Complexity and Aesthetics

Essay on complexity theory and aesthetics.
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  C O M P L E X I T Y 11 © 1998 John Wiley & Sons, Inc.  John Casti received his Ph.D. in math-ematics under Richard Bellman at the University of Southern California in1970. He worked at the RAND Corpora-tion in Santa Monica, CA, and served onthe faculties of the University of Arizona, NYU, and Princeton before becoming one of the first members of the researchstaff at the International Institute for  Applied Systems Analysis (IIASA) inVienna, Austria. In 1986 he left IIASA totake up his current post as a Professor of Operations Research and System Theory at the Technical University of Vienna. He is also a resident member of the Santa Fe Institute in Santa Fe, New Mexico, USA.IN addition to numerous technical articles and a number of researchmonographs, Professor Casti is the author of several volumes of trade science, including Paradigms Lost,Searching for Certainty, Complex-ification , and  Would-Be Worlds . BY JOHN L. CASTI Complexity and Aesthetics Is good art “complex” art?    © 1998 John Wiley & Sons, Inc., Vol. 3, No. 5CCC 1076-2787/98/05011-06 WHAT IS ART? I n the theatres of both the West End of London and on Broadway, one of the big hitsof the current theatre-going season is a play called  Art  . The surface theme of the play revolves about the main character’s purchase of a totally white-washed canvas foran outrageous sum. The character is then faced with trying to justify his extravaganceto his friends by arguing the canvas’s artistic merits.Philosophically,  Art   is interesting for its exploration of the eternally vexing issue of  just what is it exactly   that distinguishes a piece of canvas and oil paint, like Jan Vermeer’s  Allegory of Painting   as “art,” while denying that label to something like the blank can-vas in  Art  ? Or what combination of words on the page lead to the claim that Dostoevsky’s Crime and Punishment   is a work of art, while no such claims are made for an alternatearrangement of words, such as John Grisham’s The Client  ? It’s instructive to see whatsome famous thinkers of the past have had to say about the matter.Both Plato and Aristotle held to a representational theory of art, in which artworksimitate real physical objects. But they differed radically on the matter of whether it waspossible to gain either intellectual or practical knowledge about real-world things fromtheir art-world representations.In Plato’s philosophy, true reality resides in the Eternal Forms or Ideas that make itpossible to understand ordinary physical objects. Thus, according to Plato, the way togain knowledge is to directly encounter these “platonic” Forms. But since artworks areonly imitations of physical objects, which are themselves only derivatives of the Forms,a work of art cannot provide us with any knowledge. As Plato, described it in Book 10 of  The Republic  : “They [artworks] are at the third remove” from reality. So, for Plato, art was not a source of knowledge or even of reliable opinion about objects of the real world. A ristotle, although sharing Plato’s view of art as presenting likenesses of things,argued that it is natural and beneficial for humans to learn by imitating and fromcarefully crafted imitations. In the Poetics  , Aristotle noted that tragic poetry, un-like history, often expresses general truths, not just the facts of what actually took place.Rather, poetry tries to convey a feeling for what is likely to happen, generalizable truthsabout the sorts of things that probably or necessarily occur. But, he went on to say, itmay be difficult to understand events that match these general truths, especially whenthese events are taking place in real time all around us. As a result, Aristotle suggests that by composing an imitation of an action that iscarried out on stage, the dramatist can display the same truth that is being shown by the real action, but in circumstances helpful to learning about the situation. The realaction, possibly containing real death, tragedy, and destruction, might distract us from  12 C O M P L E X I T Y © 1998 John Wiley & Sons, Inc. the chance to learn. But a suitably ideal-ized imitation of the action may allow usto comprehend the principles that gov-ern human activity. This is somewhatanalogous to studying, say, the humanheart or kidney. A plastic laboratory model of these organs might facilitatelearning about their typical structuremore effectively than dissecting the realheart or kidney of an anonymous corpse.In this case, the model reproduces andemphasizes the organ’s essential struc-ture and general features, but it elimi-nates the peculiarities and possibly repul-sive and distracting aspects of a realorgan. B oth Plato and Aristotle recognizedthat an essential aspect of art is thatit is different   from real things. Theirviews part company only on the point of  whether we can learn about real thingsfrom this difference. For example, Plato would argue that there is nothing to belearned about late-19th-century Parisianlife from gazing on Renoir’s famous paint-ing Luncheon of the Boating Party  . Aristotle, on the other hand, may well ar-gue that this painting encapsulates anenormous amount of information abouthow people of a certain social class inter-acted and how they lived in  fin-de-siécle  Paris. Nevertheless, the portrait of Pari-sian life shown by Renoir is certainly notthe real thing, and to believe it is wouldbe like having a member of the audience jump up and call for the police during thescene in Shakespeare’s play Othello  whenOthello strangles Desdemona on stage. Inboth the play and the painting, a crucialaspect of understanding the artwork liesin realizing that art objects must be dif-ferent from real things.Interestingly enough, postmodernartists try to reduce the distance betweenart and real things. As an illustration, con-sider the artist Robert Indiana who paintspictures of bull’s-eye targets that are at thesame time real targets and imitations of real targets. Now suppose you hung a realtarget next to such a painting. Would itbe acceptable for an archer to shoot ar-rows at the Indiana painting? Or wouldan art aficionado object that you shouldrestrict your shooting only to the target,even though the target and the painting look exactly alike? Does the Robert Indi-ana painting tell us anything about realtargets by imitating them in paint on acanvas? That is, do we learn anything about the real system from a model thatis indistinguishable