Link Concepts

In recent posts about Bruce Lee, we looked at his technical prowess as a fighter, including his use of the one-inch punch and the stop-hit, as well as a fight that exposed the limitations of his approach. By 1964, at the age of 23, Lee had become a fighter who possessed blinding speed, incredible strength for his size, a wide array of skills, and a receptiveness to any influence that could be useful, combining to create the foundation of the legend he would eventually become. Yet his sloppy win over Wong Jack Man that year caused him to recognize that if he were to become the world’s best martial artist, those attributes were not enough. He still needed something more. His main criticism of classical martial arts was that they were too rigid. With their focus on standardized techniques, they prioritized form over function. They may have looked impressive in the training hall or when used against opponents who also adhered to classical techniques, but their formality became a weakness in the heat of battle. Real fighting was messy. It was unpredictable. In a street fight, you never really knew what your opponent was going to do. Would he stick to standard fighting tactics, or would he throw sand in your eyes? Would he bite your hand or kick you in the groin? Would he suddenly draw a concealed weapon? Classical martial arts thrived when both opponents stuck to the same rules, but unpredictability exposed their weaknesses. In fact, being unpredictable could be an advantage when fighting an opponent who only used classical techniques. For years Lee railed against the classical systems for being exclusionary. Each martial-art school had developed a framework that may have been effective within a narrow scope, and they codified their framework into a series of moves, techniques, credos, and philosophies. This codification may have been necessary to teach students and to provide tangible concepts to understand and emulate. It created a framework for articulating what each particular school stood for and, by contrast, what it stood against. It drew a line between what it was and what it wasn’t. From Lee’s perspective, this approach was self-limiting. He saw benefits in all the different schools, and he set out to liberate himself from predetermined ideas of what works and doesn’t work. He felt that no single approach to fighting would be the best approach against all opponents. He articulated the limitations of the classical schools in an article he wrote for Blackbelt magazine. “It is conceivable that a long time ago a certain martial artist discovered some partial truth… After his death, his students took ‘his’ hypotheses, ‘his’ postulates, ‘his’ method and turned them into law. Impressive creeds were then invented, solemn reinforcing ceremonies prescribed, rigid philosophy and patterns formulated, and so on, until finally an institution was erected. So, what originated as one man’s intuition of some sort of personal fluidity has been transformed into solidified, fixed knowledge, complete with organized classified responses presented in a logical order. In so doing, the well-meaning, loyal followers have not only made this knowledge a holy shrine but also a tomb in which they have buried the founder’s wisdom.” Lee’s criticism of classical schools and their masters got him in a lot of trouble. He was controversial because he called into question the deference to classical wisdom. “You think you’re the best, with your centuries of classical tradition, but you’re not,” Lee shot at the establishment. “Your way is not the best. My way is better because it includes all ways. And I’ll prove it to anyone who doubts me.” That was the challenge he issued to the community, and that challenge is what caused Jack Man to come for him. Lee’s cocky attitude sprang from his belief that he had developed the winning formula: a broader repertoire of techniques than any other opponent. His edge was forged from a diversity of styles. Until then, he had been focusing on the micro elements of the fight. “If the opponent does this, I do that.” It worked well. Very well. However, the Jack Man fight proved it was clearly not enough. What if the opponent introduced something truly novel? Even if a fighter had the most diverse arsenal of fighting techniques, that still might not make him effective against every opponent in every situation. He had to think bigger. After the bout with Jack Man, Lee entered into a period of deep introspection and self-evaluation. He pushed himself to add more to his techniques, including exercises designed to build his stamina. Eventually, he pushed himself so intensely that he injured the nerves in his spine. The injury forced him to stop all training and seek rehabilitation. So severe was his injury and so intense was the pain that they threatened to prevent him from ever being able to practice martial arts again. Keep in mind, by this point Lee was mainly known just for his work as the character Kato on the one and only season of the TV show Green Hornet. He hadn’t yet made any of the Kung Fu movies that would expose him to international audiences, and he was mostly an obscure martial arts teacher and struggling actor. Now with two young children and a potentially career-ending injury, he was forced to admit that a change was needed. While bedridden and convalescing, he spent much of his time writing the notes for what would become his book, Tao of Jeet Kune Do. By the time he recovered from his injury, an outcome that was far from certain six months earlier, he had arrived at a deep understanding of how he could flourish as a martial artist. He had been previously drawn to the archetype of water in the way it could be applied to fighting techniques: advancing, retreating, flowing, and crashing. The adaptability of water served as a good metaphor for the diversity of his fighting techniques. Now, however, he had identified another attribute of … Read more

In hand-to-hand combat, being taller has advantages, all else equal. If you are taller than your opponent, your reach will tend to be longer than your opponent’s, meaning you can strike from a distance that is outside your opponent’s range. To counter, your opponent has to lunge forward to reach you, making him more vulnerable. You can stay where you are to hit your opponent, but your opponent has to move to hit you. Clearly, you have the advantage. In hand-to-hand combat, being heavier also has advantages, all else equal. If you are heavier than your opponent, you can use your weight to tire your opponent, as wrestlers do. If you punch and kick with the same speed as a smaller opponent, your heavier punches and kicks will deliver more damage. That’s why sports like boxing, wrestling, weight lifting, mixed martial arts, and others have standardized weight classes such as Lightweight, Middleweight, and Heavyweight. These standardized weight classes help to ensure fighters get matched fairly to their opponents. In hand-to-hand combat, a fighter can make a punch or kick harder by generating more momentum. Momentum is measured by the mass of an object (like a fist or a foot) multiplied by the velocity of the object. So, to make the punch or kick harder, the fighter could increase the mass, or the velocity, or both. Bruce Lee was neither particularly tall nor particularly heavy. As a world-famous fighter, standing just 5 feet 7 inches and weighing around 135 pounds, he punched well above his weight class. Lee’s height and weight created disadvantages relative to other fighters who were larger and heavier and created obstacles standing in his way of becoming the best kung-fu fighter of his time, which was his ambition. He knew he had to find ways to overcome his disadvantages. In the movie Game of Death, which was released after Lee’s death, there is an iconic scene where he is wearing a yellow jumpsuit and he is fighting against basketball legend Kareem Abdul-Jabbar sporting aviator shades. The scene highlighted the extreme size differences between the two opponents. Abdul-Jabbar, who studied martial arts under Lee, was 7 feet 2 inches and roughly 225 pounds. He was a foot and a half taller and 90 pounds heavier. Predictably, Lee manages to overcome his size disadvantage and — “Spoiler alert!” — he beats Abdul-Jabbar. Possibly the greatest weapon that Lee possessed was his blinding speed. He was often regarded as the fastest martial artist of his time. The old kung fu master Ip Man said Lee was the fastest martial artist he had ever seen. Other champion fighters added their confirmation, including Sparring Grand Champion and fellow martial arts icon Chuck Norris. In a 2011 column in Black Belt magazine, Norris said, “Lee was lightning fast, very agile and incredibly strong for his size.” In fact, there were several occasions in Lee’s movies when his moves were so fast that they could not be properly captured by a camera shooting at the standard 24 frames per second. With the standard camera speed, Lee’s move couldn’t actually be seen by the viewer. Directors would ask him to slow down his moves for the camera or, at times, they would operate the camera at higher speeds so as to better capture his moves. If you watch the mirror-fight scene in Enter the Dragon, for instance, you are actually watching Bruce Lee moving more slowly than in real life, since the camera was shooting more than 24 frames per second for projectors that played back at just 24 frames per second. In boxing, the term to describe quickness is “hand speed.” Lee’s hand speed was arguably unbeatable. That went a long way to overcoming some of his disadvantages. Despite his below-average mass, he was able to generate above-average momentum with his exceptional velocity. Lee said the following: “A powerful athlete is not a strong athlete, but one who can exert his strength quickly. Since power equals force times speed, if the athlete learns to make faster movements he increases his power, even though the contractile pulling strength of his muscles remains unchanged. Thus, a smaller man who can swing faster may hit as hard or harder as the heavier man who swings slowly.” And yet there is another element of speed that often gets overlooked in discussions of fighting techniques. It is the acceleration of speed that reaches an apogee at the moment of impact. It is not only that the fist or foot is traveling at a blazingly fast speed; it’s that the fist or foot is traveling at an increasingly fast speed until it strikes its target. It’s fast, and it gets faster, rising to its fastest speed at the moment of impact. Since the fastest speed happens at the point of full extension, the foot or hand recoils back immediately after impact. This is analogous to the crack of the whip. In combat, this dynamic is sometimes referred to as “snap.” A snapping punch has more power than a regular punch. It is also a highly efficient transfer of energy, concentrating the fighter’s momentum at the moment of impact, and allowing the fighter’s muscles to relax the instant after impact has occurred. Employing this technique allows the fighter to conserve energy, which becomes increasingly important in fights that last longer and fatigue can potentially tip the balance in one direction or the other. So, all else equal, a fighter with superior snap delivers more punching power and retains more energy as the fight progresses. If the momentum of a punch is measured by mass times velocity times snap, Bruce Lee more than overcame his smaller-than-average mass with exceptional velocity and snap. Defense to Offense Bigger, heavier opponents, sensing they have the advantage in a fight, may be less guarded when they attack. On the rooftops of Hong Kong, Lee searched for ways to turn the attacks of his larger opponents to his advantage. He discovered ways to take their confidence … Read more

