In Sync With Nature Quotes

In our modern lives we have strayed so far from living in sync with nature that integrating natural health measures into our lives can paradoxically feel unnatural.

Instinctively, and against my better judgement, I pull her closer to me. She rests her head on my shoulder as if it is the most natural thing in all the worlds to do. But it's a mistake. I become aware of her heart beating, her lungs expanding with every breath, her skin beneath my touch. She moves, and her head slides to my chest. Shifting into sleep, she wraps her arm around my waist. Now I'm aware of my heart beating too, slowly, in sync with hers. I know I should push her away. But if my life depended on it, right now, that would be impossible.

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.

If we are in sync with nature, we will be in sync with ourselves because although we belong to Heaven, we are made from earth.

We think and believe that we are exceptional. We have created so many stories around how exceptional humans are. We were created by the hands of the divine, and the universe is our gift. We believe that it was all created to serve us, but the reality of the matter is, we are not exceptional except for our ability to kill beauty and destroy. We are not as fast as the gazelle or a cheetah; we can't fly like birds; we don't have fur to protect us in the cold; we don't have natural strength to lift heavy objects like a gorilla or an elephant. We created fables to explain our presence, even scientific ones that we can't prove. It is all unproven theories, on all sides. We are not exceptional; we are only exceptional when we work together and in sync with nature like every other creature.

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.

I am knee deep in sea water now, feeling the energy of the tidal waves as they roll inwards towards the shore. A tide that exhales life spent, across its great, red stained sea. Its waves’ beats are out of sync, as they crawl slowly towards land.

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.

Soul Mates share complementary, compatible life goals and their spiritual natures are often in sync with ours. They also experience an immense level of comfort with each other that cannot be experienced in other relationships, and they complement each other in many ways through their strengths and weaknesses.

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

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

Warriorship is an infinitely nuanced subject. A true warrior desires nothing so much as to be perfectly appropriate, “in sync” with space and time in each and every moment. The perfection of warrior timing results in a kind of invisibility. Walking between the super strings of karma, or bound activity, the warrior engages in kriya, or spontaneous action. This is the actionless action spoken of so eloquently by Krishna in the Bhagavad Gita. Only the natural perfection of kriya ensures that a warrior’s actions will be of real benefit to those she serves. Walking between and in a state of total non-distraction, a warrior’s invisibility is identical to her invincibility. In the warrior heart is a dynamic stillness that is unperturbed by any arising of this world, by any impediment or seeming obstacle. Even when we have not realized this perfection, it is our warrior hearts, still mostly unknown to us, that lead us steadily on to realization.

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.

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.

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.

The prefrontal cortex is a complex, fragile region of the brain. In its healthy state, it directs human impulses toward rational choices and away from destructive or self destructive behavior. It allows us to deal with the present moment while storing plans for the future. Yet as the newest part of the brain to develop in human evolution, the prefrontal cortex is also the region that takes the longest time to reach maturity, or maximum operating efficiency. It will not be fully functional until the person is past the age of twenty. This out of sync progress ranks among the most profound natural misfortunes of humanity. For while the prefrontal cortex is taking its time, other powerful components of the humaninprogress have raced across the finish line and function without the cortex's restraints. A young adult with a still developing prefrontal cortex will have reached .physical maturity, which of course means the capacity to reproduce and the strong hormonal drive to do so.

He wanted his birthday to disappear, dissolve in water and sink to the bottom. A day like all the others. That's how he felt about it, wanting to maneuver that day into silence, and outside of time, time lived and gone for good, so that eventually not even a scratch on his skin would remind him of the day when it occurred, or of that time; that's what gave Singer a great sense of satisfaction. Then he felt that he was once again in sync with himself and could breathe a sigh of relief while, without thinking about it, he endured yet another day in his life without noting that forty-seven years had now passed since his birth. Such is Singer's life, it proceeded without any need to mark its passage, thought Singer, moving with his own unique rhythm, yet not totally without self-awareness, in spite of everything. To be yanked out of the automechanism of life in order to celebrate his birthday as a boisterous reminder was something that broke with what Singer regarded as his essential nature.

