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                                 We Are All Programmers

[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)


The Sommer Cube (S3) is about programming.

It’s about Cybernetics quivalent of MIT model railroad network switches.

“Come play with me.”

Goodbye, Gender / Adult-Child Stereotypes. 

It's about exploration in depth of the contrapuntal possibilities inherent in a cubical maze module.  A system of programable logic blocks.

Leveraging both analogical and binary reasoning — the exoskeleton circumscribes a system of linkable tunnels. where changing questions of function, role and position determine meaning,

Each 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 of multiple simultaneous passages, changing dead-ends and thruways.

Soon, with additional S3, logic alone will fail; governing rules, consistent patterns and trends become problematic.

Thus, it’s about self-regulation of analytic and holistic thinking; a competition of rational (programming desired logic functions) and nonrational.

Compounding logical arguments

Thus, it’s about grasping everyday complex functional relationships solved and displayed 

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Changing (24 S3 attitudes), robust (multiple input / output), tunnels (tilt-switch / rule) "function box”.

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.  Causal interaction within dynamic core.  Patern-matching.

"… the logic of dichotomies ….  A container shall be provided with holes in such a way that they can be opened and closed.  They are to be open at those places that correspond to a 1 and remain closed at those that correspond to a 0.  Through the opened gates small cubes or marbles are to fall [gravity] into tracks, through the others nothing.  It [the gate array] is to be shifted from column to column as required."

                                                                            Leibniz, G.W., "De Progressione Dyadica -- Pars 1", 1679 


                  Rolling Ball “Tilt-Switch             four bit (0/1) — nibble

(Think of the ball as “ping”:  a network test for reachability.  Part of the methodological process of logical reasoning, the logical argument — ike the "function box" above.)

In operational terms, S3 with its nested reference frames creates an interdependence of analogical and binary reasoning, transformation to higher and higher levels of abstraction, much as algebra (“al-jabr”:  reunion of broken parts) converts geometry into algebra by other means (Cartesian Plane). 


A coupling between physical objects and binary information, where bits are directly manipulable and perceptible.  (Physical and Virtual Reality)

It’s 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.

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




"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.

"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 about classic toy (Tate Museums) and cognitive tool (developmental and research).

Five-year-old programs S3s at studio.


Systems Analyst                                             


It’s about patterns.

And switchiness.

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.)

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.



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

"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)

Simply put, S(a motile) is a work of art (SPACE AS ART (STEAM)of 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.  

Thus, children formulating Spatial Systems Problems in an Art Museum.

Science as the Arts by other means.

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.  STEAM.


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 … 

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 afternoon.  



                          Programming Binary Logic Gates





                               Rolling Ball Tilt-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.  

S3 is about Distributed Communication Network -- regulatory switching:  synchronizing concurrent communication / interference among S3s (each a three axis rotation problem space):  

It’s about continuous synchronous 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 (Boolean algebra -- a way of seeing new structures -- fundamental to the design of binary computer circuits and programming language).  

Note that individual S3 logic elements do not necessarily have a discrete true / false state at any given time; simple Boolean, bivalent logic is inadequate for this, thus extensions are required.


Thus, 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)





Borrowed S3 lives in Beijing  


Cog Sci 16 




University of Pennsylvania, Graduate School of Education -- Milken EDSI Workshop entrepreneurs 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