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A New Way of Understanding the World

iPad app available on iTunes Download the interactive introduction to complexity science—a whole new way of understanding our world. Each characteristic of complexity science is presented in an engaging and non-technical way.

This project has been supported by The Santa Fe Institute, The New Mexico Department of Cultural Affairs, and New Mexico Highlands University Media Arts Illustration: Gabriel Garcia Design and Layout: Rianne Trujillo Text: Mimi Roberts and James Liljenwalls Faculty Advisor: Miriam Langer Copyright: 2011, Center for Cultural Technology, NMHU Full website at : www.nmnaturalhistory.org/emergence

TABLE of CONTENTS PREFACE

EMERGENCE ADAPTATION NETWORKS SCALE RECURSION FRACTALS ROBUSTNESS

COMPLEXITY SCIENCE | 3

It was six men of Indostan To learning much inclined, Who went to see the Elephant (Though all of them were blind), That each by observation Might satisfy his mind. The first approached the Elephant, and happening to fall Against his broad and sturdy side, At once began to bawl: “God bless me! But the elephant Is very like a wall!” The Second, feeling of the tusk Cried, “Ho! What have we here, So very round and smooth and sharp? To me ‘tis mighty clear This wonder of an Elephant Is very like a spear!” The Third approached the animal, And happening to take The squirming trunk within his hands Thus boldly up he spoke: “I see,” quoth he, “the Elephant Is very like a snake!” The fourth reached out an eager hand, And felt about the knee: “What most this wondrous beast is like Is mighty plain,” quoth he, “Tis clear enough the Elephant Is very like a tree!” The Fifth, who chanced to touch the ear, Said: “E’en the blindest man Can tell what this resembles most; Deny the fact who can, The marvel of an Elephant Is very like a fan!” The Sixth no sooner had begun About the beast to grope, Than, seizing on the swinging tail That fell within his scope. “I see,” quoth he, “the Elephant Is very like a rope!”

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And so these men of Indostan Disputed loud and long, Each in his own opinion Exceeding stiff and strong, Though each was partly in the right, And all were in the wrong! —John Godfrey Saxe

This 19th-century retelling of an old fable points out the limitations of understanding something without the full picture. Is it really possible to understand an elephant by feeling only the different parts of its body separately? Of course not. But until the last few decades, scientists have been limited to exactly this approach: trying to understand living organisms and other complex systems by studying their individual parts. This approach continues to yield important discoveries and great insights, but it will never lead to full understanding because the whole really is greater than the sum of its parts. Complexity science looks at the big picture—all of the separate parts and the connections and interactions between them. The understanding of complex systems is critical to addressing key challenges in our world that are environmental, technological, biological, economic, and political.

COMPLEXITY SCIENCE | 5

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hen we think about complex patterns and behaviors, we tend to think they must be the result of carefully designed or controlled processes. Emergence is the way complex behaviors and patterns can arise spontaneously out of large numbers of relatively simple interactions. Emergent phenomena occur when individual elements combine to form a more complex system, for example a swarm of bees, a flock of birds, a school of fish, or a colony of ants. No ant is in charge of the ant colony. Individual ants carry out their tasks without direction. Each ant follows a relatively simple set of rules that governs its behavior and interactions with other ants. An individual ant modifies its behavior based on encounters with other ants. In this way the colony can determine the shortest distance to a nearby source of food or respond to changes in the environment. If you study an ant colony, there is nothing particularly mysterious about determining the rules of interaction that govern the behavior of individuals. The curious thing is that it is not possible to deduce the behavior of the collective ant colony from the rules that govern the behavior of the individuals. Those rules are necessary but not sufficient to predict emergent behavior. Applying the principles of emergence can help us gain a deeper understanding of everything from the neural connections in our brains, to the ways in which immune systems respond to invading microorganisms, to the formation and functioning of neighborhoods and cities. Scientists Harold Morowitz, Eric Smith and their colleagues are applying the concept of emergence to research on the origin of life.

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EMERGENCE

COMPLEXITY SCIENCE | 7

ADAPTATION

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o survive, species must adapt to changes in the environment. If they don’t adapt, they will go the way of the dinosaurs and become extinct. Adaptations include changes in behavior, such as new ways of getting food, and physical changes, such as the evolution of legs that allow an animal to run faster. Hibernation is an adaptation to cold. Migration is an adaptation to drought or famine. What if we could rewind the evolutionary tape and replay it? In the battle for survival, would the same groups of creatures, or species, succeed? Would the same ones become extinct? Would living things look the way they look today? The answer is No, and the reason is sometimes explained as the Butterfly Effect—the idea that a butterfly flapping its wings on one side of the world can begin a series of changes that will end up causing a typhoon on the other side of the world. Computer models show this to be true: tiny changes resulting from chance events do add up over time to produce huge differences. Thus, the smallest differences in the past would have changed the course of events, history, and evolution. So if we could roll back the tape of life and play it forward again, the world would be an entirely different place. Understanding adaptation in the natural world will help us design everything from better machines to better companies, museums, and schools.

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ADAPTATION

COMPLEXITY SCIENCE | 9

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EVOLUTION

COMPLEXITY SCIENCE | 11

NETWORKS

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ountless things are connected by web-like structures known as networks, from the nerves that carry messages between the cells in your body and your brain to the power grids that carry electricity from power plants to your home. Networks are made up of many separate parts connected by pathways. The pathways carry things back and forth—cars, food, information, energy. Networks can be big or small, and they’re everywhere. The highway system is a transportation network. The stock market is a financial network. School is a social network. The Internet is a communications network. Your brain is a thinking network.

