"Transire suum pectus mundoque potiri”     

                                              "Rise above oneself and grasp the world."  (Archimedes)                        

                              Thinking Without Boundaries

Toward a Science of Play (here defined as evolutionary regulatory arena) — cognitive and educational assessment — STEM / STEAM:  in a low-tech, high-yield, cost effective format which requires fluid intelligence, and nurtures it.


The story of the Sommer Cube (S3), a cubical maze module — leveraging binary and analogical reasoning as both classic toy and cognitive tool (developmental and research).  Analytic and holistic thinking; a competition of rational (programming desired logic functions) and nonrational.  Thinking about thinking as play.

It’s about self-regulation.  And enlightenment.

Concocting and evaluating new hypotheses:  science is a question, not an answer.  Any child knows that.


                 S3 supporters speak out at  CONSTRUCTION BLOCKS (Analog-Binary Processor)

In other words, S3 is about the need for more learning proficiency than problem solving competence:  ("tin-can”) creativity, in operational terms, and the careful construction of logical arguments, and their limitations. 


For anyone, across the age spectrum. 

What does Sdo?

It kick starts intuition, the nonrational. 


In information processing / Cybernetic terms,  "Distributed Adaptive Message Block Network", in Paul Baran’s Internet terms, in a low-tech format.  A fractal command and control, strategic and tactical planning challenge.

(Think of the ball as “ping”;  a network test for reachability.)


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).

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?)



In other words, In operational terms, Swith its nested reference frames creates an interdependence of analogical and binary reasoning, transformation to higher and higher levels of abstraction, much as algebra (“al-jabr”:  reunion of broken parts) converts geometry into algebra (and vice versa) with the Cartesian Plane.    CHALLENGES / GAMES 

Thus, Sconstruction is about seeing Play in operational intelligence terms (not silliness or behaviorist truism), as adaptability (“neurocognitive plasticity”):  cognitive payoff.  

Play = Ashby’s Cybernetic / homeostatic "good regulator" of Intelligence (like REM sleep).


            (Analogical x Binary reasoning  >>  Probabilistic reasoning  >>  Intuition.) 

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.  


“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.” 

                                     Laura E. Berk, Ph.D.  Child Development, 8th Edition (May 13, 2008, cc m.s.)

"Recognizing Spatial Intelligence", SCIENTIFIC AMERICAN (2010) 

                 S3 supporters speak out at  CONSTRUCTION BLOCKS (Analog-Binary Processor)

S3 is transformative, a kick-start, a self-generating, self-sustaining escalating causal loop:  an exploration of deep causal structure (in "hard science”, beyond behaviorist psychology descriptive terms -- think endogeneity); an evolutionary cycle of cognitive development where the manipulator is both agent and object of change. 

In operational terms, Silluminates / integrates diverse problem sets (classes) across a broad range of disciplines  CHALLENGES / GAMES  as algebra (“al-jabr”:  reunion of broken parts) facilitates the solution of geometry problems by other means (Cartesian Plane).  Like analytics.

S3 is about variations on a theme of square and circle -- flip-flop, juxtaposition across three dimensions.  A counterpoint of logic and intuition.

S3 is about 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. 


In other words, the S3 physical state embodies the binary state of the system, as well as the analogical. (think Tangible User Interface -- TUI)

                                                      Pre-K and Up  

                                                          Informal Reasoning:  "Use it or lose it”.


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.


In other words, knowledge generation that manipulator can both express and demonstrably use -- avoiding what Whitehead called “inert ideas” -- propositional knowledge that the student could express but not use.

“Summing up the formal characteristics of play we might call it a free activity standing quite consciously outside "ordinary" life as being "not serious," but at the same time absorbing the player intensely and utterly. It is an activity connected with no material interest, and no profit can be gained by it. It proceeds within its own proper boundaries of time and space according to fixed rules and in an orderly manner. It promotes the formation of social groupings which tend to surround themselves with secrecy and to stress their difference from the common world by disguise or other means.”

                                                                                         John Huizinga, Homo Ludens, 1938

Ask Albert Einstein. (CONSTRUCTION BLOCKS)


“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 uncertainty as tool.  

Thus, S3 is about levels of abstraction, pattern, "'voluntarily' reproduced and combined", the rule which governs a system or phenomenon, exactly like numeric, musical, or visual relationships; patterns of thought (and their systematic breakdown -- learning requires negative knowledge), intuition, under simultaneous mental (rational and nonrational) and manual rotation.  Apex reasoning, patterns of thought exceeding the parameters normally experienced in logical operations:  where the strategies and tactics are evolutionary. 

"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)

The question is, Machine-think or Human-think?  Remember, we can switch how we think  re-program ourselves.  We are all programmers  but not limited to programmatic thinking.  Enter S3.

Sis about the tension of switchiness (compound cognitive, perceptual, mechanical flip-flop and schedule of reinforcement — reversal learning":  analogical reasoning, instrumental learning):  switching of directed attention, relative motion and form, and navigational strategies:  thinking within a topology of paradox

Control under continuously varying context (among eccentrically rotating local" and expanding “absolute" coordinate systems) — multivariate, celestial mechanics.

