Book Review: Sync: How Order Emerges from Chaos in the Universe, Nature, and Daily Life – by Steven Strogatz (Hyperion, 2003)
This one is an interesting foray into chaos and complexity theories and tendencies toward synchronization and self-organization. Strogatz is a mathematician. The book is ‘dry’ in parts but is not overly complex for the ‘slow’ reader like myself. Synchronization occurs in nature at all scales from atomic nucleus through cosmos.
Spontaneous order is mysterious, he says. Synchronization is a kind of order - in time. He distinguishes accidental temporary sync with persistent long-lasting sync. We tend to like sync such as the rhythm of music. We tend to interpret persistent sync as a sign of planning, choreography, or intelligence. Seeing sync like schools of fish, synced fireflies, or in my case noticing that my geese and ducks (and one rooster) can be herded in sync as one unit, is fascinating. Sync among non-intelligent entities like cells and electrons is even more mind-boggling.
The science of synchrony (sync) studies “coupled oscillators.” Oscillators are “entities that cycle automatically, that repeat themselves over and over again at more or less regular intervals.” Two or more oscillators are said to be coupled if they influence one another physically or chemically. Coupled oscillators may be many things: planets, heart cells sending electrical signals, or various units of life and matter. Strogatz studies sync mathematically and notes that there are practical applications present and future, many of them medical and safety oriented.
He goes through the history of the study of synchronized firefly flashing. Biologist John Buck and colleagues discovered that the rhythm of flashing was regulated by an internal oscillator that could reset. Somehow all this internal resetting, adjusting to the flashing of others, without intelligence, accounts for the well-timed synchrony observed in many firefly species. Strogatz goes so far as to call the tendency to synchronize one of the most pervasive drives in the universe. Different syncs – say the moon’s ability to spin at the exact same rate that it orbits the earth so that we only ever see one side of it from here (caused by tidal effects) or the synchronized swimming of sperm on the way to egg or the pacemaker cells of the heart – are linked by mathematical relationships. In many ways nature is collectively precise without a leader.
The author was inspired by a book by biologist Art Winfree called The Geometry of Biological Time. Impulses often did not change smoothly. Instead they tend to jump which makes them harder to study with calculus and algebra. With multiple oscillators studying them mathematically becomes unwieldy and nearly impossible. Simulations are another method but far less precise than math. Peskin’s stroboscopic simulation method was more satisfying for the author who described the synchronization of his own experimental simulations as “spooky.”
Strogatz and a grad student describe the tendency of synchronization to be due to what they call “absorption” where one oscillator “absorbs” another in the sense that once the absorbed becomes synchronized with the absorber they stay in sync irrevocably. That is, after they hit a threshold. They may be changed by other oscillators but will change together. Absorption is how oscillators “clump” together eventually resulting in a fully synchronized system or unit. This all happens according to mathematical proofs and logic. The synchronized firing of neurons and the way an earthquake happens after stresses cross certain thresholds are other examples of sync. There are many more. Another idea called ‘self-organizing criticality’ by physicist Per Bak was found to be synonymous with sync. Even though the study of sync has been mocked as frivolous by some politicians, there have been practical benefits. Early internet routers were plagued by pulses that showed sync that causes congestion and so engineers had to devise a means to “clock” computer circuits more efficiently.
Only male fireflies flash in sync and proposed explanations for it have much to do with mating: to advertise the scale of the males available, to take advantage getting lucky by being mistaken for another male, and to not stand out as prey so much to predators. In humans, females sometimes show sync when their menstrual cycles synchronize after being together for long periods. One of the leading possible explanations for the mechanism of sync involves pheromones, chemicals that may signal to sync. Among women some experiments showed that something in their sweat (pheromones) may signal the menstrual cycles to sync. Other experiments did not verify that so that explanation is still unproven. While the pheromones certainly influence the cycles of other women those cycles do not always end up synchronized. Thus, the behavior is more complex than the sync of fireflies. The complexity is enough that synchronized menstruation is difficult to predict. Some have theorized that they do this so they can share some child-rearing and breast-feeding duties which can result in healthier offspring among mammals. Strogatz notes that the shear complexity of some systems makes mathematical modelling of them an art as well as a science.
