Current Issue: Spring 2007 (Vol I)
Certainly Uncertain: Linking Chaos and Culture
“According to cybernetics, the universe is formed by a series of
feedbacks, positive and negative. . . . From the moment that the
process is set in motion, it can only follow the logic of this chain.”
- Epigraph to “How Much Shall We Bet?”
Calvino sought, through this fabulistic story and others, to make complex scientific ideas accessible to the non-scientist without patronizing the reader or simplifying the science so much as to render it meaningless. He makes the abstract tangible: non-human characters with surprisingly human characteristics interact directly with cryptic concepts and their consequences. Beings that walk among the stars experience a wonder at their formation just the way the reader would.
The first wager Qfwfq and (k)yK place is whether a lone electron and proton flying around in the void will collide to form an atom. The universe is simple and thus easily predictable—or so Qfwfq assumes; he harnesses its uncomplicated logic to deduce future scenarios to bet upon. As the primordial cosmos becomes more complex over time, the stakes likewise become higher. At first, the companions bet on simple physical phenomena just for bragging rights. But eventually they try to foresee the actions of individuals and nations for fittingly more substantial winnings. “Conversely, the more I went ahead, the better I understood the mechanism,” Qfwfq observes, whereas the baffled (k)yK, who is not as quick and lacks imagination, simply plays along with his companion’s game.1 It is Qfwfq who initiates every wager; (k)yK’s role is simply to posit the exact opposite result.
Over billions of years, Qfwfq exploits his foreknowledge of further and further minutae to increase his winnings until his luck inexplicably turns. Qfwfq grasps for a cause: “I had worked out my calculations to their conclusions, I hadn’t overlooked a single component. Even if I were to go back to the beginning, I would bet the same way as before.”2 There is no question in his mind as to the validity of his methods.
It is no accident on Calvino’s part that Qfwfq’s deterministic worldview closely resembles that of Sir Isaac Newton, the renowned physicist whose elegantly simple laws of motion became fundamental to understanding the nature of the universe. Newton was also a devout Christian and believed that the absolute power of God guided that nature. He posited that if one could keep track of the position and movement of each and every particle in existence, one could calculate their interactions and predict the future with exact accuracy.
Nature and Nature’s laws lay hid in night:
God said, “Let Newton be!” and all was light.
It did not last: the Devil howling, “Ho,
Let Einstein be!” restored the status quo.3
Scientists discovered quickly that Newton’s equations worked in theory but were often slightly incorrect representations of physical reality. A few “fudge factors” are needed to make the equations accurately model the workings of the universe. Additionally, there are even some systems that can only be approximated with tremendous uncertainty, such as weather patterns. The interactions of innumerable variables like air currents, moisture, and temperature are so complicated that the local meteorologist can only forecast at most seven days in advance. Even then, only the first few days approach anything like accuracy. How then should scientists “fudge” their predictions in order to make them right? Like Qfwfq, forecasters have no basis for correcting their methods in the present: only in hindsight can they begin to understand exactly how reality came to deviate from their prediction. (k)yK cites a perfect example: predicting the stock market. He exclaims, “You know something, Qfwfq? The closing quotations on Wall Street are down 2 per cent, not 6!”4
In the 20th century, chaos theory was developed to help explain why such patterns go awry. This branch of science postulates that while the universe is not nearly so ideal and orderly as once thought, there is some kind of underlying order to the disorder. This is a very dense concept and will require some explication. Chaos: Making a New Science, by James Gleick, is an excellent continuing resource for those readers whose interest is piqued by Calvino’s introduction to the topic.
Chaos theory posits that systems of all ranges of complexity have an extreme sensitivity to initial conditions. Running an experiment over again inevitably gives a slightly different result. The sensitivity of the system is even greater than the scope of our measurements of the initial conditions. For example, if the starting temperature in an experiment is measured as 3000°C, then even a small variation in the actual temperature, such as 3000.01°C, will make a notable difference in the final result. This initially minute difference is compounded exponentially: the further we get from the start of our calculations, the more complex the system gets, and the harder it is to predict what will happen next. Besides the fact that we can never make a precise enough measurement, quantum physics has also shown that via the very act of measurement we influence the system and cannot completely stand apart from our observations. Qfwfq eventually becomes conscious of this inevitable progression and accepts that he has no control over it.
Contemporary sciences like quantum mechanics—which demonstrates that one can make predictions that give, at best, probable results—assert that there is a degree of uncertainty to universal truths. This is a disconcerting notion to seekers of knowledge. Qfwfq comes to reminisce about the more straight-forward early universe, literally, “the good old days,” when things were much simpler. His realization of the increase in complexity mirrors the growing prevalence of empiricism and rationalism during the Enlightenment, which cast fundamental doubt on the absolutes that guided society in its pre-modern times. For instance, an epidemic was no longer merely the wrath of God upon sinners, but the patterned spread of a dangerous virus that mutates and evolves to combat various treatment methods.