Instead of ascending to enlightened states of being that involve the denial of the self, we have discovered that ours is a journey of descent: we look deep within to reclaim forgotten aspects of ourselves. In our descent, many of us rediscover “Sophia,” which is the Greek word for wisdom. She is a feminine aspect of the divine found in the Hebrew Scriptures. Her presence in the male pantheon of gods has been obscured, but not completely eradicated. In the Gnostic writings, considered heretical by the “orthodox” church, Sophia was present at creation and escorted Adam and Eve toward self-awareness. Women are reclaiming Sophia as a representation of their own inner wisdom. No longer is “god's will” imposed from outside of their lives—wisdom unfolds from within them and is in sync with their own natural gifts and capacities. No longer available to turn their lives and wills over to gods, gurus, and experts, they’re refusing to surrender except to Wisdom's urgings. No longer abdicating responsibility for their lives, they are employing their own willfulness in harmony with Wisdom's ways.

Von Neumann, in his thought experiment about self-replication, had written that he had avoided the “most intriguing, exciting, and important question of why the molecules or aggregates that in nature really occur … are the sorts of thing they are, why they are essentially very large molecules in some cases but large aggregations in other cases.”20 Pattee suggested that it is the very size of the molecules that ties the quantum and classical worlds together: “Enzymes are small enough to take advantage of quantum coherence to attain the enormous catalytic power on which life depends, but large enough to attain high specificity and arbitrariness in producing effectively decoherent products that can function as classical structures.”21 Quantum coherence basically means that subatomic particles sync together to “cooperate” to produce decoherent products, which are particles that do not have quantum properties. Pattee notes that there is now research that supports his proposal that enzymes require quantum effects22 and that life would be impossible in a strictly quantum world.23 Both are needed: a quantum layer and a classical physical layer.

that raises a profound mystery: Scientists have long been baffled by the existence of spontaneous order in the universe. The laws of thermodynamics seem to dictate the opposite, that nature should inexorably degenerate toward a state of greater disorder, greater entropy. Yet all around us we see magnificent structures—galaxies, cells, ecosystems, human beings—that have somehow managed to assemble themselves.

Although synchrony is ubiquitous among living things, its function is not always obvious. Why, for instance, should fireflies flash in unison?

When subjects go to sleep later in their body temperature cycles, they actually sleep less, even though they have been awake longer.

alertness goes hand in hand with body temperature: It’s low when temperature is low and high when temperature is high.

during 24-hour entrainment, minimum alertness should occur around the time of the temperature trough, namely, 4 to 6 A.M. That’s a notorious time of day. The accident at the Three Mile Island nuclear-power plant occurred then, with a crew that had been on night duty for just a few days. Chernobyl, Bhopal, Exxon Valdez: All those disasters occurred in the middle of the night, and were tied to human error. Field studies show that from 3 to 5 A.M., workers are slowest to answer a telephone, slowest to respond to a warning signal, and most apt to read a meter wrong.

How does incoherence give birth to synchrony? It dawned on me one day that there was a straightforward way to frame the question as an exercise in differential equations: I needed to view incoherence as an equilibrium state and then calculate its stability.

For the Kuramoto model, incoherence is an equilibrium state; if the oscillators of each frequency are spaced evenly around the circle, they will stay evenly spaced forever. Although the oscillators run around the circle, their uniform spacing is unaltered. The nagging unsolved problem was whether this equilibrium is stable like the water in the glass, or unstable like the pencil balancing on its point. If it is unstable, it would mean that sync would emerge spontaneously, that the runners would eventually wind up in a pack.

The equations showed that the answer depends on how similar the oscillators are. If they’re identical, or nearly so, I found that the disturbances grow exponentially fast as oscillators clump together in phase, in an embryonic form of sync. Then out popped a formula for the exponential growth rate (analogous to the interest rate for how fast your money compounds in the bank). No one had ever found such a formula before.

neutral stability normally occurs only at transitions, at critical settings of a system’s parameters (the “knobs” that control its properties). But the Kuramoto model was breaking this rule. Its incoherent state was doggedly staying neutrally stable, even as we widened the bell curve to make the population more diverse. Turning that knob over a wide range of parameters made no difference.

