UNCERTAINTY AS TOOL

                                 The Hidden Architecture of Play 

It’s about self-regulation. 

Enlightenment, concocting and evaluating new hypotheses.  The power of Play (here operationally defined as evolutionary regulatory arena).


                                       Let’s Raise the Bar

This is the story of the Sommer Cube (S3), a cubical maze module:  Classic toy and cognitive tool

It's about challenging assumptions.  Integrating concepts that have been carefully examined in radically different fields.

“Normal science does not aim at novelties of fact or theory and when successful, finds none." … "puzzle solving" …  [instead of] ‘paradigm shift”.

                                                                     Thomas Kuhn, The Structure of Scientific Revolutions, 1970

It’s about Mind Waste:  systematic Early Education test bias / failure because early abstract / spatial thinking can not be discerned / measured by the conventional cognitive development model and associated research methods, and is therefore ignored in the education ladder.


Thus, STEM / STEAM gender bias against "girls and minorities”.  

It’s about the acquisition / decline of abstract concepts, in Alzheimers and Autism, not to mention spatial reasoning, and education, independent of age-spectrum, the subtleties of which would be better understood using S as diagnostic tool.  

It’s about embracing a common research benchmark employing Hands and Mind  (S3 has 24 possible orientations — “switches" reset accordinglyof manipulator-formulated "tests , as Laura Berk describes it below, “calibrating their own complexity of Play”; a nested and evolving problem universe, simplest to most complex abstract reasoningIt’s about a 3D "Rorschach Test” for Spatial Thinking.

Smethodology, producing a unified picture of the spatial manipulator in a single session:  structured, with specific spatial prompts to respond to; unstructured, constructing whatever comes into one’s head; and circumventing our conscious processes, to graphically reveal our “programming", our unconscious decision process architecture.

It’s about leveraging Binary and Analogical reasoning, from concrete to abstract (a switching of “true" and “false" logical arguments presented visually and tactilely — “sameness" and “differentness” at multiple levels of abstraction in terms of relational complexity).

Hard science cognitive and educational assessment — STEM:  in a low-tech, high- yield, cost-effective format which requires intelligence, and nurtures it.

(Note:  the GAO report (4/10/13) on STEM education points out that few of the "complicated patchwork of overlapping programs" are ever assessed for their effectiveness  & "Research Recommendations from the Spatial Thinking Journal Club”) 

We have in effect already turned the world over to the children (we gave them iphones) --  our challenge is to respect that fact and support their efforts to reinvent the world, to rethink it from the ground up.  The issue is to make the children comfortable / productive in the driver's seat  -- they are already there, and they know it.  All this in the face of adult anxiousness about loss of power in this new world.

To put it another way, do the questions (research foundation) we ask at Education Conferences reflect what the children want / feel is relevant?  Or do they reflect our own turf battles, our available skills, our future? 

It’s about more learning proficiency than problem solving competence.  Creativity, in operational terms, and the careful construction of logical arguments, and their limitations.  

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”.

Binary and analogical reasoning.   

Who will speak for them?

How to go about that?  M. S. Sommer addressed the question in "Open Systems Listening: Conversation As a Research Tool”, (Ph.D. Diss.,1988), about a paradoxical environment, a hidden architecture of inquiry.  An archiecture of paradox.

S3 is predicated on 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.

In other words, Wayfinding:  spatial problem solving critically examined as cognitive tool, in conjunction with an overdue operational definition of Play in Cybernetic regulatory terms, further developed as as a Play Means / Ends Matrix:  the hidden architecture of play.

Thus, Sis about scientifically verifiable Spatial Thinking   (space, representation, process:  multifaceted, interconnecting competencies, human and robot) tools and learning opportunities are needed, for teachers as well as students, diagnostic as well as development.



Sis about effectiveness:  the interface (invites interaction and responds to it) between hand and mind, binary and analogical thinking, the application of naive commonsense reasoning versus logical algorithms.

An eminently measurable (think signal-to-noise ratio:  mental opposed to manual rotation / neurophysiological) interface (invites interaction and responds to it), a working definition of naive commonsense reasoning (in a paradoxical environment -- hierarchies of different rules and changing order of operations, principles have to be unlearned) versus logical algorithms, "naive physics”.  

