Beauty in Organized Complexity: Towards a New Aesthetics

In 1995, Kurt Vonnegut gave a lecture in which he described his theory about the shapes of stories. He drew on a blackboard graphs of story shapes that writers have used for centuries. “The fundamental idea is that stories have shapes which can be drawn on graph paper, and that the shape of a given society’s stories is at least as interesting as the shape of its pots or spearheads,” Vonnegut said (Swanson). He plotted stories on a vertical axis, running from Good fortune to Ill fortunes of the protagonist, and a horizontal axis that represents the course of the story from Beginning to End (see fig. 1a.). One of the most popular story types is what he called “Man in Hole”: somebody gets in trouble, gets out of it, and ends up better off than where they started (see fig. 1b.). A close variant is “Boy Loses Girl,” in which a person gets something amazing, loses it, and then gets it back again (see fig. 1c.). The Cinderella story (see fig. 1d.) is the most popular arc story in the history of civilization, “every time it’s retold, someone makes a million dollars,” Vonnegut said (Swanson). He also pointed out the similarity between the story arc of Cinderella and that of the New Testament in which a person receives sudden help from a deity, is suddenly ousted from good standing, but achieves happiness in the end. Some notable works of literature have ambiguous shapes: Kafka’s The Metamorphosis starts off bad and gets infinitely worse, and Hamlet keeps us from knowing if new developments are good or bad.


Fig. 1. Kurt Vonnegut’s arcs of story. 1a. Two axes of the graph. 1b. The “Man in Hole” arc. 1c. The “Boy Meets Girl” arc. 1d. The “Cinderella” arc. Images reproduced from Swanson and Popova.

Today, with technological advances, scientists have provided empirical evidence for Vonnetgut’s outlines of story shapes. Scientists at the Computational Story Laboratory at the University of Vermont in Burlington have used sentiment analysis to map the emotional arcs of over 1,700 stories and then used data-mining techniques to identify the most common arcs (MIT Technology Review). They found six basic storytelling arcs that are the essence of all complex narratives: Rags to Riches (rise), Riches to Rags (fall), Man in a Hole (fall then rise), Icarus (rise then fall), Cinderella (rise then fall then rise), Oedipus (fall then rise then fall) (LaFrance).

Vonnegut’s theory of story shapes and these scientists’ work apply the same method—using graphical models to understand a set of data, a corpus of stories. The difference is that Vonnegut quantifies the data using his knowledge as a writer and a humanist, while the scientists use program and computer. There is not necessarily a superior method, but the two results, which overlapped, definitely complement each other.

Similarly, Frederick Turner has mapped familiar motifs of worldwide epics in Epic: Form, Content, and History, poetic meter as a universal human activity in “The Neural Lyre: Poetic Meter, the Brain, and Time,” and beauty as a pancultural, neurobiological phenomenon in Beauty: the Value of Values. Taking relatively large sets of literary works produced by distinctive individuals, even from different cultures, Vonnegut and Turner found the common denominator among them and provided us with a compressed understanding of literature spanning the history of the human knowledge. One can quickly dismiss these works as overgeneralization. Vonnegut’s theory of story arcs was rejected as a master’s thesis in Anthropology at the University of Chicago “because it was so simple, and looked like too much fun,” in Vonnegut’s words (MIT Technology Review). Yet, these works open opportunities to work cross-discipline for humanists, artists, and scientists. Taking a large set of seemingly unrelated data and making sense of its structure are common practices of science today. This essay argues that a new aesthetics in the arts and humanities is emerging from this scientific practice. Before going into this new aesthetics, we need to take an excursion into the concept of “Organized Complexity” defined by the mathematician Warren Weaver to understand the origin of this aesthetics.

The Emergence of Organized Complexity

In 1948, the mathematician Warren Weaver, who was then the director of the Rockefeller Foundation, wrote a famous essay entitled “Science and complexity” in the American Scientist magazine. Weaver described science as a way of solving problems and divided the history of science into three main periods: problems of simplicity, problems of disorganized complexity, and problems of organized complexity. According to Weaver, the sciences of the seventeenth, eighteenth, and nineteenth centuries were largely concerned with the understanding of the problems of one or two variables or problems of simplicity. One classic example is Newton’s laws of motion. While solving problems of simplicity brought us technological advances such as the telephone, the radio, the automobile, the airplane, and the phonograph, they were too simplistic to solve biological and medical problems which often involve complex systems: “The significant problems of living organisms are seldom those in which one can rigidly maintain constant all but two variables. Living things are more likely to present situations in which a half- dozen, or even several dozen quantities are all varying simultaneously, and in subtly interconnected ways” (Weaver 2).