The year was 1964. The scene was a small residential garage in Oakland, California, that served as a martial-arts school run by Bruce Lee. The space was cluttered with homemade sparring devices pieced together by Bruce’s assistant James, who was a welder by trade, making it appear like a cross between a boxing gym and a mad-science lab. James locked the door because he knew things were about to get ugly. He had stashed a pistol nearby, just in case the situation got out of control. Bruce’s wife Linda was seated to one side, her belly bulging with their first child. She was surprisingly calm for a woman whose husband was being confronted by a man who came to kick his ass. That man was Wong Jack Man, who was dressed in a traditional kung-fu robe. He had arrived a minute earlier with three associates. Bruce stood in front of him wearing jeans and a tank top. The two men sized each other up. They shared many traits. They were both 23-year-old martial artists who recently emigrated from Hong Kong. They were both fanatically committed to combat. They were both viewed as rising stars in the California kung-fu community. Despite their differences, however, Jack Man and Lee had two glaring differences. One was technical, and the other was cultural. From a technical standpoint, Jack Man employed the Northern Chinese Shaolin style of martial arts with its emphasis on legwork, kicking, and acrobatics. By contrast, Lee primarily used Southern Wing Chun that emphasized close combat, fist strikes, and redirection of attacks. Culturally, Jack Man was a traditionalist, and he viewed Bruce Lee as a heretical street punk who needed to be taught a lesson. Lee was a vocal critic of the kung-fu establishment, which he publicly roasted for being too rigid, too deferential to hierarchy, and too focused on choreographed sequences. He called the established kung-fu masters “old tigers with no teeth.” Jack Man came tonight to answer that call. Bruce Lee in 1964 was still an up-and-comer, still obscure, largely unknown outside of the California kung-fu community, and not that well known inside the California kung-fu community. It made sense that he had developed an anti-establishment worldview, considering he never really fit in. He grew up in Hong Kong, which was occupied by Japan during WWII and then taken over by the British when Japan surrendered. Being of Chinese heritage, he clearly didn’t fit into the British establishment. And yet he also didn’t completely fit into Chinese culture because he had European ancestors on his mother’s side. In 1950s Hong Kong, the kung-fu establishment only condoned teaching martial arts to students who were full-blooded Chinese. He faced prejudice from both sides. Lee’s first kung-fu master, Ip Man, came under pressure for accepting Bruce as a student. He liked Bruce, who was barely a teenager when Bruce joined his school, and he saw tremendous potential in the young student. But the old shifu had to carefully navigate the traditional cultural sensitivities. He allowed Bruce to train privately and did not actively publicize Lee’s mixed heritage. This need to tiptoe around cultural taboos enraged Bruce. He viewed the kung-fu principle of purity as regressive, upheld primarily to protect the status quo rather than produce the most effective combat techniques. He developed a chip on his shoulder about deference to tradition. It made him question the wisdom of the establishment, and in the world of martial arts so steeped in ways that dated back centuries, this stance by a young student was nothing short of radical. Lee set his sights on becoming the best fighter possible. He relished the idea that a person of mixed heritage could whoop opponents who stood for an ideal of supposed superiority because of their pure-blooded heritage, whether Chinese, British, or other. Ip Man, to his credit, taught his students to emphasize practicality. He encouraged them to test the techniques they learned by sparring with opponents outside of the formal school environment. Bruce zealously honed his techniques in street fights, which in 1950s Hong Kong often unfolded on the city’s rooftops. He began to see that much of traditional kung-fu teaching, with its emphasis on choreographed moves, pre-determined patterns, and rote memory, was unnecessarily self-limiting and ultimately impractical for real combat situations. He saw this as a weakness to exploit. Lee’s view is what Mike Tyson said about boxing decades later: “Everyone has a plan until they get punched in the face.” So Lee began looking for the best techniques wherever he could find them. He saw effectiveness in lunges and parries of fencing, in jabs and hooks of western boxing, in the nimble footwork of dancing, and elsewhere. He also championed efficient kinesthetics, expending minimal energy to create maximum speed and maximum force. In the context of singular links, he set out to combine these elements that normally exist in different domains so as to create a martial art that was more effective than all the others. In 1958, when Bruce turned 18, he was beginning to show the benefits of his prodigious training across multiple disciplines. That year he claimed the Hong Kong interschool boxing title by beating champion Gary Elms, he won the city’s cha-cha dance championship, and he defeated a number of kung-fu rooftop opponents. Unfortunately, since he was also getting into trouble with the police, and his parents predicted his street-fighting lifestyle would land him in jail or worse, they arranged for him to leave Hong Kong and join his sister Agnes in California. By the time he was standing in front of Wong Jack Man in the Oakland garage, he had spent the prior six years prolifically developing his own mash-up of techniques and philosophies under a unifying approach. The details of what happened that night remain somewhat disputed, but the outcome was clear: Bruce Lee beat Jack Man in combat, but did so in ways that exposed shortcomings of Lee’s technique. Jack Man’s retreats caused Lee to expend too much … Read more

Bruce Lee was neither tall nor heavy, but he could beat up larger opponents. What he lacked in brawn, he made up in speed, smarts, and heart. He also knew how to put on a show. The son of an opera singer and film actor, young Bruce Lee grew up in show business. He happened to be born in San Francisco while his parents were touring with the Hong Kong Cantonese Opera. He performed as a child actor and competitive dancer. In 1958, he won the Hong Kong cha-cha championship. Later, he served as dance partner and bodyguard to actress Diana Chang during her publicity tour of America, showcasing his cha-cha moves with her on stage every night. At the inaugural Long Beach International Karate Tournament in 1964, showman Bruce Lee captivated the crowd by demonstrating two-finger push-ups and a spectacle called the one-inch punch. The one-inch punch is a martial-arts strike that travels just a tiny distance before reaching its target. Lee’s demonstration surprised the audience of martial artists and combat fans not so much for the speed of his punch, which was blinding, but for the explosive power that it delivered. It sent tournament attendee Bob Baker flying backward into a chair. The punch began with Lee standing with his fist outstretched to Baker’s chest, tensed and ready for the punch. Then, a moment later, Baker was flying backward. Lee had hardly moved a muscle. Lee’s punch looked like an impossible stunt. It looked like a hoax. It looked unnatural, like Michael Jackson’s moonwalk. The punch didn’t look real. But it was real. Decades later, the TV show Mythbusters set out to investigate the one-inch punch. They conducted tests with a martial artist who allegedly studied under one of Bruce Lee’s students to deliver the performance, and they concluded that the one-inch punch was a plausible attack technique. In truth, the recreated punch didn’t look nearly as crisp or focused as Bruce Lee’s punch. The Mythbuster martial artist stood with his left foot forward, while Lee stood with his right foot forward. Lee showed much more extension from his rear left foot through his hips and shoulders to his fist. Most power punches that you see in the boxing ring travel a long distance. The puncher pushes off the rear foot and pivots the hips and shoulders to deliver power to the fist. It’s the pivot that delivers the power, like the swing of a baseball bat or a golf club. By contrast, the one-inch punch employs no pivot. Rather, it requires a chaining of muscles from the rear foot, up through the leg, hips, spine, shoulder, arm, and wrist. The power comes from an instantaneous flexing of all muscles involved so as to deliver the force from the rear foot to the front fist. Lee’s body acted like a series of signal repeater/amplifiers used to carry an electrical voice signal thousands of miles. Lee’s study of the Wing Chun style of martial arts focused on close-quarter combat mainly through hand techniques, as opposed to Northern Chinese martial arts techniques that emphasize kicking from farther away. When standing face to face with an opponent, you could see why the traditional power punch would not be optimal, considering the time it takes to draw back the fist and throw it forward. In close-quarters combat, where the difference between knocking out your opponent and being knocked out by your opponent can be measured in milliseconds, the traditional haymaker that you see in western boxing could put the attacker at a disadvantage. While the one-inch punch travels a short distance, it is like the tip of a whip that carries astonishing force. In a whip, the impulse is accelerated to supersonic speed by the time it reaches its tip. The crack of the whip is the sound of a wave traveling at supersonic speed. It is a miniature version of what happens when a jet airplane travels faster than the speed of sound. It creates a shock wave as it displaces air. It’s the sound of air molecules crashing into each other. As Lee said in his book Tao of Jeet Kune Do, “Good form is the most efficient manner to accomplish the purpose of a performance with a minimum of lost motion and wasted energy.” Like many singular links, the point of the one-inch punch is to transform the impossible into something possible.

Let’s unpack the concept of entropy, which is an abstract term loosely connected to the idea of randomness. The term “entropy” appears in different fields of study with different meanings. In thermodynamics and statistical mechanics, entropy describes the disorder or dispersion of energy in a system. In information theory, entropy measures the uncertainty of information in a message or data set; it is the ambiguity of information. In finance, entropy can be used to quantify the amount of randomness in the movement of securities’ prices or the unpredictability of performance. What’s common to all these applications is the idea that chaos exists in otherwise orderly systems. As we’ll discuss shortly, the process of creating singular links often involves harnessing chaos and reducing entropy. For a physical example of entropy, consider the internal combustion engine of the Toyota Corolla, which Wikipedia says is the world’s best-selling car. When you start your Corolla, gasoline is burned to drive the pistons, but some of the energy is inevitably lost as heat, sound, and friction as the energy is transferred to other mechanical components of the car. These losses represent an increase in entropy because energy is being dispersed rather than being used efficiently. The heat produced as a by-product of the engine’s mechanical process must be constantly dissipated to prevent overheating. Energy is not directly related to the amount of energy that is unavailable for conversion into mechanical energy. Entropy doesn’t tell you, for instance, that for every gallon of gas consumed, 5% of the potential mechanical energy is lost in the burning process. Rather, entropy is a measure of the dispersal of energy within a system. It tells you how far-flung the lost energy becomes when it is lost. Think of it in the context of a school field trip where 20 kids visit a museum, and one of the kids wanders away from the group. Entropy doesn’t tell you that one of the 20 kids got lost. Entropy tells you how far that one kid traveled while separated from the group. The entropy might be small, such as if the kid remained in the same museum but ended up in a different room. Or the entropy could be large, such as if the kid climbed on a Greyhound bus and traveled across the country. For the adults responsible for keeping track of the kids on the field trip, the difference between small entropy and large entropy could equate to the difference between gainful employment and unemployment. The laws of physics show that systems, processes, and interactions tend to evolve towards states of greater disorder and randomness over time. This concept is succinctly captured in the second law of thermodynamics, which states that in an isolated system, entropy tends to increase over time. Heat disperses as it flows from higher-temperature objects to lower-temperature objects, scattering its energy in the cooling process. The molecules in frozen water are highly ordered, but as water melts, the molecules become more disordered and move more freely. When you mix salt with water, the ions contained in the salt become more randomly dispersed in the solution than they were in the solid state. When a biological life dies, natural decomposition sets in, causing its particles to scatter. As the saying goes, “The only constant in life is change.” So, if the natural tendency of the world is towards entropy, the reduction of entropy requires activity. The historian Henry Adams said, “Chaos is the law of nature; order is the dream of man.” Much of human activity focuses on bringing order to an otherwise chaotic world. People who show up to a job interview looking tidy, with hair groomed, and wearing a pressed outfit, communicate the message, “You can count on me as someone well practiced in the skills of entropy reduction.” They might as well wear a sign that says, “Hire me: I create order from chaos.” In the next post, we’ll look at the relationship between entropy and singular links.