Next is an ode to the work of Norbert Weiner, the founder of cybernetics. Weiner was the first to point out the pervasiveness of sync in the universe. He dived into the study of brain waves suspecting them as indicative of some internal clock mechanism to coordinate brain activities that occur many times in a second. He speculated that oscillators in the brain pulled on the frequencies of individual ones to speed them up or slow them down to achieve synchronization. So, the brain waves are a kind of consensus of the mental state. He believed that this ‘frequency pulling’ was a key mechanism of ‘self-organizing.’ He failed to adequately describe this situation before his death in 1964 but a year later Art Winfree would do so. He focused on the ability of oscillators to send and receive signals. Coupled oscillators influence one another and the sensitivity to being influenced changes according to the cycle. Winfree stated that:
“At any instant, an oscillator’s speed is determined by three contributions: its preferred pace, which is proportional to its natural frequency; its current sensitivity to any incoming influences (which depends on where it is in its cycle); and the total influence exerted by all the other oscillators (which depends on where they all are in their cycles)”
That makes the mathematics very complex and the future can be predicted from the present by differential equations, or calculus. Linear differential equations are solvable but non-linear ones, including those involving competition or cooperation, are unsolvable. Winfree utilized computer simulations to attempt to solve the equations. Once some clumps begin to synchronize they can be “heard” over the background and this can lead to synchrony of the system. Group sync was not hierarchical but was not democratic either, he discovered. Winfree realized that group sync was analogous to phase transition (like the transition from liquid water to solid ice). In phase transition, at a certain temperature there is a reorganization that results in a new structure. Sync is similar, but in time rather than in space. This was an “unexpected link between biology and physics.” Non-linear dynamics and statistical mechanics could now be hybridized into a new theory. In 1975 Japanese physicist Yoshiki Kuramoto finally was able to solve the differential equations related to sync which were considered possibly unsolvable. He defined the ‘order parameter’ which gives a value of 1 to perfect sync and a value of zero to no sync. In his analysis he noted that only a total non-sync, a partial sync, or complete sync were possibilities. He realized that the oscillators must be similar enough to each other in order to synchronize. Strogatz set out in 1986 to study the Kuramoto model. He eventually used techniques developed by plasma physicist Lev Landau. Weiner’s frequency pulling turned out to be not as clear cut as thought but it was found for certain that oscillators affect the frequency of other oscillators.
Next, he delves into the sync of the human body in sleep-wake cycles. We are tuned through evolution to the day-night cycle and being out-of-sync with it due to things like working the nightshift can wreak havoc. Apparently, we have a ‘circadian pacemaker,’ a ‘neural cluster of thousands of clock cells in the brain, themselves synchronized into a coherent unit.” This cluster influences other cells and organs to do what they do at the right times. Sync in the body occurs at three levels, he notes: sync in cells within an organ, sync between organs where they ‘period match,’ and sync between our bodies and the world around us – this last one, rooted in the day-night cycle, is called external synchronization, or entrainment. There is still much to learn about these circadian rhythms. Hormone fluctuations, digestion, alertness, dexterity, and cognitive performance are all related to these daily rhythms. Experiments with people kept from the sun have shown that their body temperature cycle (changing in a 1.5 deg F range) will sync up with their sleep-wake cycle. Some circadian rhythms were found to be 26 hours, some closer to 22 hours so they vary. However, some people desynchronized radically after long periods away from the sun, typically with long wake and long sleep cycles seemingly randomly thrown in. Their body temperature cycle, however, remained the same. This became known as ‘spontaneous internal desynchronization.’ Only the sleep-wake cycle varied, while the temp and hormone secretion cycles stayed with their variation of daily. Even though the desynchronization seemed random there was logic in the data as expressed with raster plots. The beginning of long sleeps coincided with higher body temps and the beginning of short sleeps coincided with lower body temperature. Results were strong correlations that sleep length was related to phase of temperature cycle. Many other physiological and cognitive processes were linked to the phase of the temperature cycle.
