A Partnership of Puzzlement

                                      Cognitive Payoff

The Sommer Cube (S3) is Sis about the need to reexamine the prevailing taxonomy of simple puzzle and labyrinth / maze and rolling ball toy.

It’s about paradigm shift. 

A hybrid, and orchestration of ideas:  combination of simple puzzle, labyrinth / maze and rolling ball (apparently unrelated, but in equilibrium, exploiting the symmetry of geometry and algebra, to higher and higher levels of abstraction), where intuition, naive commonsense reasoning, are prerequisites:  logic is necessary but not sufficient.

It is about Apex reasoning.  

Patterns of thought exceeding the parameters normally experienced in logical operations:  where the strategies and tactics are evolutionary.


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


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 (Animal and Machine) -- balanced, opposing, and apparently random forces.

It is about synergy.

Coordinating mental and manual 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.

While Rubik’s Cube (Machine-think:  about problem solving competence), without that paradox, exercises logic, S(about human learning proficiency) demands logic and intuition.

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.


                                                     Asynchronous Analog-Binary Processor (0/1)


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.  (learning requires negative knowledge)

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.  In cybernetic terms:

"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, 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.  

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.


                    Rolling Ball “Tilt-Switch”                                    Analog-Binary Processor (0/1)


Each S3 reorientation simultaneously reprograms the four "gravity feed” tunnels differentially, nonlinearly; each acts as a binary (0/1) logic gate (rolling ball "tilt-switch") to impede (0) / allow (1) ball flow.    

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.  


                                                       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.



                                                "Smart" Playground

                               Child Designed Puzzlement


                         (checkered paths allow exit)

© Michael S. Sommer, Ph.D, 2018