Sync Quotes

“For reasons we don't yet understand, the tendency to synchronize is one of the most pervasive drives in the universe, extending from atoms to animals, from people to planets. Female friends or coworkers who spend a great deal of time together often find that their menstrual periods tend to start around the same day. Sperm swimming side by side en route to the egg beat their tails in unison, in a primordial display of synchronized swimming. Sometimes sync can be pernicious: Epilepsy is caused by millions of brain cells discharging in pathological lockstep, causing the rhythmic convulsions associated with seizures. Even lifeless things can synchronize. The astounding coherence of a laser beam comes from trillions of atoms pulsing in concert, all emitting photons of the same phase and frequency. Over the course of millennia, the incessant effects of the tides have locked the moon's spin to its orbit. It now turns on its axis at precisely the same rate as it circles the earth, which is why we always see the man in the moon and never its dark side.”
― Steven H. Strogatz, Sync: The Emerging Science of Spontaneous Order

“Whenever the whole is different from the sum of the parts—whenever there’s cooperation or competition going on—the governing equations must be nonlinear.”
― Steven H. Strogatz, Sync: How Order Emerges From Chaos In the Universe, Nature, and Daily Life

“This synergistic character of nonlinear systems is precisely what makes them so difficult to analyze. They can’t be taken apart. The whole system has to be examined all at once, as a coherent entity. As we’ve seen earlier, this necessity for global thinking is the greatest challenge in understanding how large systems of oscillators can spontaneously synchronize themselves. More generally, all problems about self-organization are fundamentally nonlinear. So the study of sync has always been entwined with the study of nonlinearity.”
― Steven H. Strogatz, Sync: How Order Emerges From Chaos In the Universe, Nature, and Daily Life

“We're accustomed to thinking in terms of centralized control, clear chains of command, the straightforward logic of cause and effect. But in huge, interconnected systems, where every player ultimately affects every other, our standard ways of thinking fall apart. Simple pictures and verbal arguments are too feeble, too myopic. That's what plagues us in economics when we try to anticipate the effect of a tax cut or a change in interest rates, or in ecology, when a new pesticide backfires and produces dire, unintended consequences that propagate through the food chain.”
― Steven H. Strogatz, Sync: The Emerging Science of Spontaneous Order

“a big, messy linear problem can always be broken into smaller, more manageable parts. Then each part can be solved separately, and all the little answers can be recombined to solve the bigger problem. So it’s literally true that in a linear problem, the whole is exactly equal to the sum of the parts.”
― Steven H. Strogatz, Sync: How Order Emerges From Chaos In the Universe, Nature, and Daily Life

“we’ve come to realize that most systems of differential equations are unsolvable, in that same sense; it’s impossible to find a formula for the answer. There is, however, one spectacular exception. Linear differential equations are solvable.”
― Steven H. Strogatz, Sync: How Order Emerges From Chaos In the Universe, Nature, and Daily Life

“Beyond serving as an inspiration to engineers, the group behavior of fireflies has broader significance for science as a whole. It represents one of the few tractable instances of a complex, self-organizing system, where millions of interactions occur simultaneously—when everyone changes the state of everyone else. Virtually all the major unsolved problems in science today have this intricate character. Consider the cascade of biochemical reactions in a single cell and their disruption when the cell turns cancerous; the booms and crashes of the stock market; the emergence of consciousness from the interplay of trillions of neurons in the brain; the origin of life from a meshwork of chemical reactions in the primordial soup. All these involve enormous numbers of players linked in complex webs. In every case, astonishing patterns emerge spontaneously. The richness of the world around us is due, in large part, to the miracle of self-organization.”
― Steven H. Strogatz, Sync: How Order Emerges From Chaos In the Universe, Nature, and Daily Life

“It’s hard to blame Representative Petri for missing the point. The value of studying fireflies is endlessly surprising. For example, before 1994, Internet engineers were vexed by spontaneous pulsations in the traffic between computers called routers, until they realized that the machines were behaving like fireflies, exchanging periodic messages that were inadvertently synchronizing them. Once the cause was identified, it became clear how to relieve the congestion. Electrical engineers devised a decentralized architecture for clocking computer circuits more efficiently, by mimicking the fireflies’ strategy for achieving synchrony at low cost and high reliability.”
― Steven H. Strogatz, Sync: How Order Emerges From Chaos In the Universe, Nature, and Daily Life