What I’ve just described is called a system of differential equations. Such equations arise whenever we have rules for speeds depending on current positions.

pack and a disorganized band of fringe oscillators. When the system was self-synchronizing, Winfree found that no oscillator was indispensable. There was no boss. Any oscillator could be removed and the process would still work.

Hopfield’s insight was that self-organized criticality might be intimately linked to synchronization in pulse-coupled oscillator systems. The tantalizing possibility of a relationship between those two areas spawned dozens of papers exploring the possible ties.

Unfortunately, our minds are bad at grasping these kinds of problems. 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.

There are various ideas about the mechanism of synchronization, but the best guess is that it has something to do with pheromones: unidentified, odorless chemicals that somehow convey a synchronizing signal.

Winfree wrote equations for his system of oscillators, describing how fast each one moves through its cycle. 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).

When you’re trying to prove something, it helps to know it’s true.

We take it for granted that we can sing and dance together, march in step, clap in unison. Sync is second nature to us. But because it comes so easily, we have poor insight about what it actually demands. It seems to involve at least a low level of intelligence, the ability to time our behavior and anticipate that of others. Which is why the reports of concerted flashing among thousands of fireflies aroused such skepticism for so many years, and why we are impressed by the chorusing of crickets or the seductive tactics of male fiddler crabs, who court a female by waving their gargantuan claws at her in unison.

Mindless, lifeless things can sync spontaneously. The sympathy of clocks taught us that the capacity for sync does not depend on intelligence, or life, or natural selection. It springs from the deepest source of all: the laws of mathematics and physics.

Quantum sync also explains how superconductivity works. The argument is tricky, because the herd behavior that we’ve been discussing doesn’t come easily to electrons. Being fermions, they are not naturally sociable. Instead, superconductivity relies on a subtle mechanism that prods the electrons to join in pairs, at which point they become bosons and lose all inhibition. These paired electrons spontaneously form a Bose-Einstein condensate, a synchronized ensemble that encounters no resistance as it carries electrical current through a metal.

The theory also showed that superconductivity is not a mere extension of ordinary conductivity. Previously it had always seemed paradoxical that the best normal conductors, copper and silver, are feeble superconductors; they do not superconduct even when the temperature is a thousandth of a degree above absolute zero. Seen in the light of the new theory, however, that finding began to make sense. Good conductors are good precisely because their conduction electrons ignore the lattice. But by encouraging the electrons and the lattice to go their separate ways, these materials never give Cooper pairs a chance to form. Remember, the pairing mechanism relies crucially on an electron’s ability to deform the lattice (like the bowling ball rolling on the waterbed) so that a second one can follow in its tracks. If the waterbed is so stiff that the first bowling ball can’t make a groove in it, there’s no chance that a second one will follow. So good conductors are lousy superconductors, because they can’t form the necessary Cooper pairs.

Finally, the theory explained why the resistance drops so abruptly at a certain temperature. It’s much the same reason that water freezes suddenly at 0 degrees Celsius. Both processes are phase transitions, victories of self-organization over random jittering. At the freezing point, water molecules calm down just enough to allow their attractive forces to bond them into a crystal. Similarly, at the superconducting transition temperature, the atomic lattice calms down just enough to allow electrons to form Cooper pairs and coalesce into a Bose-Einstein condensate. In both cases, a fraction of a degree drop in temperature makes all the difference.

Despite its technological potential, superconducting technology has been slow to materialize in the marketplace. One obstacle has always been the frigid temperatures needed to reach the superconducting state, requiring the use of elaborate refrigeration systems available only in research laboratories. That was one reason why the discovery of high-temperature superconductivity caused such a stir: The critical temperatures could now be reached by cooling with liquid nitrogen, which is both cheap and abundant. The more serious obstacle has become the difficulty of manufacturing strong, flexible wires out of the new materials; like other ceramics, they are brittle and tend to crack easily. It’s also hard to fabricate the wires in practical lengths; they tend to lose their superconductivity because of material defects when they get too long. Moreover, the most promising form of superconducting wire is encased in silver, which makes it 20 times more costly than copper wire, although the cost will decrease as demand rises.

