Three months ago I began to hear about, and then read about, and then correspond with people about the world views of Carl Jung and its resonance with quaternions. I even joined the Kristine Mann Library of very extensive Jungian materials at the Carl Jung Center on E. 38th St. in New York City.
I first probed the index books for the word quaternion — and got a false hit, where one particular German translation should have used quaternio (of a set of 4 things). A related word was quaternity, meaning a square of four entities facing and relating to each other, or a division into four principles or elements, similar to the word duality for two related elements. A quaternity was at a somewhat higher level of generality than the mathematical system of quaternions, and simply meant relationships of four-fold principles or aspects of reality. Also, one element of the four principles is usually seen as dominating the other three.
I also went through the Jung-Pauli correspondence (1932-1958 in book form) and did find a discussion by Jung of the space-time continuum quaternity, looking at it in two interesting ways — one, the traditional three dimensions of space and one of time, the other a nontraditional one dimension of fixed space and three of time — past, present, and future in parallel.
I concluded that Jung had probably seen examples of applied quaternions from Pauli, Piaget, or other researchers with whom he was in contact, but did not try to develop conceptual applied systems in cognition and personality with them. But some of his later generations of followers did, particularly the analyst/researcher, Terry Marks-Tarlow. We correspond, and learn from each other.
Terry is in Santa Monica, CA and, in her therapy, specializes in helping artists, writers, and other creative and professional people to become unblocked in their work.
Terry uses quaternions to represent 4D symbolic and integrative thinking. She also use mathematical fractal theory (interactional processes occurring across borders and between dimensions) to model play and development.
In the Jungian framework, inexact borders and paradoxes are rich opportunities for growth experiences in the interpersonal domain. Also, in line with fractal math, the Jungian world focuses on repeated patterns and looks to understand the mental archetype driving it within the person’s individuality.
In fractals, patterns are found repeated at different levels of depth and detail.
One of the striking things about quaternions is that they have been use to model processes at every level of nature, from quantum mechanics to DNA strands, from molecular docking to (animal and human) bio-logging, and from cognitive psychology to celestial mechanics.
My conjecture is that quaternion systems are reflective of an operational toolbox of nature, recurring at every level in some form, with a linkage or at least resonance between the levels.
This is also consistent with Mike Mair’s construct and theory of The Universal Template in the field of social anthropology, first developed in the 1970s under a grant arranged by Mary Douglas, who wrote Purity and Danger. Mike is hoping to resume work soon on his construct and its expression.
References:
Marks-Tarlow, T. (2004). Semiotic Seams: Fractal Dynamics of Reentry. Cybernetics & Human Knowing, 11, 1
http://www.uboeschenstein.ch/texte/marks_fractal.html
Marks-Tarlow, T. (2010). Fractal Self at Play. American Journal of Play, Summer 2010
Jung-Pauli Correspondence — letters 14J, 21P, on dimensionality interpretation of space-time.
Atom and Archetype:
The Pauli/Jung Letters, 1932-1958
Edited by C. A. Meier, 2001, Princeton University Press
http://pup.princeton.edu/chapters/s7042.html
Mair, M. W. (original paper 1981, plus revisiting later). The melody of the text – revisited (after 2002). Semioticon website
http://www.semioticon.com/virtuals/multimodality/mair.htm
“Even though the speech trajectories capture virtual world models rather than actual objects on four-dimensional trajectories (like a prey animal moving in the environment), I suggest that the trajectory of speech with movement is non-verbal, the product of the core brain forming the core to the speech act. The ‘point’ is the point. A growth point is defined as the ‘initial form of thinking out of which speech-gesture organization emerges’. (McNeill) It might also be called the ‘projection point’.
The core brain mechanisms underlying human natural story telling can now be glimpsed. Damasio’s core brain text generator in action describes the nonverbal internal structure of gesturing behaviour in speech with movement. It may have functioned projectively on 4D-space time for probably billions of years. Additional control of outcomes is achieved by adding more dimensions or variables to the modeling process, up to our present limit of 7+/-2.
I think that the ‘material’ of speech with movement, via the mechanism of mirror neurons and the shape of the trajectory itself, makes a ‘synctium’ of the communicating minds. They directly collaborate to control the outcomes of the topics in which they are immersed. The core brains are entrained, and the story is shared. However the logic is ‘projective’ on 4D space-time, and I have termed our everyday ‘logic in use’ as ‘visual projective logic’.”