Around 1900, science evolved to deal with problems involved complex systems that are more often encountered in living things and in daily life. Instead of studying problems with two variables or at most three or four, some scientists, one pioneer being Josiah Willard Gibbs, started looking at problems with million or billion variables. The methods that made this new challenge possible were powerful techniques of probability theory and of statistical mechanics. Instead of describing the motion of a single ball as Newton’s laws did, scientists were capable of building statistical models for motions of millions of balls. Weaver defines a problem of disorganized complexity as:

a problem in which the number of variables is very large, and one in which each of the many variables has a behavior which is individually erratic, or perhaps totally unknown. However, in spite of this helter-skelter, or unknown, behavior of all the individual variables, the system as a whole possesses certain orderly and analyzable average properties. (Weaver 3)

Examples of the problems of disorganized complexity are the motion of atoms, the motion of stars, Mendel’s laws of heredity, and the laws of thermodynamics. Examples outside of science are telephone companies who calculate the average frequencies of calls, and life insurance companies that calculate their financial stability from the knowledge of the average frequency with which deaths will occur.

Using probabilistic and statistical methods to deal with disorganized complexity proves to be so powerful an advance over the earlier two-variable methods that scientists leave a great field untouched, and that is the region between simplicity and disorganized complexity. Weaver describes this middle region:

The really important characteristic of the problems of this middle region, which science has as yet little explored or conquered, lies in the fact that these problems, as contrasted with the disorganized situations with which statistics can cope, show the essential feature of organization. In fact, one can refer to this group of problems as those of organized complexity. (Weaver 4)

Weaver further stresses the difference between disorganized complexity and organized complexity: organized complexity involves “dealing simultaneously with a sizable number of factors which are interrelated into an organic whole” (Weaver 5). To put it simply, one can solve the problems of complete randomness or disorganized complexity by using probability and statistics, but in a complex system with many intertwined variables, where order is inherent within complexity, science needs to make a third great advance. He suggests two developments that can help solve problems of organized complexity: first, the electronic computing devices, and second, mixed teams of scientist from different fields:

mathematicians, physicists, and engineers are essential, the best of the groups also contained physiologists, biochemists, psychologists, and a variety of representatives of other fields of the biochemical and social sciences… [M]embers of such diverse groups could work together and could form a unit which was much greater than the mere sum of its parts. (Weaver 7-8)

Weaver did not specifically mention artists or humanists in his ideal team of problem solving, but recent interdisciplinary research, such as in information science, cultural analytics, computational art history, and digital humanities, has seen an increasing trend of cooperation between scientists, artists, and humanists despite rancorous objections from academics who do not tolerate “impurity” of their fields. John D. Barrow captures this sentiment in his essay “Art and Science—Les Liaisons Dangereuses” (2003): “Most artists are very nervous of scientific analysis. They feel it destroys something about the human aspect of creativity. The fear (possibly real) of unsubtle reductionism—music is nothing but the trace of an air pressure curve—is widespread” (Barrow 1). This fear is indeed not unfounded. Many projects bridging the arts/humanities and science can be over-simplistic and meaningless, offering little to no insights compared to the traditional approaches of studying arts and humanities. But this situation suggests a great potential of working cross-discipline between the arts, the humanities, and science. Scientists and computer scientists who have the key to technical skills and logical reasoning need us—humanists and artists who can direct them into producing meaningful research, helping them moving beyond the mere applications of their technical expertise.

To sum up Weaver’s three periods in the history of science, I used two figures produced by two data visualists Kim Albrech and Manuel Lima. Albrecht’s graph in Culturegraphy situates the problems of organized complexity exactly where chaorder is, between order and chaos: just before chaos is reached, the most complex systems arise and organized complexity emerges (see fig. 2.). In Visual Complexity: Mapping Patterns of Information, Lima provides a graph explaining the three problems in science addressed by Weaver (see fig. 3.). Lima’s depiction of the problems of simplicity is two bodies with a directed vector; one object has direct influences on the other. The problems of disorganized complexity are depicted as random dots, in which one can possibly make sense of the structure by applying probabilistic and statistical models. The drawing of problems of organized complexity suggests the inherent structure among the dots, and in this case, there exists linkages among them, and thus the system is a network. To understand how modern science has tackled problems of organized complexity, one needs to take a glance into network science, a promising solution to problems of organized complexity.