All the electrical components on a computer chip are clocked to operate in sync. A microelectronic crystal beats billions of times each second, switching the digital circuitry on and off in concert, which helps the millions of circuits on the chip communicate with one another efficiently. This centralized design, with all components slaved to a tyrannical master clock, has some notable disadvantages: 15 percent of the circuitry is wasted on distributing the clock signal, and the clock itself consumes 20 percent of the power. But engineers still favor this design because of its conceptual simplicity, and because the alternative—a democracy of many local clocks, as in firefly swarms and circadian pacemaker cells—is still not well enough understood to be easily imitated in practice.

The implication is that there are two pathways from the eyes to the brain: one for conscious vision and the other for circadian entrainment. This hypothesis is consistent with the known anatomy of the mammalian brain; the neural hotline to the pacemaker is separate from the brain’s visual pathways.

Although the role of serendipity is familiar, what’s not so well appreciated is how different serendipity is from luck. Serendipity is not just an apparent aptitude for making fortunate discoveries accidentally, as my dictionary defines it. Serendipitous discoveries are always made by people in a particular frame of mind, people who are focused and alert because they’re searching for something. They just happen to find something else.

This is the key process behind a laser. It’s called stimulated emission, and you can see that it offers a way to increase the number of photons flying along a certain line. Every time a photon hits an excited atom, it duplicates itself, amplifying the amount of light traveling in that direction, which is precisely what the acronym laser stands for: Light Amplification by Stimulated Emission of Radiation. The emission is said to be stimulated (as opposed to spontaneous) because the incoming photon provoked the excited atom into spitting out the new photon. What matters most, however, is that the emitted photon is indistinguishable from the one that spawned it. If you think of these photons not as particles but as tiny waves of light, they’d be perfectly synchronized.

There’s no commonsense way to understand how stimulated emission could be possible, or why the new photon should be a carbon copy of the old one. The phenomenon is a consequence of the odd logic of quantum mechanics, the physics of the atomic and subatomic world, where our intuition from everyday life breaks down. Einstein discovered the theoretical necessity of stimulated emission in 1917, but it took another 43 years before anyone figured out how to use it to create the first working laser.

The global positioning system consists of 24 satellites orbiting about 11,000 miles above the Earth, arrayed so that any spot on the planet is visible to at least six of the satellites at any time. Each satellite carries four atomic clocks on board, synchronized within a billionth of a second of one another by the master superclock in Boulder. Any GPS receiver, like those found in expensive cars or on handheld devices, receives signals from four of these satellites (at least), and uses those four numbers to calculate its three-dimensional location and the current time.

Remarkably, the other 20 percent of blind people do manage to synchronize to the light-dark cycle. The likely explanation is that the circadian photoreceptors in their retinas are intact, even if their rods and cones are not. This allows light to work its resetting action on the clock, by striking the eyes and then traveling down the neural pathways to the pacemaker. In other words, although these people lack sight, they can still perceive light in a nonvisual, circadian sense.

This explanation was long in coming. It required more than fifty years of insights into quantum theory, and was proposed in 1957 by the physicists John Bardeen, Leon Cooper, and Robert Schrieffer. Its most surprising innovation is the idea that electrons can form pairs. Normally we would expect electrons to repel each other, since they are all negatively charged. The pairing mechanism is indirect. The interaction between the electrons is mediated by the lattice of positively charged ions. (Earlier, we referred to these ions as atoms. But since they are freely sharing some of their conduction electrons, they are positively charged and so should be called ions. Their positive charge is the key to the pairing mechanism.) When an electron moves through the lattice, it pulls the lattice toward it slightly, because of its opposite charge. That deformation creates a region of space with a tiny excess of positive charge, which tends to attract a second electron toward it. In that indirect sense, the two electrons are linked.

