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Artist's Statement in "The Derivation of the Laws. . ."
The following Statement by Roman Verostko was published in the limited edition of George Boole's Derivation of the Laws which is Chapter III, from Boole's classic work: An Investigation of the Laws of Thought.. (Macmillan, 1854). The illustrations were generated with Verostko's software, Hodos. The limited edition of 125 copies, bound in leather, was pulled by hand at the St. Sebastian Press in Minneapolis in 1990. Each copy has original, "one of a kind", tipped in front and end pieces which were plotter drawn in the artist's studio. The work was also issued in paperback, in February 1991 (ISBN 1-879508-07-9). The press is no longer active. The artist retains a limited number of copies of each edition. © Roman Verostko For more information on this project click here.
STATEMENT. Early in this century a number of artists became intensely interested in unfolding a universe of visual form which did not "re-present" the world we see around us. Wassily Kandinsky strove to create "improvisations" based on "inner necessity", something like the structure of harmony in music. Paul Klee observed that he wished to "make visible the invisible" - perhaps the process of a flower blooming. And Piet Mondrian sought a "dynamic equilibrium" through the visual equivalence of opposites - an opposition he observed most profoundly in the relationship of the vertical and the horizontal elements in the landscape. These and many others - Frantisek Kupka, Kasimir Malevich, Barbara Hepworth, and the pioneering constructivist brothers Naum Gabo and Antoine Pevsner - all shared one thing in common - they sought to make visible a reality which was not visible.
Each in his personal way searched for forms which some have called the "new reality" - a world of forms without reference to the visual vocabulary of our everyday world. Terms such as "non-objective art", "concrete art" and more generally "abstract art" have been used to refer to this work. Within the first generation of these artists, we have experienced many marvelous moments: recall the lyrical biomorphic forms in the sculpture of Jean Arp - the vibrating power of interacting colors in the work of Joseph Albers and Victor Vasarely - and the expressive wonder in the organic worlds sculpted by Isamu Noguchi.
Within the past fifteen years, experiments with worlds of unseen visual form have crossed a new threshold. The pioneers who opened our eyes to such forms have been mathematicians and physicists whose images of complex dynamic systems have amazed the discoverers themselves.
The hidden worlds of visual adventure were either unknown or not able to be visualized before the advent of computers. One world filled with visual adventure, which lay largely unseen before computers, was brought to visualization through the work of Benoit Mandelbrot (Note 2). Surprisingly this hidden world emerged from the need for a geometry for measuring and describing the forms of nature. How do we describe mathematically the shape of a cloud, a coast line, or a mountain? Not with the cones and spheres of Euclidian geometry! Mandelbrot identified a new geometry of fractal shapes. This geometry, aided by a computer, can be used to visualize the form of the phenomenon it defines. This revolutionary new geometry, still in its infancy, has seized the imagination of many artists involved with computer graphics.
For now, it is clear that geometries, both old and new, coupled with the power of the computer, have sown the seeds for a revolution in the arts. The next generation will see magnificently articulated improvisations as artists learn how to use dynamic iterative techniques. Both the frontispiece and the endpiece in this book are hard copy examples of such improvisation.
Each is an original "one of a kind" in a "family" of forms. For example, the brush stroke, in the frontispiece, presents the key shape which controls all the other "self-similar" strokes. No other book in this edition has a frontispiece evolved from the same shape Thus the final form is unique in every book. On the other hand, every frontispiece, sharing the same parameters and instructions, belongs to the same form family - each has a true "familial" resemblance to every other work in the edition. (Note 1)
There are many remarkable analogues between computing processes and biological processes, e.g. software generations, computer viruses. We can expect these analogies to become more apparent as computers evolve further. We assume that the "rulebook" in our universe is the same for every information processing system whether it be the mind of a human or a chimpanzee, an abacus or a computer operating system.
This "rulebook" fascinated George Boole. He was convinced that if the laws of logic "are really deduced from observation, they have a real existence as laws of the human mind independently of any metaphysical theory . . .". He sought to identify those rules of thought and give them algebraic expression.
