A Partnership of Puzzlement

                                     Cognitive Payoff

The S3 is a hybrid:  combined puzzle and maze and rolling ball device, where intuition is a prerequisite:  logic is necessary but not sufficient.

Sis about navigating three-dimensional problem space, with Hands and Mind.

A simple block and ball networking system which leverages full-spectrum cognitive / perceptual processing, learning algorithms, and the art of design, with an emphasis on advanced thinking and intuition -- and its reflection upon itself (not "mere facts", but principles):  functional relations, particularly goals and feedback (What are my assumptions? Are they justified?)

S3 is about paradigm shift, the need to reexamine the prevailing taxonomy of simple puzzle and maze and rolling ball toy, a demonstration of conceptual synthesis:  cognitive payoff for the manipulator is as important as hierarchy of form and function.

“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 

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.

Operationally, S"combinatory play" simultaneously requires 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, overcoming entropy by using noise as positive feedback), exciting curiosity: topology of paradox.  A cognitive development tool.  While Rubik’s Cube, without that paradox, exercises logic, Sdemands logic and intuition.

Instead of viewing space as fixed, a passive arena (simple games, puzzles and mazes), the S3 network architecture uses space and geometry as active participants in the problem universe.

S3 is about awareness of environment, modifying self-behavior on the basis of experience, through the optimization of multiple simultaneous paths, in a constant stream of evolving problems, within a topology of paradox.

Consequently, S3 demands recognition of sequence / pattern of repeating events formed in accordance with a definite rule(s) -- but different individuals can perceive the same pattern differently, reach different generalizations.  It’s mysterious.


                                                                        Binary Processor (0/1)

S3, in Norbert Wiener's Cybernetics-Teleology parlance, is a technological mechanism employing non-linear feedback controlled purpose.

"Cybernetics deals with all forms of behavior insofar as they are regular, or determinate, or reproducible.  The materiality is irrelevant …."

                                             Ashby, W. Ross, An Introduction To Cybernetics (1956)  

Pattern.  Machine.  Animal 



Rolling ball construction, works of kinetic art, simple toy to playground size should provide the manipulator with nested and evolving contradictions and the opportunity to control them:  a cognitive / perceptual partnership.


                                                  (checkered tunnels show paths)

Such a partnership of inquiry and discovery is missing with conventional rolling ball devices, offering only variations of gravity in action: a ball moving downhill (rolling / bouncing / teetering / speeding up / slowing down, on a series of abrupt / gentle inclined planes / helices), and ultimately carried back up to the top: a simple display of gravity.  

There is no mystery in that and no collaboration, no puzzlement.  No failure; no learning.

The whole point of having a ball, the fun of that relationship, is that we can control it: bounce it, throw it, lose control of it, recover it, etc.  It offers a dynamic problem-solving experience:  the exploration of symmetry, influences among parts and whole, square and circle — adaptation to accelerating rates of change and complexity of system and environment.

"Another test asks the child how it would find a ball in a field: out of all the possible paths the child must select one of the suitable few. Thus it is not impossible that what is commonly referred to as “intellectual power” may be equivalent to “power of appropriate selection”.  Indeed, if a talking Black Box were to show high power of appropriate selection in such matters — so that, when given difficult problems it persistently gave correct answers — we could hardly deny that it was showing the behavioral equivalent of “high intelligence”. 

                                                                         Ashby, W. Ross, An Introduction To Cybernetics (1956)

To put it another way, the Alexander Calder stabile here on the Parkway, with its countless possible configurations, evoked a sense of fulfillment and awe; Calder shared control of the work with the air, the breeze.  Its actions were unpredictable.

In the same way, a rolling ball system, playground size or simple toy should share a balance of competitions to create uncertainty, the need to question, to focus on process, an interplay of inductive (& abductive) and deductive reasoning, not just outcome.


The Sdoes exactly that.  And much more.  

It is not only a router, a “flying junction” (an over-and-under junction of tunnels which weave past each other), but also  a dynamic system of binary switches


housed within a cubical exoskeleton with multiple axes of rotation creating unpredictable, manipulator-controlled ball trajectories.


                                                                        Binary Processor (0/1)

Thus, the Smanipulator derives the additional satisfaction / cognitive development benefits of the working scientist creating, continuously reformulating / calibrating dynamic systems problems with changing ground rules, and then solving them -- no small task.  A rich cognitive experience.  A transformative experience.


                                                "Smart" Playground

                               Child Designed Puzzlement


                         (checkered paths allow exit)

Another partnership.

                                                       Sommer Mobius Helix

                                                                  Dual Path Helical Ramp

                                            (two balls illustrate mobius path, junctions) 



                                                                  Just like Escher's Ants

A dynamic router.  

A dual path helical ramp consisting of a wire rail formed as a helix, 

a straight rail, 

a closed transparent cylindrical wall rail,

and a ball. 

Multiple axes of rotation create unpredictable, manipulator-controlled ball trajectories.



© Michael S. Sommer, Ph.D. 2015