Just as Qfwfq was discomforted by the growing uncertainty he saw in the universe, even cutting-edge theorists find a limit to how much they themselves can tolerate. Einstein made world-changing scientific contributions in the 20th century such as the theory of relativity, but he proclaimed that “God does not play dice with the universe.” By this he meant that he too believed in a higher order that governed the universe. He could not bring himself to accept the strangeness and chance of quantum mechanics. Joseph Ford, a prominent 20th century physicist, later responded to Einstein’s aphorism with a chaos theory quip of his own: “God plays dice with the universe, but they’re loaded dice.”5 Ford asserted that it was physics’ task to figure out by what rules those divine dice were loaded; it takes Qfwfq some eons to realize that his craps shoots are fixed, but he does not seek out the rules that Ford intuits.
Despite its name, chaos theory strongly suggests a deeper relational structure, albeit an unexpected one. One of the most counter-intuitive aspects of chaos theory is that complex systems can have simple causes and simple systems can have complex causes. We are used to the opposite: in a fixed volume, say a propane gas tank, as the temperature is increased, the pressure should increase proportionally (until the tank can no longer withstand the force and explodes). This is a linear relationship. Through chaos theory, however, we can see non-linear relationships: a small change in one variable can have extraordinarily large effects, and the network of interactions between variables can become so compounded that the links between cause and effect are distorted to immense proportions. A variation on the oft-repeated chaos theory question is, “Can a butterfly flapping its wings on one end of the planet cause a hurricane on the other?”
Everyday experiences now become appropriate inquiries for science; pondering the formation of clouds in the sky or snowflakes in a blizzard was once considered silly daydreaming. Elucidating the origins of snowflake structures is a good example of gaining new insights into the mundane. It is commonly said that every snowflake is unique, and it is hard to disagree in light of the amazing complexity of their patterns of six-sided symmetry. Scientists have developed a model of their formation that shows “a delicate balance between forces of stability and forces of instability” between the surface tension of water, previously thought to be negligible, and the diffusion of heat.6 In this way, the rules of formation are very deterministic; but there are an innumerable number of paths of falling through the sky as well as wind conditions, air pollutants, and other factors that influence the balance of forces differently, adding an indeterminate element of randomness.
In the story, Calvino draws a parallel to this method of chaos theory, because the cosmic beings, too, use a complex system of events to examine a simple, almost arbitrary, action. Qfwfq challenges (k)yK to a bet on which direction a young Italian woman in 1926 will turn as she leaves her home. Qfwfq must take into account all of the minute things leading up to that moment in the woman’s life to guess what she will do. She must have a destination and so will determine a path for herself, but whether she takes the long way or the short way could only depend on her mood. Perhaps, she will take a longer stroll because her day had been delightful. Or maybe she was warned to take care when alone in the evening and will move swiftly.
Gleick notes that each snowflake “records the history of all the changing weather conditions it has experienced, and the combinations may as well be infinite.”7 The young Italian herself is a living record of all of her experiences and is thus unique as well. A central aspect of post-modern perceptions of history is that every person experiences a different history, and because of this fact, there cannot be one God’s-eye view, just as there is no one form that can summarize all the possible snowflakes.
The question for the post-modern historian then becomes: What events remain relevant in a history? This discussion of chaos theory suggests that every little detail has an impact, although it is sometimes seemingly invisible. Keeping track of everything could, however, lead to an information overload and a perception of the present that
Qfwfq describes as “intrinsically illegible, a doughy mass of events without form or direction, which surrounds, submerges, crushes all reasoning.”8
Nevertheless, Qfwfq, for all of his eons of experience, has missed the applications of chaos theory despite deducing its influence. We must not worry ourselves over direct causes, but must sift through the “doughy mass” for what are called “strange attractors” in chaos theory, the patterns that guide which type of chaos results from a process. One of the primary lessons from chaos theory is that every apparent collection of random gibberish is not necessarily equivalent to every other one. Perhaps immensely complex parts of history like the movement to genocide or war repeat themselves despite obvious lessons from the past because of a strange attractor like tribal loyalties, which can drive people to do unexpected and chaotic things.
With its strict doctrinal emphasis on rational investigation of natural phenomena, science has come to represent a new post-Enlightenment source of absolute knowledge for the lay modern. The oft-made assertion is that, given enough time, scientists will discover all of the secret inner-workings of the natural world; humanity will master and dominate its environment, destroying the scourge of cancer and harnessing the very weather itself. What is daunting, even to trained scientists, is the realization that this is very likely a false hope; developments like chaos theory have not only exposed many new limits and restrictions to how much we can know, but also questioned how much raw information we can process in order to fathom that limited knowledge. We are faced, then, with a new strangeness of reality, but despite the lack of preparedness we seem to have for it, we still possess a strange attractor to guide our perceptions of our chaotic world. Indeed, modern science exhorts us to “expect the unexpected.”
1. Italo Calvino, Cosmicomics, trans. William Weaver (New York: Harcourt Brace Jovanovich, 1976), 88.
2. Ibid., 91.
3. N.C.C. Sharp, “Nature’s laws revealed in rhyming couplets,” Nature 413 (2001): 108.
4. Italo Calvino, 93.
5. James Gleick, Chaos: Making a New Science (New York: Penguin Books, 1987), 314.
6. Ibid., 309.
7. Ibid., 311.
8. Italo Calvino, 93.
Damien Croteau-Chonka is a senior in the school of Arts and Sciences Honors Program majoring in Biochemistry. He is interested in making science accessible to the common person, especially in light of the growing presence of science and technology in everyday life. He will be continuing on to graduate school in the fall to study computational biology and bioinformatics.