It takes effort and intention to take control of our environment and behaviors to bring our brain clock and body clocks back in sync and as close to the natural 24-hour light/dark cycle as we can. Sleep hygiene, like using blackout curtains to keep the bedroom dark, taking a hot shower or bath an hour before sleep to jump-start a temperature change in our body, shutting off devices and screens an hour before bed or using blue (and green) light-blocking glasses, or journaling or meditating for 20 minutes before bed can profoundly help rewire our clocks and reset our circadian rhythm.

Superfluid helium is a realization of the hypothetical quantum liquid that we imagined when performing the thought experiment with the buckets on the staircase. Its behavior is almost surreal.

This weird behavior is a manifestation of quantum sync. All liquids become highly ordered when cooled to very low temperatures. Normally they freeze into a crystal. But the two isotopes of helium, helium-3 and helium-4, never solidify, at least not at ordinary pressures. They remain liquids all the way down to absolute zero.

Over the past 40 years, a number of practical applications have been found for these remarkable manifestations of quantum sync. Josephson’s superconducting sandwiches, now known universally as “Josephson junctions,” have spawned the most sensitive detectors known to science. For instance, a device called a SQUID (for superconducting quantum interference device) takes advantage of the extreme sensitivity of a supercurrent to a magnetic field. A SQUID can measure a displacement a thousand times smaller than an atomic nucleus, or a magnetic field 100 billion times weaker than Earth’s. SQUIDs are used in astronomy, to detect faint radiation from distant galaxies; in nondestructive testing, to spot hidden corrosion beneath the aluminum skin of airplanes; and in geophysics, to help locate sources of oil deep underground.

The principle underlying a SQUID is that variations in a magnetic field alter the phase difference between the quantum waves on either side of its two junctions, and therefore change the supercurrents tunneling through them. Just as ripples on a pond can either add up when they collide (if a crest meets a crest) or cancel each other out (if a crest meets a trough), the quantum waves in the two arms of a SQUID interfere in a way that depends sensitively on their phases, and hence on the amount of magnetic flux passing through the loop. In this way, a SQUID transforms tiny variations in magnetic flux into measurable changes in current and voltage across the device, allowing ultrafaint electromagnetic signals to be detected and quantified.

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.

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.

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.

Spiral waves are now recognized to be a pervasive feature of all chemical, biological, and physical excitable media.

Now we see the connection to the Josephson junction. This sine function is the same one that appeared earlier in the direct-current Josephson effect, where the supercurrent is proportional to the sine of the phase across the junction. That’s the analogy: The phase across the junction is like the angle of the pendulum. As it turns out, all the other terms in the equation have counterparts as well. The flow of normal electrons corresponds to the damping of the pendulum caused by friction. The pendulum’s mass is like the junction’s capacitance. And the torque applied to the pendulum is like the external current driving the junction.

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.

If we make things even more complicated and allow the torque itself to vary in time, like the back and forth agitation of a washing machine, the pendulum’s whirling can become chaotic, rotating this way and that, changing direction haphazardly. The verification of the corresponding electrical spasms in a Josephson junction was one of the early experimental triumphs of chaos theory. Before that, physicists had always seen the pendulum as a symbol of clockwork regularity. Suddenly it was a paradigm of chaos.

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.

We each had our own clocks on either side of the bed. They were old wind-up clocks from our Ann Arbor days. His was a Big Ben and mine a Little Ben. Naturally the Big Ben’s ticking was lower than mine, and louder, the father of the clock family. Mine was staccato, shrill, as if it was panicked by the passage of time. They didn’t tick in sync, and Howard’s was always set fast. I remember waking up and thinking the clocks were sparring, that they would battle over their precious minutes and the way to tick until they exhausted themselves and wound down and just quit.

