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                                     Space As Dialectic 


                                      A Conspiracy Of Pattern

The Sis about navigating three-dimensional problem space (like flying), with Hands and Mind.

Sis a work of art of bare utility, like mobile and stabile, and offers abstraction of form and function, as well as cognitive payoff, for the manipulator.


Sis mysterious:  Sand manipulator are engaged in a joint process of change -- the collapse of the expectation of a logical universe.   Art as the promise of change, and self-reflection. 

 “The most beautiful thing we can experience is the mysterious.  It is the source of all true art and all sciences.”

                                                                                                     Albert Einstein, Living Philosophies (1931)


Sachieves this by leveraging full-spectrum cognitive / perceptual processing, advanced thinking and intuition -- and its reflection upon itself.  Contradiction between action and environment.  

More on that below.  

"I shall understand the term "art" in its broadest connotations--perhaps broader than the American Society for Aesthetics would normally recognize: I shall understand art to include all artifice, all human invention.

                                                               Daniel Dennett, Memes and the Exploitation of Imagination

                   Potential Energy -- Form and Its Negation


“One must first of all study geometric forms: the cone, the cube, the cylinder, the sphere.”

                                                                                  Paul Cézanne, Letter to Emile Bernard 


                                                                                                                             Binary Processor (0/1)

 "[The universe] cannot be read until we have learnt the language and become familiar with the characters in which it is written. It is written in mathematical language, and the letters are triangles, circles and other geometrical figures, without which means it is humanly impossible to comprehend a single word.” 

                                                                                                        Galileo Galilei, Opere Il Saggiatore, 1623

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.   

S3 are "pattern blocks", which create porous polyhedron "chains" formed by distinct collections of figurative elements:  circles and squares.

Consequently, S3 demands recognition of sequence / pattern of repeating events formed in accordance with a definite rule(s) -- but different individuals can perceive the same pattern differently, reach different generalizations.  It’s mysterious.


“Symmetry and order do not make a composition.  It is the apparent accident to regularity which the artist actually controls, by which he makes or mars a work.”

                                                                                                                   Alexander Calder: Interview

"The scientist is always working to discover the order and organization of the universe, and is thus playing a game against the arch enemy, disorganization."

                                                Norbert Wiener, The Human Use Of Human Beings, 1950


Symmetry under transformation.

Juxtaposition of square and circle across three dimensions.

A self-generating, self-sustaining, escalating causal loop, where objects / ideas are taken to pieces, analyzed, and reassembled (a cycle of cognitive development where the manipulator / observer is both agent and object of change).

Thus, S3 as art in action, in process, consistent with Albert Barnes’ idea that "fine art consciously undertaken as such is peculiarly instrumental in quality ... a new training of modes of perception.”  Hands and mind.




The S3 universe consists of an architecture of nested dichotomies:  contradictions of reason and perception, frames of reference, of logic, pattern and process, motion and stasis -- that "game against the arch enemy, disorganization."

But instead of viewing space as fixed, a passive arena, the S3 network architecture uses space and geometry as active participants in that problem universe.  It embodies Braque’s "hankering … to touch things”, that union of hand and mind, the art work of the Cubists, and others as far back as the dark world of the Patagonia, Lascaux, and Altamira Cave paintings (30,000 BC).  


Thus, Sis a dialectic engine of paradox, developing logic and intuition; a tangible, lucid demonstration of basic behaviors (consciousness) of the brain through mechanical, instrumental concepts: a contradiction.  It overrides the human interaction with complex cognitive and perceptual content in paradoxical ways.   Like the the Stone Age cave paintings (variations of pigment intensity to create chiaroscuro, and use of natural cave contours to convey subject three-dimensional effect).

It disturbs.

“Conflict is the gadfly of thought.  It stirs us to observation and memory.  It instigates invention.  It shocks us out of sheep-like passivity, and sets us at noting and contriving…conflict is a sine qua non of reflection and ingenuity.”

                             John Dewey, Human Nature and Conduct: An Introduction to Social Psychology, 1930



                                                                                  Tessellating Space

The eye presents the mind with that conflict: competing interpretations, paradox; none is satisfactory.  We can be conscious of that tug of war and think about it, and play with it -- the collapse of our expectation of a logical universe.