It has also been found that the REM cycle during sleep is also entrained with the body temperature cycle. It is most likely to be initiated just after the body is coldest which is why it more often occurs near the end of the sleep cycle. Other cycles such as the short-term memory cycle, release of the hormone melatonin, and other cognitive and physiological functions maintain phase relationships with the body temperature cycle and with one another. The biological clock ties everything together. The cells of organs also display circadian rhythms. Eventually, the suprachiasmatic nuclei, two clusters of neurons in front of the hypothalamus was identified as where the circadian pacemaker resides. Built in to our daily cycles are times of drowsiness corresponding to the siesta in the day (1-4PM) and the zombie zone at night (3-5AM). These are times when accidents are likely to occur. Times of maximum wakeness were also found, their peaks being 10AM and 9PM. Night shift workers tend to have trouble with synchronization and there are some things they can do to help. Light has a strong synchronizing effect. 80% of blind people suffer from some form of sleep disorders. The other 20% likely have intact circadian photoreceptors in their retinas, even if they can’t see.
An example of circadian sync is that of leaves of plants opening in the day and closing at night. Several trees do this. In 1665 Dutch physicist Christiaan Huygens noticed that two pendulum clocks (he invented them) would synchronize their pendulum swings within a half-hour no matter where they started from. There are many other examples of non-living things spontaneously synchronizing. Lasers, utilized in many things including CDs, laser surgery, and supermarket scanners, rely on synchronized light emissions. Even our regional power grids utilizing different power generators or power plants end up operating in sync.
Atomic clocks, the most accurate clocks we have, rely on sync. They “count the transition of a cesium atom as it flits back and forth between two of its energy levels.” Atomic clocks made possible GPS systems which can pinpoint positions in space from far away with accuracy. GPS allows synchronization better than a millionth of a second which is also useful for coordinating financial transactions. Each of the 24 global positioning satellites carries 4 atomic clocks synchronized within a billionth of a second of one another by a master clock in Boulder, Colorado.
In the wider universe, another example of inanimate sync is orbital resonance. In the case of two linked planets orbiting a star one version is where one will orbit the star at exactly twice the rate as the other. Even more remarkable is the case of our own moon that spins on its axis at exactly the same rate it orbits the earth, which is why we only ever see one side of the moon. In that case the earth’s gravitational pull of the moon is balanced by the moon’s centrifugal force at the center of the moon. The moon’s weight distribution (it is bottom-heavy) provides the corrective torque to bring it back into sync. Another example of astronomical sync (orbital resonance) is the calculated orbital periods of asteroids in the asteroid belt between Mars and Jupiter, which are always precisely mathematically related to the orbital period of Jupiter. The point of closest approach of the asteroid to Jupiter always occurs in the same place of both of their orbits, similar to Huygens’ pendulum clocks synchronizing.
Quantum choruses is the next chapter. Superconductivity showed that perpetual motion was possible near but slightly above a temperature of absolute zero, which defies the laws of classical physics. The new theoretical science of quantum mechanics would mathematically solve this riddle and many others. Electrons pairing up and cooperating in sync would be the key to superconductivity. In 1995 physicists at a lab in Boulder, Colorado were able to get temperatures down to less than a millionth of a degree above absolute zero (mind-boggling) and this showed that atoms began behaving as one super-atom. This is ‘quantum phase coherence,’ the basis of the laser. Electrical resistance drops to zero at a certain low temperature, which is the basis for hopes of superconductivity as the basis of a much more efficient form of electrification. Apparently, this has to do with the “communal behavior” of paired electrons. With materials research in the search for superconductivity, which was a major research issue in the 1980’s, it was found that some materials could be coaxed into superconducting behavior at much higher temperatures, but unfortunately, not high enough to be feasible in the real world. There are many other hurdles as well.
A young grad student, Brian Josephson, in the early 1960’s discovered that “supercurrent” could have a counterintuitive mathematical relationship (like many quantum-level processes). Physicist Richard Feynman soon discovered that these “Josephson effects” in superconductivity could theoretically occur for many “phase-coherent” systems. In 1997 one was found: superfluid helium. Strange quantum effects account for the Josephson effects, like quantum tunneling and quantum sync. “All liquids become highly ordered when cooled to very low temperatures.” Josephson’s theory involved sandwiched superconducting materials that later became known as “Josephson junctions.” They have led to the most sensitive detectors in science known as SQUID – superconducting quantum interference devices. They have been developed and used to great success in medical imaging and show potential for supercomputers, or rather superconducting computers. Josephson received a Nobel Prize in 1973 but soon thereafter devoted his work to paranormal research, thinking that one day quantum theory could explain telepathy. This was not well received by his physicist colleagues, but Josephson believes (if he is even still alive) that it is possible. It was noticed that Josephson junctions, like the motion of pendulums. Is non-linear. The motion of a pendulum is affected by gravity, angles, and torque. Josephson junctions are affected by phase. Breakthroughs in chaos theory aided in the study of sync with the development of non-linear dynamics.