Josephson junctions have also been considered as possible components for a new generation of supercomputers. One attractive feature is their raw speed: They can be switched on and off at frequencies of several hundred billion cycles per second. But perhaps even more important, Josephson transistors produce a thousand times less heat than conventional semiconductors, which means they can be packed tighter on a chip without burning themselves up. Dense packing is always desirable because smaller computers are faster. By using less wire, they are less burdened by the speed of light, which ultimately determines the time it takes for signals to travel from one part of the circuitry to another.

Although a single Josephson junction produces only about a microwatt of power—too puny to be practical for anything—its output could be greatly amplified by cooperation. Just as an audience clapping in sync makes a lot more noise than any individual person, a synchronized array of Josephson junctions would be a much more potent source of radiation than any solitary one. For example, if you could find a way to coax a thousand junctions to oscillate in phase, the power delivered to another device—a “load” in parallel with the array—would be amplified a millionfold. (The combined power is proportional to the square of the number of junctions.) The hard part is figuring out a way to sync them.

There, staring us in the face, was the Kuramoto model—an enigma like the monolith in 2001: A Space Odyssey, buried under the soil, waiting for us apes to find it, beckoning, the key to sync. Until now, the Kuramoto model had been thought to be nothing more than a convenient abstraction, the simplest way to understand how groups of dissimilar oscillators could spontaneously synchronize, and under what circumstances. It was born out of pure imagination, concocted as a caricature of biological oscillators: crickets, fireflies, cardiac pacemaker cells. Now here it was, unearthed, in the dynamics of superconducting Josephson junctions. It reminded me of that wonderful feeling that Einstein talked about, the recognition of hidden unity. Soon

Since 1996, the Kuramoto model has turned up in other physical settings, from arrays of coupled lasers to the hypothesized oscillations of the wispy subatomic particles called neutrinos. We may be catching the first glimpses of a deep unity in the nature of sync. Whether there will be any practical applications remains to be seen. Given how many diseases are related to synchrony and its disruption (epilepsy, cardiac arrhythmias, chronic insomnia) and how many devices rely on synchrony (Josephson and laser arrays, electrical power grids, the global positioning system), it seems safe to say that a deeper understanding of spontaneous sync is bound to find practical benefit.

The widespread occurrence of the Kuramoto model raises the question of why this particular mathematical structure should be so common. To be honest, it probably isn’t all that common. I have focused on it because it is the only case of spontaneous synchrony we understand well. On theoretical grounds, one can show that it arises only whenever four specific conditions are met, and is not expected otherwise. First, the system in question must be built from an enormous number of components, each of which is a self-sustained oscillator. That is already a strong constraint. The individual elements must have extremely simple dynamics: pure rhythmicity along a standard cycle, without chaos or turbulence or anything complicated, just repetitive motion. Second, the oscillators must be weakly coupled, in the sense that the state of each oscillator can be characterized by its phase alone. If the coupling is strong enough to distort any oscillator’s amplitude significantly, the Kuramoto model will not apply. The third condition is the most restrictive: Each oscillator must be coupled equally strongly to all the others. Very few systems in nature are literally like that. Oscillators normally interact most strongly with their neighbors in space, or with a collection of virtual neighbors defined by a network of mutual influence. Finally, the oscillators must be nearly identical, and the amount of dispersion in their properties should be comparable to the weakness of their coupling.

The mathematician Stanislaw Ulam once said that calling a problem nonlinear was like going to the zoo and talking about all the interesting nonelephant animals you see there. His point was that most animals are not elephants, and most equations are not linear. Linear equations describe simple, idealized situations where causes are proportional to effects, and forces are proportional to responses. If you bend a steel girder by two millimeters instead of one, it will push back twice as hard. The word linear refers to this proportionality: If you graph the deflection of the girder versus the force applied, the relationship falls on a straight line.

But linearity is often an approximation to a more complicated reality. Most systems behave linearly only when they are close to equilibrium, and only when we don’t push them too hard. A civil engineer can predict how a skyscraper will sway in the wind, as long as the wind is not too strong. Electrical circuits are completely predictable—until they get fried by a power surge. When a system goes nonlinear, driven out of its normal operating range, all bets are off. The old equations no longer apply.

