At first it may not seem obvious how developments in mathematics have affected the direction of the arts and the evolution of our culture, let alone how they can influence our own practice and how we contextualize our work. I, for one, used to wonder in school how math could be relevant to my life.

A brief look at history reveals a deep underlying relationship between the inspirations and aspirations of mathematicians, scientists, and artists. For one thing, we are all trying to explain the world around us.

The Greeks thought the true nature of the universe was to be found in ratios of numbers. Pythagoras¹ saw all things as relationships defined by the void between them ², in the same way that the spaces between beats in a piece of music determine its rhythm and tempo. This is where we get our concept of “rationality”.³

The “Golden Ratio” was particularly cherished by the Greeks and can be defined as a rectangle that is constructed such that the removal of a square equal to its height from one end will leave a smaller rectangle of the same proportions.

Architectural historians have identified the use of this ratio in the design of the Acropolis, and so mathematicians refer to this proportion by the first letter of the name Phidias (Gr. Phi, or ), as he is the architect of the Athenian Temple complex.

Further popularized in Luca Pacioli’s 1509 book Divina Proportione (which was illustrated by Da Vinci and includes the famous picture of the Vitruvian Man, see animation). This “Golden Ratio” was rediscovered during the Renaissance by artists as a guide to producing works with pleasing proportions. It has been seen as emblematic of the ideals of rationality. Ironically, is also an irrational number.

Studies of perspective in the early 1400’s by Filippo Brunelleschi (1377-1446) produced a  geometrical formula for two dimensional representation of the three dimensional world that became the standard model for the realistic depiction of space from the Renaissance onward.

The development of calculus by Isaac Newton gave the finishing touches to the Copernican heliocentric paradigm and bequeathed a powerful set of tools to astronomy and physics. This emboldened society to believe that, if these laws could be mastered, the universe could be controlled.

With the earth removed from the center of the universe, the church lost its monopoly on science and art. Armed with a new mechanistic world-view and with a set of mathematical tools that seemed to have unlimited predictive powers, the western world entered what was called the “Age of Enlightenment”. This was an echo of the Renaissance and of the Golden Age of Pericles, during which Phidias had worked. The “Enlightenment Thinkers” believed in the perfection of mankind through accumulation of knowledge.

So we see that, for each of these time periods, the cultural understanding of mathematics had both a direct and an indirect influence on the culture’s self-expression, providing practical tools, useful paradigms, and areas for further endeavor.

What is the mathematical metaphor that dominates us in the post-modern age? How will the math of today affect our cultural future?

I propose that the Science of Complexity, also known as Chaos Theory, provides many concepts which help to give insight into the context and direction of contemporary culture, as well as providing new technologies, methodologies, and metaphors for the production of valid work and theory.

What tools can it provide us, both practically and intellectually? Perhaps we should first ask what it is that we look would look for in such a paradigm.

A useful paradigm for artistic discourse should fulfill a few basic requirements:

It should contextualize our work in history: It should provide a historical and geographical overview of cultural phenomena which is inclusive of the diversity of human experience. It should provide tools for understanding society; past and present, and it should contextualize current trends and indicate future developments. It should help make some sense of apparent paradoxes, contradictions and disparities.

It should give direction to movements and to individuals: It should provide motivation and direction to groups, individuals and specific works, just as ideals rooted in mathematics have, throughout the ages, inspired people to believe in the power of Art to elevate and enlighten.

It should provide tools and technology: It should enhance or provide new avenues of expression and distribution. Just as the mathematics of optics provided optical devices that allowed painters to analyze what they saw and lead to the eventual development of the cameras and the scanners we use today.

It should provide metaphors and tools for critique and analysis: It should provide a language for understanding new concepts and relationships , just as the science of optics has given us the concepts of “focusing our attention” and “getting things in perspective”. It should also have the capability of self-analysis ⁴ .

It should open significant areas of endeavor: It should provide areas for artists and critics to direct their investigations and their works, in the same way that modernism opened the door to the study of contemporary life and ultimately art itself.

Chaos theory is the study of simple iterative formulae that produce complex, unpredictable results. In common usage the word “chaos” implies disorder or randomness but this sense it means an underlying, unpredictable order from which patterns emerge over time.