(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.) PLAY AS THINKING — “DEFRAGMENTATION" / OPTIMIZATION

Toward understanding cognitive development by capturing patterns of changing binary and analogical abilities. 

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, Sconstruction is about Play without boundaries, seeing Play in operational intelligence terms (not silliness or behaviorist truism), as adaptability (“neurocognitive plasticity”): cognitive payoff.

                   How Do We Define / Capitalize On Play

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.  

“Play scholars” are missing the point, in the sense of Steven Weinberg’s "anything can be explained, and no explanation can be verified”.  The salient issue is the absence or presence of cognitive benefit, cognitive payoff.

We need to focus on play as something humans do to insure survival of the species over time, serious business (not playfulness).  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.  

Is anyone else taking up his point?  

S3 is. 

The question is:  What invisible forces are driving Play, and intuition?

                           Peel the conceptual onion to follow Slinks in science.

                                                  What it is.  What it does. 


The perspective:  Brain as evolutionary union (the whole) of analogical and binary processes, biology and experience (the parts).  The Gestalt engine (de Kreyser’s “we are furious pattern-matchers”), resolving dissonance by escalating perception:  bird’s-eye view — like Zen.

The hypothesis:  Play as evolutionary regulatory arena (survival of the fittest) for neural housecleaning (rearranging / loosening’ rigidly held intellectual content” — “pruningunused synapses), a harmony-seeking oscillatory activity; regulation of neural binary and analogical computation and plasticity.

It’s about survival of the creativist.

Play = Ashby’s Cybernetic / homeostatic "good regulator" of Intelligence (like REM sleep):  a dynamic development equlibrium. 


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

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.  

Thus, S(cognitive tool) leverages analogical and binary harmony (coherent states of opposition are preserved while that decoherence is maintained, in an evolutionary fashion).

And intuition — the nonrational — is the cognitive payoff.

S3 is combinatory play.

Ask Einstein.

"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  

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.

"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 .… viewing the brain (and hence the mind) as one organ among many, a relatively recent usurper of control, whose functions cannot properly be understood until we see it not as the boss …"

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

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)

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

S“Combinatory Play”) simultaneously demands, in C.S. Peirce’s Pragmatism terms: 

A) flip-flops of abduction (intuition) / deduction / induction, a dynamic cycle (or spectrum) of inquiry only understandable as a whole, 

B) systematically impeded by gestalt figure / ground illusion flip-flop (active resistance, error).

With Hands and Mind.

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. 

Sis about making assumptions -- making assumptions about assumptions, engaging rule-based as well as analogical based reasoning.  Reasoning relates to the sense of touch, which overrides the human interaction with complex cognitive and perceptual content in paradoxical ways.  S3’s robust integration of haptics / Hands and Mind, mental and manual rotation. 

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 exceeding the parameters normally experienced in logical operations:  Apex reasoning (think Bayesian inference -- subjective probabiity as epistemic tool).  Where the strategies and tactics are evolutionary.

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.

Sis about relative motion (flip-flop of manipulator frame of reference:  egocentric  >>  allocentric) and patterns of thought (higher levels of abstraction) in a paradoxical environment, and why and how to get the most out of them:  partnership of feedback and symmetry.  Strategies for learning and control under continuously varying context (among eccentrically rotating local" and expanding “absolute" coordinate systems) — multivariate, celestial mechanics.  

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


                 Hands and Mind — Back to Basic Research

                              Innovation -- Not Doctrine

Normal science does not aim at novelties of fact or theory and when successful, finds none."                                                                                             

                                                                                     T. Kuhn, The Structure of Scientific Revolutions (1970)  

                      "Motor Processes in Mental Rotation"

          "Is Rotation of Visual Mental Images a Motor Act?"

"The relationship between the mechanisms of visin and of visual mental imagery, such as mental rotation, has been well established. The relations between mental rotation and motor action, on the other hand, have hardly been studied …."

"Two vs Three-Dimensional Presentation of Mental Rotation Tasks"

                  Think Low-tech -- Reciprocity of Hands and Mind


                        "Manual Training of Mental Rotation in Children"

                                                  "Mental and Manual Rotation"

"The Contributions of Egocentric and Allocentric Reference Frames in Haptic Spatial Tasks"

"Assistive Technology for Cognition" - Alzheimer's / Autism (ASD)

"The increasing use of technology to help individuals compensate for cognitive impairments is one of the most notable advances in neuropsychological rehabilitation in recent years (Wilson, 2009) .... ATC refers to a range of tools that includes low-tech and mainstream devices as well as specialized technology."