The author began a collaboration in 1990 with Kurt Wiesenfeld, studying the non-linear dynamics of Josephson junctions. They developed a method of study and representation involving two-dimensional graphs that made interesting geometrical shapes. They were shocked to find that “every solution is periodic.” They suspected a “secret symmetry” in the equations. What they discovered was essentially the Kuramoto model! The Millenium Bridge opened in 2000 in England but when hundreds of people began walking on both sides of it, it began to sway and increased its swaying to the point where the bridge was shut down. Apparently, people walking to catch their balance in response to the sway was amplifying the sway. It was Josephson who figured out the sync mechanism that was causing the amplified swaying.
Next, he delves more into chaos theory and non-linear dynamics with accounts of Lorenz coming up with his equations back in 1963. Chaos theory overlaps with complexity theory as chaotic systems are mathematically complex. He refers to the “second wave” of chaos theory where it was discovered that chaotic systems exhibit a new kind of order. Chaos now had laws. James Gleick’s 1987 book, Chaos, brought chaos theory to the masses (I have read most of it and one day may finish it for a review here). Chaotic systems mostly defy predictability, but it has been found that two chaotic systems can sync up. Synchronized chaos shows that chaotic systems only appear to be random. In reality they are subject to certain laws.
“These, then, are the defining features of chaos: erratic, seemingly random behavior in an otherwise deterministic system; predictability in the short run, because of deterministic laws; and unpredictability in the long run, because of the butterfly effect.”
The butterfly effect is simply the observation that in chaotic systems small discrepancies or disturbances can end up changing the whole dynamics of a system, rendering it non-predictable. A chaotic system requires precision in the initial measurement of the system to get predictability, but only short-term predictability.
“Just as a circle is the shape of periodicity, a strange attractor is the shape of chaos.”
In both cases dynamics are converted into geometry. On a practical level, chaotic systems provided the means for “chaotic encryption” of electronic communications, which is unpredictable enough to defy decryption.
Next, the author explores sync in three dimensions. He goes back to 1982 when he accepted a summer job with Art Winfree at Purdue University to study topology – the study of continuous shape, among other topics. Winfree was the author of many scientific papers relating biology and mathematics, particularly geometry. Another topic of their study was the chemical waves produced in a “Zhabotinsky soup,” a chemical reaction that supports excitatory waves much like those that trigger heartbeat. Chemical waves are like neurons that have three states: quiescent, excited, and refractory (incapable of being excited for a time). One might also compare them to the human sexual response. Zhabotinsky soup (more accurately known as the BZ reaction) allows the unfettered study of wave propagation in excitable media. This led to discovery of a new kind of rotating, self-sustaining wave, shaped like a spiral. Such waves are responsible for tachycardia and the ventricular fibrillation that can result in sudden cardiac death. The waves tend to annihilate on collision with other waves. Strogatz and Winfree were studying these spiral waves in 3D. They helped define scroll waves, scroll rings, and twisted scroll rings, and the rules of such structures. Knots were more difficult. With modern supercomputers there is now much more known about spiral waves and scroll waves and their twisted and knotted forms. They continued to be studied for their role in cardiac arrhythmias.
The next subject is small-world networks. We know that networks have organizing principles and seek to discover them. Even the corpus of scientific knowledge is a network of sorts. Networks are made up of individuals but exhibit network properties, group properties. One version is the so-called “six degrees of separation” that connects us to one another and to others.
“Whenever nonlinear elements are hooked together in gigantic webs, the wiring diagram has to matter. It’s a basic principle: Structure always affects function. The structure of social networks affects the spread of information and disease; the structure of the power grid affects the stability of power transmission. The same must be true for species in an ecosystem, companies in the global marketplace, cascades of enzyme reactions in living cells. The layout of the web must profoundly shape its dynamics.”
