Nature is so predictable. Or is it? On Monday, August 21, 2017, thousands will travel to see the first total solar eclipse in the contiguous United States since 1979. Peering back into the minds of our ancestors, we often recount ancient eclipse memories as omens of chaos.
And yet, harbingers of chaos to some were signals of regularity to others. For ancient civilizations such as the Chinese and the Greeks, eclipses underscored the periodicity of nature and the triumph of human forecasting. The accuracy of eclipse forecasting culminated with English astronomer Edmund Halley’s prediction of the solar eclipse of May 3, 1715 within four minutes of its actual occurrence. Halley’s historic prediction, based on recently invented Newtonian physics, broadcast the deterministic nature of the universe to all humanity. Nature works like clockwork. We need only understand the laws of nature to extrapolate the positions of all objects to the end of time.
“Even hours before the eclipse, the befuddling surprise of defiant weather is possible.”
Or do we? We know with the greatest possible human certainty that a rare solar eclipse will occur this year on August 21. Yet we are ironically mocked by the elusiveness of something as mundane as a weather forecast. One journeying to see the eclipse can be certain of its occurrence, but not of weather permitting its observation. Even hours before the eclipse, the befuddling surprise of defiant weather is possible.
Befuddling surprise was central to the work of Swiss artist Jean Tinguely, whose sculptures and “méta-matics” were capable of creating music, chaos, and self-destruction. Tinguely shocked the art world when his infamous Homage to New York deliberately burst into flames before a crowd at the Museum of Modern Art in New York in 1960.
Less known is Tinguely’s humble but elegant Bascule XIII, a moving sculpture which closely resembles what physicists call a double pendulum. A long blade with 360 degrees of movements is hinged to the short blade of fan, dancing chaotically when the fan is turned on. Similarly, the physicist’s double pendulum elegantly demonstrates the concept of chaos theory. A simple pendulum, like the one you might remember from high school physics class, is entirely predictable. Yet attach a second pendulum to the bob of the first pendulum, and a chaotic dance of motion ensues.
There’s no magic here. The chaotic dance is, in principle, entirely choreographed and predictable. Yet its motions are so sensitive to the starting position that errors in its measurement yield errors in prediction that, like the weather forecast, grow exponentially the further one looks into the future. Tomorrow’s weather forecast? Safe bet. Next week’s forecast? Don’t count on it. Next month’s forecast? Don’t bother.
As we observe chaos outside us, there is chaos within us as well. On the continuum from eclipses to weather, where do our brains fall? Like coupled pendula, the electrical rhythms of coupled cells in the brain seesaw back and forth with the utmost sensitivity to a plethora of conditions. The human brain boasts as many neurons as our galaxy does stars, and predicting each cell’s activity would be an exercise in futility.
Yet individual neurons do not a person make. From studying chaos, scientists can deduce general principles that transcend parts of a system. One pattern of activity seen in the brain, called “pink noise,” has been understood through a computer model that began with many coupled pendula arranged in a grid. Avalanches of activity spread through the grid, much like bursts of activity seen in the brain. Such avalanches may allow the brain to switch between states of activity or rapidly make choices as cells reach a decisive crescendo.
Art imitates life. In similar spirit to Bascule XIII are a series of works by Tinguely such as Méta-Matics No. 14. In this and similar sculptures, a pen is jostled across a sheet of paper by wild, chaotic movements. The pen traces the contours of chaos, resulting in a pattern of swirling lines that closely resembles what physicists call a strange attractor.
Attractors show all states of a system and offer understanding of its motion. For planets and simple pendula, the signature of regularity is a circular attractor. But so called strange attractors were discovered when meteorologist Edward Lorenz, attempting to understand the weather, found that the atmospheric attractor appeared beautiful and complex, like the wings of a butterfly. Soon after, Lorenz summarized the essence of chaos theory in a talk titled “Does the Flap of a Butterfly’s wings in Brazil Set Off a Tornado in Texas?” The Butterfly Effect was born.
Neurons are capricious beasts indeed. By transforming small The potential energy between two points in space felt by an ... changes into large spikes, neurons sow the very seeds of chaos. Indeed, nonlinearity—large effects triggered by small causes—is the foundation of chaos theory. Brain cells sleep like dragons, switching between deep slumber and light sleep. These phases are known as down states and up states, respectively. During a down state, the The functional unit of the nervous system, a nerve cell that... stands stoically against turbulent inputs. But during an up state, the neuron is especially hot tempered. The smallest signal from a neighboring cell may awaken the beast into a fury of A series of repetitive action potentials generated by one or.... While not quite the hurricane imagined by Lorenz, neurons are known to fire chaotically when pushed to their limits.
“…chaos is woven into the very fabric of the brain’s inner workings.”
Single neurons are usually predictable, but the billions of neurons in the human brain are a symphony of chaos. Indeed, the seemingly random outbreak of an epileptic seizure may have its roots in the chaos of the brain. And yet, this mocking unpredictability may be one of the brain’s great strengths. As the physicist Emerson Pugh said: “If our brains were simple enough for us to understand them, we’d be so simple that we couldn’t.” Indeed, work by the late neuroscientists Walter Freeman III suggests that chaos is woven into the very fabric of the brain’s inner workings.
While art, brains, and weather descend to chaos, we look to the heavens for dependability and regularity. That we can predict solar eclipses more than a millennium in the future seems like evidence of our celestial omniscience.
Yet this is not so. The Solar System moves slowly, and a millennium is merely a millisecond on a cosmic scale. While the motions of planets and moons are often regarded as the paragon of stability, the Solar System, too, is chaotic. Like next month’s weather forecast, the position of Earth in its orbit ten million years from now is anyone’s guess. That means ten million years from now (in orbits) might not really be ten million years from now (in days). And catastrophic possibilities may await. In a twist of interplanetary self-destruction echoing Tinguely’s self-sabotaging sculptures, gravitational influences between planets could fling Mercury into the Sun or the Earth in a few billion years. The butterfly flaps her wings, and the planets cower in fear.
Rejoice. Chaos rules all.
Eclipse artwork by Jooyeun Lee, adapted from photograph by Wikimedia Commons user Luc Viatour.
Bak, P., Tang, C., & Wiesenfeld, K. (1987). Self-organized criticality: An explanation of the 1/f noise. Physical review letters, 59(4), 381.
Beggs, J. M., & Plenz, D. (2003). Neuronal avalanches in neocortical circuits. Journal of neuroscience, 23(35), 11167-11177.
Millman, D., Mihalas, S., Kirkwood, A., & Niebur, E. (2010). Self-organized criticality occurs in non-conservative neuronal networks during/up/’states. Nature physics, 6(10), 801-805.
Laskar, J. (1989). A numerical experiment on the chaotic behaviour of the solar system. Nature, 338(6212), 237-238.
Laskar, J. (2013). Is the solar system stable?. In Chaos (pp. 239-270). Springer Basel.
Laskar, J., & Gastineau, M. (2009). Existence of collisional trajectories of Mercury, Mars and Venus with the Earth. Nature, 459(7248), 817-819.
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