Contradiction of Action and Environment


“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)


The S3 is Mysterious.

S3 is about mental and manual rotation, in the face of contradiction of action and environment:  an illogical universe, and its implications.

In Zen terms, embracing the contradiction (instead of accepting the Law of Non-Contradiction) creates the necessary tension to escape from the underpinning concepts -- to see them as dynamic patterns, part of a process of transformation.

Thus, Sis about “operationalizing” the collapse of our expectation of a logical universe (ike the Frame Problem:  no boundary for what information is relevant, what will change, what will remain the same), and how to adapt (we don't know the rules until the game evolves) by advanced thinking and intuition -- and reflection upon those processes:

Thinking as play.

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 [emphasis mine] 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 

S"combinatory play" simultaneously demands a spiral of pattern recognition (inductive - abductive / deductive flip-flop) while impeding it (gestalt figure / ground illusion flip-flop) introducing active resistance, error (in “new" Cybernetic terms, overcome entropy by using noise as positive feedback), exciting curiosity:  topology of paradox. 

Thus, Sis about continuous synchronous switching:  nested, dynamic, switching of cognitive and perceptual and mathematical dichotomies, where the manipulator must constantly re-examine reigning assumptions, transcend and control nested and evolving recursion and contradiction, by inventing new propositions.

S3 is about pattern, "'voluntarily' reproduced and combined”, the rule which governs a system or phenomenon, exactly like numeric, musical, or visual relationships -- and its simultaneous mental and manual rotation.


Patterns, a dynamic visuospatial (analogical mapping and processing) cycle of concrete and abstract reasoning:  think Rene Descartes's analytic geometry -- nested coordinate systems; Albert Einstein’s “Combinatory Play”;  Mathematics  -- the science of patterns:  nothing but patterns  …  "Omnia apud me mathematica fiunt."

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

Sis about functional relations, particularly goals and feedback

All of this relates to the dialectical premise of the S(cognitive tool for individual -- internal dialogue, below), and are embedded in the original Synthesis of Cybernetics and Systems Thinking:  Optimizing communication network / signal operating in an unfriendly (blocking) environment, approaching Complexity (something you cannot predict)and was introduced in “Open Systems Listening:  Conversation As a Research Tool” Ph.D. Diss.,1988 (cognitive research methodology for group, the Listening Post: -- external dialogue -- "What people hear is not what is going on”).

" … request for conversation is … the cornerstone of our misunderstanding …. It implies a simple (means / ends) as opposed to a joint causality [S3] .... Not just a crude, inept version of written propositional statements, e.g., "what they were trying to say is … rather multi-layered messages in which a communication about the nature of the exchange is negotiated on many levels."  

                   M. S. Sommer, "Open Systems Listening: Conversation As A Research Tool", Ph.D. Diss.,1988 

Contradiction of action and environment.



Both of these tools, the Sand the Listening Post, capitalize on contradiction / paradox and are rooted in the idea and operation of “wholeness", the relation of whole and parts, structure of systems and their behavior, laws of regulation, and recursive processes of self-observation and self-reference in the service of reasoning, Animal and Machine. 

S3 exemplifies Animal and Machine at the intersection of that robust philosophy; 

"automata ... coupled to the outside world both for the reception of impressions and for the performance of actions.”

           Wiener, Norbert,  Cybernetics:  Or Control And Communication In The Animal And The Machine (1948)

Regulation of things with “purpose”, joint causality; a multi-layered "conversation" in which the nature of the exchange is negotiated on many levels. 

topology (properties and relations unaffected by continuous change -- symmetry under transformation) 

of paradox (contradictory cognitive and perceptual signals / messages at different levels, where acknowledgement of that contradiction is forbidden).  

An exploration of symmetry, influences among parts and whole, square and circle -- adaptation to accelerating rates of change and complexity of system and environment.

