“A too restricted view of human nature … even though only briefly ascendant, can significantly alter the expectations and, hence, the behavior of men and societies and may thus provide its own bogus validation.”

                                                                                                Geoffrey Vickers, The Art of Judgment, 1965



Contradiction of action and environment.*


Michael S. Sommer:  Systems Design

Ph.D. in Systems Thinking / Operations Research:  Strategic Planning / Intelligence

Wharton / University of Pennsylvania  


(Systems Scientist / Management Consultant / Photographer)  >>

(Wiener-Ashby Animal-Machine / cognition / perception)  >>

(geometry / navigating Topology of Paradox)



                           Cybernetics / Systems Thinking 

Note:  Gregory Bateson, Steps Toward An Ecology Of Mind, 1972; Harry Stack Sullivan, The Psychiatric Interview, Norton, 1954; Fred Emery, Systems Thinking, Volumes I and II, Penguin Books, 1969 / 81; Mitchell Waldrop, Complexity:  The Emerging Science at the Edge of Order and Chaos, Simon & Schuster, 1993; Ludwig Von Bertalanfy, General Systems Theory: Foundations, Development, Applications, George Braziller, 1968; Ross AshbyAn Introduction To Cybernetics, Methuen & Co,1956; Norbert Wiener, Cybernetics:  Or Control and Communication in the Animal and the Machine, MIT Press, 1948; Norbert Wiener, The Human Use of Human Beings, Avon,1967;  Robert M. Pirsig, Zen and the Art of Motorcycle Maintenance, William Morrow, 1974; Douglas Hofstadter, Gödel, Escher, Bach: An Eternal Golden Braid, Basic Books,1979; John Conway and Richard Guy, The Book of Numbers,1996.   

The S3 began in the late sixties for me with George Braque, the Tangram and Harry Stack Sullivan, which took me to Gregory Bateson and Norbert Wiener, which took me to Double Bind.  Those ideas turned into a management consulting practice, which took me to Wharton / PENN, Systems Thinking / Operations Research and interesting real world paradoxical organizational problems, and the need for more learning proficiency than problem solving competence.  I tried out the thinking on Anheuser-Busch / Budweiser and got a Ph.D for my troubles.  Then, all these years later, I took all that and put the S3 together -- topology of paradox.

My interest in Toy is tricky:  it’s more child as systems scientist, from inception, and capitalizing on that power, as opposed to small creature just having “fun”.

Now I've got a mission: I would like to see it out in the world at the lowest possible price to reach the greatest number of children.  The Zen mechanics (cognitive flip-flop) are important.  

Still trying to get Sto a wide audience, especially in an educational context for children and for potentially developing its integration within programs and research of a Children’s Spatial Thinking and Learning Laboratory  (/ Children’ s Museum).

Still trying to get the word out to manufacturers -- still no sale.  But writing about it has been fun, and very rewarding -- for me -- it is yet to be seen whether anyone else gets something good out of it.

Festina Lente.     


  Isaac Newton and Leibnitz (stripes) formulate The Calculus            Children formulate a Systems Problem

                    (hydrodynamic drag) — (Poohsticks

The Cybernetics equivalent of a model railroad network.

The Zen koan (cognitive flip-flop) mechanics of enlightenment (contradiction).

Mind and Machine as fugue.

                                                               Angular velocity and acceleration.


             Play of Ideas        

The challenge:  navigation in a topology of paradox, where the strategies and tactics are evolutionary.  Key is the difference between objective and subjective reality, and factoring that in. 


Thus, S3 is about adaptation to uncertainty:  unleashing the instinct to think, with Hands and Mind; play, with freedom of means and ends, and why it is important, in scientific terms.  A challenge to prevailing assumptions, integrating concepts that have been carefully examined in radically different fields.

Peel the conceptual onion to follow Sin science.


”I’ve always been interested in systems in the real world that are nonlinear because they can do more interesting things.  Of course that makes them harder to solve because the unexpected can happen.”

                                            Alwyn Scott:  “Straight Man For Nonlinearity”, 1984

“The psychical entities which seem to serve as elements in thought are certain signs and more or less clear images which can be 'voluntarily' reproduced and combined... this combinatory play seems to be the essential feature in productive thought before there is any connection with logical construction in words or other kinds of signs which can be communicated to others."

