The Geometry of Dialogue

A visual way of understanding

interpersonal communication and human development

Book and drawings by Dennis Rivers, MA


This book records my ongoing quest for visual models of human unfolding. By that I mean to ask, what sort of diagrams might help us understand human interaction and development in such ways that we would be able to interact with one another, and develop as persons, more creatively, successfully and nurturingly?

The geometry of dialogue is a field of inquiry, and also the title of my book and of a set of mandala-like drawings that I have produced over a period of about ten years Many cultures have used geometry and diagrams to represent and understand important aspects of life. Among the most notable examples are Dine(Navajo) sand paintings, Hindu and Tibetan mandalas, ancient Greek mystery teachings centering on geometry, and the designs of cathedral windows.

Such diagrams have been found helpful because they allow us to model a complex set of relationships or interactions which would be difficult, if not impossible, to describe using the long-string-of-ideas structure of everyday language. My work draws inspiration from these ancient traditions, as well as from architectural drawing, computer programming data flow diagrams, and the work of modern mandala makers of various schools, including my father, the architect Hector V. Tate (1915-1991), and my father’s friend, the 20th century metaphysical painter, Hubert J. Stowitts (1892-1953). It is a characteristic of mandalas that they often represent an effort to put everything important about human life into a single drawing or painting, and I notice that yearning in myself as well.

One crucial moment in the evolution of this book was my discovery that it is possible to use Adobe Acrobat to display “zoom-able” line drawings on the Web in high resolution with relatively small file sizes. This has allowed me to make my visually-intensive work available on the Web. (If you do not already have the free Adobe Acrobat Reader 8 installed on your computer, please download it from The entire text of the book and high resolution editions of the major drawings, are available below free of charge in PDF format.

When you look at the drawings with the Acrobat Reader, please go to Edit Menu> Preferences> Display and turn on all three “smoothing” options. Then use the Zoom Lens tool to zoom in on any part of a drawing to see the details.

In The Geometry of Dialogue (consciously) and my other communications book, the Seven Challenges Workbook (implicitly), explore the interweaving of at least three truly fundamental ideas:

The first is that cooperation is a more complex and mentally demanding activity than domination. That idea, from the work of developmental theorist Robert Kegan, strongly suggests to me that a more peaceful world will also be a more cognitively complex and mentally demanding world. The quest for a more peaceful family, workplace or world thus brings with it the task of modeling the complexity of cooperation, one crucial step toward generating it.

The second idea is that in order to guide a process, a person has to be able to observe it. Therefore, in order to improve one’s communicating, one has to gradually develop the ability to be both a participant in, and an observer of, one’s own conversational activities. I have learned much from Kegan’s work on the evolution of self-observation over the course of a lifetime.

The third idea concerns model building in everyday life. It is that we have a very difficult time perceiving what we can’t conceive. It does not seem to be the case that we see something it its fullness and then set about to think about it. Current understandings of thought and perception strongly suggest that observing and conceiving co-evolve over time. In relation to communication skills all this means that the quest to observe one’s conversational activity brings with it a need to have a framework of understandings about conversations, a model of various conversations, and some way of sorting out all that is going on between people. This has also been described as a “mental coat rack” on which to hang new experiences.

In The Geometry of Dialogue , and my ongoing diagramming explorations such as “Eighteen Intertwined Ellipses,” you will observe me trying to weave these themes together in a way that encourages the evolution of communication skills learning, communication skills training, and human evolution toward awareness, self-awareness and compassion. I hope the drawings, and the entire book, will inspire you to become an even more active and successful encourager of cooperation and reconciliation in a world full of conflict. I welcome your comments and suggestions on all these topics. You can send them to me by clicking here .

Dennis Rivers

January, 2008
The Geometry of Dialogue (all sections in PDF format) Copyright 2002-2007 by Dennis Rivers.May be reproduced for non-profit educational purposes.
1. Introduction : My quest for a facilitative model of interpersonal communication
2. Methodology and justification : Why build a multidimensional model of interpersonal communication
3. An overview of the Six Dimensions/Five Transformations model of interpersonal communication.
4. Dimension 1 : The elements of experiencing
5. Dimension 2 : Intentions in conversation and interaction
6. Dimension 3 : Fundamental forms of communicative interaction [as verbs]
7. Dimension 4 : Styles of action and interactions [as adverbs]
8. Dimension 5 : Self-awareness and exploratory self-questioning
9. Dimension 6 : The inner resources we use to shape our experience and responses
10. The evolving persons in interpersonal communication
11. Summary and postscript : A search for an action-facilitating geometry of dialogue
Selected bibliography
ENTIRE BOOK: The Geometry of Dialogue: A visual way of understanding interpersonal communication and human development   (210-pages. 10MB PDF file)

Illustrations and exploratory work as separate PDF files

DRAWING: A Six Dimensions/Five Transformations Model of Conversation (PDF format diagram, 8 1/2″ x 11″, 22k)
DRAWING: The Multiple Contexts of Interpersonal Communication (PDF format diagram, 8 1/2″ x 11″, 75k)
RECENT WORK DRAWING 2003: Twelve Intertwined Circles: The Geometry of Dialogue in Teaching and Learning (PDF format diagram, 8 1/2″ x 11″, 25k) This model has been replaced by the one shown below, and is included here for the sake of showing the evolutionary steps in my thinking. DRAWING 2007: Eighteen Intertwined Ellipses: A Model of Cooperative Learning, Teaching and Becoming (PDF format diagram, 8 1/2″ x 11″, 189k) This latest diagram incorporates Lev Vygotsky’s idea of the “proximal zone of development,” that is, what we are ready to learn next in the presence of a helpful person, given what we know. or can do, now. I have also incorporated Kuhn’s idea of paradigms, in the sense of the horizon of generally accepted knowledge, inside of which we progress to accumulate knowledge and abilities that make sense to our culture.
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