Symmetry Under Transformation

                                   Cubical Maze Module

                                              a necessity


                          To Support and Strengthen the Disposition to Go On Learning Throughout Life 




"Steve Jobs:  The Next  Insanely Great Thing." 

"I used to think that technology could help education.  I've probably spearheaded giving away more computer equipment to schools than anybody else on the planet.  But I've had to come to the inevitable conclusion that the problem is not one that technology can hope to solve.  What's wrong with education cannot be fixed with technology.  

"No amount of technology will make a dent."

                                      Steve Jobs (as quoted by Gary Wolf, The Wired Interview, 1996)

The sense of touch overrides the human interaction with complex visual content in important ways.  The power of touch is missing in computer learning -- a computer learning deficit. 

TABLE OF CONTENTS --  follow multiple scientific perspectives with Links. 

REVIEWS                                                                                 MODELS OF MIND

PROGRAMMERS                                                                                COGNITIVE TOOL (low-tech)

IDEA                                                                                                     INQUIRY / DISCOVERY

          ARCHITECTURE / ENGINEERING                                            MATH / RATCHET

          BLOCKS  / HANDS & MIND                                                       LOGIC

          PUZZLEMENT                                                                           PROBLEM SPACE

          SPACE  AS ART                                                                        RESEARCH

                                                                                                             STEM WITHOUT BOUNDARIES

          QUAD PROBLEM                                                           PLAY  AS THINKING

          CHALLENGES                                                                          ALGEBRAIC PLAY 

                    COMBINATIONS / GAMES                                             “CREATIVITY” / INNOVATION 

                    COURTYARD                                                       ROOT / SYSTEMS THINKING

                    AIR BALL TOWER                                                APPENDIX - PHOTOS



                                                                              open your mind


The Smart Block.    The Upgrade.        "What’s in your child’s playroom?"

The operation of abstraction, self-challenge: the Sommer Cube (S3).

"… 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.”    (del, Escher, Bach)


A robust, low-tech cognitive tool: thinking with Hands and Mind (note manual / mental rotation studies -- unlike "mouse learning" / computer learning).  "Brain Games are Bogus.

A system that leverages cognitive / perceptual processing, algorithms, and the art of design with an emphasis on advanced thinking.

The embodiment of Albert Einstein's "Combinatory Play"

(visuospatial:  analogical mapping and processing);

Especially Mathematics (science of patterns) Play (without symbols) --

a geometry of paradox (asymmetric, nested self-reference and contradiction).


From developing mind to powerful intellect:

infant, child or world-class mathematican. 


The "transformative" nature of Its challenges and games

(dynamic cycle of concrete and abstract reasoning),



From manipulation (manual and mental rotation) to research 

(Autism, Alzheimer's, visuospatial, etc),


The S3 offers a true "parallelism of general cognitive fields", 


"I'd like to see the S3 in every preschool and elementary school classroom, and in the home of every family with young children.”  

                                                                             Laura E. Berk, Ph.D.  Child Development, 8th Edition (cc mss)


crucial to the development / exercise of visuospatial reasoning in

Science Technology Engineering Mathematics (& Art), 

(particularly in the formative years).

How to think. 

Freedom to think.

And it's fun.



                         Cognitive Tool / Classic Toy


    (S3s in every pre-K “block corner” / elementary school: explore abstract concepts)

PROGRAMABLE LOGIC BLOCKS ("binary" -- Combinational Gate Array)

    (“Levels:  High School (9-12), College, Research …  

     Math Topics:  Higher-Dimensional Geometry, Topology”)









wall flower 2 crop copy crop 2

                                                                           "l'espoir vis en moi'


(3” X 3” X 3”)

(6” X 6” X 6”

(12” X 12” X 12”) 



© Michael S. Sommer, Ph.D. 2014