                                           Albert Einstein:  letter to Jacques Hadamard,

                                                     The Psychology of Invention in the Mathematical Field, 1945 

"The scientist is always working to discover the order and organization of the universe, and is thus playing a game against the arch enemy, disorganization."

                                Norbert Wiener, The Human Use Of Human Beings, 1950 

“Normal science does not aim at novelties of fact or theory and when successful, finds none." … "puzzle solving" …  [instead of] paradigm shift”.

                                                       Thomas Kuhn, The Structure of Scientific Revolutions, 1970


The system viewpoint has penetrated, and has indeed proved indispensable, in a vast variety of scientific fields …. the parallelism of general cognitive fields."  …. the name 'general systems theory' is here used broadly ….  It is the introduction of a new paradigm that matters." 

                                           Von Bertalanfy, Ludwig, General Systems Theory: Foundations,    

                                                       Development, Applications, George Braziller, 1968

"It takes as its subject-matter the domain of "all possible machines" .... What Cybernetics offers is the framework on which all  individual machines may be ordered, related, or understood."  

                                                       Ross Ashby, An Introduction To Cybernetics, 1956

"The first rule of discovery is to have brains and good luck. The second rule of discovery is to sit tight and wait till you get a bright idea."

"Analogy pervades all our thinking, our everyday speech and our trivial conclusions as well as artistic ways of expression and the highest scientific achievements."

"… the main achievement in the solution of a problem is to conceive the idea of a plan.” 

                                                                       G. Polya, How to Solve It (1945)

"You can turn ideas around in your mind to examine them from different perspectives until you find one that works for you.  And that's what we mean by thinking." 

                                                        Marvin Minsky, "Commonsense-based Interfaces", CACM (2000)

"Logic is a poor model of cause and effect.

                                                                        Gregory Bateson, Mind and Nature: A Necessary Unity, 1979

“The most beautiful thing we can experience is the mysterious. It is the source of all true art and all sciences.”

                                                                       Albert Einstein, Living Philosophies (1931)

“Painting isn’t an aesthetic operation; it’s a form of magic designed as mediator between this strange hostile world and us.”

                                                                       Picasso, Quoted in Mario Livio, The Golden Ratio (2002)

"A set is a collection of definite, well-distinguished objects of our intuition or thought.”

                                                                       Georg Cantor, Math. Am., 46 (1895)



In musical (math / pattern) termsSis about polyphony:  simultaneously combining modules, independent in melody (rhythm and contour of ball trajectory) yet interdependent harmonically (periodic variations upon a theme).

Sis simply about variations on a theme of square and circle    -- flip-flop, a counterpoint of logic and intuition.  Symmetry, and feedback, under transformation. 

Navigation as play, Spatial Thinking,  the holistic approach (space, representation, process:  multifaceted, interconnecting competencies -- human and robot), manifested by a cubical maze module, the Sommer Cube (S3) and its partner the Listening Post (EPISTEMOLOGY).

S3 is about exploration of feedback and symmetry, influences among parts and whole, square and circle -- adaptation to accelerating rates of change and complexity of system and environment:  a cognitive development tool (manual / mental rotation studies).  

Control under continuously varying context. 

S3 is about architecture of nested dichotomies:  contradictions of reason and perception, frames of reference, of logic, pattern and process, motion and stasis -- self-referential.

Architecture of complexity.

Like Listening Post; a partnership of feedback and symmetry, thinking within a topology of paradox, Watzlawick’s "contradiction that follows correct deduction from consistent premises”.  Reasoning as play:  invitation to double feedback loop learning (intrinsically destabilizing, Open Systems Thinking).

Sis predicated on the tension of switchiness (compound cognitive, perceptual, mechanical flip-flop and schedule of reinforcement):  switching of directed attention, relative motion and formand navigational strategies.  

A dialectic. 

A contradiction of action and environment -- dissonance of conflicting cognitions / actions.


                                                                                                  Rolling Ball “Tilt-Switch

To repeat, Sis simply about variations on a theme of square and circle -- flip-flop, a counterpoint of logic and intuition.  Symmetry, and feedback, under transformation. 

A powerful cognitive catalyst; and it’s fun.

                                                        "On the road again …"

           Putting today’s "education-minded consumer" into the strategic planning / intelligence driver's seat.



© Michael S. Sommer, Ph.D, 2017