“Simulation is no substitute for math—it could never provide a proof—but if Peskin’s conjecture was false, this approach would save me a lot of time by revealing a counterexample. This sort of evidence is extremely valuable in math. When you’re trying to prove something, it helps to know it’s true. That gives you the confidence you need to keep searching for a rigorous”
― Steven H. Strogatz, Sync: How Order Emerges from Chaos In the Universe, Nature, and Daily Life

“Simulation is no substitute for math—it could never provide a proof—but if Peskin’s conjecture was false, this approach would save me a lot of time by revealing a counterexample. This sort of evidence is extremely valuable in math. When you’re trying to prove something, it helps to know it’s true. That gives you the confidence you need to keep searching for a rigorous proof. Programming”
― Steven H. Strogatz, Sync: How Order Emerges from Chaos In the Universe, Nature, and Daily Life

“Here, it seems to me, is where sync has been uniquely successful. As one of the oldest and most elementary parts of nonlinear science (dealing, as it does, with purely rhythmic units), sync has offered penetrating insights into everything from cardiac arrhythmias to superconductivity, from sleep cycles to the stability of the power grid. It is grounded in rigorous mathematical ideas; it has passed the test of experiment; and it describes and unifies a remarkably wide range of cooperative behavior in living and nonliving matter, at every scale of length from the subatomic to the cosmic. Aside from its importance and intrinsic fascination, I believe that sync also provides a crucial first step for what’s coming next in the study of complex nonlinear systems, where the oscillators are eventually going to be replaced by genes and cells, companies and people.”
― Steven H. Strogatz, Sync: How Order Emerges From Chaos In the Universe, Nature, and Daily Life

“Although scientists are still struggling to understand the neural basis of human thoughts and feelings, it has recently become possible to eavesdrop on the mind as it recognizes a face, remembers a word, or snaps to attention. Neurobiologists have discovered that such acts of cognition are linked to a brief surge of neural synchrony, in which millions of far-flung brain cells suddenly switch on and off in precise lockstep at about 40 times a second, and then just as rapidly unravel to allow the next thought or perception to occur. If this view is right, a flash of insight is literally a burst of electrical synchrony, an instant when separate parts of the brain begin to harmonize.”
― Steven H. Strogatz, Sync: How Order Emerges From Chaos In the Universe, Nature, and Daily Life

“In particular, the creeping advance of an improbable cascade near the second tipping point is reminiscent of a low-budget hit that starts out slowly and builds by word of mouth.”
― Steven H. Strogatz, Sync: How Order Emerges From Chaos In the Universe, Nature, and Daily Life

“Here’s what’s going on, intuitively. Lurking within the network is a connected subset of nodes that Duncan calls the vulnerable cluster. The geometric structure of this cluster—the way it percolates through the rest of the network—is what matters. In marketing language the vulnerable cluster is composed of “early adopters”: not innovators themselves but nodes that are poised and ready to tip, if just one of their neighbors has already toppled. Close to the second tipping point, the vulnerable cluster is spindly and almost invisible—it occupies a very small percentage of the whole network—so the odds of igniting it with a random seed are small. But once ignited, it spreads a slow-burning fire to its neighbors, enough of which pass it on to their neighbors, continuing inexorably until the entire giant component (the vast, interconnected meshwork of nodes that dominates the system) is engulfed in flame.”
― Steven H. Strogatz, Sync: How Order Emerges From Chaos In the Universe, Nature, and Daily Life

“With further increases in connectivity, the cascades at first become even larger and more likely, as one might expect, but then—paradoxically—they become larger yet rarer, suddenly vanishing when the network exceeds a critical density of connections. This second tipping point arises because of a dilution effect: When a node has too many neighbors, each of them has too little influence to trigger a toppling on its own. (Remember that each node compares its threshold to the fraction of its neighbors that have tipped, not the absolute number. The more neighbors there are, the less impact any one of them has, in a fractional sense.)”
― Steven H. Strogatz, Sync: How Order Emerges From Chaos In the Universe, Nature, and Daily Life

