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The Union of the Imaginary and the Real:

the Ring i


Presented by Robert Matthews, PhD


This program will not be recorded.


Sunday,  June 20, 2021, 4:00 - 6:00 pm PDT (UTC -7)

The ring i is a mathematical function, the complex exponential, which sits at the heart of quantum mechanical calculations.  It appears at the end of an active fantasy by Wolfgang Pauli (who worked closely with C.G. Jung and Marie-Louise von Franz) entitled Die Klavierstunde (The Piano Lesson); perhaps you have heard of this often mentioned fantasy.  What is less often discussed is an earlier dream of Pauli’s that was also concluded with the ring i. (This can be found in an appendix to the Jung-Pauli letters Atom and Archetype edited by C. A. Meier.)  


The image of the ring i has the appearance of a mandala.  But appearance does not make it a symbol, it is the reaction of the observer.


As a physicist, the ring i was well known to me, but although it is a function with quite remarkable properties, it had little meaning beyond its mathematical utility. So I was quite surprised when it appeared in my dreams, even more surprised when I found it had also arisen in Pauli’s dreams.  Curiously, the ring i always seems to arise as the conclusion of a cosmic viewpoint.


I have pondered its meaning for some three years now, a meaning that is deeply complex (pardon the wordplay) and brings us into that nexus between physics and psyche that was so richly discussed in the letters between Jung and Pauli. The ring i appears to carry, in mathematical form, a paradoxical world view, not only of the outer world, but of the inner world too – the real and the imaginary.  It may be one of those images that appears synchronistically to help heal the split we are all subject to in this time of rational materialism. 

Learning objectives:


  • Give an example of how an image becomes a symbol.

  • Explore if a symbol can simultaneously carry a world view of both the outer and inner world, the real and the imaginary. 

  • Learn about the nexus between physics and psyche that fascinated Jung and the physicist Wolfang Pauli.

Robert Matthews, PhD, is a senior lecturer in the School of Education, University of Adelaide, Australia, where he prepares beginning teachers for classroom practice and their interactions; teaches post-graduate studies in neuroscience and psychology of education; and supervises at the post-graduate level.  Prior to this, Dr. Matthews was a post-doctoral theoretical physicist at Flinders University.  He is near completion in his training as a Jungian analyst at the Zentrum für Tiefenpsychologie, Switzerland.  This diverse background offers fascinating insights into the areas of education, depth psychology and quantum physics, the nexus of which forms his research interests.




Pre-registration is REQUIRED.  You will not be admitted to the Zoom session unless you have pre-registered.  Use this link to pre-register for this program.  After registering, you will receive a confirmation email containing information about joining the meeting.

Continuing Education (CE)

This course meets the qualifications for 2 CE hours for LMFTs, LCSWs, LPCCs, and/or LEPs.


  • Use the CE Registration Form to pay $15 and register to be awarded 2 CE hours for this program.  

  • Attend the entire program (Zoom records the attendance times of attendees).

  • Submit the online program evaluation form which will be emailed to registrants who have completed the program.

  • A Certificate of Completion will then be emailed within ten days.

For more information about the awarding of continuing education units, visit our CE web page.

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