Cognitive Tool 

                     Full-spectrum Cognitive Engagement 


                                      Informal Reasoning:  "Use it or lose it”.

This is the story of the Sommer Cube (S3), a cubical maze module — leveraging binary and analogical reasoning in a hybrid toy:  a cognitive tool.  Analytic and holistic thinking; a competition of rational (programming desired logic functions) and nonrational.  

What does Sdo?

It kick starts intuition, the nonrational. 

Exploration in depth of the contrapuntal possibilities inherent in a cubical maze module.


S3 is about creativity -- playfulness, imagination and rigor -- in the face of real and abstract variables:  coordinating mental and manual environment, modifying self-behavior on the basis of experience, through the optimization of multiple simultaneous paths (make most paths begin / cross within a single S3), in a constant stream of evolving problems, within a topology of paradox.  (“How complex environments push brain evolution”

Sis about the tension of switchiness (compound cognitive, perceptual, mechanical flip-flop and schedule of reinforcement):  switching of relative motion and form, and navigational strategies.

Simultaneous mental (rational and nonrational) and manual rotation, giving form to binary and analogical information, a coupling between physical objects and binary information where bits are directly manipulable and perceptible.


                                                                       Rolling Ball “Tilt-Switch

A story of Spatial Thinking    (space, representation, process:  multifaceted, interconnecting competencies, human and robot), the holistic approach —  manifested by a cubical maze module, the Sommer Cube (S3) -- the rational in conflict with the intuitive, and why it is important.

In particular, Wayfinding:  spatial problem solving critically examined as cognitive tool, in conjunction with an overdue definition of Play, in operational intelligence terms, as adaptability:  cognitive payoff.  

Unleashing the instinct to think.

S3 is about the need for more learning proficiency than problem solving competence:  situation awareness, creativity, and the careful construction of logical arguments, and their limitations. 



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?)

Thus, S3 is about challenging assumptions.


                      The Smart Block.

                                                        Binary and Analogical Reasoning

                                                        (switch from fixed to changing values).

                                                        The Upgrade.     


S3 is about variations on a theme of square and circle -- flip-flop, a counterpoint of logic and intuition.


“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 

Mindwealth management.

Toward understanding cognitive development by capturing patterns of changing binary and analogical abilities.  A construction block, a cognitive tool for the education-minded consumer.

Sis about exploration of symmetry, transformation of parts and whole, square and circle --  adaptation to accelerating rates of change and complexity of system and environment, a cognitive development tool, unlike Rubik’s Cube (Machine-think:  about problem solving competence) cognitive “exercise” without paradox (according to MIT / Rubik’s Cube"Solving the cube becomes almost trivial once a certain core set of algorithms, called macros, are learned.”)

In constrast to "creativity tools" ("Brain Games are Bogus’) such as the Nine-Dot Problem ("functional fixedness" / "closed view of a problem") with, arguably, "creativity"-generating "outside-the-box" / divergent thinking and single, two-dimensional reference frame,  


                                                                   just thinking "outside the box"

each S3 is a dynamic, hierarchial Open System of interdependent, multiple, three-dimensional reference frames -- an interaction of fourteen squares and circles [not to mention reorienting connecting chiral, gravity-dependent, tunnels] to be remembered and adjusted. 

Sis about modifying self-behavior on the basis of experience (feedback), through the optimization of multiple simultaneous paths, in a constant stream of evolving problems, within a topology of paradox.  (learning requires negative knowledge)

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.

A combinational (technically “permutational", like a combination lock) logic block which contains four tunnels, effectively an array of unconnected switches to be programmed by the user as the block is rotated in space, which can be connected to other logic blocks to create multiple adaptive, simultaneous, routes by reconfigurable interconnects.

A dynamic router, an Analog-Binary Processor:  a system of programmable binary (0/1) switches, a “flying junction” (an over-and-under junction of tunnels which weave past each other) housed within a cubical exoskeleton with multiple axes of rotation and alternative, manipulator-controlled ball trajectories, offering exit in all orientations: a topology of networks.

In Cybernetic terms the S3 is a tangible demonstration of basic behaviors (consciousness) of the brain through mechanical concepts (switches / logic gates); 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 choosing patterns and networking the S3s chiral tunnels (each with its independent set of twenty-four “logic gate” orientations) there are no absolute choices, only relative choices -- the nested, interactive possibilities of the S3 change with each rotation. Everything must be questioned: 


                        Asynchronous Binary Processor (0/1)  /  three axis rotation problem space                                                                                                      

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.

(Note that Snonlinearity -- change in one variable which does not produce a directly proportional change in the result -- even in the single S3, is effectively a nonlinear expression / experience which allows one to intuitively graph the output as a curve -- very exciting stuff for the manipulator with a questioning mind.   And that’s just the first S3.)

                                  Why Corporate Play?

One fifth of employee time must be used to work on personal projects / art -- an essential part of GOOGLE'S work culture:

"Our founders built Google around the idea that work should be challenging, and the challenge should be fun … creative approaches to work, play, life."