from it? Hard ques-tions. W hat about complexity? Is there aconsistent relationship betweenthe perceived “quality” of a pieceof art and any reasonable measure of itscomplexity? Is a complex artwork moreaesthetically satisfying than one that is“simple?” To even pose this question im-plies that we have some type of complex-ity measure that is intrinsic to the pieceof art itself, and which does not dependon the person ob-serving the painting,sculpture, or what-ever other type of artwork may be un-der consideration.Dubious as such anhypothesis may be,let’s follow throughits implications. GENERATIVE ART One of the most well-developed ap-proaches to char-acterizing the com-plexity of patternsis algorithmic com-plexity theory, which takes thecomplexity of apattern to be thelength of the short-est computer pro-gram that will reproduce the patternunder study. Since this shortest lengthmay vary, depending on the particularcomputing machine and computer lan-guage used to describe the situation, it’scustomary to fix these variables by as-suming that we use a universal Turing machine, together with the limited setof standard instructions appropriate forsuch a gadget. I won’t worry about thesetechnical fine points here, as they’re notimportant for the issues we want to ex-plore. In fact, instead of a universal Tur-ing machine and its language, let’s con-sider a real computing machine and thepopular programming language LISP tolook at the complexity of some piecesof art. A few years ago, computer scientistKarl Sims had the idea of regarding ex-pressions in the LISP programming lan-guage as genotypes in as evolutionary process [1]. When executed on the com-puter, the result can be thought of as thephenotype generated by the LISP ex-pression. Sims’s goal was to create aprocess of artificial evolution using these symbolic expressions. In this pro-cess, the LISP expressions open up theopportunity for the emergence of agenuinely new developmental rule orparameter value beyond the bound- FIGURE 1 The output from the simple LISP functions 1–9. Is there a consistent relationship between the perceived “quality” of apiece of art and any reasonable measure of its complexity? Is a complexartwork more aesthetically satisfying than one that is “simple?”  C O M P L E X I T Y 13 © 1998 John Wiley & Sons, Inc. aries of what may have been set by theprogrammer at the outset of the experi-ment. It’s not really important for us toknow the exact meaning of these LISPexpressions, other than that each of them takes a specific number of argu-ments and returns an image of black-and-white or color values for each pixelon the computer’s terminal screen.Nevertheless, it is of interest to exam-ine a few of the expressions Sims used just to get a feel for what he had in mind with these experiments.In Sims’s work, the LISP expressionscould be formed of combinations of any of the following common LISP func-tions:1.  X  2. Y  3.( abs X) 4.( mod X   ( abs Y  ))5.( and XY  )6.( bw-noise .2 2  )7.( color-noise .1 2  )8.(  grad-direction ( bw-noise .15 2  ) .0 .0  )9.( warped-color-noise ( *X .2  )  Y .1 2  ) F igure 1 shows the type of image eachof these functions produces from aninitially black square, where thefunctions 1—9 are read left to right, topto bottom.Sims began his experiments by creat-ing a LISP expression that combined arandom number of these functions. Suchan expression was then translated by aLISP interpreter into a graphic image, thephenotype associated with this symbolicgenotype. Since LISP expressions can be written as tree structures, the mutationof such an expression proceeds by tra-versing the tree, node-by-node, and ap-plying one or another mutation schemesat each node. A typical such schememight say that if the node is a functionlike ( abs X  ), it might mutate into a differ-ent function like, for instance, ( cos Y  ). Inaddition, symbolic expressions can bereproduced with “sexual combination” by combining the parent expressions in vari-ous ways. Figure 2 shows the effect of 19mutations of this sort on a parent in theupper left-hand corner. This figure showsonly the surface image of a three-dimen- FIGURE 2 A parent with 19 mutations. FIGURE 3 Evolved phenotypes and their corresponding genotypes.  14 C O M P L E X I T Y © 1998 John Wiley & Sons, Inc. sional structure that Sims created by add-ing a volume texture operation that cal-culates color values for each point inthree-dimensional space.By starting with randomly generatedgenomes and applying a variety of typesof mutations, Sims played the role of Fa-ther Nature, selecting those mutationsthat would be allowed to live on to thenext generation. After anywhere from 5to 20 generations, a remarkable set of graphic images emerged. Figure 3(a—c)shows a small sample of Sims’s art gallery,along with the LISP genotypes that codedfor these pictures. If you’re wondering  why there is no genotype displayed forFigure 3c, it is because this phenotype was created before Sims added a geno-type-saving subroutine to his program.Figure 3c is what one might call an extinctspecies in this world of evolutionary artforms. It’s a point worth pondering tonote here how 186 characters of the al-phabet can code for a complicated artis-tic object like part b of the figure.So what does this exercise tell usabout complexity and art? Is thepicture in Figure 3b more aesthetically satisfying than that in Figure 3(a), forinstance? It’s certainly more complex, atleast by the measure of program length.But perhaps program length isn’t such agood measure after all, since by such acriterion for complexity the most com-plex objects are those that have no pat-tern at all! The totally random objectshave the highest complexity, and com-pletely randomness is definitely not what we have in mind when it comes to sepa-rating great works of art from the pretend-ers. Perhaps another standard of com-plexity is called for. CONNECTIVITY AND ART A n almost self-evident feature of  works of art of all types is that they represent a connective structure atmany different hierarchical levels. The col-ors and shapes of a painting are integratedinto substructures, which in turn formparts of even larger substructures until weencompass the entire work in one, grandpattern. To a mathematician, this kind of pasting together of local patterns to formglobal structures is very reminiscent of  what topologists do in order to create glo- FIGURE 4 M.C. Escher, Sky and Water   (1938). FIGURE 5 Shapes in Sky and Water  .
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