“Barabási and his team pointed out that scale-free networks also embody a compromise bearing the stamp of natural selection: They are inherently resistant to random failures, yet vulnerable to deliberate attack against their hubs. Given that mutations occur at random, natural selection favors designs that can tolerate haphazard insults. By their very geometry, scale-free networks are robust with respect to random failures, because the vast majority of nodes have few links and are therefore expendable. Unfortunately, this evolutionary design has a downside. When hubs are selectively targeted (something that random mutation could never do), the integrity of the network degrades rapidly—the size of the giant component collapses and the average path length swells, as nodes become isolated, cast adrift on their own little islands.”
― Steven H. Strogatz, Sync: How Order Emerges From Chaos In the Universe, Nature, and Daily Life

“The challenge now is to decode the underlying meaning of small-world and scale-free architecture, if there is any. In one recent attempt, Solé has observed that electronic circuits tend to be wired in a small-world fashion, and he thinks he knows why. Whether he was analyzing the latest digital microchips or the clunky circuits found in old televisions, he found that all the components were just a few electrical steps from one another, yet they were much more clustered than they would have been in an equivalent random circuit, thanks to the modular design favored by engineering practice.”
― Steven H. Strogatz, Sync: How Order Emerges From Chaos In the Universe, Nature, and Daily Life

“From a purely mathematical perspective, a power law signifies nothing in particular—it’s just one of many possible kinds of algebraic relationship. But when a physicist sees a power law, his eyes light up. For power laws hint that a system may be organizing itself. They arise at phase transitions, when a system is poised at the brink, teetering between order and chaos. They arise in fractals, when an arbitrarily small piece of a complex shape is a microcosm of the whole.”
― Steven H. Strogatz, Sync: How Order Emerges From Chaos In the Universe, Nature, and Daily Life

“And the fundamental idea is that your close friends are wonderful for all kinds of things—for giving you support, for helping you when you’re sad, for doing favors that other people wouldn’t do for you—but as sources of information they’re not very good, because your close friends tend to know the same people you know. Whereas people who are just your acquaintances—who might not help you out if you were in desperate trouble—are still better sources of information because they know so many people you don’t know. They’re really your windows on the world, because they’re linked up to different circles from your own.”
― Steven H. Strogatz, Sync: How Order Emerges From Chaos In the Universe, Nature, and Daily Life

“Though we couldn’t see how to explain these results mathematically, an intuitive explanation suggested itself: The shortcuts were providing high-speed communication channels, enabling mutual influence to spread swiftly throughout the population. Of course, the same effect could have been achieved by connecting every oscillator directly to every other, but at a much greater cost in wiring. The small-world architecture apparently fostered global coordination more efficiently.”
― Steven H. Strogatz, Sync: How Order Emerges From Chaos In the Universe, Nature, and Daily Life

“To test that prediction, we needed empirical examples. They weren’t easy to find. Any candidate had to be fully characterized, its wiring diagram known down to the last detail, every node and link documented, or we couldn’t calculate the clustering and average path length. Then I remembered that Koeunyi Bae, a student in my chaos course the year before, had done a project about the Western States power grid, a collection of about 5,000 electric power plants tied together by high-voltage transmission lines across the states west of the Rocky Mountains and into the western provinces of Canada. Koeunyi and her adviser Jim Thorp provided the data to Duncan. It contained a great deal of detailed information that an engineer would find crucial—the voltage capacity of the transmission lines, the classification of the nodes as transformers, substations, or generators—but we ignored everything except the connectivity. The grid became an abstract pattern of dots connected by lines. To check whether it was a small-world network, we compared its clustering and average path length to the corresponding values for a random network with the same number of nodes and links. As predicted, the real network was almost as small as a random one, but much more highly clustered. Specifically, the path length was only 1.5 times larger than random, whereas the clustering was 16 times larger.”
― Steven H. Strogatz, Sync: How Order Emerges From Chaos In the Universe, Nature, and Daily Life

