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                                 We Are All Programmers

The Sommer Cube (S3) is about "dynamic modeling”, constantly updating and making adjustments to one’s own thinking:  learning from myriad and nonlinearly increasing “permutations” of dead-ends, and decreasing thruways, where the evolving errors of interdependent feedback loop information serve as teacher, revising behavior and blueprints for thinking.

"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(April 10, 2008, cc m.s.)

It’s all variations on a theme of square and circle -- flip-flop, a counterpoint of logic and intuition.


                 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.)

(Note that Snonlinearity -- change in one variable which does not produce a directly proportional change in the result -- even in the single S3, is effectively a nonlinear expression / experience which allows one to intuitively graph the output as a curve -- very exciting stuff for the manipulator with a questioning mind.   And that’s just the first S3.)

                          Programming Binary Logic Gates





                                Rolling Ball Switch                             Asynchronous Analog-Binary Processor (0/1)



Thus Sis about the essence of programming; 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.

In other words, we are all programmers — but not limited to programmatic thinking.

A programmable logic component (In Field Programmable Gate Array terms); think of bus architecture, plug-ins, simple logic circuits.  


[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)

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 tsk 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.

                                                                     Peter Norvig, “Teach Yourself Programming in ten Years” (2001)

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?)

S3 is a combinational (technically “permutational”, like a combination lock) logic block which contains four tunnels, effectively an array of unconnected, gravity-dependent switches / routers to be programmed (with or without a ball) by the user as the block is rotated in space, which can be connected to other logic blocks to create multiple adaptive, simultaneous routes (network theory), depicted physically or logically.  An architecture of nested dichotomies.

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.

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.

"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)

In other words, programming is more than binary / logical manipulation.

Simply put, S(a motile) is a work of art (SPACE AS ARTof bare utility, like mobile and stabile (remember Calder’s play circus), a machine which offers abstraction of form and function, as well as cognitive payoff, for the manipulator.  

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. 


Thirty 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 … 

                 Goodbye, Gender / Adult-Child Stereotypes. 

Hello, Science Technology Engineering Mathematics. 


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.




"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.



Cog Sci 16 


 Systems Analyst                                             




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


And Businessman


University of Pennsylvania, Graduate School of Education -- Milken EDSI Workshop entrepreneur face S3 CHALLENGES.




To repeat, each S3 reorientation simultaneously reprograms the four "gravity feed” tunnels differentially; each acts as a binary (0/1) logic gate (rolling ball "tilt-switch") to impede (0) / allow (1) ball flow.

That is, negotiating conflict, efficiently directing multiple concurrent interactions, resources and asynchronous procedures, in an expanding distributed network.

Discovering and representing a system of rules;

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.

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) 

Sis 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 attentionrelative motion and formand navigational strategies.

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:  a partnership of feedback and symmetry.


                                                                                                  Rolling Ball “Tilt-Switch

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

(From child to super-mathematician, the Smanipulator has only one path:  reason / intuit up the original "evolution of mathematics” ladderfrom things, to abstractions of things, to binaryness, to geometryness, to algebraness, to setness -- create more sophisticated problem models, know what the laws are.) 


Kinko’s playroom.

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

I reached out (I was sitting 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 (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?                                                        *REDO.pdf*REDO.pdf

Low-tech cognitive tool.  Intelligent toy.

Hands and Mind. 

S3 Play.  


                    The Smart Block

                                                        Binary and Analogical Reasoning

                                                        (switch from fixed to changing values).

                                                        The Upgrade.       

© Michael S. Sommer, Ph.D, 2018