Networks are made up of nodes, or connection points. Studying networks with mathematics involves calculating the number of links between nodes. Strogatz and grad students designed simulations to study network connectivity. They defined a term to address a network’s evolving structure – the average path length, which is the number of lengths in the shortest path between two nodes, averaged for all nodes. They found that, counterintuitively, what they call small-world networks are both highly clustered and small, which is apparently different than bigger networks that are often highly clustered and small ones which are typically not highly clustered. The power grid and the nervous system both qualify as small-world networks. Social networks are also likely to be small-world networks, as the experiments in ‘six degrees of separation’ suggest.
“The importance of small-world connectivity is even clearer for processes of contagion. Anything that can spread – infectious diseases, computer viruses, ideas, rumors – will spread much more easily and quickly in a small world.”
Small-world networks have a tendency to self-organize. Statistically speaking, there are networks that organize regardless of scale. These are called scale-free networks and have similar self-organizing properties to the small-world networks.
“At an anatomical level – the level of pure, abstract connectivity – we seem to have stumbled upon a universal pattern of complexity. Disparate networks show the same three tendencies: short-chains, high clustering, and scale-free link distributions. The coincidences are eerie, and baffling to interpret.”
Scale-free networks have been shown to be resistant to random failures yet vulnerable to attacks on their hubs. In a study of the network of protein interactions in yeast it was found that the most highly connected proteins are the most important ones for the cell’s survival.
The last chapter addresses the human side of sync. The author was contacted by the actor Alan Alda, who read his Scientific American article about sync. Alda had long studied fads, a fascination of his. Likely spurred by Richard Dawkins’ idea of memes as a psychological equivalent to genes, he sensed mysteries of group human behavior to be discovered in the study of fads, possibly being some form of sync. Mobs, riots, traffic, and music or sports spectators all exhibit group behavior that sometimes seems to sync up. Sociologists and behavioral economists study group behavior too. Sometimes it’s called herd behavior – since the behavioral choices of others influence one’s own behaviors. We tend to do what our neighbors do. Companies tend to do what their competitors do, often to avoid falling behind or losing market share or profitability. There seems to be a threshold where if enough of one’s neighbors adopt a behavior then we will adopt it as well. Explanations involve ideas like ‘tipping points’ and ‘vulnerable clusters.’ Complexity theory has even been applied to highway traffic where sync does indeed happen when enough vehicles are confined to a certain space. We tend to adjust our speed to the traffic around us. Audiences clapping in unison is another example of social sync. The synchronized marching of German Nazis is another example, not so flattering. Some people see coincidences as a form of sync but the evidence is lacking or perhaps just harder to find. Some suspect sync is even involved in how the brain gives rise to the mind, a major problem in brain science and psychology. Now that we can correlate human thoughts and emotions with activity in different parts of the brain, we can arrive at neural correlates of consciousness. Cognition has been linked to brief outbursts of neural synchrony. Sync may well be a way of binding things together in our minds. Experiments have found that:
“… synchronized neural activity is consistently associated with primitive forms of cognition, memory, and perception.”
The question is perhaps whether sync is essential to cognition or simply just associated with it. Recognition of faces hidden in otherwise meaningless pictures has been definitely associated with synchronized neural activity.
Strogatz sees science as changing from the excessive study of parts to a new holistic study of whole systems. Crafting parts into a whole often involves apparent choreography and that of course suggests sync. The non-linear sciences: cybernetics, sync, complexity theory, chaos theory, etc. are systems sciences. The chemist Ilya Prigogine thinks thermodynamics will come (somehow) to explain the non-linear subjects. Metabolism, as optimal use of energy, does indeed explain some processes.
As noted, this book was tough to grasp and a little boring in parts but overall quite fascinating. The final paragraph of the book goes like this:
For reasons I wish I understood, the spectacle of sync strikes a chord in us, somewhere deep in our souls. It’s a wonderful and terrifying thing. Unlike many other phenomena, the witnessing of it touches people at a primal level. Maybe we instinctively realize that if we ever find the source of spontaneous order, we will have discovered the secret of the universe.”