Hands and Mind

                                      Back to Low-Tech


                                                             Classic toy                          

                                               Full-spectrum Cognitive tool  

The Sommer Cube (S3) is about exploration of situation awareness, transformation of parts and whole, square and circle, feedback and symmetry -- adaptation to accelerating rates of change and complexity of system and environment:  a cognitive development tool (manual / mental rotation studies):  a topology of paradox. 

Variations on a theme of square and circle -- flip-flop, a counterpoint of logic and intuition. 

Spatial Thinking   (space, representation, process:  multifaceted, interconnecting competencies, human and robot).

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?)


It's a big secret:  

Thinking is good for you.

"The first rule of discovery is to have brains and good luck. The second rule of discovery is to sit tight and wait till you get a bright idea."

"Analogy pervades all our thinking, our everyday speech and our trivial conclusions as well as artistic ways of expression and the highest scientific achievements."

"… the main achievement in the solution of a problem is to conceive the idea of a plan.” 

                                                                       G. Polya, How to Solve It (1945)

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

About levels of abstraction, pattern,   


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.

As any dog, cat, infant, child can tell you, there is nothing more fun than a ball,

especially a ball that seems to have its own mind and keeps getting away:  a cognitive / perceptual partnership.  Like S3

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”.  

If this is so, and as we know that power of selection can be amplified, it seems to follow that intellectual power, like physical power, can be amplified.  Let no one say that it cannot be done, for the gene-patterns do it every time they form a brain that grows up to be something better than the gene-pattern could have specified in detail. What is new is that we can now do it synthetically, consciously, deliberately."

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


Mixing that fun with stacking things, putting things inside of things, on top of things, testing things, getting frustrated and figuring the mess out, the manipulator experiences the wonder of inquiry / discovery through the S3voluntary behavior is modified and maintained by its consequences (intermittent reinforcement).

Not just step-by-step deductive reasoning (rule driven / top down), but also flashy inductive and abductive (intuition) reasoning (discovery driven / bottom up), looking for patterns, mentally “color-coding” paths, taking specific issues and deriving generalized conclusions when we are allowed to find things out for ourselves.

"The native and unspoiled attitude of childhood, marked by ardent curiosity, fertile imagination, and love of experimental inquiry, is near, very near to the attitude of the scientific mind 

                                                                                                     John Dewey, How We Think, 1910

Thus, the human mind is capable of connecting events causally long before it can formulate that level of abstraction verbally, the emerging infant begins life as a working “scientist" faced with contradictions: a creative problem solver, sucking up every bit of conceivable information, manipulating concrete objects and abstractions, making inferences and hypotheses, challenging assumptions, testing and failing, adjusting and succeeding.  (learning requires negative knowledge)


All this relates to long standing formal ideas / implementations concerning Child Development, particularly Constructivism (process discovery / task-based learning) which with rare exceptions (e.g., Friedrich Froebel, 1837, with his “sphere and cube linked by an elucidating cylinder”) never reach the child’s hand and mind.  

"The irony is that the real educational toys are not the flashy gadgets and gismos with big promises, but the staples that have built creative thinkers for decades.” ....

                                                                                 Roberta Golinkoff:  Science Daily, 2000“ 

This is S3 turf:  

Mental and Manual Dialectic:  operation and activity of abstraction, contradiction of Pattern and of Process. 



"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

                                           Why is S3 Disorienting?

S3 manipulator must, by logic and intuition, naive commonsense reasoning, mentally and manually rotate the S3 and its dynamic, interdependent, parts and hierarchical reference frames about multiple axes of rotation, while coping with ambiguous contradictions of pattern and of process. 


"Whenever one encounters a new situation (or makes a substantial change in one's viewpoint [S3 rotation] he selects from memory a structure called a frame:  a remembered framework to be adapted to fit reality by changing details as necessary....  Attached to each frame are several kinds of information… how to use the frame… what one can expect to happen next… what to do if these expectations are not confirmed …. a simplified frame-system to represent the perspective appearances of a cube." 

                                                                   Minsky, Marvin, The Psychology of Computer Vision

                                                                   McGrawHill, 1975  

In other words, S3 process and architecture of nested, confusing distinctive-feature information is paradoxical.  While the S3 exterior has six faces (three sets of opposing faces), each "quartered" face with one or two holes (mismatched hole quadrants between modules are dead-ends, and proliferate erratically), the S3 interior has four intertwined chiral tunnels (each tunnel with independent logic gate orientations) with eight entrance / exits.


                                                                      Rolling Ball “Tilt-Switch

To cope with / coordinate the resulting dynamic, tangled control structure / flow, and order of operations -- to optimize multiple simultaneous paths -- the manipulator must simulate the future, conceptually "drill down" through nested coordinate systems.

To discover order in what is seemingly random.

In other words, navigation of nested levels of abstraction (sets: binary and analog), mental discrimination / integration of different problem models, starkly contrasting conceptual frameworks (each with its own set of rules):  

CUBE exoskeleton (six faces)  >>  

HOLES quadrant (eight holes)  >>  

TUNNELS / HOLES (four couplingsgravity gate array; (four binary switches)  >> 

TUNNEL / HOLES (one binary switch). 


                  Asynchronous Analog-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.  (Think Field Programmable Gate Array.)

Each of these nested frames of reference establishes conditions / opportunities as the focal point of each frame is moved in any of three perpendicular directions.

A dynamic cycle of abstractionnested recalibration and reflection:  analogical mapping, consistently “structured representations made up of objects and their properties, relations between objects, and higher-order relations between relations.” (Structure-Mapping Theory, Dedre Gentner, 1983, 1988)

Binary and Analogical Reasoning (switch from fixed to changing values).

A structure-mapping, domain-traversing relational engine for Hands and Mind.  

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. 

In celestial motion termsthe S3 manipulator (unlike the computer-focused manipulator) faces “inherent retrograde motion”, a dynamic, immersive, mental and manual rotation of nested and interdependent frames.  It becomes increasingly confusing to formulate the problem.

"… Copernicus, who, when he did not make good progress in the explanation of the celestial motions if he assumed that the entire celestial host revolves around the observer, tried to see if it might not have greater success if he made the observer revolve and left the stars at rest”

                                                                           Kant, I., Critique of Pure Reason, (Preface to B)


                   allocentric / egocentric flip-flop spatial processing (route following, piloting, ded reckoning) 


The ability to imagine object rotation is limited by a flip-flop of rotational motion of egocentric, object-intrinsic (S3 dynamic hierarchy) and allocentric reference frames, a perceptual "relativity” of local and universal coordinate systems (moving backgrounds create the illusion of self-motion).

Everything is recursive / self referential: solutions depend on chains of solutions to smaller, and smaller, etc., sub-problems; part always requires reference to whole, over and over again. 


Consequently, successive mental and manual rotations create loss of situational awareness, failure of visuospatial reasoning.  You just keep getting stymied.

A topology of reciprocal influence of Hands and Mind.



A topology of paradox which simultaneously impedes and encourages path development, (remember, the ball must obey the law of gravity) as options, with no obvious external / internal reference frames, change in nonlinear ways.

And that’s why the S3 is disorienting.

© Michael S. Sommer, Ph.D, 2017