"Acquisition of Internal Models of Motor Tasks in Children with Autism" (ASD)

      "… Visualization In Learning and Teaching Mathematics" 

“What is the structure and what are the components of an overarching theory of visualization for mathematics education? ….

"An ongoing and important theme is the hitherto neglected area of how visualization interacts with the didactics of mathematics. Effective pedagogy that can enhance the use and power of visualization in mathematics education (Woolner, 2004) is perhaps the most pressing research concern at this period: very few studies have addressed this topic since Presmeg (1991) reported the results of her study of classroom aspects that facilitate visualization….

“The role of visual imagery in mathematical problem solving remains an active question in educational research” (Stylianou, 2001, IV p. 232). And not only in mathematical problem solving, but in the interactional sphere of classroom teaching and learning of mathematics at all levels, the need for research on visualization remains strong."

From "Research On Visualization In Learning and Teaching Mathematics": Norma Presmeg, in Handbook of Research on the Psychology of Mathematics Education:  Past, Present and Future, 2006.

"Simultaneously develop Lower and Higher-Order Thinking Skills"

"Lower-order exercises are fairly common in existing curricula, while higher-order thinking activities are much less common. Higher-level thinking tends to be difficult for students because it requires them not only to understand the relationship between different variables (lower-order thinking) but also how to apply—or transfer—that understanding to a new, uncharted context (higher-order thinking)" ….

Hong Kong and Shanghai, two of the highest-performing systems in the world, moved away from the transmission model [teachers transmit factual knowledge to students through lectures and textbooks] a decade ago."

          "Are Constructivism and Computer-Based Learning       

                            Environments Incompatible?"

"Calls for the widespread use of computer-based educational technology often justify themselves by the potential to support some version of constructivism, seen to be a major improvement in education over more behaviorist or information transfer notions of teaching. The strong claim that computer-based educational technologies are inherently constructivist cannot be sustained because current technology largely fails to provide four key components of a constructivist environment: an engaged learner, hands-on interaction with the materials of the task, an authentic problem-solving context, and human interaction during the learning process…."

     Stephen Gance:  "Are Constructivism and Computer-Based Learning Environments Incompatible?", 2002



              Low-tech / High-tech Interface (TUI) Assessment

                        (physical cubes, etc., with input / output devices)



Sis about continuous synchronous and asynchronous 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.

Hands and Mind.

Sis a demonstration of Hegelian dialectics of pattern and of process, a mixing of different levels of abstraction, self-reference.


                                                      Asynchronous 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.

S3 is a dialectic engine of paradox, developing logic and intuition, naive commonsense reasoning; a tangible, lucid demonstration of basic behaviors (consciousness) of the brain by 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.


                                                                   Rolling Ball “Tilt-Switch

The S3 manipulator must, by logic and intuition, mentally and manually rotate the S3 and its dynamic, interdependent, parts and hierarchical reference frames about multiple axes of rotation (easily calibratable), while coping with ambiguous contradictions of pattern and of process -- and plan accordingly.  

That is, the manipulator must continuously focus on the binary (0/1) issues (part) of a given tunnel, proceed upward through the logic hierarchy to the S3(s) (whole), and then go back down the hierarchy and repeat the process (while coping with contradiction of action and environment).

An oscillating, intermittent restriction of cognition and perception within a dynamic logic hierarchy (contradictory cognitive and perceptual signals / messages at different levels, where acknowledgement of that contradiction is forbidden:  Double Bind).

Thus, S3 is transformative, a kick-start, a self-generating, self-sustaining, escalating causal loop:  an exploration of deep causal structure; an evolutionary cycle of cognitive development where the manipulator is both agent and object of change.

In behaviorist, operant conditioning terms, the S3 manipulator is both experimenter and experimental subject (rewarded with a falling ball), while the pigeon manipulator in Skinner’s Box (a topology of axioms) is simply experimental subject (rewarded with a falling ball of food); S3 switchiness: compound switching -- cognitive, perceptual, mechanical flip-flop -- and compound schedule of reinforcement (seminal issue). 