While Rubik’s Cube (Machine-think:  about problem solving competence)without that paradox, exercises logic   

(according to MIT / Rubik’s Cube"Solving the cube becomes almost trivial once a certain core set of algorithms, called macros, are learned.”)S(about human learning proficiency) demands logic and intuition. (note "Brain Games are Bogus.) 

The key is cognitive payoff. 


                                     But, What is Play?

                            Why is Adult Play Important? 

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."

Think particularly Einstein’s seminal "Combinatory Play” above, play with the opportunity for simultaneous high-level reasoning, and manual experience, Hands and Mind (note mental and manual rotation studies), essential in the very early years. 

Thus, seminal question:  What is the functional significance of the difference states of play?  Does state make a significant difference?  Why?  

Why quibble?   

Ask Humpty Dumpty.

"When I use a word," Humpty Dumpty said in rather a scornful tone, "it means just what I choose it to mean -- neither more nor less." 

"The question is, “ said Alice, "whether you can make words mean so many different things." 

"The question is,” said Humpty Dumpty, "which is to be master -- that's all."

                                                                                                       Lewis Carroll, Alice In Wonderland, 1865

Ask Cybernetics’ Ashby.

"It might seem that one could make practically any assertion one likes ... and then ensure its truth simply by adjusting the definitions. 

                                                       Conant / Ashby, "Every Good Regulator of a System Must Be a Model of That System” 1970 

(Experts are missing the point, in the sense of Steven Weinberg’s "anything can be explained, and no explanation can be verified” [the supernatural]:  “Intelligence" and “Play” are analytically isolated, made into equivocal benchmarks, instead of synthesized as dynamic equilibriumparts of a whole (intelligence) regulating cognitive benefit, cognitive payoff.) 

Einstein’s thesis, "combinatory play seems to be the essential feature in productive thought” (as distinct from simple hypothetical reasoning) should be rigorously examined experimentally, particularly in the face of todays ubiquitous computer-focused learning / play, and the unfortunate prevailing wisdom that "playful attitude" has some kind of predictive value.

In a sense, the snowstorm of uses of the term Play, in behavioral psychology descriptive terms, is the problem (think endogeneity) with inevitable confusion across the aging spectrum and cost of lost opportunity:

The words we use today to describe play severely diminish the importance of the mental activity involved — the evolutionary regulatory activity (it’s about survival) in a no holds barred arena.

Like the children below playing at recess.



The present terminology reinforces the notions of silliness and stifles interest in a scientific definition of play:

Educational "Play"  vs. "Free Play"  vs. "Playfulness" vs. "Playful Learning"  vs. "Old Fashioned Play", etc.

Not to forget other "expert” terms: 

Active Play; Arts Play; Associative Play; Collaborative Play; Competitive Play; Communication Play; Construction Play; Cooperative Play;
 Creative Play; Deep Play; Developmentally supportive Play; Directive Play; Diversional / Recreational Play; Dramatic Play; Exploratory Play; Fantasy Play; First Pretend Play; Functional Play; Group Play; Imaginative Play; Imitative Play; Independent Play; Language Play; Large-motor Play; Locomotor Play; Manipulative Play; Mastery Play; Motor / Physical Play; Non-Directive Play; Object Play; Onlooker Play; Parallel Play; Physical Play; Pretend Play: Quiet Play; Recapitulative Play; Risk-taking Play; Role Play; Rough and Tumble Play; Rule-governed Play; Sensory Play; Small motor Play; Social Play; Social Bids Play; Socio-Dramatic Play; Solitary independent Play; Structured Play; Substitute Play; Symbolic Play; Therapeutic Play; Unoccupied Play, etc. 

Instead, let’s approach it in "hard science" terms — exploration of deep causal structure.

Seminal researchable question:  Does increase / decrease in Play (like REM sleep) make a difference?  Why?  


                          The Hidden Architecture of Play 

                                    Play Without Boundaries

Remember, this is the story of a "Distributed Adaptive Message Block Network", in Paul Baran’s Internet terms, in a low-tech format. (Think of the ball as “ping”:  a network test for reachability.)


Play in operational intelligence terms, as Adaptability (neurocognitive plasticity):  cognitive payoff.    


             Play = Ashby’s Cybernetic / homeostatic "good regulator" of Intelligence.

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

Think of play as “defragmentation" / optimization (balancing discrete parts of a dynamic development equlibrium -- intelligence whole -- with Hands and Mind).  A self-regulation, load reduction:  "… NFB (neurofeedback) tunes brain oscillations toward a homeostatic set-point which affords an optimal balance between network flexibility and stability”, "Tuning pathological brain oscillations with neurofeedback”.  

In other words, mental processes reach beyond brain.  Play capitalizes on that.

Let's look at it as simply as possible:  play with freedom of means and ends,  “free” play / learning.