Fig. 2. This visual interpretation of Weaver’s essay positions the problems of organized complexity between order and chaos. Just before chaos is reached, the most complex systems arise and organized complexity emerges. Reproduced from Albrecht’s Culturegraphy.


Fig. 3. Visualization of Weaver’s three periods of history. Problems of Organized Complexity differ from Problems of Disorganized Complexity because there is inherent structure among the elements of the former. Reproduced from Lima’s Visual Complexity: Mapping Patterns of Information, p. 45

Network Science and the Arts

 The network of interactions between genes, proteins, and metabolites in live cells—the cellular network, the wiring diagram of connections between neurons—the neural network, the interconnection of one’s social ties—the social network, cyber interaction between people through the internet—communication networks, economic exchange—trade networks: these are all examples of network science (Barabasi 1.2). The official definition of network science is “the study of network representations of physical, biological, and social phenomena leading to predictive models of these phenomena” (the United States National Research Council). In visual representation, which is essential to the study of network science, distinct elements are represented as nodes or vertices, and the connections between the elements as links or edges (see fig. 4.).

Fig. 4. An example network (or graph as people use it interchangeably).
Courtesy of Google Image.

This new science has received increasing attention since the last decades of the 20th century. Fig. 5. shows the frequency of use of the words “evolution,” “quantum,” and “network” in books since 1880. The plot was generated by Google’s ngram, which calculates the frequency of these words in the Google book corpus. Since 1980, usage of the word “network” surpasses that of “quantum,” referring to quantum mechanics, and that of “evolution,” referring to Darwin’s theory of evolution. The plot indicates the exploding societal awareness of networks in the last decades of the 20th century. The impact of network science can also be seen through citation patterns (see fig. 6). The plot compares citation numbers over time of high-impact papers in the field of complex systems. In the 60s and 70s, the field was dominated by Edward Lorenz, Kenneth G. Wilson, and Samuel F. Edwards and Philip W. Anderson. In the 1980s, the community has shifted its focus to Benoit Mandelbrot’s work on fractals and John Hopfield’s work on neural networks. The spikes in recent years are the two most cited papers in network science by Watts and Strogatz and by Barabási and Albert.

Fig. 5. The frequency of use of the words “evolution,” “quantum,” and “network” in the Google book corpus since 1880. The plot indicates the increasing awareness of networks in the last decades of the 20th century. Reproduced from Barabási’s Network Science.


Fig. 6. Comparing citation numbers over time of high-impact papers in the field of complex systems. Reproduced from Barabási’s Network Science.

While network science has emerged as a separate discipline only in the 21st century, one can trace its root to the Biblical tree of knowledge of good and evil, or to the Porphyrian tree, the oldest known type of a classification tree diagram. A classic visualization of a network is Darwin’s illustration of the great Tree of Life in The Origin of Species (1859). It is the only graph included in the book, and so critical to Darwin’s theory of evolution that he included a note to the publisher to explain the importance of the diagram. Darwin’s description of this tree of life is so beautiful that it is usually considered an evidence that The Origins is more a piece of literature than a piece of scientific writing. The Tree of Life is a metaphor for the relationships between all creatures of the same class:

As buds give rise by growth to fresh buds, and these, if vigorous, branch out and overtop on all sides many a feebler branch, so by generation I believe it has been with the great Tree of Life, which fills with its dead and broken branches the crust of the earth, and covers the surface with its ever branching and beautiful ramifications. (Darwin 127)

The tree illustrates Darwin’s concepts of species divergence and extinction. Evolution is like a big tree: many branches emerge from a common trunk, some branches die off, representing extinction, other branches multiple and diversify over time.

