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

A simple block and ball networking system which leverages full-spectrum cognitive / perceptual processing, learning algorithms, and the art of design, with an emphasis on advanced thinking and intuition -- and its reflection upon itself (not "mere facts", but principles):  functional relations, particularly goals and feedback (What are my assumptions? Are they justified?)

Sis a combinational 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 programmable logic component (In Field Programmable Gate Array terms).



[Programming] "From the perspective of a user, the crucial factor is not whether the problem is intrinsically complex (suitable software can make even complex problems seem simple), but rather the cognitive resources that the user is prepared to devote to solving the problem."

                                                          Alan F. Blackwell, ˆWhat is Programming?” (2002)

             What Does SHave To Do With Our New world?  

"The S3 “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.”                                                                

                                                                   Laura E. Berk, Ph.D., Child Development, 8th Edition

Sdevelops the cognitive resources necessary to program a computer (0/1) -- but without the computer.  There is too much computer, not enough peopleness.  That is, unlike the iPhone, etc., the S3 allows us to hold on to some of the things we are losing … (see also Norbert Wiener’s, The Human Use Of Human Beings)

"Programming … The key is deliberative practice: not just doing it again and again, but challenging yourself with a task that is just beyond your current ability, trying it, analyzing your performance while and after doing it, and correcting any mistakes. Then repeat.  And repeat again." [Ratchet]

                                            Peter Norvig, ˆTeach Yourself Programming in Ten Years” (2001) 


The S3 is about pattern


the rule which governs a system or phenomenon, exactly like numeric, musical, or visual relationships -- and its simultaneous mental and manual rotation.

"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."   

                                                                                        Marvin Minsky, "Frames Systems Theory", 1975

S3 is a tangible demonstration of basic behaviors (consciousness) of the brain through mechanical concepts (switches / logic gates): 

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.

While the S3 exterior has six faces (three sets of opposing faces), each "quartered" face with one or two holes (mismatched hole quadrants block path exit between S3s), the S3 interior has four intertwined chiral tunnels (each tunnel with independent  “logic gate” orientations) with eight entrance / exits.

                          Programming Binary Logic Gates



                                Rolling Ball Switch                                              Binary Processor (0/1)


"Consider all the different things that children do, when they play with their blocks. To build a little house one has to mix and match many different kinds of knowledge: about shapes and colors, space and time, support and balance, stress and strain, speed, cost, and keeping track. An expert sometimes can get by with deep but narrow bodies of knowledge - but common sense is, technically, a lot more complicated."

                                                                   M. Minsky, "Why People Think Computers Can't", AI (1982)

S3 is about the essence of programming (declarative and imperative); it demands, gently at first, the manipulator simultaneously plan and direct multiple lines of thought, "factors of variation" (orientation, clutter, etc.), to mentally and physically rotate, differentiate and process dynamic parts and wholes, separate evolving tasks into manageable, recursive subsequences, all within evolving layers of abstraction.

Discovering and representing a system of rules (non-linear S3 code arrays; genuine vs. illusory patterns -- square / circle);

Storing operations in anticipation / preparation of patterns;

Making assignments. 

Thus, the manipulator is directly, by manual and mental rotationmanipulating things, learning algorithms and "specifying behavior to occur at some future time”, key to the thinking required to program a computer:

In Systems Analysis terms:  cyclical, dynamic process of analysis (separation into constituent parts) and synthesis (fusion of parts into whole), verification and correction, expressed as programming steps, from formulation to execution.*REDO.pdf




Picture an eleven-month old boy, holding his mother's hand, carefully watched me arrange S3s on the floor for bubble-wrapping at a Kinkos / FedEx.

I reached out (I was on the floor) and offered him the ball.  

He stared at me, then slipped out of his mothers hand and crawled over, took the ball in his hand, and stared at the S3 and the numerous options.  And he stared.  Then with great precision / confidence he placed the ball into a hole, and sure enough the ball exited (a self-checking process; it does not always exit).  

Then he looked at me as if to say, "I knew I could do that."  

By then his mother had noticed what he was doing and apologized for his disturbing us.  

Does that child [every child] have that challenge of abstract reasoning in his daily life?

Why Not?

                                      The Smart Block.      The Upgrade.*REDO.pdf

                                 We Are All Programmers


Princeton Math Department Common Room -- world-class mathematician works all day with S(on the QUAD problem) using Group Theory in mathematics (no ball) -- his son arrives late in the afternoon.  

A blonde five-year-old programs S3s at studio “... challenging players of any age and spatial-skill level.”   





      Paralegal                                                                           Entrepreneur 


"Separating Science From Stereotype"

"Sex Differences in Cognitive Functions"

"Why Are There Still So Few Women in Science?"

"Two- vs. three-dimensional presentation of mental rotation tasks: Sex differences and effects of training on performance and brain activation."



 Systems Analyst                                             




University of The Arts -- Inventor (Touchscreen Swipe)                   Innovator


And a businessman


The children and I were seated on the floor, each with a name tag, all more or less at eye level.  I began by introducing myself and explaining that “We are all inventors here.”  They were quiet as mice.  Each child had been required to bring his / her invention and explain it to the group.  Each child had to stand when presenting the device and its reasoning (MIT has never had a more serious presentation of mechanical devices and their underlying processes).

When they were finished, I stood and explained my own little idea (S3), using their own explanations as a foundation to get a little more technical, which they quietly absorbed. 

Then they broke into small groups, and began manipulating S3s, focusing on the idea that principles can evolve into working process -- just like their own inventions (for one example:  a rock which fell on a stick, which moved a leaf, which released a feather) — but in the face of paradox.  And they had fun.

Their faces tell the story … 

S3 Day at Pennsylvania Academy of the Fine Arts -- thirty children, six to twelve years old, program S3s for three hours at Inventor's Class. 

image-18 med

University of Pennsylvania, Graduate School of Education -- Milken EDSI Workshop entrepreneur face SCHALLENGES.


                 Goodbye, Gender / Adult-Child Stereotypes. 

Hello, Science Technology Engineering Mathematics


Low-tech cognitive tool.  Intelligent toy.

Hands and Mind. 

S3 Play.  

© Michael S. Sommer, Ph.D. 2015