Logical-mathematical intelligence                 S3              benchmark

Verbal-linguistic intelligence

Spatial-visual intelligence                              S3              benchmark

Naturalist intelligence

Musical intelligence                                      

Interpersonal intelligence                               S3

Intrapersonal intelligence                               S3

Bodily-kinesthetic intelligence                        S3  

(Howard Gardner)

"Children play naturally, and it is through natural play that children practice reasoning. Children who are manipulated into play by teachers who think that this will improve their reasoning will soon learn to resist the manipulations.  Play, in the long run, is only play if it is self-chosen and self-directed. Children practice reasoning in their own ways, through their own self-chosen play; we can't do it for them and shouldn't try.

                                                Peter Gray, "The Value of Play II: How Play Promotes Reasoning”

Thus, to repeat, S3 is about levels of abstraction:  abstraction of pattern, "'voluntarily' reproduced and combined", the rule which governs a system or phenomenon, exactly like numeric, musical, or visual relationships; patterns of thought (and their systematic breakdown -- learning requires negative knowledge), under simultaneous mental and manual rotation.

                   The Smart Block

                                                        Binary and Analogical Reasoning

                                                                        (switch from fixed to changing values).

                                                        The Upgrade.     

The Cybernetics equivalent of a model train set.

The Zen koan mechanics of enlightenment.

Mind and Machine as fugue.


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

                    (hydrodynamic drag) — (Poohsticks 

"In terms of definition, play behavior is characterized as an unstructured self-amusement activity that has a goal in itself, and it can either be governed or not by prior rules (Brougère and Wajskop, 1997; Bomtempo, 1997; Biscoli, 2005).  Also characterized as free play are the activities that include the child’s voluntary decision, i.e., it is the child who decides when, how, where and, if necessary, with whom to play (Queiroz et al., 2006)."

                                                              Cordazzo, Almeida, Vieira (2011) Educational Research

Scientifically verifiable Spatial Thinking tools and learning opportunities are needed, for teachers as well as students, diagnostic as well as development.

Science Technology Engineering Mathematics -- the future of the U.S. is on the line.

STEM development should be about power -- first, the power of abstract reasoning and then its practical application -- right from the beginning (bottom-up, in addition to top-down).  Spatial processing -- (teaching and learning).

"Spatial ability and STEM:  A sleeping giant for talent identification and development.

                                                    "What is Play?"   

                                                             "What is Playtime 12?”

                                                               "Play As Mathematics"

                                   "How Play Promotes Reasoning

The core process of abstract reasoning (the barber pole below), both manual and visuospatial skills (independent of disciplines), should work together as the learner moves up the education ladder. 

The computer and the S3 learning / play process are natural partners:  both are needed, for different reasons, and should be seen as complementary, not competing. (RESEARCH) 

             Marriage of Constructivism and Computer Learning

                          Full-Spectrum Cognitive Partners   


                             Across the Aging Spectrum

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."

                 Self-determination:  "The Project Approach"

                     Critical Mass:  S3 "Play With Learning" 

Behaviorist / Cognitivist / Constructivist / Experiential / Social and Contextual



                "A Mandate for Playful Learning in Preschool: 

                               Presenting the Evidence"

Executive Summary

“Play has become a 4-letter word.  In an effort to give children a head start on academic skills like reading and mathematics, play is discouraged and didactic learning is stressed. This book presents the scientific evidence in support of three points: 

1) Children need both unstructured free play and playful learning under the gentle guidance of adults to best prepare them for entrance into formal school; 

2) academic and social development are so inextricably intertwined that the former must not trump attention to the latter; and 

3) learning and play are not incompatible; learning takes place best when children are engaged and enjoying themselves.

 “The argument is organized into three chapters.  The first describes the current crisis in preschool education and suggests that the lack of attention to play and playful learning lies at its core.  We propose that there exists a false and counterproductive dichotomy between play on the one hand and learning on the other.  This dichotomy is echoed in society at large as parents are influenced by the media and the marketplace to buy “educational” toys and restrict free play.  While supporting the need for accountability and assessment, we suggest that the current emphasis on assessment in higher grades has lead to narrowly defined curricula objectives in the preschool.  Curriculum development has been more responsive to the practical constraints of assessment than to the findings of evidence-based pedagogy. 

 “The second chapter presents the evidence that play and playful learning enhance academic, social, and emotional outcomes in preschool. Playful learning, and not drill-and-practice, engages and motivates children in ways that enhance developmental outcomes and life-long learning.  After defining play and playful learning, we examine assumptions about how children learn and suggest that preschools are no longer teaching the “whole” child.  The weight of the evidence, from random assignment to correlational to intervention studies, suggests that both free play and playful learning create optimal environments for achievement.  Additionally, children in developmentally appropriate classrooms often show less anxiety and stronger social skills.  

 “The epilogue moves from data to application, presenting seven principles that are derived from the science that inform preschool pedagogy.  These principles reflect consensus across the learning sciences for how children learn best.  If followed, these principles can contribute to the creation of preschools that will be equipped to educate the work force and citizenry for this new century." 

In press, Oxford University Press:  Kathy Hirsh-Pasek, Temple University; Roberta Michnick Golinkoff, University of Delaware; Laura E. Berk, Illinois State University; Dorothy G. Singer, Yale University.


© Michael S. Sommer, Ph.D, 2018