The S3 is about regulatory switching (synchronizing concurrent communication / interference among rotating S3s), a heuristic routing (ball or vector) system (in Paul Baran’s Distributed CommunicationAdaptive Message Block Network terms):  seeking best paths (optimization) in an unfriendly (blocking) network / environment of switchable links; where dynamic programming is required to optimize incompletely understood and changing systems (using locally implemented full switching at all nodes, not a hierarchy of routing control centers). 


Think of the ball as “ping”:  a network monitor / troubleshooting tool testing reachability.


                        Binary Processor (0/1)

Sis a topology of reciprocal influence of Hands and Mind. 

Sis holistic, Hegelian, an Open System:  an evolution among parts and whole -- a kind of incompleteness.    

Play of causal inference, joint causality.

               S”Parallelism of General Cognitive Fields”

“A too restricted view of human nature … even though only briefly ascendent, 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 Judgement, 1965

The Srepresents a long overdue paradigm shift away from that compression of reality: Marcuse's "Happy Consciousness”  (“the belief that the real is rational and that the system delivers the goods -- reflects the new conformism …")

"Logic is a poor model of cause and effect.

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

According to the S3 reciprocity of Hands and Mind epistemological premise, not to mention common sense, the current focus of educational technology, all things computer -- The “Silver Bullet”, “The Fix -- and the assumptions supporting it, are too constricted:  Marcuse’s  pattern of “One-dimensional Thought”.

"Conventional education in physics, biology, or the social sciences treats them as separate domains … each specialty becomes a triflingly small field, unconnected with the rest.

"In contrast, the educational demands of training “Scientific Generalists” and of developing interdisciplinary "basic principles"  [STEM] are precisely those General Systems Theory tries to fill.” … interdisciplinary synthesis and integrated education." 

                                                                 von Bertalanfy, Ludwig, General Systems Theory: Foundations, 

                                                                  Development, Applications, George Braziller, 1968

"While in the past, science tried to explain observable phenomena by reducing them to an interplay of elementary units investigable independently of each other, conceptions appear in contemporary science that are concerned with what is somewhat vaguely termed 'wholeness', i.e. problems of organization, phenomena not resolvable into local events, dynamic interactions manifest in difference of behaviour of parts when isolated or in a higher configuration, etc.; in short, 'systems' of various order not understandable by investigation of their respective parts in isolation. Conceptions and problems of this nature have appeared in all branches of science, irrespective of whether inanimate things, living organisms, or social phenomena are the object of study.”

                                                      von Bertalanfy, Ludwig, General Systems Theory: Foundations, 


From this platform, the S3, with its unique "dynamic interactions" (Norbert Wiener,  Cybernetics:  Or Control And Communication In The Animal And The Machine, 1948)), leverages cognitive / perceptual processing to a higher level of abstraction through robust integration of Hands and Mind (mental and manual rotation), 

"Nature appears to have built the apparatus of rationality not just on top of the apparatus of biological regulation, but also from it and with it.

                                                      (Daniel Dennett’s ReviewAntonio Domasio, "Descarte’s Error”, 1995

Thus, Sis a tangible demonstration of of those processes at work, basic behaviors (consciousness) of the brain through mechanical concepts (switches); a cubical maze module (four tunnels = four binary (0/1) switches = gate array) offering a development of choices (control flow) to create linearly independent / dependent paths, using a ball, or symmetry in mathematics.

In Cybernetic terms, Sis a Leibniz  "germinis machinea rationcinatrix.”

A dynamic domain (Wiener Animal-Machine Control and Communication) of variety increasing, nested and recursive structures / functions / processes, a tangible, lucid demonstration of Cybernetics / Systems Thinking -- goal systems of circular, regulatory chains influencing each other.

In Fine Arts terms, Sis

"… a kind of Strange Loop, an interaction between levels in which the top level reaches back down towards the bottom level and influences it, while at the same time being itself determined by the bottom level.”    Gödel, Escher, Bach


“Art is made to disturb.  Science reassures.  There is only one valuable thing in art:  the thing you cannot explain …”  "tactile … manual space …. This answered to the hankering I have always had to touch things and not merely see them…. "  

                                                                                                        Georges Braque, Illustrated Notebooks

"The hankering.”  Like an infant who hungers to touch to understand.  