And then came the second wave of chaos theory, which revealed that chaos itself, belying its misleading name, contained a stunning new kind of order. The pivotal discovery was made by the physicist Mitchell Feigenbaum, who showed that there are certain universal laws governing the transition from regular to chaotic behavior. Roughly speaking, completely different systems can go chaotic in the same way. His predictions were soon confirmed in experiments on electronic circuits, swirling fluids, chemical reactions, semiconductors, and heart cells. It was as if the old Pythagorean dream had come true: The world was not made of earth, air, fire, and water—it was made of number. Feigenbaum’s laws transcended the superficial differences between heart cells and silicon semiconductors. Different materials, the same laws of chaos. Other universal laws would soon be discovered.

A depressing corollary of the butterfly effect (or so it was widely believed) was that two chaotic systems could never synchronize with each other. Even if you took great pains to start them the same way, there would always be some infinitesimal difference in their initial states. Normally that small discrepancy would remain small for a long time, but in a chaotic system, the error cascades and feeds on itself so swiftly that the systems diverge almost immediately, destroying the synchronization. Unfortunately, it seemed, two of the most vibrant branches of nonlinear science—chaos and sync—could never be married. They were fundamentally incompatible. Plausible as it sounds, the argument outlawing synchronized chaos is now known to be wrong. Chaos can sync.

The discovery of synchronized chaos also enriched our understanding of sync itself. In the past, sync had always been associated with rhythmicity. The two concepts are so tightly linked that it’s easy to overlook the distinction between them. Rhythmicity means that something repeats its behavior at regular time intervals; sync means that two things happen simultaneously. The confusion occurs because many synchronous phenomena are rhythmic as well. Synchronous fireflies not only flash in unison, they also flash periodically, at fixed intervals. Cardiac pacemaker cells fire in step, and at a constant rate. The moon turns once as it orbits Earth; both its spin and its orbit follow cycles that repeat themselves regularly.

But we all know that, at least in principle, sync can be persistent without being periodic. Think of the musicians in an orchestra. All the violins come in at the same time, and stay in sync throughout. Yet they are not periodic: They do not play the same passage over and over again.

In colloquial usage, chaos means a state of total disorder. In its technical sense, however, chaos refers to a state that only appears random, but is actually generated by nonrandom laws. As such, it occupies an unfamiliar middle ground between order and disorder. It looks erratic superficially, yet it contains cryptic patterns and is governed by rigid rules. It’s predictable in the short run but unpredictable in the long run. And it never repeats itself: Its behavior is nonperiodic.

More generally, when a nonchaotic system is disturbed slightly, the disturbance either doesn’t grow at all or else grows very mildly, increasing in proportion to how much time has passed. One says that the errors grow no faster than linearly in time.

In a chaotic system, the required precision in the initial measurement grows exponentially, not linearly.

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.

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.

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.

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.)

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.

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.

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.

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.

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.

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.

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.

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.

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.

Young women have an advantage because they are also in sync with the lunar cycles. It is an advantage, but a lot of them treat it as a curse. It is a fantastic possibility that your body is both connected to the solar and the lunar cycles. Nature has granted this advantage to a woman because she has been entrusted with the responsibility of propagating the human race. So she has been given some extra privileges, which unfortunately have been perceived socially as disadvantages. People do not know how to handle the bonus energy generated at that time and hence treat it as a curse, and even a kind of madness. (The word “lunatic” is derived, as we know, from “lunar.”)

I look down at my list of fruits and recite the names under my breath, syncing into the rhythms of nearby batucada drummers. Softly chanting, I close my eyes, and feel a sense of peace. For a moment, I forget everything. I forget my name. I forget why I came here. All I know is abacaxí, açai, ameixa, cupuaçu, graviola, maracujá, taperebá, uva, umbu.

Only once all the fish and birds and mammals were in sync were we, their human descendants, born—each creature and plant and ancestor dependent on one another, intrinsically linked. The Kumulipo is not only a map of our genealogy but our core agreement to the world we were brought into: it’s the Kānaka’s kuleana, or duty, to respect nature’s harmony. This union is our life force.