When observing singular links, you see one thing joining to another thing to create some new thing. Sperm joining egg creates a zygote. A spark joining gunpowder creates ignition. A hot poker from the fireplace joining water creates steam. In each of these cases, the joining process suddenly creates something new. Take a moment to consider the fact that sudden changes such as these are relatively unusual. Sudden change is far less common in the world than gradual change. Most changes that you witness unfold in sequential steps, from A to B to C to D, not from A to D in a single step. The sun gradually rises and sets. Winter gradually turns to spring, which gradually turns to summer. You are born, gradually grow up, and mature, and you can look at the photos of yourself at various stages (remember that haircut?). Geological erosion, evolution by natural selection, succession in ecosystems, urbanization, and most everywhere you look, when things change, they pass through a series of intermediary steps in the process. However, some of the most interesting changes, and many of those associated with singular links, happen very rapidly or in a single jump step, rather than through gradual, iterative processes. Let’s look at some of them. Volcanic eruptions and earthquakes are geological examples of rapid change. Hurricanes, while not instantaneous, create extensive damage and change in a matter of hours. Tornadoes can do the same in a matter of minutes. A tectonic shift at the bottom of the ocean can happen rapidly, resulting in tsunamis that crash on shores hundreds of miles away. Lightning strikes can be measured in millionths of a second. What do all these have in common? They all involve the release of pent up energy. For volcanoes, molten magma rises to encounter resistance from the earth’s surface, building pressure until it suddenly erupts. For earthquakes, there is an immediate release of stress along faults in the earth’s crust. Tornadoes spring from a significant buildup of energy stored in the earth’s atmosphere. Lightning erupts from static energy in thunderclouds. Many mechanical devices also deploy the release of stored energy to initiate rapid change. Think of a mousetrap, a jack-in-the-box, firearms, automobile airbags, electric circuit breakers, or electric speakers whose diaphragms react to changes in electrical energy, moving rapidly to produce mechanical energy in the form of sound waves. A catalyst that releases pent up energy can create singular links. Another type of rapid change happens in the form of exponential growth. For instance, if you plotted the growth of the human population over 100,000 years, from roughly 98,000 BC to 2,000 AD, the line would look more or less flat as you moved from left to right, with a sudden spike at the end. For the first 99,600 years until the year 1,600, the human population had grown to an estimated 550 million people. Then it took a little over 200 years for that number to double to around 1 billion. By the time the next 200 years had elapsed, the human population had rocketed to a whopping 7 billion. In what would be considered a blink of the eye in planetary terms, the human population leapt from insignificant to highly significant. If you could somehow have set a time-lapse camera in space pointed at the earth for the same 100,000 years, you would have seen a planet that was pitch black at night for a long long time. It would have been a very boring movie. However, eventually, just a moment after you noticed some faint flickers of light in New York, London, and Paris around the late 19th century, the time-lapse movie earth would suddenly light up like the giant incandescent bulb it is today. This is exponential growth. To be clear, the term “exponential growth” is often used to mean, simply, rapid growth, but their meanings are different. Exponential growth and rapid growth are two different forms of growth. Not all rapid growth is exponential and not all exponential growth is rapid. Rapid growth just refers to something growing at a fast pace. For instance, if a town of 1,000 people grows by 1,000 people per year, that may be rapid, but not exponential. By contrast, exponential growth refers to something whose growth is proportional to its population. So, the larger the population, the more it grows. Eventually, as the population of a town becomes sufficiently large, if it continues to grow exponentially, its population will jump by huge amounts from one year to the next. It might add hundreds of thousands or even millions of people in any given year. Meanwhile, the other town that continues growing by a fixed number, rapid as it may be, will add just 1,000 new people each year. Children’s ability to acquire language follows a similar exponential growth curve. When a child first learns to mimic the words “mama” or “dada,” the growth of her language skill is modest as she picks up a few new words here and there. Eventually, she starts using more words, stringing them together in phrases, then sentences, and then suddenly – boom – she becomes a chatterbox. Her language increases exponentially. Exponential change exists in the world all around. Think of epidemiology, bacterial colonies, technological advancements, compound interest, social networks or, in the case of exponential decay, radioactive decay and carbon dating. Here’s the key point: even if something changes exponentially, it changes modestly for long periods and changes dramatically for a short period. In the case of the human population, for most of the past 100,000 years, growth was modest, until it wasn’t. In the case of a bacterial infection, symptoms may be so slight as to be undetectable for long periods, until the exponential growth forces the patient to the emergency room. Then, after she receives antibiotics resulting in exponential decay of the infection, the bacterial population declines exponentially at the beginning, followed by long periods of modest reduction thereafter. So, while something may appear … Read more

When two elements join together to propagate something new, there exists a certain reciprocity in the relationship. The term reciprocity speaks to the way they interact and the way they influence each other. You can see examples of reciprocal relationships everywhere in the natural world. Take the reciprocal relationship among bees and flowers. Bees visit flowers to gather pollen, and they transfer pollen to other flowers, helping the flowers to reproduce. Bees get honey and flowers get baby flowers. In the ocean, fish visit cleaning stations where cleaner shrimp crawl all over them to feed on the parasites attached to their skin. There is a reciprocal relationship between the two parties. The fish get detailing and the shrimp get dinner. Fish may reciprocate the favor with the hippo at the San Antonio Zoo. The hippo stands asleep in the water with just its nostrils above the surface, its mouth open, with colorful little fish enthusiastically exploring the hippo’s teeth, tongue, and gums. The fish enjoy yummy algae and food particles while the hippo enjoys good dental hygiene. Reciprocity also exists within species themselves. Consider cooperative hunting. Lions or wolves are limited in the prey they can catch on their own. However, when they work together, they can be more successful to catch larger prey, contributing to the prosperity of their packs and prides. Reciprocity is an ancient concept that has helped to inform the earliest civilizations. The Code of Hammurabi, ostensibly written by King Hammurabi of the First Dynasty of Babylon around 1750 BC, is known for exemplifying the “eye for an eye” principle. One of its laws says, if a man puts out the eye of another, his eye shall be put out. Another says, if a man breaks a hole in another man’s house to steal his possessions, he shall be put to death in front of the hole. Yet another says, if fire breaks out in a man’s house and another man steals the homeowner’s property while endeavoring to put out the fire, that man shall be thrown into the self-same fire. Hammurabi didn’t mess around when it came to matters of theft. For the Babylonians, theft was a capital offense. In contemporary times, reciprocity is the glue that holds together principal-agent relationships, as when one party hires another party to carry out specific tasks. If you want to start a company, for instance, you may hire a lawyer to draft and file the articles of incorporation. You, as the principal of the company, hire the attorney to act as an agent on your behalf. You receive the benefits of legal services, and your lawyer receives a commission for her services. You may repeat a similar arrangement with your accountant, your website designer, and any number of other professionals needed to help run your business. In each case, the parties enjoy mutual benefit. The concept of mutuality is key. Both parties contribute something of value and receive something of value in return. Flowers provide pollen and bees repay them with their fertility services. Entrepreneurs provide paychecks to lawyers, and lawyers repay them by birthing new corporate entities, perhaps a different type of fertility service. If only one side benefited, the relationship would be lopsided or, in extreme cases, predatory. Going back to the pack of wolves, reciprocity exists among the wolves, not between the wolves and their prey. Wolves need food, such as the deer in the open field. The deer needs nothing from the wolves except to be left alone. That relationship is not reciprocal. The relationship between wolves and deer is unilateral. The wolves say to the deer, “Stop running,” and the deer says to the wolves, “I’ll stop running when you stop chasing me.” The episode will end with either the wolves catching the deer or the deer escaping, at least for the time being. The relationship is unidirectional, not bi-directional. Reciprocal relationships also have an element of interdependence. Each party needs the other party to maintain their side of the bargain. If one party withdraws, the collective benefits collapse. If the bees don’t show up, the flowers don’t reproduce. Or, if the bees show up and there are no flowers, they have to find pollen elsewhere for their honey. In the principal-agent relationship, the business owner needs the expertise of agent professionals in order to launch and run the business. Without them, the business might not get off the ground or, if it does, it might not survive. By the same token, the agents need principals to hire them for their services. If the principals go out of business, the agents also suffer. They need each other. They are interdependent. Another characteristic of reciprocal relationships is specificity. Each party brings the exact something that the other party needs. That is why the relationship works. If either party didn’t possess that certain something that the other party needed, the relationship wouldn’t work. Consider again the entrepreneur who wants to file articles of incorporation to get her business off the ground. She needs a lawyer with knowledge and experience related to the formation of a company. The entrepreneur might be approached by other skilled individuals offering to help her with her business, but if they didn’t bring the specific legal skills necessary, the relationship would be fruitless. Imagine a shoemaker, for instance, who says, “I hear you want to start a business. I can help. You need shoes. I can make them for you.” The entrepreneur says, “I don’t need a shoemaker, I need a lawyer. Can you file articles of incorporation for my company?” The shoemaker says no. Conversation over. Specificity of contribution is a necessary element of the reciprocal relationship. In the context of singular links, where a combination propagates an outcome that has greater scope or scale, reciprocal relationships also enjoy another characteristic. That characteristic is synergy, where the interaction produces a result that is greater than the sum of their individual parts. Each party catalyzes an aspect of the other … Read more