Those patterns are called fractals and they have a number of special attributes which make them different from Euclidean geometrical shapes.

One unique aspect is that their borders are infinitely convoluted, so that it is impossible to predict if points in the vicinity are inside or outside of the shape. This complexity means that fractals occupy fractional dimensions (they can occupy a dimensionality between 2 and 3D for example) (Burger/Starbird 507).

Fractals also demonstrate self-similarity at different scales. Patterns may be contiguous or have many elements that are not connected. Their patterns display infinite with infinite differentiation.

The equations that create fractals do not generate patterns in a linear fashion, as in Euclidean geometry where adjacent points are determined successively. Patterns emerge chaotically, so that it is impossible to predetermine if subsequent iterations will generate points which will fall within the shape or not. The final outcome of many iterations is radically affected by tiny changes in the initial conditions.

Chaos theory doesn’t espouse a deterministic, Newtonian idea of linear causality, but one of emergence. As such, “things” can be regarded, on one level, as structures and on another level as processes (Young 5).

Complexity theory also denies the concept of the objectivity, or separation of the observer from the observed (Young 11).

How can an understanding of Chaos be helpful in a cultural analysis? Culture is a non-linear dynamical system. The development and propagation of ideas is an iterative process. The repetition of concepts, both verbally and concretely, forms the evolution and the canon of our culture. This process has accelerated since the development of reproduction technologies like the printing press, and it is now increasing exponentially through digital information technologies. It is reasonable to expect a massively iterative system such as this to produce complex, non-linear results. How best to understand this complexity? I believe Chaos theory meets the criteria set forth earlier:

It contextualizes our work in history: The contemporary practice of referencing the distant and recent past in the forms of irony, parody, homage, reruns, remakes, takeoffs, mash-ups, outtakes, rip-offs, revivals, samples, loops, cover versions, re-mixes and reissues etc. is one of the defining features of Post-modernism. We have inherited this practice directly from the Modernist mandate for self-analysis, which has been multiplied by the subsequent proliferation of industrial technologies for image making, replication and distribution. Fractal models help us understand the post-Internet de-centeralization of expertise, authority, and distribution in all realms of expression.

It gives direction to groups and to individuals: The open source movement, wikis, and distributed computing, are new forms of massively collaborative endeavor that are best understood as non-linear dynamical systems. Democratized distribution like YouTube and peer-to-peer file sharing circumvent the traditional top-down distribution models, and allow the appearance of “viral memes” and other emergent phenomenon. Complex systems like these are subject to the Butterfly Effect”, i.e. final outcomes are critically dependent on tiny changes in the initial conditions. This means that all of society can be affected by the actions of individuals and small groups.

It provides tools and technology: The tools of chaos are those that allow us to produce, reproduce, alter, sample, loop, feedback and distribute information. Computers, whose sole function is to cycle thousands of times per second and store millions of iterations of ones and zeros are ideal, but so are cell phones, wireless devices, smart appliances, and samplers to name a few others. Chaos algorithms are used to create realistic textures to 3D animations, encrypt sensitive data, and cut down noise in transmissions.

It provides metaphors and tools for critique: Unlike the Newtonian Paradigm, Chaos theory and cybernetics ⁶ integrate the concept of circular causality. Simple loops where A causes B, and B causes A are found throughout the art world. For example, the relationship between artist, critic, and audience, between inspiration and work, as well as perfomative and improvised scenarios all have these kind of “chicken/egg” relationships.

The fractional dimensionality of emergent phenomena and the uncertainty of their border regions suggest what socio-cyberneticist TR Young called “fractal facticity”; meaning that more than one thing can be true simultaneosly depending on one’s point of view in time and space. This approach helps us to understand, in a holistic fashion, the postmodernist de-centeralization of cultural discourse from the various perspectives of post-colonialist / post-structuralist / Marxist / feminist /queer / etc. theory.

A complex analysis of works would be done done with an eye for self-similarity at different scales, rather than looking for linear connections and Euclidean constructions with their connotations (“right” angle, “golden” rule, getting “straight to the point” etc.). For example, Pollock’s paintings have been been interpreted in terms of their fractal properties (Peterson). Emily Zants has used complexity theory to study French literature’s evolution in relation to cinema (Zants)⁷.