In Proposition IV he identified "the fundamental law of thought" as Aristotle's principle of contradiction - that "it is impossible for any being to possess a quality and at the same time not to possess it" (Note 4). George Boole argues from its algebraic equivalent that "what has been commonly regarded as the fundamental axiom of metaphysics is but the consequence of a law of thought, mathematical in its form."
From this foundation he evolved a symbolic logic for the "essential laws of human language". He achieved the first successful application of algebraic methods to logic, an achievement which provided the foundation of all subsequent developments in the field. "Boolean" Logic, refined by his successors and essential to switching theory, has been the cornerstone for developing the circuitry and software for the modern computer.
If George Boole were living today he would stand in wonder and amazement pondering the magnificent machine language that has evolved since the publication of the "Laws" in 1854. I think especially that he would be transported to near ecstasy seeing the binary 1's and 0's in computer assembly language which symbolize the "on' and "off" bits. This is his Proposition IV evolved into a machine language that controls the electronic circuits in everything in our daily world from cash registers, airplanes, and washing machines to Cray supercomputers.
The illustrations in this book have evolved from procedures made possible by Boolean logic. For several illustrations I adjusted my algorithms to use terms from Boole's symbolic logic for the graphic improvisation. In those cases the 1's and 0's were distributed randomly around a center of attraction. The visual effects are intended to suggest the dynamism inherent in logical systems. It is a tribute to Boole who perceived the value of a symbolic language of logical equivalence in advance of computer languages.
As a final note I want to place this work in historical context. In the early 15th Century Filippo Brunelleschi developed linear perspective and Leon Battista Alberti documented its theory and practice in his work "Della Pittura" (1435). The perspective of the 15th century was more than a re-tread of the perspective practiced in the Roman empire. Alberti's treatise emerged along with the growth of empirical observation as a learning method and an interest in the study of optics as a key to that learning.
Furthermore, Alberti believed that mathematics and logical order were essential for the practice of art. Subsequent development in the theory and practice of perspective altered the art of western culture. Indeed, Renaissance perspective provided the tools of visualization essential for the development of modern western civilization.
I think that we stand at a similar threshold today as we face the future. The computer provides the artist with a seemingly limitless power to transform and improvise. And, like renaissance perspective it provides us with a new window on our world - one that is altering the way we perceive that world.
Over the years I have gained a respect (and even affection) for the machines I use. My plotters, named Alberti and Brunelleschi, are with my computer, my excellent companions in exploring these new perspectives. (Note 3)
They help me explore visual analogues of probability, forms which were hidden from view before we had these machines. Through the computer we have gained access to a visual domain filled with mystery, a domain that was invisible before. For many the energy and growth patterns of these forms echo processes lying at the core of the unfolding universe. My work explores a faint echo of this cosmic landscape. For me, the computer and its companion plotters, provide a new pathway to "making visible the invisible".
Now, in the summer of 1990 we recognize that electronic art is still in its infancy. But, as in the early 15th century, there are artists now wrestling with the problems of the transformation and creation of art forms with computers. The new geometries and new technologies will surely bring a revolution as we approach the next century. This book is a tribute to George Boole whose work helped make this new adventure possible.
Roman Verostko, Minneapolis, 1990
Note 1. Original, "one of a kind", works for the frontispiece and end-piece were plotted in the studio for the "hand pulled" letterpress edition only. Special reproduction works were created for the litho paperback edition.
Note 2. B. Mandelbrot The Fractal Nature of Geometry (NY: 1982) which is a revision of Fractals: Form, Chance and Dimension (1977).
Note 3. Since 1990 the studio, having grown to a network of workstations, has become more of a "digital scriptorium" with the plotters working as digital scribes. Even so, the artist "companion-like" atmosphere prevails.
Note 4. The original Greek text was noted in George Boole's edition and also in the limited edition. (Click here for Greek text). To pay for his education George Boole tutored students in classical languages. It is remarkable that his knowledge of the classics provided the keystone for the Boolean operators that lie at the heart of electronic logic circuits!
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