There is a riddle that asks how a prisoner could escape over a high wall without leaving any evidence. How could he pull it off? The name of the riddle reveals how. It is called the Ice Block Wall Escape. The prisoner freezes water to form an ice block, stands on the ice to climb over the wall, and the evidence disappears when the ice melts. Remember, a singular link is a combination that changes the scope or scale of its product. In the riddle, the prisoner creates a singular link by pooling the water in the shape of a block and allowing it to freeze. Changing the scope of the water, the prisoner uses it to literally scale the wall. Let’s look at some other examples of changing scope or scale. You could use canvas fabric to create a tent, and it might be effective in many environments. However, in heavy rainfall, the canvas would absorb the water, leaking rainwater into your otherwise cozy shelter. What’s the solution? Wax. You could melt the wax, brush it onto your canvas, and the waxed canvas would repel the water. Presto! Canvas on its own isn’t waterproof. Wax on its own has no form. The combination of canvas and wax creates waterproof material. Teflon coating on pots and pans works the same way. When cooking with metal pots and pans, food tends to stick to their surfaces. Coating the metal with Teflon, which has an exceptionally low coefficient of friction, reduces the propensity of foods to stick. Metal cookware on its own is sticky. Teflon on its own has no form. The combination of cookware and Teflon creates a non-stick solution for cooking. If you wash your car at the automated car wash, one of the final applications after the standard soaps and foams is “spot-free rinse.” This, I assume, is some chemically softened water whose properties reduce the likelihood that spots will form when the water dries. This is not just a regular rinse but rather an enhanced rinse. Its scope has changed. When you begin looking for examples of combinations that change the scope or scale of their products, you will start to see them everywhere. Apply window tint to your car windows to block the sun’s ultraviolet radiation. Add SPF sunblock to skin products. Galvanize metal pipes by covering them with a layer of zinc to prevent them from rusting. Soundproof the walls of a room to help absorb sound waves, deadening them and preventing them from bouncing to other surfaces. All these examples begin with surfaces that are in some way vulnerable — windows, walls, pipes, delicate skin — and after they are chemically altered, they become more resilient. The treatment changes their properties. In these examples, each element provides a property that the other lacks, and together they create recipricity. In the Ice Block Wall Escape riddle, water was manipulated to create an escape. In fact, water frequently serves as a catalyst for singular links. Think of concrete, Plaster of Paris, or ceramic clay. Each one begins as a powder. When you add water, you create a material that can be manipulated, pressed, injected, trammeled, or skimmed. Later, when the moisture is gone, the result is a hard surface. Mixing powder and water creates a pliable substance capable of new applications. Controlling the ratio of powder and water generally controls the durability of the final product. This is most evident in the industrial applications of concrete, where the mixing ratios, their curing conditions, and other environmental factors could mean the difference between a skyscraper that stands for hundreds of years and another that crumbles under its own weight. Humidity can be used for all manner of manipulation. Adding moisture to wood makes it more pliable, as in the case of furniture making. Moisture can be used to induce corrosion such as a uniform patina of rust on industrial signage. Moisture also conducts electricity, as you know all too well if you have ever accidentally spilled a glass of water onto your phone or computer keyboard. The process of torrefaction, in which moisture is removed from lumber, changes the wood’s chemical and physical properties. It creates a chemically altered wood that is lighter, more stable, less vulnerable to decay and, in the case of musical-instrument manufacturing, is more resonant for sound vibrations. Yeast turns flatbread into leavened bread, grape juice into wine, and tea into kombucha. A grain of sand in the soft tissue of an oyster induces pearl cultivation. The right combination of carbon, pressure, and high temperatures results in diamonds. In each of these examples, a precise combination is required to achieve the desired outcome, with slight variations producing vastly different outcomes. A tiny change in the fermentation of wine could be the difference between a delicious Bordeaux and a glass of vinegar. In the case of diamonds, a slightly different geological environment could produce a wide spectrum of products from rubies or emeralds to plain old charcoal. Encryption is another example of a singular link. The process of encryption converts a text message into an indecipherable blob of nonsense by applying an encryption algorithm. The recipient of the encrypted message applies the reverse algorithm to decrypt the text, thereby translating the nonsensical blob back into a legible message. There is a unique relationship between the plaintext and the ciphertext, and that relationship is uniquely explained in the algorithm. If anything in the algorithm were to change, the relationship would be corrupted. Looking at it from this perspective, the creation of singular links is like cracking a safe or breaking an encryption. Approximate combinations are insufficient. Only exact combinations create the required change of scope or scale to satisfy the definition of a singular link.

When I moved to New York City in my twenties, I was determined to forge a career as a working artist. In that Darwinian pool of ambition, the most successful artists were the ones who could generate a dependable stream of original work. They seemed to always be developing multiple ideas simultaneously. It was tempting to believe they were the ones who came into this world blessed with some unearthly natural talents, as someone might inherit a certain eye color or blood type. As it turns out, they didn’t receive some rare gift from the gods, or a crate of secret scrolls, or a muse shackled to the radiator of their studio apartment. The prolific artists were just curious people who had a knack for noticing connections in the world around them, and a dedication to developing those connections to find out where they might lead. They started their process by making connections. Some years later I discovered a love for the capital markets and, in particular, the psychology that makes people value some things more than other things. I noticed that although a loaf of bread is mostly just flour, water, yeast, and salt, some loaves could command 20 bucks at the grocery store, while others would go stale on the shelf if their prices rose above two. What makes one loaf more valuable than another? Or one car or one phone or fizzy drink or magazine subscription? At the end of the day, the answer is related to the way consumers connect the product in question to some impact on their life, real or perceived. Again, it’s about making connections. In the investment world, I have had the good fortune to work with professional money managers who forged luxurious careers by being the ones who spotted trends before others. Being among the first to invest in those trends, they benefited when others caught on, invested their funds in turn, and drove up the price of their investments. On Wall Street, as in other places, there’s a premium for being the first to make a connection. Many of the Fortune 500 companies got their start by linking a solution to some market need. In the early 20th century, Henry Ford set out to make car ownership affordable, creating the Model T, and helping to not only fuel the economy but also birth that societal structure known as the suburb, complete with its picket fences, tidy lawns, and garden gnomes. Cars made suburban sprawl a possibility, or possibly, an inevitability. From a business perspective, Ford’s push to democratize car ownership also led to innovations in manufacturing. If the Model T was going to be affordable enough for average people to buy, it had to be manufactured economically. So, instead of employing workers to assemble entire vehicles one at a time, Ford introduced the concept of assembly-line production. This cut costs and improved output. It scrapped the need to transport heavy car parts to a single area of the plant for assembly. Additionally, since workers focused on single areas of production, they could develop their skills, speed, and specialization, making them more efficient and making their work more consistent. Ford linked affordability to manufacturing efficiency. IBM saw there was a nascent market for personal computers, deviated from its focus on large mainframe devices, and released its DOS-based IBM PC (which had a whopping 16 kilobytes of total memory). The Sony corporation, seeing that music lovers wanted a convenient way to take their music on a walk, created the Walkman. Netflix, upon noticing increasing feasibility for in-home video streaming, pivoted from the traditional DVD-by-mail business model. The common link in these companies was their ability to change strategy to meet changing consumer lifestyles. As I began working in research, I noticed clients would pay handsomely for someone to tell them what they didn’t know. It turns out that having your blind spots revealed is valuable. It gives you a greater context for your decision making and helps to answer the question, should we go full steam ahead or change course? In business, the consultants who really command the Midas touch are those who not only alert the client to some new information, but also advise on how to monetize that knowledge. Success in so many fields hinges on being able to make connections. Strategic planners, journalists, research scientists, business consultants, attorneys, detectives, doctors, first responders, and more, all these occupations involve making links and acting upon them. In fact, there seem to be more vocations that rely on making connections than those that don’t. Keep in mind, however, not all links are singular links. Not all links create a transformative result. A singular link is a connection that births a unique outcome, an outcome that is fundamentally different from its constituent parts. Folding sushi into a seaweed wrap and calling it a sushi burrito is not a singular link. It’s sushi wrapped in seaweed. Taking a plastic spoon and adding some teeth is not a singular link, it’s just a spork. Making a cowboy movie in Italy and calling it a spaghetti western isn’t a singular link, it’s just a different kind of cowboy movie. Singular links are more rare and more powerful when they occur. They may be surprising, inspiring, or shocking. If you take some household bleach and mix it with ammonia, you create chlorine gas. And if you’re not wearing a respirator, that’s a singular link that can kill you. If you take a copper penny, touch it to a galvanized nail, and immerse them in lemon juice, you create an electrical current. This is a singular link that can illuminate an LED light bulb. Go ahead and try it! Our ancestors created a singular link when they discovered that a piece of flint struck with pyrite would create sparks. These sparks could ignite tinder and create controlled fire, possibly the most consequential discovery in human development. Bleach plus ammonia equals chlorine gas. Copper plus zinc plus lemon … Read more

singular [ sing-gyuh-ler ] adjective being one of a kind; unique exceptional; extraordinary; remarkable unusual; conspicuous link [ lingk ] noun a bond between one part and another anything serving to connect two things or situations, especially where one may affect the other singular link [ sing-gyuh-ler lingk ] noun phrase a novel construct derived by linking unrelated elements or ideas the transformative result of a creative or intuitive combination a connection that produces something fundamentally different slink [ slingk ] verb a contraction of the term “singular link“ to make a connection resulting in an enhanced, heightened or unexpected outcome slinker [ sling-ker ] noun a person who makes singular links someone who engages in the practice of slinking

Let’s talk about music. Let’s talk about how musical notes can create singular links. When you play a note on a piano or any instrument, you are actually hearing several notes wrapped together. Let’s say you play what piano players call the A2 note on a standard-size keyboard. This note is below middle-C, two octaves above the lowest note. The loudest pitch you hear is called the note’s fundamental. In the case of A2, the fundamental vibrates at 110 Hertz, or 110 times per second. In addition to the fundamental, you also hear other harmonic notes, or overtones, that work together and complement the fundamental. These overtones vibrate at higher frequencies. However, their volumes are lower than the fundamental, so their contribution to the overall sound is more subtle. The first overtone of A2 is A3, which is an octave above the fundamental, and it vibrates 220 times per second. The second overtone is E3, a perfect fifth above A3, vibrating 330 times per second. Then there’s A4, which vibrates 440 times per second and is the reference note for “standard 440 tuning” or “concert tuning.” The next overtone is C-sharp, two octaves plus a major-third above the fundamental, and it vibrates 550 times per second. All these notes ring simultaneously when you play that single A note on the piano, and together they create a rich, blended sound. Whichever note you play on the piano, the fundamental will be accompanied by several overtones.

