Knot being: to be or knot to be

Composing and Engendering the Future: Presenting the Future (Part 4) (Part #3)

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In addition to celtic patterns, many contemporary artists and designers have crafted knotted shapes of unusual aesthetic appeal -- increasingly with the assistance of math visualization programs. As with the classic mobius strip, these weave continuously around themselves modelling a finite but unbounded space. They may model, more realistically than a sphere, the complex multidimensional space in which we experience the moment (cf Ron Atkin, **) especially if they are recognized as representing a dynamic, standing wave, flow condition. Some may suggest a fourth dimension and how it is woven coherently into the other three. Finalizing a fundamental relationship, such as marriage, may be described as "tying the knot".

Knots themselves have been studied extensively by mathematicians for the last hundred years (see http://www.earlham.edu/*peters/knotlink.htm). Recently they have proven to be of great interest to theoretical physicists and molecular biologists (http://www.wspc.com.sg/books/series/skae_series.html). One of the most peculiar things which emerges is how a category of objects as simple as a knot could be so rich in profound mathematical connections (http://www.c3.lanl.gov/mega-math/workbk/knot/knot.html).

Although knots are a common metapor in a number of schools of spiritual development, the relevance of knots to the problematique of the person was highlighted in a much-cited study by psychiatrist Ronnie Laing (Knots, 1970):

There is something I don't know that I am supposed to know. I don't know what it is I don't know, and yet am supposed to know, And I feel I look stupid if I seem both not to know it and not know what it is I don't know. Therefore, I pretend to know it. This is nerve-wracking since I don't know what I must pretend to know. Therefore, I pretend to know everything.

Curiously a particular form of knot, reminiscent of a common celtic pattern, has been used by Jacques Lacan to model an understanding of the person basic to his particular school of psychiatry. The borromean knot is of the same class as the interlinked rings on the Olympic flag. According to Lacan the body is only an imaginary consistency, not an actual concrete whole. It is pierced by losses that give rise to the desire to replace the lost object which, in turn, gives rise to the scopic, invocatory, oral and anal partial drives which seek to close up the "holed " body with substitute objects in the world. Lacan places such an object at the center of the intertwined Borromean knot of real, imaginary and symbolic orders -- something then returns from the primordial experience of it which one can never regain as conscious memory or narrative. (http://www.academyanalyticarts.org/Ragla1.html)

Borromean knot	Traditional Celtic pattern

The approach has proven of interest to postmodern theories of crime as evidenced by the work of Bruce Arrigo (1996) on the psychic configuration of existing crimoinological reality. Lacan's later works examined Borromean knots as topological constructions. His interest in such figurations was in providing a re-tooling (a different graphing) of the psychic apparatus and the constitution of sense. In that topography, Borromean knots are homologous; that is, they are corresponding and interpretive devices which explain how sense production occurs, how it is reproduced, and, therefore, how it ensures the stabilization of hierarchically constituted discursive formations. Such knots are instructive mechanisms for further appreciating the limitations of existing criminological theory to produce discourses and narratives inclusive of a culturally diverse criminology. Lacan was also interested in the use of borromean knots as a way of cultivating mythic knowledge. Put another way, these knots were a critical means of discovering replacement discourses; that is, grammars more compatible with the jouissance of those whose voices and ways of knowing remain silenced (http://www.tryoung.com/archives/pomo-crm.htm#20b)

But Lacan's approach has been criticized from a feminist perspective by semiotician Julia Kristeva (1980) using social theory that is a blend of linguistic and psychoanalytic theory. She believes in the potentially revolutionary force of the marginal and repressed aspects of language. She identifies the semiotic with a repressed feminine libidinal system, and the symbolic with a masculine libidinal system. Others have extended this dichotomy to higher dimensional chaos and lower-order lococentricity respectively. The semiotic is anarchic, pre-Oedipal, and polymorphous erotgenically, maternally oreinted, and involves primary processes. The symbolic is Oedipalized, paternally oreinted, and involves secondary processes. It is "order superimposed on the semiotic. The semiotic overflows its boundaries . . . in madness, holiness and poetry.", and avant-guarde art and texts (see http://www.blueberry-brain.org/chaosophy/kristeva.html). She cautions that: "Current attempts to put an end to human subjecthood (to the extent that it involves subjection to meaning) by proposing to replace it with space (Borromean knots, morphology of catastrophies), of which the speaker would be merely a phenomenal actualization, may seem appealing." If language and language acquisition can impose limitations (subjugations) on an individual, the use of sytems theory (catastrophe theory), may not entirely liberate the subject (individual).

Clearly the imagination is enticed by intuitions of possibilities associated with such strange shapes and their dynamic implications (http://www.cs.ubc.ca/nest/imager/contributions/scharein/KnotPlot.html). The guidelines to writers of one fantasy tale specify that by "tesseracting" an individual is able to move from one point to another without passing through the intervening space -- reminiscent of properties attributed by physicists to wormholes. With the enhancement of the quality of visual graphics, much creativity will be unelashed into giving form to spaces with unusual properties that resonate with subjective experience (for example, for knotting software, see http://www.earlham.edu/*peters/knotlink.htm).

The Union of International Associations is exploring possibility that the complex networks of international organizations (30,000), world problems (56,000), and strategies (32,000) in response to them, which it profiles and visualizes might indeed be usefully understood and portrayed through knot theory. This might provide radical new insights into "untangling" the Gordian Knots of the social problematique that characterizes the present.

The isomorphism between the basic borromean 3-fold knot, the classic Venn diagram and some celtic patterns offers an interesting mapping of the experienced relationship between past, present and future. They draw attention to the different interfaces between all three. These may also be explored as a form of temporal phase diagram. Similary there are intriguing similarities between 4-fold mandalas and knots (extensively linked on the web) which suggest, in the light of their articulations in celtic patterns, the existence of stabilizing feedback loops and transformations linking the psychic functions symbolized in depth psychology by earth, air, fire and water. Further vital complexifications are suggested by the relationship between mandalas and the dynamics of the enneagram (John Fudjack and Patricia Dinkelaker, 1999 http://tap3x.net/EMBTI/j4selfb.html)

The celtic spiral symbol (above) from New Grange (Ireland, circa 2,000-1,000 BC) suggests continuous movement, the twin base spirals never meeting, always opposed, interwoven, inseparable and interdependent, contained within a closed but endless spiral. Whether or not this was a key to Celtic religious thought, and the need of the two opposites for each other, their containment within the evolutionary third, and the unity of the system makes good sense of an age-old pattern.

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