Synchrony and spontaneous order

Summary: The world is filled with examples of spontaneously emerging order.

Humans are familiar with order: people order homes by placing belongings in one place; people also watch football games with players who follow orders given by a quarterback who directs the play. There are many examples of order in nature. Birds and fish order themselves by flying in flocks and swimming in schools. How is order created in a complex system with many parts? Experience indicates that order emerges from the actions or directions of a leader, just as the quarterback is the leader of a football team. It is possible, however, for a system to be ordered without the help of a single leader—an attribute that occurs in a spontaneously ordered system. Systems have a global (group) level and a local (individual) level. A school of fish is made up of thousands of individual fish, and a laser is a collection of particles of light (photons) that are emitted from trillions of atoms. When a system is spontaneously ordered, the order occurs because of local level interactions without global level direction. Imagine a spontaneously ordered football team. The quarterback on this team does not need to direct or call a play. This team is able to organize and execute plays simply by communicating with each other (individually) as each play unfolds. There will likely never be a team like this, but spontaneously ordered phenomena are all around if one knows where to look.

When multiple events are ordered in time, the result is “synchrony.” Without synchrony, life would be very different. People would not enjoy watching a football game with unsynchronized players who run in different directions after—or before—the ball is snapped. Many of the technological devices that people use, including GPS, cell phones, and lasers, rely on synchrony to work properly. Scientists have even published evidence of synchrony in cloud patterns. When spontaneous order occurs, the result is often synchrony. Mathematicians and statisticians are involved in the collection of data that help define important variables related to synchrony and fuel the development of theories and models, as well as the formulation of mathematical models to describe and explain synchrony. This work draws from many areas of mathematics, including logic, probability, decision theory, geometry, and statistics, as well as related scientific fields.

Examples of Synchrony and Spontaneous Order

In some regions of Southeast Asia, large numbers of male fireflies flash on and off at the same time, creating a spectacular array of synchronized lights. It is believed that the males are flashing in unison to attract females. Physiologically, these fireflies have an internal firing mechanism that can generate a rhythmic flashing sequence. Experiments with individual fireflies demonstrate that the timing of their flashes can be altered to mimic that of an external stimulus, which is flashing rhythmically. This suggests that synchronized firefly flashing is the result of a spontaneously ordered process. To test this hypothesis, mathematicians Renato Mirollo and Steven Strogatz created a simple mathematical model by using an equation to describe an individual firefly as a biological oscillator (just as a plucked guitar string is a mechanical oscillator). They coupled multiple, identical oscillators together to form a system. Their mathematical model is a system of coupled differential equations. Mirollo and Strogatz analyzed the system and proved that in almost all cases, no matter how many oscillators there are or how the oscillations are started, synchrony is the result.

Fish often travel in schools. One advantage of this behavior is to allow fish to better avoid predators by performing highly synchronized, evasive maneuvers. Experimental data suggests that schooling fish have a preferred distance, elevation, and orientation relative to their nearest neighbor. Scientists Andreas Huth and Christian Wissel have modeled fish schooling as a spontaneously ordered system. They assume that schooling originates not because of a particular fish directing the group’s movements but because of simple behavioral rules for individual fish. Their assumptions include that each fish desires to be close (but not too close) to another fish, each fish moves according to its perception of the position and orientation of neighboring fish, and individual fish movement is random. Huth and Wissel tested different movement rules for their model since there are no data that supports specific movement rules for schooling fish. They used the data generated from computer simulations of their model to determine the average direction of movement as a group and the average angular deviation by individual fish from the group’s direction, which is defined as the “polarization” of the school. The polarization is a way to quantify the synchrony of the school because the larger the polarization, the more disoriented the school is. Since polarization depends on the movement rules, they used polarization to find movement rules for which their model best simulated synchronized schooling.

A fluorescent light bulb consists of a long tube filled with an inert gas. The light that we observe originates from the atoms in the gas. Each atom has multiple electrons that exist at specific energy levels. Electricity forces electrons through the tube and these electrons collide with the atoms in the gas. The collision raises the energy level of the atom’s electrons, which then spontaneously revert back to a state of lower energy. This loss of energy causes a light particle (photon) to be emitted and the light that we see is from the emission of millions upon millions of photons. The light from a fluorescent light bulb consists of many different wavelengths and is scattered in many directions. Alternatively, the light from a laser, which stands for “light amplification by stimulated emission of radiation,” is highly synchronized with a single frequency, direction, and phase. The first laser was constructed in 1960, but in 1917, Albert Einstein developed the quantum physics that predicted how a laser is able to synchronize the photons. When lasers were invented no one knew what to use them for.

Today, laser light is used for everything from grocery store checkout scanners to eye surgery. Just as with fluorescent light, raising and lowering the energy levels of individual electrons generates the light from a laser. An external energy source (such as electricity) continually stimulates electrons and raises them from lower energy states to higher energy states. Initially, when the laser is turned on and some electrons spontaneously fall back to their lower energy states, the emitted photons move in random directions. But a laser has mirrors at both ends and the photons are trapped between the mirrors for a long period of time before they can escape. Furthermore, a laser is constructed so that the photons will perfectly synchronize and amplify a light wave with a specific frequency and direction while filtering out the other light waves. One of the mirrors allows some of the light to escape in the form of a laser beam, an example of synchrony that we encounter each day.

Bibliography

Camazine, Scott, Jean-Louis Deneubourg, Nigel R. Franks, James Sneyd, Guy Theraulaz, and Eric Bonabeau. Self-Organization in Biological Systems. Princeton, NJ: Princeton University Press, 2001.

Haken, Hermann. The Science of Structure: Synergetics. New York: Van Nostrand Reinhold, 1981.

Strogatz, Steven. SYNC: The Emerging Science of Spontaneous Order. New York: Hyperion, 2003.