we are playing with a toy train set on a carefully arranged environment:Powerful, expansive moments of harmony within the self and within human interactions can be imagined as experiences of the transcendent function by Jungians. With the movement towards the infinite either through winding the logarithmic spiral into miniscule turns or alternatively widening it out into the galaxy, size may be variable but shape remains consistent. Note that in the path of ever decreasing size of the curves an approach to infinity through the small, the infinitesimal, is revealed. The point of origin within the most minute turn is framed as the “eye of God.” This place, which dynamically is also a moment, echoes Jung’s descriptions of the transcendent function when couched in an emergentist model; it is inherent in nature as both an archetypal structure evident in the golden rectangle and as dynamic archetypal process seen in the golden spiral. With containment and boundaries of specific proportions, energy can move along the spiral shape archinward the infinitely small or toward infinite expansion outward with ever widening loops.
There are particular moments in the analytic process in which the co-created relationship hits a special note where consciousness of both partners is dyadically expanded; proportions within and between are harmonious; it is a moment of transcendence.Read More:http://www.institutcgjungbcn.cat/joecambray.htm
Evidently, we live in a world in which there are many connections between geometry and art. There is a fascination with the golden ratio, with the story of projective geometry arising from painters’ perspective prior to it becoming a pure mathematical subject. Even the cave paintings at Lascaux invoked the use of geometry and the continued considerable impact of mathematics on art in the twentieth century through cubism and Escher for example into the bewildering array of symbols and logos that make up today’s pop culture.
But, this predominance of the psychology of mathematical thinking does pose some issues about creative thinking and whether it is actually limiting the creative process and acting as a barrier to a connection with a higher unconscious.
In the arts it has been employed, consciously or unconsciously, throughout millennia, as in the “Great Pyramid” at Giza, and the Parthenon. The painter mathematicians of the renaissance including Piero della Francesca, Leonardo da Vinci and Albrecht Dürer all made extensive, deliberate use of the golden mean in their work and one of Piero’s students Luca Pacioli popularized this in his book the Divine Proportion. Read More:http://www.institutcgjungbcn.cat/joecambray.htm
I wish to add another ‘complaint’ here; the posthumous co-opting of the past by the present, in order to render mathematical styles apparently less temporal. By labelling a particular formulation as Lagrange’s or Cauchy’s theorem, for example, is to recruit their work into a modern idiom, into ‘our’ style of doing mathematics. I believe it is done, in part, to make them one of ‘us’. In this way, the ‘timelessness’ of the notions, formulations and even styles of proof themselves become buttressed by the past and, thus, rendered invisible. What we lose (and are meant to lose) is a contingent and historical sense of our present-day mathematics. How can someone nowadays read Cayley or Jordan, having studied a course in group theory which included ‘Cayley’s theorem’ and the ‘Jordan-Hölder theorem’, and not assume that they were addressing the same objects, seen in the same axiomatically-specified way. In the Ancient Greek world, there was considerable discussion of the ‘timelessness’ of geometry and the permanence of geometric knowledge versus the genesis (coming–into-being) of mathematical objects by means of constructions… Read More:http://www.icme10.dk/proceedings/pages/regular_pdf/RL_David_Pimm.pdf
A better connection would be to the philosophical tendency towards abstraction through mathematics that is part of the Dutch tradition. Mathematics is a way of expressing the realities of the world in numerical terms. Numbers immediately abstract and universalize the particular and subject the local to the universal logic of abstract though. Equally Dutch was the tendency to eliminate the incidental in favor of abstraction, as exhibited in the iconoclasm of the Puritans in the sixteenth and seventeenth centuries. One can better understand De Stijl from viewing a painting of the bare and stripped interior of a Protestant church by Emmanuel De Witte. De Stijl removed iconoclasm from its religious origins, eliminated nature, and substituted a more universal and absolute quest for a utopian harmony. “The art of painting,” van Doesburg said, “can be explained only by the art of painting.”
Cubism suggested to the De Stijl painters that it was possible to move into abstraction. Bart van der Leek stated, “Modern painting transmutes physicality into flatness by reducing the natural to the terms and proportions of the flat plane; and through the understanding of space, painting achieves relationships.” The Dutch artists seemed to understand that Cubism, particularly that of Braque and Picasso, suggested that line and color and form could be used as signifiers instead of as describers. If that was the case, then Cubism had created a new visual language that substituted ideas or concepts for resemblances. The Cubist artists themselves were unwilling to take the final step into total abstraction and to relinquish their hold on reality, but the De Stijl artists were concerned with concepts that were abstract compared to the more mundane sources of Cubism. In addition, Cubism was a pre-War movement and De Stilj was a post-War movement with the goal of rethinking the world. But the impact of Cubism upon De Stijl would be a strong one, particularly the author of the 1920 series of articles on “Neo-Plasticsm,” Piet Mondrian, who used cubist ideas as a vehicle through which he made concepts concrete through painting. Read More:http://www.arthistoryunstuffed.com/tag/theo-van-doesburg/