Seven Bridges of Konigsberg

The concept of networks originated over 300 years ago with the riddle of the Seven Bridges of Konigsberg. In this German village, a small island was connected to the rest of the town by seven bridges. Each bridge charged a toll, so some people wondered how to find a route that would allow them to walk back and forth across each bridge only once and pay the least toll. The Swiss mathematician Leonhard Euler (1707-1783) reduced this problem to what we now call a network by drawing a picture using dots for land and lines for bridges. Analyzing the network, Euler came up with a surprising result: there is no perfect path.

Six Degrees of Separation

Scientist Duncan Watts (b. 1971) applied mathematics to understand how people interact in social networks. If you’ve heard the expression “six degrees of separation,” then you’ve heard something about his research. Watts concluded that any two persons, even if they’re on opposite sides of the world, are likely to be separated by no more than six friends or acquaintances—a friend of a friend of a friend of a friend of a friend of a friend. He didn’t say this is true of any two persons but that it is likely to be true.

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NETWORKS

COMPLEXITY SCIENCE | 13

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SIX DEGREES of SEPARATION

COMPLEXITY SCIENCE | 15

SCALE

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ave you heard the expression “economies of scale”? This expression usually refers to the cost advantages of business expansion—the average cost per unit goes down as the scale of output goes up. It turns out that there are universal scaling laws that pervade economics and also biology. As species get bigger—from a tiny mouse to a huge whale—the pulse rates slow down and the life spans get longer. The number of heartbeats during an average life span tends to be roughly the same, around a billion. A shrew just uses them up more quickly than a whale. These universal scaling laws provide a mathematical framework for understanding fundamental issues in biology ranging from cell size, growth, and metabolic rates, to the structure and dynamics of ecosystems, as well as questions at the forefront of medical research such as aging, sleep, and cancer. Scientist Geoffrey B. West and his colleagues are exploring how the application of the principles of scale in complex biological systems can help us gain a deeper understanding the structure and dynamics of social organizations such as corporations and cities. They are studying the relationships between economies of scale, growth, innovation and wealth creation and their implications for long-term survivability and sustainability.

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ECONOMIES of SCALE

COMPLEXITY SCIENCE | 17

RECURSION So, Nat’ralists observe, a Flea Hath smaller Fleas that on him prey, And these have smaller fleas to bit ‘em, And so proceed ad infinitum —Jonathan Swift, 1733

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e’re not sure why, but in 1202 the mathematician Leonardo of Pisa, better known as Fibonacci (c. 1170-1250), set out to calculate how fast rabbits would multiply under ideal conditions. Fibonacci used a process now called recursion. In recursion, you create a series of numbers by starting with one number, apply a rule to this number to get the next number, apply the same rule to the new number to get the following number, and so on. For his increasing population of rabbits, Fibonacci came up with the following series: 1, 1, 2, 3, 5, 8, 13, 21, and so on. We now call this the Fibonacci series, and, as you can see for yourself, it is generated by a very simple rule: add together the last two numbers to get the next. But there’s much more to Fibonacci numbers that this. For instance, if you start at the beginning of the series and divide each number by the one before it, you will get closer and closer (but never exactly equal) to an irrational number (known as Phi) approximately equal to 1.6180339. When interpreted as the ratio between two magnitudes, this number appears throughout nature—for instance, in the patterns of branches in plants, in the arrangements of flower petals and seeds, and in the spirals of pinecones and seashells.

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FIBONACCI RATIO

COMPLEXITY SCIENCE | 19

FRACTALS

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ore than seven hundred years after Fibonacci, the American mathematician Benoit Mandelbrot (1924-2010) used recursion in a different way. He had never learned the alphabet and had never memorized the multiplication tables past the fives, but he wondered what it would mean to measure the size of a cloud and how you would do it. In pursuing this question, Mandelbrot would invent an entirely new branch of mathematics. Instead of applying recursion to numbers, he applied it to equations that generate geometric patterns. The computational process was so complicated it would have been impossible without computers. The result was the Mandelbrot Set, which generates a special kind of recurring patterns Mandelbrot named fractals (from the Latin word for fragments). When we look at things through a microscope or a telescope, they usually look entirely different at different scales or magnifications. Fractals, however, look similar at different scales. The crystals that make up a snowflake, for instance, resemble the snowflake itself. The veins of a leaf look like tree branches. A whirlpool is made up of smaller swirls containing still smaller swirls. Broccoli flowers are made up of tiny buds that resemble the whole flower. Understanding how objects change or remain the same at different scales is an important key to understanding a vast number of different kinds of things. Scientists now use fractals to uncover patterns in everything from the weather to the stock market.

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COMPLEXITY SCIENCE | 21

ROBUSTNESS

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ockroaches have a bad reputation, but they are the living embodiment of “robustness”—the ability to survive under changing, often threatening conditions. Cockroaches first appeared on Earth millions of years ago, long before humans, and they are likely to be here long after we’re gone. Cockroaches are robust in many ways. They can survive on almost any food. They can run fast, and they know where to hide. Their hard exoskeletons protect them from predators and injury. And they live in groups and cooperate to perform complex tasks that promote survival and reproduction. Cockroaches even appear more likely than most living things to survive nuclear war. That is because for most animals, cell division takes place continuously, which makes them highly vulnerable to the effects of nuclear radiation. Cells in cockroaches, however, divide only during molting (when they shed their exoskeletons), which makes them less vulnerable to these effects. That is why some people say “cockroaches will inherit the Earth.” Understanding what makes cockroaches so robust can help us design organizations, social systems, even robots and will help human beings survive and thrive in an increasingly complex and dangerous world.

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COCKROACH

COMPLEXITY SCIENCE | 23


Complexity Science: A New Way of Understanding the World