A phenomenon like the replication, distribution and display on the Web of the self-similar frames in a QuickTime video over millions of hard drives and screens can be viewed as a vast fractal distribution intersecting both cyberspace and real space/time.

It opens significant areas of endeavor: Aside from the use of fractals for their 2D and 3D graphical properties there are many applications where iterative systems can be applied. Artists who produce work that demonstrates emergent behavior, like David Rokeby and Norman White, exploring complexity and chaos creatively.

Artificial intelligence, massively collaborative on-line virtual spaces, ubiquitous computing and image recording with democratized distribution; these are all chaotic systems.

The convoluted fractal boundaries between doing and being; between the real and the imagined; between the idea and the art; between the artist and the viewer; between the public and the private; these are areas of infinite richness to be explored, and what better tools than the Aesthetics of Chaos to navigate them?

Bibliography

Burger, Edward B. and Starbird, Michael The Heart of Mathematics: An invitation to effective thinking
Key College;2 edition (August 18, 2004)
Peterson, Ivars Jackson Pollock’s Fractals 1999
https://www.maa.org/mathland/mathtrek_9_20_99.html

Rokeby, David Installation Artist
https://homepage.mac.com/davidrokeby/home.html

White, Norman The Normill
https://www.normill.ca/

https://en.wikipedia.org/wiki/Pythagoreanism
https://en.wikipedia.org/wiki/Hippasus

Young TR CHAOS THEORY AND HUMAN AGENCY
https://www.critcrim.org/redfeather/chaos/chaosindex.html

Zants, Emily Chaos Theory, Complexity, Cinema and the Evolution of the French Novel
1998 Edwin Mellen Press ISBN13: 978-0-7734-8789-5
1 – Pythagoras (c. 580-500 BCE), the Greek philosopher/mathematician who is known for the theorem explaining the relationship between the lengths of the side of a right triangle, also originated some profound ideas about the nature of space and time which influenced thinkers from Plato on for many centuries.

 

2 – Aristotle (384-322 BCE) (wiki/Pythagoreanism) explains the Pythagorean concept of how Form emerges from Void by creating relationships in space and time.

The void distinguishes the natures of things, since it is the thing that separates and distinguishes the successive terms in a series. This happens in the first case of numbers; for the void distinguishes their nature.

3 – So much did the Greeks cherish their rationalism that legend has it that when Hippasus discovered that the square root of 2 could not be represented as a ratio of two natural numbers, and was therefore irrational, he was drowned at sea and the information was kept secret by the Pythagoreans.

4 – Clement Greenberg wrote in the 1970s that Modernism was the culmination of a social project of self analysis. He said it started with the empiricism of Enlightenment philosopher Immanuel Kant and manifested as a science-like self-analytical approach in the arts that culminated in Post Painterly Expressionists, like Morris Louis, who avoided the intervention of the brush by simply pouring paint on the canvas. But by then postmodernism was already underway.

5 – This effect discovered by Edward Lorenz in the 1960s. When he re-ran a computer weather simulation, after rounding the initial parameters off to 2 decimal places from 3 or 4, he got radically different results, leading him to say it was as if the flapping of a butterfly’s wing in the forest had caused a hurricane on the other side of the world.(Burger/Starbird 490)
6 Cybernetics is the study of communication and control systems in machines and nature and important area of research is into positive and negative feedback where complex and unpredictable results are produced by self-limiting iterative systems.

7 – In the introduction of her book Zants states:
“…novels developed techniques and structures such as fragmentation, doublings, flashbacks, or metaphorical representations that are cinematic because they engender a sense of spatial and temporal simultaneity, whereas the traditional novel is condemned to the linearity of words.(Zants)”

Abstract of a talk given at ISEA98 on Sept 6, 1999 in Manchester.

We are approaching the end of the age of reason. Science has matured as a philosophy to the point where it recognizes the existence of the unknowable. No longer labouring under the naive Newtonian assumption that all the universe can be measured or predicted Science turns to the study of Chaos in an attempt to gain insight into the inner workings of the world.

Communications technologies allow culture to instantaneously encircle the world and feedback on itself. Sampling and looping its way into the next millennium, the iterative nature of post-modern humanity makes it impossible to predict. Artists can embrace Chaos as a tool for deciphering and forging the new world disorder.

