We already do this to a remarkable extent. Even the simplest activities of everyday life involve much more cooperation than you might think. Consider, for example, stopping at a coffee shop one morning to have a cappuccino and croissant for breakfast. To enjoy that simple pleasure could draw on the labors of a small army of people from at least half a dozen countries. Delivering that snack also relied on a vast number of ideas, which have been widely disseminated around the world down the generations by the medium of language.
Now we have remarkable new insights into what makes us all work together. Building on the work of many others, Martin Nowak of Harvard University has identified at least five basic mechanisms of cooperation. What I find stunning is that he shows that the way we human beings collaborate is as clearly described by mathematics as the descent of the apple that once fell in Newton’s garden. The implications of this new understanding are profound.
Global human cooperation now teeters on a threshold. The accelerating wealth and industry of Earth’s increasing inhabitants—itself a triumph of cooperation—is exhausting the ability of our home planet to support us all. Many problems that challenge us today can be traced back to a profound tension between what is good and desirable for society as a whole and what is good and desirable for an individual. That conflict can be found in global problems such as climate change, pollution, resource depletion, poverty, hunger, and overpopulation.
As once argued by the American ecologist Garrett Hardin, the biggest issues of all—saving the planet and maximizing the collective lifetime of the species Homo sapiens—cannot be solved by technology alone. If we are to win the struggle for existence and avoid a precipitous fall, there’s no choice but to harness this extraordinary creative force. It is down to all of us to refine and extend our ability to cooperate.
Nowak’s work contains a deeper message. Previously there were only two basic principles of evolution—mutation and selection—where the former generates genetic diversity and the latter picks the individuals best suited to a given environment. We must now accept that cooperation is the third principle. From cooperation can emerge the constructive side of evolution, from genes to organisms to language and the extraordinarily complex social behaviors that underpin modern society.
The Law of Comparative Advantage
Dylan Evans
Lecturer in behavioral science, School of Medicine, University College Cork, Ireland; author, Introducing Evolutionary Psychology: A Graphic Guide
It is not hard to identify the discipline in which to look for the scientific concept that would most improve everybody’s cognitive toolkit; it has to be economics. No other field of study contains so many ideas ignored by so many people at such great cost to themselves and the world. The hard task is picking just one of the many such ideas that economists have developed.
On reflection, I have plumped for the law of comparative advantage, which explains how trade can be beneficial for both parties even when one of them is more productive than the other in every way. At a time of growing protectionism, it is more important than ever to reassert the value of free trade. Since trade in labor is roughly the same as trade in goods, the law of comparative advantage also explains why immigration is almost always a good thing—a point which also needs emphasizing at a time when xenophobia is on the rise.
In the face of well-meaning but ultimately misguided opposition to globalization, we must celebrate the remarkable benefits which international trade has brought us and fight for a more integrated world.
Structured Serendipity
Jason Zweig
Journalist; personal finance columnist, Wall Street Journal; author, Your Money and Your Brain
Creativity is a fragile flower, but perhaps it can be fertilized with systematic doses of serendipity. The psychologist Sarnoff Mednick showed decades ago that some people are better than others at detecting the associations that connect seemingly random concepts. Asked to name a fourth idea that links “wheel,” “electric,” and “high,” people who score well on other measures of creativity will promptly answer “chair.” More recently, research in Mark Jung-Beeman’s cognitive neuroscience lab at Northwestern has found that sudden bursts of insight—the Aha! or Eureka! moment—come when brain activity abruptly shifts its focus. The almost ecstatic sense that makes us cry “I see!” appears to come when the brain is able to shunt aside immediate or familiar visual inputs.
That may explain why so many of us close our eyes (often unwittingly) just before we exclaim, “I see!” It also suggests, at least to me, that creativity can be enhanced deliberately through environmental variation. Two techniques seem promising: varying what you learn and varying where you learn it. I try each week to read a scientific paper in a field new to me—and to read it in a different place.
New associations often leap out of the air at me this way. More intriguing, others seem to form covertly and lie in wait for the opportune moment when they can click into place. I do not try to force these associations out into the open; they are like the shrinking mimosa plants that crumple if you touch them but bloom if you leave them alone.
The sociologist Robert Merton argued that many of the greatest discoveries of science have sprung from serendipity. As a layman and an amateur, all I hope to accomplish by throwing myself in serendipity’s path is to pick up new ideas, and combine old ones, in ways that haven’t quite occurred to other people yet. So I let my curiosity lead me wherever it seems to want to go, like the planchette that floats across the Ouija board.
I do this remote-reading exercise on my own time, since it would be hard to justify to newspaper editors during the work day. But my happiest moments last year came as I reported an investigative article on how elderly investors are increasingly being scammed by elderly con artists. I later realized, to my secret delight, that the article had been enriched by a series of papers I had been reading on altruistic behavior among fish (Lambroides dimidiatus).