Let’s dive deeper into the topic of emergent properties, which are the unique characteristics that result from connecting some underlying components. The high school student creates emergent properties by mixing vinegar and baking soda to simulate the frothing lava of a volcano science project, for instance. The frothy properties do not exist in either of the underlying components. Rather, they emerge from the interaction of the components. Consider the Pointillist painting style developed by artists Georges Seurat and Paul Signac. The technique involves painting thousands of tiny dots to create an image. If you stand close to a painting such as Seurat’s A Sunday Afternoon on the Island of La Grande Jatte, you don’t actually see an image because you are too close. All you see on the canvas is a swarm of little painted splotches. As you step back from La Grande Jatte, however, your eyes begin to recognize certain images such as a woman with a parasol and a quirky 19th-century French skirt, various dogs, and sunbathers laying lazily on the lawn. Each little paint dot on its own is trivial, but it is the clustering of dots that creates the emergent properties of a Pointillist image. The same is true for Roy Litchenstein’s pop art pieces like Whaam! From far away they look like large comic book images, but up close they are just clusters of colored Ben-Day dots. Same with the giant photorealistic portraits of Chuck Close. Far away you’d swear they were photographs. Close up, however, they look like multicolored cell clusters. You step back a couple of steps, and then step back once more to locate the exact point where you see the face beginning to form in the soup of cell clusters. And then you step forward again to see the transformation again from face to cell clusters. Walk backward far enough and the property that emerges from Close’s cell clusters is the property of a lifelike human portrait. The same holds true for murals made of tiny ceramic shards. The analog in music is percussive rhythms comprised of the clackety-clack of drum beats. A single clack is not music. Rather, music is created by assembling multiple clacks to form a rhythm. The analog on a computer monitor is the retro video game comprised of blocky pixels (think, Pong, Space Invaders or Asteroids). Zooming in on one section of the mural or one phrase of the percussions or one corner of the video-game monitor, you encounter the basic building blocks of the work. Zooming out to a larger portion of the work, your senses will start to infer patterns, and you recognize the artist’s inherent order. These examples show that sometimes the success of singular links is less about what elements are combined, and more about how they are combined. In each of these examples, the individual components are basic, simplistic, elementary. But it’s the method of combining those components that creates emergent properties. Chuck Close’s portraits, when seen from afar, are jarringly lifelike. They reflect a shimmering luminosity, especially in the eyes, making the subjects appear animated, just like breathing, living giants peering at you from outside a window. You can see the Subject’s human character in his portraits. But as you go closer, the illusion of aliveness disintegrates, revealing itself as an optical illusion on a flat canvas, delivering a subtle, lucid reminder of the fleeting impermanence of a person’s life. That’s an amazing lesson from a cluster of paint splotches! Think about Seurat’s painted dots. His fine aesthetic only works because the dots are tiny and uniform in shape and size. If the painted dots were larger and more irregular, the image would inevitably appear cruder and more pixilated. If Seurat had been forced to work with ever-larger paint brushes, eventually he wouldn’t be able to create a discernible picture on a canvas of fixed size. This observation branches out to several realizations. First, the size of the paint brush is related to the size of the image. I guess that’s just another way of saying, If you want to cram more information onto your canvas — or onto any fixed piece of real estate — you need to shrink the size of your information. The more dots crammed into a fixed-size image, the smaller the dots need to be. Second, the size of the paint brush is related to the quality of the image. When I say quality, I’m not talking about whether it is inherently good or bad. I’m talking about how refined or crude the image is. The larger the paint brush for a given image size, the cruder the image will be. The smaller the paint brush, the more refined the image can be. Third, abundance and randomness are related. Sometimes two elements randomly come together and just work as a singular link. In other words, when they join together randomly they create emergent properties. For example, I don’t know… For example, your cat bumps against two drinking glasses on the kitchen counter, and one makes a sound whose pitch is a major third above the other, forming a pleasing spontaneous harmony. That’s a kind of random interaction that has emergent properties. The moment is so interesting that it strikes you and you forget to shush the cat for being on the kitchen counter. That’s a fascinating idea, that two random elements can work together. Can more than two random elements spontaneously combine to form emergent properties? Sure, it’s possible. This dynamic is captured in lots of adventure movies involving chase scenes, and as the characters scurry through their environment, they capitalize on the random intersection of people, vehicles, objects, and luck to excite and delight the viewers. However, in the world that plays out beyond the movie screen, the more elements you’re hoping to link, the less likely they can be chosen randomly and still work successfully together. A good example is the use of words. A single word is a tiny packet of information. … Read more

Let’s unpack the concept of orthogonal influences that we introduced in a recent post. Everyone is familiar with the word diagonal, but the word orthogonal could use a little introduction. Diagonal describes a line that intersects one or more lines to form one or more angles, like the line that connects two opposite corners of a square forming two 45-degree angles. Orthogonal describes a line that intersects another line at a right angle. For instance, the two lines that form the corner of the square are orthogonal to each other. They meet to form a 90-degree angle. In statistics, orthogonal describes two factors or variables that are not correlated. The movement of one is unrelated to the movement of the other. In computer science and signal processing, orthogonal describes techniques or functions that are independent of one another. You get the point. The term orthogonal has a broader application in the context of singular links. It speaks to things that are unrelated, whether they are in the same domain or not. They may be objects, ideas, elements, or influences that exist on different planes, in different dimensions, in different regions of the map or on different maps; they may hail from different families, different generations, different species; they’re not necessarily in the same ballpark and maybe not even in the same sport. They are unalike, unassociated, unfamiliar, and distinct. That’s why pairing them with one another can create uniqueness. Importantly, things that are orthogonal are not opposite to one another. Opposites are very different but are most certainly related to each other. Heads and tails are opposite but related. Yin and yang are opposites but related, as are male and female, hero and villain, beauty and beast, heaven and hell, life and death, truth and lies, order and chaos. Opposites define each other. Each exists in opposition to the other. They are not orthogonal. Zero and infinity are very far apart but they are mathematically related. Zero and infinity are symbolic quantities that exist beyond quantification, as improbable as that may sound, numbers beyond enumeration. If we were to count backward toward zero, searching for the smallest non-negative number in the universe, the teeniest, barely existing essence of the vanishingly tiniest fraction of a hint of a number… Well, zero is even smaller than that. If we were to count upward, searching for the largest number in the universe by counting all the tiniest elements of the universe such as protons and neutrons and electrons and all the mysterious quarks in the vastness of space, and then if we were to exponentiate that number to gargantuan proportions, exploding the size of that number larger and larger, and if we were to repeat that process a billion billion times over and over again every nanosecond from now until the last of our great great grandchildren breathed their last breath, creating a mind-bendingly huge number beyond our wildest imaginations… Well, infinity is even larger than that. Zero and infinity are far apart — exceedingly far apart — but they are not orthogonal. They both exist on a numerical continuum. Infinity and zero share the same kind of special relationship as do the dualities of everything and nothing (the absence of everything), light and darkness (the absence of light) and sound and silence (the absence of sound). They are opposites but they are related. Orthogonal influences are emphatically not related. Orthogonal influences are all around us if we look for them. They are everywhere, in fact, and far too numerous to list. The number of discrete pairings of orthogonal influences is infinite (there’s that word again), and that would be true even if humanity wasn’t continually creating new information, which it is. The domain of collective human knowledge is expanding faster than our ability to assimilate the new knowledge and apply it to the things we already know. The things we know are a form of order in our lives, and the new things that influence what we know are a form of chaos. It is in this interplay of order and chaos where singular links are born.  Given the infinite potential of singular links, the vastness of linkable ideas that swirl around us all the time, we need to start somewhere, and the best places to start are the places we already know. We begin with a field of familiarity, and then we introduce new, unfamiliar influences. We start with something known, and we introduce something new. We start with order, and then we inject a dose of chaos. That’s when things start to get interesting. Look at the world of biomimicry in engineering. Biomimicry seeks to create designs by imitating natural systems and structures. Velcro was inspired by burrs that grew on bushes and tenaciously stuck to clothes. The Japanese bullet train was inspired by the aerodynamic bill of the king fisher bird. Spider webs and silk from silk worms have inspired researchers to make filaments stronger without adding proportionate weight. Designers of wind turbines borrowed the biological design of humpback-whale fins whose tubercles along their leading edges reduce drag and increase lift. In each of these examples designers took what they knew (order) and introduced orthogonal influences from nature (chaos) to create engineering breakthroughs. The classic example of orthogonal elements is the duality of form & function. Form pertains to the attractiveness of something. Function pertains to its usefulness.  Form is the Tiffany diamond, the plunging back line of the bride’s dress and the bouquet of intricate sugar flowers on the wedding cake. It’s the groom’s symmetrical, toothy smile, his silk pocket square, the panache of his flare-rim glasses. Function is the credit card used to pay for the ballroom, the wedding-guest list, the marriage certificate, and the prenuptial contract. Form is the elegant angled headlight of a sports car. Function is its gas pedal and its brake pedal. Form is the the dreamy landscape zipping past the window of the moving train and the sound of the surf … Read more

Remember the story of Italian engineer and Nobel Prize winner G. Marconi, inventor of radio. As radio equipment began to get more powerful, he could transmit signals across greater distances. He thought that if he had strong enough equipment, he could beam signals across entire countries, possibly across continents and oceans. I’ll tell you ’bout Texas radio and the Big Beat. Soft, driven, slow and mad, like some new languages The WASP (Texas Radio and the Big Beat) – song by The Doors The first “border blaster” radio station was the legendary XED located across the Mexican border from McAllen, Texas. In the 1920s as broadcast technology became more powerful, the American FCC put a cap on the power levels of radio stations. In response, some enterprising broadcasters moved south across the border and set up shop in less-regulated Mexico. In 1930, XED broadcast with a power of 10,000 watts which was the most powerful transmitter in Mexico at that time. Soon other stations popped up all across the Mexican border, increasing their broadcasting power to 250,000 watts and more. Their signals were so powerful they could be heard emanating from wire fences and bed springs by listeners across North America, often overpowering the signals of local stations whose broadcast power was capped by regulators. Border blasters helped introduce country music to Johnny Cash and Waylon Jennings, and John Brinkley’s fake goat-gland cure for male impotence to a generation of flaccid consumers. During the Cold War the US government funded the border blaster Radio Free Europe to bombard the Soviet Union with Western messsaging and anti-communist propaganda. Rewind the tape to the time before border blasters, to the early days of radio when signal-generation was limited to short ranges. Marconi said if he had equipment that was strong enough and precise enough, he could transmit across the Atlantic. Other scientists ridiculed him, saying it would never work. The curve of the earth would cause his transmissions to veer off into space, they argued. But that’s not what happened. As amplification became strong enough to broadcast over longer and longer distances, the signals did in fact reach their receivers, seemingly bending around the slope of the earth’s surface. How could this happen? It happened due to one of the earth’s properties that was unknown at the time of Marconi’s early broadcasts: the ionosphere. When radio waves reached the upper layer of the earth’s atmosphere, this ionized layer reflected them back down to be received on the earth’s surface.  In other words, Marconi’s theory was correct, but for the wrong reasons. Inverting the saying, “I’d rather be approximately right than precisely wrong,” Marconi ended up being approximately wrong and precisely right! History is filled with similar examples. Alfred Wegener claimed the earth’s continents had previously all been joined together, and proposed a mechanism that pushed them apart. As it turns out, his mechanism was incorrect, but he paved the way for the accepted geological theory of plate tectonics. Gregor Mendel’s conclusions from breeding pea plants were incorrect, but his work gave rise to the scientific laws of inheritance that form the basis of modern genetics. Sir Isaac Newton’s experiments with prisms led to his mistaken belief that colors were inherent properties of light. This led to his discovery of the color spectrum and created a foundation for our understanding of optics. The Marconi story illuminates the idea of “failing but not quitting.” When on the hunt to find new ideas, we have to be prepared to make mistakes. Mistakes are proof of effort. Embrace the imperfections. They may lead to unexpected discovies.  Fail forward.