Emergent robotic behavior, genetic algorithms, and fractal mathematics are just a few of the approaches being taken. After more than 2000 years of living under Euclidean rule our head space is changing. The shortest distance between two points is no longer a straight line but a point of view.

Just as Euclid planted the seeds for an age ruled by logic, we are inoculating a culture of intuition. Try to imagine the world after one or two millennia of Chaos. What happens when feedback is produced as DNA starts to sample and manipulate itself? When an idea is as easily spread to the whole race as it is to conceive? When personal experience is not tied to the body?

Revolution becomes evolution and thought becomes reality. We become Meta-human and culture moves into the Noosphere.

More on this subject…

Introduction by Steev Morgan

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For many years the clichés of Hollywood and science fiction have formed the popular conception of robots. HAL of Kubrick and Clarke’s 2001: A Space Odyssey typifies the persona: autonomous and intelligent, sometimes malicious and often possessed of their own agenda. These modern embodiments of the Frankenstein myth usually prove to be the nemesis of their creators.

On the other hand the industrial reality of robots offers a rather more prosaic image. These robots are entirely predictable and dependable.

They are capable of performing dangerous or repetitive tasks quickly and tirelessly without end. The only threat they pose is to the jobs of assembly-line workers and the only thrill is for those who monitor the bottom lines of corporate ledgers.

The most interesting applications by artists in this field use robots more as a means than an end. The artist, being unconcerned with mere functionality or plot-line, is free to create complex systems and set them in motion to observe the emergent order that manifests itself.

Norman White has demonstrated that artists can create devices imbued with sets of functions which might be seen as abilities or freedoms rather than restrictions. If these functions are tuned carefully and allowed to run free, then the robot can develop what may be described as behavior. Unlike the actions of a simple mechanical devise, these behaviors are often unpredictable. These in turn can often be seen to tell us a lot about ourselves, and our relationships with each other and our machines.

In this exhibition White brings together a number of works which attempt to shatter some of the clichés generally held about automata and expand the commonly held preconceptions about artists and their relationship to their works.

At their simplest these works demonstrate the order to be found within chaos. The more complex pieces display, through a juxtaposition of function and limitation that parallels will and vulnerability, the emergence of rudimentary personalities.

Artists included in the show included:

	Facing Out Laying Low Norman White
	autARKy Steev Morgan – Catherine Orfald
	Sticks Doug Back
	Fingerprints from Birth of Essence Erlich, Robert T.
	The Wanderer David Rokeby

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NAFAA HOME || ALOIO HOME || EXHIBITION

To find the pieces for this show I did not have to search far. The artists are all members of a group that shares a long history. They have been friends, lovers, mentors, acolytes, and collaborators for a period spanning, in some cases, two decades.

The works chosen for this exhibition are representative of this history and of the direction we are headed in as individuals and as a group. Despite a shared history, these artists represent a diversity of viewpoints and approaches from the raw metal and visceral harmonics of Victoria Scott’s “Coil Room” to the subtle responses of David Rokeby’s “Very Nervous System”.

One of the challenges faced when creating and exhibiting these types of works is a reluctance of the main stream art media to deal with them. Artists working in the field of new media often get the feeling of working in a vacuum. The only thing worse than a bad review is no review at all.

It seems to me this lack of coverage is due mainly to two factors. The first is perhaps a perceived ignorance of the technology and issues being dealt with. Art critics are reluctant to comment on works they feel they don’t fully understand.

I believe these works should be judged by the same standards as are all works of art. What makes something a piece of “art” is that, in addition to having craft and content, it provides context — a new way of looking at the world.

Of course an understanding of the crafting of a piece can allow the viewer a deeper appreciation of it. However, if one does not understand the techniques involved in the construction of a work, then one must attempt to look beyond this to the other aspects of the piece. Just as photography could not be accepted as an art form until the novelty of the medium wore off, so too these new media must lose their “Gee Whiz” appeal and be judged for their ability to convey a deeper meaning.

I am optimistic that, as the new technologies permeate our everyday lives, an acceptance for this kind of work will grow. Conversely, I also believe that an appreciation for the non-conventional uses of these technologies will help prevent us from becoming slaves to the machine.