“Neither Duncan nor I could see how to solve that problem by pure mathematics, so we used a computer to simulate the morph on networks of large but manageable size, starting from pristine rings with 1,000 nodes and 10 links per node. To chart the structural changes in the middle ground, we graphed both the average path length and the clustering as functions of the proportion of links that were randomly rewired. What we found amazed us. The slightest bit of randomness contracted the network tremendously. The average path length plummeted at first—with only 1 percent rewiring (meaning that only 1 out of every 100 links was randomized), the graph dropped by 85 percent from its original level. Further rewiring had only a minimal effect; the curve leveled off onto a low-lying plateau, indicating that the network had already gotten about as small as it could possibly get, as if it were completely random. Meanwhile, the clustering barely budged. With 1 percent rewiring, the clustering dropped by only 3 percent. Connections were being yanked out of well-ordered neighborhoods, yet the clustering hardly noticed. Only much later in the morph, long after the crash in path length, did clustering begin to drop significantly.”
― Steven H. Strogatz, Sync: How Order Emerges From Chaos In the Universe, Nature, and Daily Life

“Our analysis revealed that whether the nodes in the network are neurons or computers, people or power plants, everyone is connected to everyone else by a short chain of intermediaries. In other words, the “small world” phenomenon is much more than a curiosity of human social life: It’s a unifying feature of diverse networks found in nature and technology.”
― Steven H. Strogatz, Sync: How Order Emerges From Chaos In the Universe, Nature, and Daily Life

“Spiral waves are now recognized to be a pervasive feature of all chemical, biological, and physical excitable media.”
― Steven H. Strogatz, Sync: How Order Emerges From Chaos In the Universe, Nature, and Daily Life

“In many ways, this chemical medium behaves like the human sexual response. Sexual arousal and recovery depend on the properties of nerve tissue, which, like Zhabotinsky soup, belongs to a general class of systems called excitable media. A neuron has three states: quiescent, excited, and refractory. Normally a neuron is quiescent. With inadequate stimulation, it shows little response and returns to rest. But a sufficiently provocative stimulus will excite the neuron and cause it to fire. Next it becomes refractory (incapable of being excited for a while) and finally returns to quiescence. The parallels with chemical waves extend to action potentials, the electrical waves that propagate along nerve axons. They too travel without attenuation, and when two of them collide, they annihilate each other. In fact, all of these statements are equally true of electrical waves in another excitable medium: the heart. That’s the beauty of this abstraction—the qualitative properties of one excitable medium hold for them all. They can all be studied in one stroke.”
― Steven H. Strogatz, Sync: How Order Emerges From Chaos In the Universe, Nature, and Daily Life

“In technical terms, his scheme can be described as follows: Take two copies of a chaotic system. Treat one as the driver; in applications to communications, it will function as the transmitter. The other system receives signals from the driver, but does not send any back. The communication is one-way. (Think of a military command center sending encrypted orders to its soldiers in the field or to sailors at sea.) To synchronize the systems, send the ever-changing numerical value of one of the driver variables to the receiver, and use it to replace the corresponding receiver variable, moment by moment. Under certain circumstances, Pecora found that all the other receiver variables—the ones not replaced—would automatically snap into sync with their counterparts in the driver. Having done so, all the variables are now matched. The two systems are completely synchronized.”
― Steven H. Strogatz, Sync: How Order Emerges From Chaos In the Universe, Nature, and Daily Life

“Pecora started the transmitter and receiver in different states, and then asked the computer to predict their behavior far into the future. As the numbers poured out, they bobbled erratically—the aperiodicity expected of chaos—but amazingly, their values converged toward each other. They were synchronizing. By driving the receiver with a chaotic signal transmitted from a duplicate of itself, Pecora had coaxed them to fluctuate in lockstep.”
― Steven H. Strogatz, Sync: How Order Emerges From Chaos In the Universe, Nature, and Daily Life

“Lyapunov time sets a horizon beyond which acceptable prediction becomes impossible. For a chaotic electrical circuit, the horizon is something like a thousandth of a second; for the weather, it’s unknown but seems to be a few days; and for the solar system itself, five million years.”
― Steven H. Strogatz, Sync: How Order Emerges From Chaos In the Universe, Nature, and Daily Life

“In a chaotic system, the required precision in the initial measurement grows exponentially, not linearly.”
― Steven H. Strogatz, Sync: How Order Emerges From Chaos In the Universe, Nature, and Daily Life

“The amount of time we can successfully predict the state of a chaotic system depends on three things: how much error we’re willing to tolerate in the forecast; how precisely we can measure the initial state of the system; and a time scale that’s beyond our control, called the Lyapunov time, which depends on the inherent dynamics of the system itself.”
― Steven H. Strogatz, Sync: How Order Emerges From Chaos In the Universe, Nature, and Daily Life