If I do my job right, my regular readers will never realize that I spend a fair amount of my leisure time reading Current Biology, The Journal of Neuroscience, and Organizational Behavior and Human Decision Processes. If that reading helps me find new ways to understand the financial world, as I suspect it does, my readers will indirectly be smarter for it. If not, the only harm done is my own spare time wasted.
In my view, we should each invest a few hours a week in reading research that ostensibly has nothing to do with our day jobs, in a setting that has nothing in common with our regular workspaces. This kind of structured serendipity just might help us become more creative, and I doubt that it can hurt.
The World Is Unpredictable
Rudy Rucker
Mathematician; computer scientist; cyberpunk pioneer; novelist; author, Jim and the Flims
The media cast about for the proximate causes of life’s windfalls and disasters. The public demands blocks against the bad and pipelines to the good. Legislators propose new regulations, fruitlessly dousing last year’s fires, forever betting on yesterday’s winning horses.
A little-known truth: Every aspect of the world is fundamentally unpredictable. Computer scientists have long since proved this.
How so? To predict an event is to know a shortcut for foreseeing the outcome. A simple counting argument shows that there aren’t enough shortcuts to go around. Therefore most processes aren’t predictable. A deeper argument plays on the fact that if you could predict your actions, you could deliberately violate your predictions, which means the predictions were wrong after all.
We often suppose that unpredictability is caused by random inputs from higher spirits or from lowdown quantum foam. But chaos theory and computer science tell us that nonrandom systems produce surprises on their own. The unexpected tornado, the cartoon safe that lands on Uncle George, the winning pull on a slot machine—odd things pop out of a computation. The world can simultaneously be deterministic and unpredictable.
In the physical world, the only way to learn tomorrow’s weather in detail is to wait twenty-four hours and see, even if nothing is random at all. The universe is computing tomorrow’s weather as rapidly and as efficiently as possible; any smaller model is inaccurate, and the smallest error is amplified into large effects.
At a personal level, even if the world is as deterministic as a computer program, you still can’t predict what you’re going to do. This is because your prediction method would involve a mental simulation of you that produces its results slower than you do. You can’t think faster than you think. You can’t stand on your own shoulders.
It’s a waste to chase the pipe dream of a magical tiny theory that allows us to make quick and detailed calculations about the future. We can’t predict and we can’t control. To accept this can be a source of liberation and inner peace. We’re part of the unfolding world, surfing the chaotic waves.
Randomness
Charles Seife
Professor of journalism, New York University; former journalist, Science; author, Proofiness: The Dark Arts of Mathematical Deception
Our very brains revolt at the idea of randomness. We have evolved as a species to become exquisite pattern-finders; long before the advent of science, we figured out that a salmon-colored sky heralds a dangerous storm or that a baby’s flushed face likely means a difficult night ahead. Our minds automatically try to place data in a framework that allows us to make sense of our observations and use them to understand and predict events.
Randomness is so difficult to grasp because it works against our pattern-finding instincts. It tells us that sometimes there is no pattern to be found. As a result, randomness is a fundamental limit to our intuition; it says that there are processes we can’t predict fully. It’s a concept that we have a hard time accepting, even though it’s an essential part of the way the cosmos works. Without an understanding of randomness, we are stuck in a perfectly predictable universe that simply doesn’t exist outside our heads.
I would argue that only once we understand three dicta—three laws of randomness—can we break out of our primitive insistence on predictability and appreciate the universe for what it is, rather than what we want it to be.
The First Law of Randomness: There is such a thing as randomness.
We use all kinds of mechanisms to avoid confronting randomness. We talk about karma, in a cosmic equalization that ties seemingly unconnected events together. We believe in runs of luck, both good and ill, and that bad things happen in threes. We argue that we are influenced by the stars, by the phases of the moon, by the motion of the planets in the heavens. When we get cancer, we automatically assume that something—or someone—is to blame.
But many events are not fully predictable or explicable. Disasters happen randomly, to good people as well as to bad ones, to star-crossed individuals as well as those who have a favorable planetary alignment. Sometimes you can make a good guess about the future, but randomness can confound even the most solid predictions: Don’t be surprised when you’re outlived by the overweight, cigar-smoking, speed-fiend motorcyclist down the block.
What’s more, random events can mimic nonrandom ones. Even the most sophisticated scientists can have difficulty telling the difference between a real effect and a random fluke. Randomness can make placebos seem like miracle cures, or harmless compounds appear to be deadly poisons, and can even create subatomic particles out of nothing.
The Second Law of Randomness: Some events are impossible to predict.
If you walk into a Las Vegas casino and observe the crowd gathered around the craps table, you’ll probably see someone who thinks he’s on a lucky streak. Because he’s won several rolls in a row, his brain tells him he’s going to keep winning, so he keeps gambling. You’ll probably also see someone who’s been losing. The loser’s brain, like the winner’s, tells him to keep gambling. Since he’s been losing for so long, he thinks he’s due for a stroke of luck; he won’t walk away from the table, for fear of missing out.