Thus, S3 is about uncertainty as tool.

The Smanipulator has the additional incentive / cognitive development benefits of a working scientist formulating a dynamic systems problem, and then solving it -- no small reward.

In other words, Sis about reference frame: allocentric (locations with respect to perspective of perceiver vs. egocentric (locations within frames external to and independent of perceiver) -- spatial processing switching -- an architecture of nested uncertainty, of constant and unexpected contradiction. 


                                                 allocentric / egocentric flip-flop spatial processing 

                                                            Come Fly Me 

                                                            Like Hand-Flying




Sis about coordinating mental and manual environment, 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, in Bateson's terms, a “Double Bind” paradox:  an environment of contradictory signals / messages at different levels, where acknowledgement of that contradiction is forbidden. 

(In Zen Koan Master tells student: "If you tell me this stick is real, I will beat you. If you tell me  this stick is not real, I will beat you. If you say nothing, I will beat you." Student escapes the paradox by changing the "level of communication”.  She takes the stick from the teacher, and breaks it.  Thus,  Zen mechanics (cognitive flip-flop) of enlightenment, with an implicit injunction forbidding discussion of the contradiction -- the sanity / wisdom of the Master.)

The same issues were addressed years ago in another form (Michael S. Sommer, “Open Systems Listening:  Conversation As a Research Tool”Ph.D. Diss.,1988):  which describes the discovery and avoidance of an unintended paradoxical environment, its inherent research bias (the system of rules, the blocking environment of paradoxical verbal / nonverbal messages) of what is called the Focus Group (a topology of paradox, with one-way mirror and "Chilling Effects of Surveillance"Philip Zimbardo / Gregory White’s “aversive surveillance on opinion inhibition).  What people hear is not what is going on (think signal-to-noise ratio:  orientations to solution, etc.) 


Exactly what are the effects of a topology of paradox (Sor cockpit) on Animal / Machine?              

Is discovery through paradox a significant tool?  It is for the followers of Zen (cognitive mechanics).

Does the Constructivist Theory of Learning (APOS) support / address S^3 levels of abstraction ?  

Does the switching, the SDialectic (mental and manual rotation), repetitive flip-flop”, abrupt, continuous change in context (gestalt illusion), structure of reasoning (inductive - abductive / deductive), etc., develop / impede the decline of abstract thought?  Why?


What are the benefits of the S3 demand for visuospatial reasoning by simultaneous mental and manual (unlike computer assisted learning) rotation?  How is it different from TUI (Tangible User Interface)?

Is the absence of that simultaneous mental and manual visuospatial training a significant weakness in computer assisted learning, particularly before middle school? 

What are implications of mental and manual rotation, analogical connection of high-level perception in visuospatial terms across the age-spectrum, for the study / amelioration of Alzheimers / Autism (ASD)?

Light can be shed on these questions by "asking" Smanipulators to describe their frames of reference, their reasoning for their reasoning, regarding their wayfinding ability / navigation strategies.  ("Ask" by "subtextual" word and deed in such a way that the evident superiority of the expert is minimized -- the subject is the expert, the researcher must be “ignorant.”

The dialectical epistemological premise, uncertainty as tool, of the S(cognitive tool for the individual -- internal dialogue) is rooted in Synthesis of Cybernetics and Systems Thinking: communication / signal operating in an unfriendly (blocking) environment, was introduced in “Open Systems Listening:  Conversation As a Research Tool”, 1988  (Listening Post:  cognitive research methodology for group -- 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 

A topology of paradox.

"… 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


Protocall analysis:

"Ask" why they learn best (seeing things, or touching things, or thinking about things) -- their own learning / cognitive strategies.

“Disciplined first-person accounts should be an integral element of the validation of a neurobiological proposal, and not merely coincidental or heuristic information.

                      Varela, F., "Neurophenomenology:  A Methodological Remedy To The Hard Problem” (1996)

Frame / calibrate those "naive" insights along simple, commonsense, researchable axes (how / why / what they did, tried to do, failed / succeeded in doing, etc.

Calibrate S3 manipulation and those insights against base-line (visuospatial / creative thinking / abstraction, etc.). 


© Michael S. Sommer, Ph.D, 2018