S3 is all about that magic moment, crossing the bridge between Hands and Mind, the Sciences and Art, a continuing source of fascination / puzzlement with the human experience, and its utility, from different perspectives.  

       Sas Marriage of Constructivism and Computer Learning

The core process of abstract reasoning, both motor and visuospatial skills, should work together, independent of disciplines, as the learner moves up the education spiral.

“I was particularly taken with the possibilities the S3 offers for strengthening spatial, mathematical, and problem-solving skills in children, beginning in the preschool years.  The S3 readily engages and captivates children, sustains their attention, and challenges and stretches them cognitively. Moreover, it enables children to calibrate their own complexity of play--making the S3 ideal for any age and age-mix of players, child-child or child-adult.  We have much scientific evidence to indicate that children benefit enormously from such collaborative endeavors, both cognitively and socially.”  (May 13, 2008, cc m.s.)

                                                                    Laura E. Berk, Ph.D. [Child Development, 8th Edition] (RESEARCH)

The S3 eliminates barriers by  demanding the manipulator visualize and resolve evolving spatial sets and hidden patterns, generating a succession of new mental models.


"The child must not only apply operations to objects -- in other words, mentally execute possible actions on them -- he must also 'reflect' those operations in the absence of the objects which are replaced by pure propositions.  This 'reflection' is thought raised to the second power.  Concrete thinking is the representation of a possible action, and Formal thinking is the representation [abstract thought] of a representation of possible action [with consequences]."

                                                                         Jean Piaget, "The Mental Development of the Child", 1968

These evolving transformations are self-initiated and self-regulated (Ratchet).  By allowing the manipulator to calibrate problem complexity (unintended consequences) the S3 generates abstract, discretionary and flexible thought across a wide range of intuitive-to-logical conceptual understanding.  

In other words, the manipulator must constantly re-examine and adjust chains of contradictory reference frames (boundaries which shape our thought), those of the observer as well as the observed system itself. 

"Attached to each frame are several kinds of information … 

how to use the frame … 

what one can expect to happen next … 

what to do if these expectations are not confirmed."   

                                                                                        Marvin Minsky, "Frames Systems Theory", 1975

By continuously tackling fundamental, increasingly complex and dynamic hypotheticals, the S3 manipulator is “re-inventing” mathematics, manipulating higher levels of abstraction without symbolic / numeric tools (programming evolving goal-directed patterns and relationships of square and circle):

Propositions, not just objects [simple blocks];

Ideas within a hierarchical structure; and 

Alternative possibilities within a combinational array.

In short, the S3 manipulator must develop / intuit sets of rudimentary patterns and operations, inductive (& abductive) and deductive, then revisit and reconstruct them, a spiraling step by step reconceptualization, from operational rigor to comprehensive abstraction.

Back to basics.

Reciprocity of Hands and mind.

                              The Smart Block.    The Upgrade.

                                                                    SAs Liberator

                 "Steve Jobs:  The Next Insanely Great Thing"

"I used to think that technology could help education.  I've probably spearheaded giving away more computer equipment to schools than anybody else on the planet.  But I've had to come to the inevitable conclusion that the problem is not one that technology can hope to solve.  What's wrong with education cannot be fixed with technology.  

"No amount of technology will make a dent."

                                      Steve Jobs (as quoted by Gary Wolf, The Wired Interview, 1996)                                            

As Steve Jobs says above (Is anyone listening?), Hi-Tech by itself is necessary, but not sufficient; computer learning and the S3 learning / play process are interdependent, natural partners:  both cognitive tools are needed, for different reasons, and should be seen as complementary, not competing. 

           "A Silicon Valley School That Doesn’t Compute"

"The Underlying Assumptions of Educational Technology Implementation"


                             Removing Arbitrary Barriers

Pre-K and up, arbitrary barriers between school subjects restrict the development of abstract  reasoning.

© Michael S. Sommer, Ph.D. 2015