Contrary to what our brains are telling us, there’s no mystical force that imbues a winner with a streak of luck, nor is there a cosmic sense of justice that ensures that a loser’s luck will turn around. The universe doesn’t care one whit whether you’ve been winning or losing; each roll of the dice is just like every other.
No matter how much effort you put into observing how the dice have been behaving or how meticulously you have been watching for people who seem to have luck on their side, you get absolutely no information about what the next roll of a fair die will be. The outcome of a die roll is entirely independent of its history. And as a result, any scheme to gain some sort of advantage by observing the table is doomed to fail. Events like these—independent, purely random events—defy any attempts to find a pattern, because there is none to be found.
Randomness provides an absolute block against human ingenuity; it means that our logic, our science, our capacity for reason can penetrate only so far in predicting the behavior of the cosmos. Whatever methods you try, whatever theory you create, whatever logic you use to predict the next roll of a fair die, there’s always a 5/6 chance you are wrong. Always.
The Third Law of Randomness: Random events behave predictably in aggregate even if they’re not predictable individually.
Randomness is daunting; it sets limits where even the most sophisticated theories cannot go, shielding elements of nature from even our most determined inquiries. Nevertheless, to say that something is random is not equivalent to saying that we can’t understand it. Far from it.
Randomness follows its own set of rules—rules that make the behavior of a random process understandable and predictable.
These rules state that even though a single random event might be completely unpredictable, a collection of independent random events is extremely predictable—and the larger the number of events, the more predictable they become. The law of large numbers is a mathematical theorem that dictates that repeated, independent random events converge with pinpoint accuracy upon a predictable average behavior. Another powerful mathematical tool, the central-limit theorem, tells you exactly how far off that average a given collection of events is likely to be. With these tools, no matter how chaotic, how strange, a random behavior might be in the short run, we can turn that behavior into stable, accurate predictions in the long run.
The rules of randomness are so powerful that they have given physics some of its most sacrosanct and immutable laws. Though the atoms in a box full of gas are moving at random, their collective behavior is described by a simple set of deterministic equations. Even the laws of thermodynamics derive their power from the predictability of large numbers of random events; they are indisputable only because the rules of randomness are so absolute.
Paradoxically, the unpredictable behavior of random events has given us the predictions that we are most confident in.
The Kaleidoscopic Discovery Engine
Clifford Pickover
Writer; associate editor, Computers and Graphics; editorial board, Odyssey, Leonardo, and YLEM; author, The Math Book: From Pythagoras to the 57th Dimension
The famous Canadian physician William Osler once wrote, “In science the credit goes to the man who convinced the world, not to the man to whom the idea first occurs.” When we examine discoveries in science and mathematics, in hindsight we often find that if one scientist did not make a particular discovery, some other individual would have done so within a few months or years of the discovery. Most scientists, as Newton said, stood on the shoulders of giants to see the world just a bit farther along the horizon. Often, several people create essentially the same device or discover the same scientific law at about the same time, but for various reasons, including sheer luck, history sometimes remembers only one of them.
In 1858, the German mathematician August Möbius independently discovered the Möbius strip simultaneously with another G
erman mathematician, Johann Benedict Listing. Isaac Newton and Gottfried Wilhelm Leibniz independently developed calculus at roughly the same time. British naturalists Charles Darwin and Alfred Russel Wallace both developed the theory of evolution by natural selection independently and simultaneously. Similarly, Hungarian mathematician János Bolyai and Russian mathematician Nikolai Lobachevsky seem to have developed hyperbolic geometry independently and at the same time.
The history of materials science is replete with simultaneous discoveries. For example, in 1886, the electrolytic process for refining aluminum using the mineral cryolite was discovered simultaneously and independently by American Charles Martin Hall and Frenchman Paul Héroult. Their inexpensive method for isolating pure aluminum from compounds had an enormous effect on industry. The time was “ripe” for such discoveries, given humanity’s accumulated knowledge at the time the discoveries were made. On the other hand, mystics have suggested that a deeper meaning adheres to such coincidences. Austrian biologist Paul Kammerer wrote, “We thus arrive at the image of a world-mosaic or cosmic kaleidoscope, which, in spite of constant shufflings and rearrangements, also takes care of bringing like and like together.” He compared events in our world to the tops of ocean waves that seem isolated and unrelated. According to his controversial theory, we notice the tops of the waves, but beneath the surface there may be some kind of synchronistic mechanism that mysteriously connects events in our world and causes them to cluster.
We are reluctant to believe that great discoveries are part of a discovery kaleidoscope and are mirrored in numerous individuals at once. However, as further examples, there were several independent discoveries of sunspots in 1611, even though Galileo gets most of the credit today. Alexander Graham Bell and Elisha Gray filed their own patents on telephone technologies on the same day. As the sociologist of science Robert Merton has remarked, “The genius is not a unique source of insight; he is merely an efficient source of insight.”
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