A topology of paradox.

"Topology is therefore more than a branch of geometry, or geography, or medicine. It deals with art, language, and perception. It is a dialectical space in which ontology and topography meet."

                                                                                  Ben Stol Tzfus, "Robbe-Grillet's Dialectical Topology" (1982) 

"… 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.”   

                                                                                                   Douglas R. HofstadterGödel, Escher, Bach


“Art is made to disturb.  Science reassures.  There is only one valuable thing in art:  the thing you cannot explain …”  "tactile … manual space …. This answered to the hankering I have always had to touch things and not merely see them…. "  

                                                                                                        Georges Braque, Illustrated Notebooks

The “hankering.”  Like an infant who hungers to touch to understand.  

S3 is all about that magic moment, navigating space, crossing the bridge between Hands and Mind, continuing fascination / puzzlement with the human experience: 

In the beginning there was only the nipple, greedy cognition and perception.  Change, and the promise of more change, and self-reflection.

                                       "The Hankering  


                                                Mind and Machine (as Fugue)

                                                                                  S3 Sculpture 


                                                           Maquette   ”trompe l’oeil / trompe l’esprit" 


                                           Mind And Plane

91055-CT~Philosopher-with-an-Open-Book-1625-7-Posters x

The Sabove, with its conspiracy of pattern, selected Michael Sommer photos, and numerous works of Cubist and Renaissance art shown below all comment on / demonstrate potential energy: stored energy of position, juxtaposition of perception and cognition: recursion, and optical illusion; void, solid, motion, stasis; form and function; symbol and object. 

Some engage the viewer in the collapse of the expectation of a logical universe:  the promise of change, and self-reflection.  All interdependent, equal in value, ambiguous and contradictory -- equally figural and important.   Equally false.  Equally self-referential.

To put it another way, it’s about what is not there, “a kind of Strange Loop.”

Like the images below ...



"It turns out that an eerie type of chaos can lurk just behind a facade of order - and yet, deep inside the chaos lurks an even eerier type of order.”  

                          Douglas R. Hofstadter, Metamagical Themas: Questing For The Essence Of Mind And Pattern


                                                                            What is Happening?

                          Barnes Foundation Study Group 

       Studio Lecture / Demo  --  S3  /  Michael Sommer Photos

 MG 8715



                MG 8717

"— scientific method as intelligence in operation, art, education — are all bound together in A SINGLE ORGANIC WHOLE. To put the matter in other terms, all genuine experience is 

intelligent experience, experience guided by insight

derived from science, 

illuminated by art, and 

made a common possession in education.

                                                                                  Albert C. Barnes (regarding John Dewey's philosophy)

                 Potential Energy -- Stored Energy of Position

                                    Topology of Paradox

"We believe that great painting --painting that is illustratively full, substantial, and real -- was born with the Renaissance and grew with its flowering …. something about the essential difference between the imagery and intentions of abstract painting and those of representational painting makes it very hard for us to relate abstraction to the past."

                                                                                                        Frank Stella, Working Space 

                        Visual Illusion / Analytic Abstraction


Planar art is about navigating space, and time, without benefit of the union of Hands and Mind.

Architecture of nested dichotomies:  contradictions of reason and perception, frames of reference, of logic, pattern and process, motion and stasis -- self-referential.

Sometimes a sly joke, or a question.  Always a tension.


  Rembrandt circles / planes.  Why circles?                      Braque geometry / planes  



                                                                          geometry / planes                                                      



                                                                          energy: critical mass 

“Painting isn’t an aesthetic operation; it’s a form of magic designed as mediator between this strange hostile world and us.”

                                                               Picasso, Quoted in Mario Livio, The Golden Ratio (2002)


                      geometry /  time                                                             geometry / motion 


                    Rembrant helix / circles                                     geometry /  time


              points of reference / parallax                                               geometry /  time



                         Cezanne motion / space                                        Botticelli motion / space 



                                          Piranesi                                                        Escher

                                                                play of cognition / perception


                                                                           What is Happening?