These pieces are not “avante-garde” in the same sense as the revolutionary art of the turn of the century. That tradition exposed us to the irrational impulses underlying a staid and rigid society. The Dadaists, for example, perhaps as a reaction to the industrial revolution, applied mechanical processes to images and words. Their works revealed the often frightening under current of the subconscious mind. Quite the contrary, I think the pieces in this show apply organic, human methods to machines and by so doing attempt to make some sense of and give hope to an increasingly irrational world.

Another explanation for the reticence of the mainstream media to deal positively with technology-based art is that the dissemination of communications technology to the people marks the end of the media’s long standing monopoly on the mediation of information. The invention of movable type threatened the powerful hold of church and crown over the spread of ideas, allowing pamphleteers to publish the last words of radical thinkers from the steps of the gallows. The industrialization of the press and the development of broadcast technologies eventually put that power in the hands of the industrialists. They would rather divert us with pretty images designed to stimulate consumption and distract us from the fact that there are actually some things very wrong with our society. The catalytic power of the modem, the fax machine and the PC have already proven themselves in Czechoslovakia, the former USSR, and China. The powers of the West are misleading themselves if they think it can’t happen here.

These technologies were originally created as just another bunch of consumer goods, but I see them as a Pandora’s box. No matter how much the media warns us of the dangers of playing with the Promethean fire of unregulated, uncensored communication, the misfortunes cannot be contained. As in the myth, hope remains behind even though the gods are always angered when humans become more free.

Another positive aspect to this change is the fact that it is an evolutionary process. It reinforces my faith in human nature that at this time when the planet is no longer able to sustain the rabid material consumption that we have been raised to expect, society is spontaneously moving toward an economy based on information consumption.

As I mentioned earlier I feel that the pieces in this exhibition attempt to put a human face on the new technology. Each artist comes to terms with their chosen medium on a personal level. To best give specific examples it is convenient to divide the exhibition into three parts along the lines of similarities in style, theme and medium.

Net@Works
(A Show of Interactive Computer Installations)

Interactive works require the participation of the viewer to be complete. It can be argued that, like the tree that falls unheard in the forest, they are not fully art until they are seen and heard. The demands of the works in this show range from the mere presence of spectators to actual aerobic exertion.

Perhaps it is the nature of this interaction that fascinates these artists, because the pieces in this part of the show are also about the interconnection between individuals and crowds, their physical surroundings and their cultures.

We came up with “Net@Works” as a name for a show that was at the same time about our own community and about expanding and connecting with other communities. The word “network” is both a noun, meaning a system of interconnected people or computer systems and a verb, which means the act of creating or connecting networks . The process of building networks produces a series of nested self referential systems not unlike iterative nature of fractals. As such, it is a good metaphor for a type of work that looks both inward and outward of it’s inspiration and it’s expression.

Three of the pieces deal with the dynamics of individuals and communities. Mary Alton’s CD ROM “Critical Mass” takes the viewer on a journey from within the self and looks at the crowd as an organism unto itself, greater than the sum of it’s parts and superseding even the will of the individual. “The Gathering Space” by Tom Leonhardt and myself invokes the common denominator of humanity which unites all people at all times.

Graham Smith’s “Welcome to the Electric Skin” involves the actual creation of a new virtual community. “Cyberspace” has been described as “the place where a telephone conversation takes place”. If that is true then Graham’s piece is an attempt to colonize that space in the classic pioneering tradition.

Nancy Paterson’s “Bicycle TV” seems to warn us that too much fascination for this Brave New (Virtual) World can lead us to neglect the real physical world that our bodies must still inhabit. Though no substitute for the real thing, one can still enjoy the illusion of a bicycle trip through rural Ontario. This type of interface must surely be more natural than the usual computer mouse.

“Very Nervous System” by David Rokeby springs directly from his frustration tools the industry has given us it interact with our computers. Keyboards are a very unlike the voices they replace and the mouse is good for pointing and not much more. When all one can do is point ones expression is necessarily objective. David has spent many years perfecting an interface which is capable of responding to the subtlest and the broadest of physical gestures.