Fig. 7. The Tree of Life, from Charles Darwin, The Origin of Species (1859). Distinct species are labelled A – L on the horizontal base line. These species labels, positioned above broken lines at different angles, suggest that they have diverged from one or more common ancestors. On the vertical axis, labels I – XIV represent a thousand generations. From A, diverging lines show continuous and varied deviation from the original species. Some of new deviations become extinct; some continue to diverge. After ten thousand generations descendants of A have become distinct sub-species: a10, f10, and m10.

Networks are not just a scientific metaphor, the concept has influenced painters, sculptors, architects, and designers in recent years. Manuel Lima coined the term “networkism” to refer to the new art movement driven by network science. The movement can be most clearly seen in new fields such as information science and data visualization, but several traditional artists also take up on the challenge. Sharon Molloy infused her skill as a painter with her curiosity about modern science to create mesmerizing paintings that are not unlike scientific graphs one usually comes across flipping through Nature or Science magazine (see fig. 8.-.9.). Exhibited in the museum, the artworks attract us not only because of the intricate lines, the interconnected structure, the rhythm of the brushstrokes, the appealing colors, or the familiar resemblance to natural patterns, they also call our attention to the impact modern science has on our lives.


There is a recurrent association between the depiction of complex networks and one particular art movement: abstract expressionism, in which Jackson Pollack is the key figure. Pollock’s drip paintings evoke large-scale views of networked systems, where the individual part is lost in the density of interconnectedness. Fig. 10. and fig. 11. show a striking resemblance between the dripping trajectories of Pollock’s paintings and the detailed view into a rat’s neuronal network. Fig. 12. and fig. 13. show similarity between Pollock’s Number 5 and an image of ten thousand neurons in a single neocortical column generated by IBM’s Blue Gene supercomputer. Of course, correlation does not mean causation; Pollock might or might not have been inspired by complex networks, but the juxtaposition of the images suggests a natural affinity between science and the arts.


In architecture, the avant-garde architectural style parametricism reflects a heavy influence of technological advances and network science. Parametricism relies on programs, algorithms, and computers to manipulate equations for design purposes. It avoids rigid forms, simple repetition, and isolation of entities. According to Patrik Schumacher, partner at Zaha Hadid Architects, the most well-known advocate of the style, parametricism mimics the soft organic form of nature and requires all parts of a building correlated to reflect the network society that we are living in. Parametricism displays a very modern beauty that can be intimidating and alien compared to our familiar living and working space, but it also shows the courage of architects who readily embrace science to make a strong artist statement, and to extend the boundaries of architectural designs.

There have been some points of contact between science and the arts in the past, but opportunity to cross-pollinate between the arts and science has never been ampler given recent technological advances, especially the computer’s exponentially increasing computational capacity. From organized complexity and network science emerged a new aesthetics: a beauty that is situated between order and chaos, between simplicity and disorganized complexity, between the arts and sciences, and between the traditional and the avant-garde. Manuel Lima captured the beauty of “Networkism” in his book: “Networks show that there is order in disorder, that there is unity in diversity, and above all, that complexity is astonishingly beautiful” (Lima 243).

Works Cited

Albrecht, Kim. “Visualizing Memes: Culturegraphy – Culture – Memes – Visualization.” Accessed April 24, 2017.

Barrow, John D. “Art and science—les liaisons dangereuses.” Art and complexity (2003): 1-20. Barabási, Albert-László. Network Science. Accessed April 24, 2017.

Committee on Network Science for Future Army Applications (2006). Network Science. National Research Council.

Darwin, Charles. The Origin of Species: By Means of Natural Selection of the Preservation of Favoured Races in the Struggle for Life. Signet Classics, 2003.

Emerging Technology from the arXiv. “Data Mining Reveals the Six Basic Emotional Arcs of Storytelling.” MIT Technology Review. Accessed April 24, 2017.

LaFrance, Adrienne. “The Six Main Arcs in Storytelling, as Identified by an A.I.” The Atlantic, July 12, 2016.

Lima, Manuel. “Visual Complexity. Mapping Patterns of Information.” (2011).

Popova, Maria. “Kurt Vonnegut on the Shapes of Stories and Good News vs. Bad News.” Brain Pickings, November 26, 2012.

Swanson, Ana. “Kurt Vonnegut Graphed the World’s Most Popular Stories.” Washington Post. Accessed April 24, 2017.

Weaver, Warren. “Science and complexity.” Facets of Systems Science. Springer US, 1991. 449-456.