Last night the moon appeared as a tiny sliver. Above it was one bright star. Someone proclaimed the star was actually the planet Venus. My mind likened the crescent moon to a smiling mouth in the sky. Then I realized Venus was an eye. Venus and the moon together formed a face. The face of the night sky. This is a Singular Link. And once I saw it, I could not unsee it. Can you see it?

It’s hard to look at something familiar and see it in a new way. But that is what we often must do when we work with the same material over and over again. Musicians use the same 12 notes. Artists use the same forms of composition. Painters use the same primary colors as the source of other colors. Comedians use the same joke structures. One way to jump-start the creative process is to recognize the relationship between simple and complex elements. If you have ever visited LEGOLAND, you may have seen a display that asked the question, How many different ways are there to assemble six LEGO bricks that have eight studs (the standard rectangular LEGO brick)? The answer may be surprising – a whopping 103 million different ways! LEGO patent The reason there are so many ways to combine six LEGO bricks is, the LEGO brick is very simple. Its simplicity makes it simple to work with and simple to adapt. If it were more complex, it would be less adaptable, and would be more limited in its usage. Let’s look at it from a different perspective. Instead of starting with the building blocks and seeing how they could be assembled, let’s instead look at an assembled object and then see how it could be deconstructed. For example, let’s look at a simple drawing of a stick figure. Let’s divide this stick figure into its head and body. If we were trying to describe how these elements fit together, it would be pretty simple: the head connects to the top of the body. Looking at the body, we see that it is made up of different elements, including the torso, arms and legs, and we can further separate each of these elements from the others. The body as a whole is more complex than each of the elements that comprise the body.  If we wanted to describe how each of these stick-figure elements fit together it would still be pretty simple (it is just a stick figure after all), but we would need to create more instructions. We couldn’t just say, “the head connects to the body.” Now we would say, “The head, arms and legs connect to each other by connecting to the torso.” But even with these simple elements and simple instructions, different people assembling these parts would produce somewhat different versions of our stick figure. What can we observe from this exercise? The relationship of the head to the body is simple. The relationship of the head to each of the simple elements of the body is more complex. To generalize, the more complex the elements, the simpler their relationship. The simpler the elements, the more complex their relationship. Stated more succinctly, the simplicity of the relationship is inversely proportional to the simplicity of its parts. Back to LEGOLAND, the eight-stud brick is very simple, and so the relationship of six bricks is very complex. The number of possible ways to combine them makes your head spin. Math professor Soren Eilers visited LEGOLAND with his daughter and wondered how they had calculated that number, 103 million. Recognizing a mathematical challenge, he set out to calculate it himself. As it turns out, he discovered that LEGOS’ own number was far too small. He established that there are, in fact, 915,103,765 different ways to combine six simple LEGO bricks. Why, you may ask, is this relevant? It is relevant because, when we are actively searching for breakthroughs in our work, we can deconstruct our work into its elements and their relationships. Knowing there is a trade-off between element-complexity and relationship-complexity, we can choose to keep one aspect simple. And suddenly, our task is less difficult. Going back to our stick figure, if we choose to keep the relationships simple, we can switch heads and keep the same body, or switch bodies and keep the same head. Alternatively, if we wanted to break the stick figure into simpler elements (head, torso, arms and legs), we suddenly have a lot more ways to combine them. We could overlap them at different angles, omit one or more elements, stretch or squash them, rearrange them, or relate them to each other in any number of ways. The paradox is this: the more we simplify, the more complexity become available.

If our definition of a Singular Link is the union of unrelated elements resulting in something new, the epoch-making Link of our era has been COVID-19. Think about it. Over the course of about a year the virus went from something that affected zero people to something that affected 8 billion people. It influenced the lives of everyone. Everyone. Every. One.  Its impact was unimaginably vast. It changed the science of pharmaceuticals (mRNA), the engines of commerce (global recession), the way we think about our neighbors near and far (contagious). It accelerated changes in the way we speak to each other (Zoom), educate each other (Zoom), date each other (Zoom). People literally began using the same app for their Bible-study group and for their next hookup! “There’s a app for that!” Let’s consider how the pandemic affected one tiny sliver of the population: early Gen-Z.  If you were born in the late ‘90s, you were a young adult when the COVID lockdowns hit. Maybe you were still in school, or you recently joined the workforce, or you were considering your options, looking for direction. No matter, your adult trajectory was still in its early stage. And then — BANG! — suddenly your trajectory was nothing like what you envisioned just a few years earlier in high school. If you were born in the early aughts (or, what the British call “naughties”), you may still have been in high school when the lockdowns went into effect. Your adult trajectory hadn’t even begun. By 2023, you were back out in the world, mostly mask-less, feeling like your life had skipped ahead a couple of years, just like everybody else. Except your experience wasn’t just like everybody else. For people younger than you, they were still kids when the lockdowns ended. And for people older than you, they were already adults when COVID began. It’s your group that stands out because you came of age during COVID. Your experience seems to carry a teeny extra tinge of regret. When the lockdowns hit, you were just a kid; and when the lockdowns ended, you were suddenly an adult. You came out of lockdown carrying adult weight on your shoulders. Many people born around Y2K share a common heartache for lost childhood. “I wish I had more fun.” “I wish I had gone out more.” “The last few years seemed to slip away so fast.”  Perhaps your sorrow of lost innocence is no greater than it was for those who came before you. But the thing that makes your group stand out from others is your generationally shared perception that the pandemic ended your childhood. It was the Singular Link that collided with your childhood resulting in… adulthood. This shared experience could have a profound and lasting impact just as the Great Depression impacted those who came of age in the late 1920s. The Depression gave young adults first-hand experience of economic hardship and the challenges of entering a workforce in turmoil. It fostered political and social awareness, a strong work ethic, and a mistrust of institutions. Without knowing it, you Gen-Zers may be following in the footsteps of your great grandparents.

There are popular myths that claim some creative works manifest spontaneously in their final, completed form like stars falling from the sky. The Beatle Paul McCartney allegedly woke up one morning with the song Yesterday in his head, and that song went on to become the most recorded song in history. However, what gets lost from the Yesterday origin story is the fact that after McCartney woke up with the song’s melody, he toiled over the tune for months before it was finished and ready to be recorded. Corbis / Getty Images Projects don’t just spring into the world fully formed. Their creation involves an act of will. When we listen to a tune or read a story or view a painting, the existence of that work is a testament to the intentionality of its architect. Creative works stem from creative processes. Sometimes these processes start with a cluster of ideas already developed, like McCartney’s melody. Sometimes they start with just a single influence like an intuition, an image, a riff, faint spark, a packet of seeds, a germinal concept, or a few words. Sometimes they start with a little accident that, for whatever reason, presents itself as a possible new angle to be developed rather than a goof to be erased. Sometimes they start with nothing at all except the will of some creative person to improvise something new. The dancer/choreographer Twyla Tharp in her book The Creative Habit describes how she learned to improvise. “I played some music in the studio and I started to move. It sounds obvious, but I wonder how many people, whatever their medium, appreciate the gift of improvisation. It’s your one opportunity in life to be completely free, with no responsibilities and no consequences. You don’t have to be good or great or even interesting. It’s you alone, with no one watching or judging. If anything comes of it, you decide whether the world gets to see it. In essence, you are giving yourself permission to daydream during working hours.“ When we improvise, we brainstorm. We take an idea and we start unpacking. We develop, excavate, elaborate. We create variations on the idea. We look for patterns. We try inversions, consider related ideas and patterns, look for relatives, look for opposites. Watching someone fully absorbed in improv is a wonderful sight. Athletes do it all the time when they are forced to break from their pre-rehearsed plays. Think about professional basketball, soccer or tennis players. So much of what they do is improv. Their specific actions are rehearsed but their broad movements spring from split-second decisions and reactions to the activity of the ball.  Sometimes we say people who are fully absorbed in improv are “in the zone” or “in the flow.” They appear to be oblivious to the outside world. Their manner is both intense and yet relaxed. Their activity absorbs all of their focus. Being in the flow is a state of meditation. While focused on our activities, amazingly, time may seem to compress. We immerse ourselves in the flow, and when we emerge, the clock has taken a giant leap forward.  As Tharp says, “It’s you alone, with no one watching or judging.” This is an important point. No judgement! A sure-fire way to break us out of the zone is if we interrupt our focus to judge our work. The moment we start asking ourselves if our work is any good, the flow ceases. We go from the singular state — pure doing — to a dual state — doing/judging. We become self-conscious. We begin to filter our work, to censor it. Our judgement confines our focus, boxes it in. Judging ourselves equates to inhibiting ourselves. We plummet from a world of imagination, which is vast and whimsical and free, to a world of measurement, which is limiting. Many writers talk about the writing process involving two subroutines that employ different parts of the brain. The first routine is just about getting ideas on the page; and the second routine is about refining those ideas. We have to be able to shut out the judgement when we’re in the first routine. Improvisation requires a safe space, a judgement-free space. If our inner judge creeps in, it stifles the creative process. Improvization reaches towards inspiration, bottles it like a firefly, and carries it back to share with others. This improvisation subroutine is largely where the project becomes a project. Before this stage it is just a spore of an idea. Only the nucleus exists. It is no more a project than an acorn is a tree.  As creators, our task is to pioneer paths to undiscovered lands and come back with evidence. The Silk Road was a network of trade routes with vibrant activity connecting the East and the West for 13 centuries. Travelers from Europe ventured out along its routes and came back with exotic new goods such as silk, teas, and porcelain; explorers from Asia returned home with honey, wine and horses. The Silk Road brought curious and sometimes frightening individuals from far-off lands wearing strange clothes, speaking peculiar languages, and exhibiting perplexing customs. The Road cross-pollinated commercial, cultural, political and religious influences, and it changed the course of history. As creators, our task is to pioneer paths along our own Silk Road and return to relay our experiences. In his book The Soul’s Code – In Search of Character and Calling, author James Hillman reminds us, “Let us not forget that societies are elevated and rewarded by those who are inspired.”