Northern Lights
(A Show of Holography)

Toronto has one of the largest and most active communities of art holographers in North America and perhaps the world. This is due largely to courses taught at the Ontario College of Art and facilities maintained by collectives and artist run centers such as The Photon League of Holographers and Fringe Research. This show consists of pieces from four artists, all of whom work in other media as well. In these pieces they have used holography as part of multimedia works and thus taken the medium beyond the mere representation of three dimensional objects.

I have often heard holographers criticized for not producing art but merely making interesting 3D pictures of sculptural maquettes–holography for holography’s sake. This is due partially to the aforementioned “Gee Whiz” phenomenon and it is true that sometimes even the artists themselves fall under it’s spell. All of these works are exceptions to that generalization. They integrate traditional media and use holograms to utilize properties that cannot be reproduced in any other way.

A common theme which seems to link all these works is “life”–its beginnings, its tenaciousness, its transience, and our resistance to let it pass.

Catherine Orfald’s work, invokes creation myths and goddesses to pay tribute to the beginnings of life.

“The Mother of Songs,
the mother of our whole seed,
bore us in the beginning.”

Fused in light the bodies of Father and Mother, Mother and Child bear witness to the duality and the unity of the family and of life.

Bruce Evans’ “Puddle” juxtaposes nature and civilization using objects, sounds, and images. Our entry into the space provokes a play of light that transforms a pot hole into a living pond.

“The Sappho Project” interplays light, music, and representations of the ancient poetess with translations of her words. Mary Alton has chosen poems which capture the elusive passage of time and the impermanence of temporal existence.

Tonight I’ve watched the moon and then
the Pleiades go down;
the night is now half gone; youth goes
I am alone in bed

The urge to write and create images is, in itself, a reaction against that ceaseless change.

To expose a holographic plate takes a very brief time, measured in millionths of a second. In that time the image is recorded over its entirety in such a way that it can be broken into pieces and each piece still holds the entire image. In this sense the hologram is sometimes used as a metaphor for how the brain stores memories. In “The Eternal Nanosecond” Laura Kikauka preserves a sentimental memory of herself, taking that brief moment and making it last forever.

“I Sing the Body Electric”
(A Show of Kinetic And Robotic Sculpture)

Ever since the first primitive tools were invented the machine has been an extension of the human body. Conversely the state of the art of any age has given its contemporaries a new mirror in which to view themselves and their surroundings. Take for example the model of steam technology which parallels Freud’s imagery of the mind as made up of compartments building up pressures and venting into and displacing one another.

This era dominated by telecommunications, computers, and robotics is no different. The artists in this show have all spent plenty of time bending and welding metal, designing and soldering circuits, and programming computers. One can clearly see in the humor, ingenuity, and beauty of these works that the artists share a fascination for, even a love of things electronic and mechanical. They give us works which speak about some of the important issues of concern to our age. Do machines have too much influence over our lives? Do they intermediate our interaction to the point of threatening the family and the human relationship as we know it? Are machines destroying and replacing nature as our habitat?

Doug Back’s “Small Artist Pushing Technology” is a simple, clear analogy for the plight of the new media artist or for anyone who has to work with technology. A little bit like a modern day Sisyphus, the tiny figure pushes the medium and at the same time pushes his whole world.

Simone Jones reconciles the organic and the mechanical in her piece “Transformation #1” By distilling forms and movement from natural phenomenon and translating them into motor driven sculptures she pays homage to nature and points toward a beauty hidden in unexpected places (like a field of oil derricks or the concerted movements of a factory assembly line or automated tortillaria).

Victoria Scott’s “Coil Room” redefines the female principal not in the traditional sense of passive as opposed to active, but as a cyclic as opposed to vector based energy. If the gun or the rocket can be seen as technologies representative of maleness, Scott sees the A/C motor, the oscillator, and the ones and zeros of the digital world as paralleling the rhythmic nature of female energy.

Norman White’s “Helpless Robot” turns the tables on us, reversing the traditional roles of man and machine. This robot has the ability to learn but rather than “artificial intelligence” it might more accurately be described as “artificial stupidity”. It can learn but it cannot do for itself. The more help it gets, the more it demands. It cannot escape its dependence on humans to get what it wants. Could this be a metaphor for our growing dependence on technology?

Steev Morgan, July 22, 1995, Toronto