                              Entrepreneurial Thinking

“Entrepreneurs are simply those who understand that there is little difference between obstacle and opportunity and are able to turn both to their advantage.”

                                                                                                                   Niccolo Machiavelli, The Prince

                                                                May The SBe With You.         

                      “Think Reliably and Even Gracefully 

                          About Really Hard Questions.”

"Try to acquire the weird practice of savoring your mistakes, delighting in uncovering the strange quirks that led you astray. Then, once you have sucked out all the goodness to be gained from having made them, you can cheerfully set them behind you, and go on to the next big opportunity. But that is not enough: you should actively seek out opportunities to make grand mistakes, just so you can then recover from them.

                                                               Daniel C. DennettIntuition Pumps and Other Tools for Thinking


                                 “Creativity” Training?

     Effectiveness of Creativity Training / Cognitive Skills and Heuristics … , Scott, Leritz, Mumford


   "Brain Games Are Bogus"


    "Innovation is a Discipline, Not a Cliche" 


     IBM Training  /  Mobley


   "How to Plan Innovation" … Listen to the Consumer, Carefully


      Review of Torrance Creative Thinking Tests (TTCT) / Kim


                          "Creativity:  Method or Magic?"

"Creativity may be a trait, a state or just a process defined by its products. It can be contrasted with certain cognitive activities that are not ordinarily creative, such as problem  solving, deduction, induction, learning, imitation, trial-and-error, heuristics and "abduction," however, all of these can be done creatively too. There are four kinds of theories, attributing creativity respectively to (1) method, (2) "memory" (innate structure), (3) magic or (4) mutation. These theories variously emphasize the role of an unconscious mind, innate constraints, analogy, aesthetics, anomalies, formal constraints, serendipity, mental analogs, heuristic strategies, improvisatory performance and cumulative collaboration. There is some virtue in each, but the best model is still the one implicit in Pasteur's dictum: "Chance favors [only] the prepared mind." And because the exercise and even the definition of creativity requires constraints, it is unlikely that "creativity training" or an emphasis on freedom in education can play a productive role in this preparation….    

"Creativity is a phenomenon with both external and internal contraints. The external ones concern the historical state of the problem domain and the role of the unpredictable. The internal ones concern how prepared and how "favored" (endowed) a mind is. Although there are some heuristic methods that one can attempt (such as trial-and-error induction and analogy), the best strategy one can adopt to maximize the likelihood of creativity is to maximize preparation. Maximization is not the same as a guarantee, however; although it is not magical, creativity will always remain mysterious because of the essential rule of unexpectedness and unpredictability in its defining conditions. Preparation can only provide a favorable setting for chance, not a certain one. Moreover, it is unlikely that chance or freedom -- i.e., an independent propensity for the fortuitous -- can be tutored. Apart from problem-specific preparation and open-mindedness, one's only remaining strategy is to be prepared, given one's mental, physical and experiential resources, to move on (temporarily or permanently) to other potential creative problem domains if a sufficiently dedicated and patient effort ends in unproductive, perseverative loops: Finding one's creative calling (if it exists) may itself call for some (prepared) trial-and-error sampling, guided, perhaps, by the native or acquired dictates of one's aesthetic judgment, but ever dependent for success on the vagaries of chance.

"Suggested Readings: Black, Models and Metaphors; Hadamard, The Psychology of Invention in the Mathematical Field; Harnad, Metaphor and Mental Duality; Hesse, Models and Analogies in Science; Stravinsky, The Poetics of Music; Polya, How To Solve It."

                                                         Steven Harnad, ˆCreativity: Method or Magic”, 2007


          Techniques to Spur "Creativity" -- Negative Impact.

"According to University of Oklahoma professor Michael Mumford, half of the commonly used techniques intended to spur creativity don’t work, or even have a negative impact. As for most commercially available creativity training, Mumford doesn’t mince words: it’s “garbage.” Whether for adults or kids, the worst of these programs focus solely on imagination exercises, expression of feelings, or imagery. They pander to an easy, unchallenging notion that all you have to do is let your natural creativity out of its shell."

                                                                   Po Bronson / Ashley Merryman -- Newsweek, 2010


                                 Failure of Imagination

"Business men go down with their businesses because they like the old way so well they cannot bring themselves to change.  One sees them all about -- men who do not know that yesterday is past, and who woke up this morning with their last year's ideas."

                                                                                                                 Henry Ford (Hoffman, American Icon)



                                            In Praise of the Uncluttered Mind



Mobley  ...                    

I am developing Thinking Skills.  I am one year old.  I am comfortable with that.

1)  I am not “creative” (whatever that is) – But, I have an open mind.

2)  My “assumptions” are not to be trusted – I am a baby.

3)  I must change / develop.

4)  I must “focus on questions”, not answers (whatever that is).

5)  I am “allowed to be wrong” (I am usually wrong).

6)  I must be “comfortable in an unsystematic, unstructured problem environment.”

 All my friends are babies, too.      


                                  Innovation Sandbox    



                                                S3 Play, High-tech -- Low tech

                                              (open ends / open means)



© Michael S. Sommer, Ph.D, 2017