I love to fly. This is fortunate, I suppose, because I seem do it a lot. Perhaps I was a bird in a previous life. The most interesting part of airplane travel is the ascent from the ground up to the clouds. That’s the time when all the commonplace objects like trees and cars and buildings recede in space, shrinking as if by shrink-rays to become miniature objects in a diarama. They granulate from their familiar, imposing hunks of mass to almost invisible details on the skin of the world like tiny mites on the forehead of a giant. Sometimes it’s just as interesting to descend from the clouds. That’s the time when the tiny green specks sprout up to become full-sized maple trees and teeny colored toys become full-sized Corollas and Impalas and F-150s. (And, on the very occasional flight, if you’re lucky, you might even see the miniature shadow of your own airplane zipping along the terrain below, and you watch it as it grows, slowly, dependably approaching you, until it finally reaches out to catch the plane as it touches down on the runway.) I remember when I was a kid I saw a short animated movie from the National Film Board of Canada called Cosmic Zoom. It begins with a boy in a row boat with his dog. And then the shot zooms out, farther and farther and impossibly farther until the lake, the land and all the world shrinks into the distance of space, and eventually the whole galaxy shrinks as the shot keeps zooming out until all the galaxies in the universe minify to become tiny insignificant flotsam and jetsam floating in vast darkness. Then the zoom stops and after a pause, it begins to reverse itself. Eventually it returns to the boy, and then zooms in on his arm where there is a mosquito and keeps zooming in deeper into a mocrospcopic journey down to the subatomic realm that also appears to be mostly comprised of darkness and emptiness, similar to the perspective we had all the way out there in space. The extreme macro and the extreme micro bring us to the same perspective — that’s a link! Different perspectives converge on the same picture. Questions abound. Is every atom its own universe? Is every universe its own atom? Are there limits to the smallness of the physical world or limits to the bigness of the physical world? What is the smallest unit we can measure? What is the largest? Eventually, as we reach the physical limitations of our ability to measure things, further analysis leaps over into the theoretical realms of the spiritual, the philosophical, the mathematical… The Dalai Lama wrote a book called The Universe in a Single Atom where he discusses the overlap of Buddhism and science. He asserts that Buddhism and science share a common commitment using empirical evidence to understand the nature of reality. That’s a link! Coming back to your airplane travel, those cars that you see out the window are simultaneously dainty toys and two-ton machines, depending on your perspective. Those trees are simultaneously tiny and enormous, depending on your perspective. Single objects can be simultaneously trivial and monumental. That’s a link! Any person is simultaneously a singular, unique individual in the span of the universe and also just another monkey who puts on pants one leg at a time. A person is simultaneously important to some people, and also unimportant to others. Every life is simultaneously a fascinating movie and a boring statistic. That’s a link! And so it is with everything. Your perspective shows how things are, and what things are in relation to each other and in relation to yourself, the viewer of things. This is an empowering thought, because it means you can choose to actively change your perspective. The term “coming at something from a different perspective” usually describes a situation where someone establishes a unique observation. When people don’t “see eye-to-eye,” that means they seem to have different perspectives of the same subject. When someone has “a new take on an old theme,” that person introduces a new perspective to a familiar topic. You may have had the experience of visiting a place that held special significance in your childhood – such as the giant diving board at the swimming pool or the giant slide at the play park – and when you revisit it you realize it was not so grand as you had remembered it. When you see it later in life, you think to ourself, “This is it? It looks so much smaller now. I remember it seeming so intimidating back then.” The same landmark creates divergent perspectives. That’s a link! In these situations, the places and the objects remained the same, but the thing that changed was you. You grew up, you got older, you lived through more experiences, more references, more ways of seeing the world. You left the life you had as a child and, coming back to your childhood landmark years later, you see it from a new perspective. Here’s something to chew on: If you could travel into an atom deep enough, impossibly deep, on a scale that equates the tiny atom to the vastness of our known universe, would you discover a subatomic solar system containing a subatomic planet earth containing a subatomic neighborhood containing a subatomic version of you yourself reading these words on your subatomic device? Whether the answer is yes or the answer is no, that’s a link!

Once you start noticing lucky links, when individuals stumble upon something that was completely unexpected, previously unimagined, and altogether novel, we begin to see how frequently they appeared in history. In fact, many recipients of the Nobel Prize in Physics were just such individuals. The first Nobel Physics prize winner was German professor Wilhelm Röntgen who accidentally discovered X-rays. Röntgen was researching cathode rays (aka electrons) using a fluorescent screen painted with barium platinocyanide, an early radiation detector. He was using a Crookes tube to generate the rays, and he had wrapped the tube in black cardboard to prevent the tube from emitting visible light into his lab.  However, Röntgen noticed something curious. He noticed his radiation detector was glowing, which led him to conclude that some of the rays were passing through the cardboard, though not visible as light. These mysterious rays also passed through papers and books. He called them X-rays, and later made a photographic picture of his wife’s hand using these mysterious rays. Upon seeing the picture, Mrs Röntgen allegedly exclaimed, “I have seen my death!” The professor won the first Nobel physics prize in 1901. French physicist Henri Becquerel also journeyed into the world of mysterious X-rays to see if they were connected to the topic of his life’s work, phosphorescence. He had inherited a supply of uranium salts from his father who was also a physicist. He soon discovered that uranium salts could be made to affect photographic plates, and this new discovery was spontaneous radioactivity. He shared the 1903 Nobel prize with Pierre and Marie Curie who were also investigating Becquerel radiation. Lucky links in physics abound. Percy Spencer was an American physicist and inventor working for the defense contractor Raytheon during World War II. His job was to make radar systems more efficient, a project that was the  second-highest priority US war effort, just behind the Manhattan project. He used magnetrons, power tubes that manipulate electrons (remember Röntgen). One day he also noticed something curious: the candy bar in his pocket had melted. Yes, apparently WWII physicists used to carry around candy bars in their pockets. He investigated how the magnetron could be used to heat other foods including an egg (which exploded all over the face of his lab partner) and, what else, popcorn! Co-workers were soon lining up to heat their food with Percy’s new invention, the microwave oven. The Nobel committee did not give Percy an award. Jump forward to the 1960s. Bell Labs had built a giant antenna in Holmdel, New Jersey to amplify radio signals for a satellite-transmission system. When radio astronomers Arno Penzias and Robert Wilson began working with the antenna, they were annoyed to discover some background noise interfering with their signals. They racked their brains to uncover the source of the noise, with possible explanations ranging from urban interference to extra-terrestrial radio signals to seasonal disturbances to bird shit in the hardware. None of these explanations were sufficient. There was, however, a theoretical explanation: The Big Bang. If the universe had been created by The Big Bang, the theory suggested, there should be low-level background radiation everywhere. And this low-level background radiation would manifest in the exact type of noise that Penzias and Wilson were hearing in their Holmdel antenna. This was the discovery of cosmic microwave background (CMB) radiation, which tipped the scales of science away from the steady-state model of cosmic evolution (which essentially claims the universe is practically the same at all places and all times) and towards the Big Bang singularity model (which essentially claims the universe was at one time a singularly compact speck containing all matter and energy). Penzias and Wilson won the Nobel prize in 1978. So, from microwaved popcorn (“Pop!”) to X-rays (“Zap!”) to the birth of the universe (“Bang!”), each of these lucky links involved scientists looking for one thing and then stumbling into something completely different that ended up changing the fundamental stock of knowledge. In future posts we’ll discuss that each of these scientists had something in common with each other and with many others who work with Singular Links, a receptiveness to changing direction as new information came to light.

History is crowded with countless individuals who set out to find something but ended up finding a variation of what they were seeking. Columbus happened upon the Americas while looking for the Spice Islands of Asia. Edison discovered that bamboo was a more efficient material for the light-bulb filament than cotton. These discoveries were part of an iterative process. The discoverers knew what they were looking for, more or less, and they made informed decisions to guide their way. However, history is also populated with many individuals who happened upon something that was completely unexpected, previously unimagined, and altogether novel. Let’s call these episodes of history “lucky links.” There are two types of the lucky link. The first type happens when a breakthrough creates a new and previously unimagined application. The analogy is someone traveling down a road and then unexpectedly discovering a new road that leads to a new destination. The second type of lucky link happens when a new and previously unimagined element provides a breakthrough to solve a solution. The analogy is someone traveling down a road and then unexpectedly discovering a new vehicle that transports them to their destination, like maybe a helicopter, jet pack, or magic carpet. An example of the first type is Viagra. Yes, I’m talking about the little blue pill that for decades has delivered new excitement to relationships, new material for rappers, comedians and politicians, and new spam to your email in-box. The potent ingredient in Viagra is called sildenafil and it was first synthesized by researchers working for the pharmaceutical company Pfizer. The substances helped dialate blood vessels in lab-test animals and showed promise as a treatment for high blood pressure and cardiac ailments. However, when researchers tested it on men, it gave rise to something else. It gave rise to an unexpected, a reliable erection. Pfizer thought they had a blood-pressure pill, but they realized they had a boner pill. In this way, Viagra can be considered both a “lucky link” and also a “get lucky link.” An example of the second type of lucky link in the world of pharmaceuticals is penicillin. In 1928 Scottish physician Alexander Fleming went on vacation and returned to make an astonishing discovery. Some mold had grown in a petri dish that he had been using for research on the flu virus. The mold appeared to be inhibiting the growth of the Staphylococcus bacteria in the dish. As it turns out, the mold produced a chemical that could kill bacteria. He named the chemical penicillin. Fleming said, “One sometimes finds what one is not looking for. When I woke up just after dawn on September 28, 1928, I certainly didn’t plan to revolutionize all medicine by discovering the world’s first antibiotic, or bacteria killer. But I suppose that was exactly what I did.” You may view Viagra and penicillin as simply random occurrences that came out of the blue, as incidents that were beyond the influence of the individuals involved. You may be tempted to view them as things that happened to the individuals, rather than things that the individuals created. They may seem to be unrelated to your own activities. But this view overlooks a crucially important element: intent. Both examples highlight unexpected developments in work that was already in progress. Dr Fleming and the Pfizer researchers were already deeply involved in their work when the lucky links occurred. They remind me, luck is the intersection of preparedness and opportunity. Or, stated differently, the harder you work, the luckier you get.