                                                                  play of fugue - Die Kunst Der Fugue                 


                                                                                beginning / end



Giovanni Piranesi -- engineer, architect, etcher (rearranged reality: "capriccio" / multiple view points / experience of real space / spatial movement / planar characteristics of objects)

Georges Braque -- sculptor, painter (geometricization of motion and form / succession of viewpoint -- reduction by cube, sphere, cylinder, cone as building blocks / "tactile … manual space …")

Alexander Calder -- sculptor; stabile / mobile (flowing energy / succession of viewpoint / "drawing in space")

Sandro Botticelli -- painter (rearranged reality / flowing energy, tactile movement and sense)

Rembrandt -- painter (illusion of form and tactile space / opposition of light and shadow: chiaroscuro / geometric clarity)

Paul Cezanne -- painter (flowing energy / succession of viewpoint -- reduction by cube, sphere, cylinder, cone as building blocks / sculptured, combinatory, "tactile … manual space")

M. C. Escher -- graphic artist (mathematical / visual relationships / manipulation of space: viewpoint, recursion and symmetry -- spheres, cubes, rings and spirals) SPATIAL ENGINEERS     

                                   Art / Play As Learning

                     Pennsylvania Academy of the Fine Arts 

SDay  Lecture / Demo — Inventor's Class (six to twelve year olds)

image-18 med

" … fine art 

consciously undertaken as such is peculiarly instrumental in quality.  It is a device in experimentation

carried on for the sake of education.  

 it exists for the sake of a specialized use, use being a 

new training of modes of perception.

                                                                              John Dewey, Experience and Nature, 1929

"A growing body of data suggests that connections between the art and science of learning are rigorously supportable by quantitative studies. Contemporary research is beginning to explore explicit neuroscientific hypotheses concerning the beneficial effects of activities such as musical performance, drawing, visual aesthetics and dance observation."  

                         Tyler, C., Levitin, D., & Likova, L., "Art, Creativity, and Learning" / NSF (2008)

“Art” does not create the forms; it is their selection and organization in such ways as to enhance, prolong and purify the perceptual experience.  It is not by accident that some objects and situations afford marked perceptual satisfactions; they do so because of their structural properties and relations.  An artist may work with a minimum of analytic recognition of these structures or “forms;” he may select them chiefly by a kind of sympathetic vibration.  But they may also be discriminatively ascertained; and an artist may use his deliberate awareness of them to create works of art that are more formal and abstract than those to which the public is accustomed.

 "Tendency to composition in terms of the formal characters marks much contemporary art, in poetry, painting, music, even sculpture and architecture.  At their worst, these products are “scientific” rather than artistic; technical exercises, sterile and of a new kind of pedantry.  At their best, they assist in ushering in new modes of art and by education of the organs of perception in new modes of consummatory objects; they enlarge and enrich the world of human vision.

“Thus, by only a slight forcing of the argument, we reach a conclusion regarding the relations of instrumental and fine art which is precisely the opposite of that intended by seclusive estheticians; namely, that fine art consciously undertaken as such is peculiarly instrumental in quality.  It is a device in experimentation carried on for the sake of education.  It exists for the sake of a specialized use, use being a new training of modes of perception.  The creators of such works of art are entitled, when successful, to the gratitude that we give to inventors of microscopes and microphones; in the end, they open new objects to be observed and enjoyed….

"In creative production, the external and physical world is more than a mere means or external condition of perceptions, ideas and emotions; it is subject-matter and sustainer of conscious activity; and thereby exhibits, so that he who runs may read, the fact that consciousness is not a separate realm of being, but is the manifest quality of existence when nature is most free and most active.”

                                                                                                 John Dewey, Experience and Nature, 1929


Albert C. Barnes —  Cognition and perception (seeing and learning from art)

William James -- Psychology, (anticipated much of Cognitive Psychology) human subjectivity (Umwelt / self-world) (primacy of space perception)

John Dewey -- Psychology, philosophy, and educational reform (new way of thinking)

Georg Hegel -- Philosophy (contradiction / opposition) (unfolding of the idea in space)

Marvin Minsky -- Artificial Intelligence (one of the fathers of)  (new way of learning) (advanced technologies for exploring cognitive / perceptual space)


© Michael S. Sommer, Ph.D. 2015