Depression is supposed to be this genetic disease. Really? What does it mean to depress something? It means to push it down. What gets pushed down in depression? Your feelings, your emotions. Why would a person push down their feelings? Because they are too painful, they are too much to bear. In other words, the pushing down of feelings becomes a coping mechanism in an environment where you are not allowed to feel because your feelings threaten your attachments. So you learn to survive by pushing down your feelings and then 15 years later or 30 years later you are diagnosed with depression. Now, as a medical, biological problem, they give you a pill. I'm not here to fight against pharmacology. I've taken anti-depressants and they've helped me. They work sometimes. But they are not the answer. Because the answer is how does that childhood experience manifest in your life today. If you understand all of these historical, cultural, familial stresses imposed certain behaviors on you, certain self-view, certain patterns of emotional relating, now you can do something about it. Now it is not longer "there is something wrong with me", it is just that "this is how I adapted to what happened to me." And therefore I have the capacity now, as a conscious human being, to become aware of all this and to transform myself. It's not so easy to transform yourself because, of course, these adaptions that I've talked about, originally related to our very survival as young children and so we think we have to be that way. And we don't know any other way of being, except there's something telling us that "this is not right." Something is telling us. So we can see individual problems like depression or ADHD or multiple sclerosis or anything else as problems to get rid of or we can look at them as warning signs that we are out of sync with our true nature, that we are misaligned somehow with actually who we are. And that something in us is trying to wake us up.

In springtime when I lived at the White House, we used to plant what’s called a “three sisters” vegetable patch in our garden on the South Lawn, mixing a crop of corn, beans, and squash together in one place. This is a traditional Native American method for growing food in a resourceful way, one that’s been used for many hundreds of years and is based on the idea that each type of plant has something vital to offer the others: The corn grows tall and creates a natural pole for the bean plants to climb. The beans provide nitrogen, a nutrient that helps the other plants grow more efficiently, and the squash stays low to the ground, its large, spreading leaves helping to block weeds and keep the soil moist. The plants grow at different rates; the vegetables harvest at different times. But the mix provides a system of mutual protection and benefit—the tall and the small continually working together. It’s not just the corn, and not just the beans, but rather the corn and the beans and the squash combined that yield a healthy crop. The balance comes from the combination. I’ve started to think about both my life and our wider human community in these terms. We are here to share benefits and protection. Our balance rests upon this ideal, the richness of these combinations. If I begin to feel out of sync, if I’m feeling unsupported or overwhelmed, I try to take stock of what my garden holds, what I’ve planted and what I still need to mix in: What’s feeding my soil? What’s helping to block the weeds? Am I cultivating both the small and the tall?

I hit a low place,” she began. “Perhaps it was the idea that fifty was looming. I don’t know, but I felt off. Out of sync with myself.

The last of his irritation disappeared instantly as Dean’s body folded against his perfectly. Sloane was never sure if their bodies fit so well naturally or if he and Dean were so in sync that it just happened. Personally, Sloane didn’t care what it was. It was one of the best feelings in the world.

Preparation. Because of their consistent and often intense training, successful risk-takers are prepared for any contingency. And that’s because they have the requisite education to recognize exactly what the contingencies are. They are aware of the best way to respond to different risky situations. They understand how even the smallest change in the environment can change the entire risk-taking equation. They spend an inordinate amount of time training and practicing so what they do feels like second nature. All that learning—and deliberate practice—syncs up their fast- and slow-thinking systems, which leads to smarter decision-making.

The surya namaskar is essentially about building a dimension within you where your physical bodily cycles are in sync with the sun’s cycles, which run about twelve and a quarter years. It is not by accident but by intent that it has been structured with twelve postures. If your system is in a certain level of vibrancy and readiness, and in a high state of receptivity, then naturally your cycle will be in sync with the solar cycle. Young

Nature paces its change in gradual steps, and in this time of renewal, I danced in sync to the rhythm of life.