A singular link is the fusion of independent elements that together form something novel. One classic archetype of a singular link is the romantic couple. Two people unite to create the relationship, which is its very own entity: the couple-entity. The couple has two constituents (person A and person B) which together develop certain characteristics of coupledom. You may notice this when your friend starts dating someone new and suddenly his behavior changes. He may start wearing different clothes and styling his hair in exotic new ways. His habits meld to the habits of his new partner. He may suddenly take up inexplicable new activities. When a friend of mine started dating, he and his girlfriend took up skydiving together. The lives of each of the individuals involved in coupledom exist on the same continuum of time that predated their coupledom. Each of them came into this world as little human blobs, grew up, learned some things about how humans interact, and then met to form their romantic relationship. You might say that each person persisted until they met their romantic partner. You might call each of them a persistent element. Why would you call them that? Isn’t that just an unnecessarily convoluted label to describe two people? Well, yes, it is, but it helps to make a point. Stick with me for a minute. The romantic couple is a singular link with two persistent elements. That is, two elements that persisted until they linked together. However, not all singular links involve two persistent elements. Often they involve one persistent element linking with something spontaneous — let’s call it a spontaneous element. At the beginning of the classic movie 2001: A Space Odyssey, we see a tribe of monkeys getting their monkey butts kicked by a rival tribe until one encountered The Monolith, a tall, smooth stone slab whose presence was baffling to monkeys and movie audiences alike. The Monolith prompted one of the monkeys to realize that a bone could be used as a club, and specifically it could be used to club the leader of the rival monkey tribe and thereby seize the territorial upper hand. Monkey + Monolith = singular link. Previously, the monkeys had been suffering through their precarious monkey-existence, desperately clinging to life. They had managed to persist, however perilously. But then, the Monolith appeared. From the perspective of the persisting monkey, the Monolith was a spontaneous element. So, unlike the example of the romantic couple, which is a singular link comprised of two persistent elements, the monkey example is a singular link comprised of a persistent element and a spontaneous element. This paradigm of persistent + spontaneous is common in the art world where artists may spend years developing their work, searching for their voice, until — ah-ha! — a spontaneous influence suddenly changes their trajectory. The breakthrough is coined by such aphorisms as, “Luck is what happens when preparation meets opportunity,” and “The harder I work, the luckier I get.” Consider human fertility in this context. A woman’s ovulation, which occurs more or less every 28 days during her years of fertility (so I am told), is a persistent element. The egg makes its way to the fallopian tube exclaiming, “Ta-da! Here I am, ready for business!” Most of the time this ovo-persistence is uneventful, at least to the outside world. But every once in a while, when conditions are just right, that persistent element is joined by a spontaneous element. Or, if you will, it is joined by thousands of spontaneous elements swimming frantically as if their lives depended on it because, after all, actually their little cellular lives do depend on it. When the conditions are just right, persistent + spontaneous = baby. Sometimes we see things from the perspective of the spontaneous element. Just look at the astronautical activity known as the gravitational slingshot. When sending spacecraft long distances, scientists have been known to hurl their contraptions in the precise vicinity of planets, moons and other extraterrestrial bodies so as to affect their trajectories. The Voyager 1 space probe was launched in 1977 and as of the time of this writing, it has travelled 14.8 billion miles (that’s not a typo). It harnessed the gravitational pull of Jupiter, Saturn, and Saturn’s largest moon to help hurl it through space, changing and increasing its velocity as it interacted with the gravitational field of each giant space mass. Clearly, when measuring events in astronomical units of time, the planets are the persistent elements and the man-made space probe is the spontaneous element. Spotting a rainbow also shows the link between persistence and spontaneity. When meteorological conditions are just right, sunlight shines from behind you to be refracted through water droplets that are located in front of you.  The sunlight is the persistent element and the humid air and your orientation to it are the spontaneous elements. In fact, nature abounds with examples. A spontaneous burst of lightning strikes a tree that persisted for hundreds of years. A meteor (spontaneous) crashes into the Yucatán Peninsula (persistent) to result in the decimation of the dinosaurs, who were persistent until they weren’t. A volcano’s eruption (spontaneous) forms an island in the ocean (persistent). A hurricane scrambles an area’s topology. An interesting question to explore is, How can you introduce spontaneous influences into your life? Or, if you prefer to view your life as a spontaneous element, How can you link your life with the persistence that exists around you? A good way to begin is with The Four-C Process of Ideation.

“An amazing number of ideas that shape our 20th century lives came first as inspirations in dreams. Philo T Fransworth dreamed the basic idea for t.v. When he was still a kid in high school. Elias Howe invented the sewing machine while trying to escape from cannibals in his nightmare. Albert Einstein first figured out the Theory of Relativity while riding downhill on his dream sled. Mohandas Ghandi had the brainstorm for the first religiously inspired general strike in India in a dream, to mention only a few.” -Jeremy Taylor “Savoring the Rare Bits”, Introduction to “Rabid Eye – The Dream Art of Rick Veitch” Henri Rousseau – The Sleeping Gypsy Everybody dreams. Everybody. Even if you’re one of those people who thinks you don’t dream, you do. Even blind people dream. Even people in comas who later recovered report memories of dreaming while unconscious. Even animals dream. Just ask my dog. Ask her when she wakes up, because she’s currently laying on the real blue carpet on the real floor in the real bedroom twitching her paws, likely chasing a dream squirrel. She’ll probably never catch that squirrel in her dream, just as she never catches squirrels when awake. Dreaming is a universal experience that spans time and culture. That may be why it’s so evocative when someone begins a story by saying, “I had the most curious dream last night…” The average person dreams about two hours per night, with each dream lasting five to 20 minutes. That’s a whopping six to 24 dreams per night, on average. Women tend to recall dreams more frequently than men. Recording dreams immediately after waking helps to retain dream information. One of the many interesting things about the dream world is, it offers new experiences. It allows you to see, feel, hear, taste, smell, and think about things differently than you do in your waking life. A dream can be a source for creative insights, a source for singular links. The author Isabel Allende described how one of her dreams revealed how she should conclude her first novel The House of the Spirits. She had been struggling with the ending, and she had already re-written the last 15 pages more than ten times. One night around 3:00 a.m., she awoke from a dream in which her deceased grandfather was lying on his bed. “When I woke up from the dream, I realized that I had been telling this story to my grandfather all the time,” she told Naomi Epel in the bok Writers Dreaming. “The tone of the whole book was his voice and my voice talking… The dream gave me that.” History brims with episodes of people waking from dreams with newly acquired information related to their waking-life projects. You yourself may have experienced such things, when pertinent information came to you in a dream. I recently heard a story that the actor Mark Ruffalo heard a voice in his dream one night, and that voice told him, “You have a brain tumor.” That was odd. He didn’t have any symptoms but he somehow sensed that the information was true. Sure enough, a brain scan confirmed that it was true. The topic raises so many intriguing questions. Where does dream information originate? Is it messaging from your subconscious mind trying to get the attention of your conscious mind? Is it just the random firing of ideas as your brain tries to metabolize all the stimuli you absorb in your daily life? Is it a revalation from a larger pool of human experience – a collective unconscious – of which you and I and all of us are a part? These questions open doors to even more questions. Is dreaming involuntary or can you will yourself to dream? Can you seed or incubate your dreams with specific people, places or experiences (“candle-lit dinner with \*insert beautiful celebrity here\*”)? If you become aware that you are dreaming (aka, lucid dreaming), how much can you steer the narrative? These are all juicy questions and here are some hypotheses to help answer them. Hypothesis 1) Dreams are just random In this explanation, dreams are just the flotsam and jetsam our your life’s experience. You could try to infer meaning from your dreams, but it would be the mental equivalent of spotting animal shapes in the clouds. Dreaming is like picking some random experiences out of a hat, and then asking an AI algorithm to stitch them together in the form of a story. No wonder dream stories evolve in outlandish Alice In Wonderland logic. Neuroscientist Indra Viskontas says bizarre dream content is “just the result of your interpreter trying to create a story out of random neural signaling.” Author James W Kaleb says, “[A] dream represents the brain’s effort to make sense of sparse and distorted information… The cortex combines this haphazard input with whatever other activity was already occurring and does its best to synthesize a story that makes sense of the information.” If you believe that dreams are just random neurological firings, however, that doesn’t mean they are unimportant. I remember an episode from my childhood vacationing with my family in Mexico. We spent a kaleidoscopic day visiting the Mercado Libertad in Guadalajara with its kiosks of fresh-cut flowers, bolts of vivid woven textiles, pyramids of papaya and dragon fruit and prickly pear, restaurant cauldrons boiling with aromatic broths beside goat skulls sporting limes in their eye sockets, all unfolding to the perpetual one-two-three, one-to-three soundtrack of Mariachi music. That night I tossed and turned as dream after dream replayed the vibrant stimuli that had wormed its way into my mind. The subjects of my dream-movies were the subjects of my day-movies. The experience suggested the randomness of my dreams can potentially be seeded by the experiences in my waking life. This is intriguing because it suggests that dreams can be guided or at least influenced by choices made in waking life. If you want to dream about the beach, spend time … Read more

“Genius is one percent inspiration and ninety-nine percent perspiration.” This quote, attributed to Thomas Edison, emphasizes the importance of dedication, of commitment, of stick-to-itiveness. Those are fine qualities for a person to possess. But to me, the really interesting question is, Where does that one percent come from? What is the source of the idea? What triggers the epiphany? What are the ingredients of insight? Where does creativity originate? In ancient Greece Archimedes shouted “Eureka!” when his bath water showed him the connection between the density of an object (in his case, the king’s crown) and its chemical composition (pure gold). When Einstein was stuck on a particularly thorny math problem, he achieved occasional breakthroughs while playing his violin. Google founder Larry Page dreamt he could download the entire internet and, waking from his dream, he set out to build a search engine to do just that. Each of these stories involves an individual who encountered an “orthogonal influence.” In this context, “orthogonal” means something that intersects at a right angle, or is unrelated, or comes straight out of left field. It is a singular influence which, when linked to something else, creates a novel combination. The mission of Singular Links is simple — to explore how unique connections can birth unique outcomes. We investigate how ideas merge to create breakthroughs. We examine the dynamics in which linking ideas creates novelty. We catalog ways for you and me and all of us to harness the linking process in our daily lives. Singular Links is a metaphor for the birthing process. It is the hatch-farm of ideation. Read on!