What do ant colonies, cities, and the computer program StarLogo have in common? They're all complex and they're all organized. Where does this organized complexity come from? Ants create colonies. People create the streets and neighborhoods that make up cities. The individual turtles in StarLogo affect each other's behaviors, creating the patterns that appear on the screen. In each case the end results are more than the sum of the parts. A highly sophisticated output is being formed from very simple behaviors created from a few simple rules.

The movement from low-level rules to high-level complexity is called emergence. Emergence is not just a pattern-a flock of birds sitting on a line, say-or mere connectedness, like the World Wide Web. Emergent patterns are created when the elements that make them follow simple rules that lead to complex effects at a higher level. Take a bunch of moving dots, and give them two rules: "get as close as you can to the center of all the dots" and "stay exactly one dot-width away from all other dots. "A disc of evenly-spaced dots forms. The rules said nothing about discs. The disc emerges on a higher level than the dots.

Take an ant colony. There are tunnels and nurseries, a secluded queen, a garbage site, and a cemetery. Worker ants move from building to cleaning up to foraging for food to feeding the pupae in perfect harmony. No one is telling them what to do. This is a key feature of emergence-there is no commander with a perfect plan. The individual ants are responding to simple signals they receive from other individual ants. No ant is able to assess the overall situation of the whole colony, and yet the work they do comes together in a coordinated way. The behavior that leads to emergence is decentralized, and depends on feedback between the elements.

Take a city. Although cities come with mayors and councils, it's not City Hall that decides which area of town will turn into a neighborhood of specialty shops, or where the crime rate will be higher. An overall order arises out of many local interactions. The decisions that ordinary city-dwellers make about which shops to pop into or which blocks to walk down on their way from the bus stop add up. These decisions are not made with any plan for the future in mind, yet tomorrow's city is not just affected, but formed, by the behaviors of today's residents. Emergent behavior accumufates effects over time.

And what happens if, in a StarLogo traffic simulation, you add a police car to the side of the highway?

-R.P.

The Life and Times of Slime

You are walking in a cool, damp part of the woods when you almost step into a squishy orange puddle, a couple of inches across. What is it? Is it toxic waste? Dog vomit? Is it alive?

It is alive, and the first person to name this organism called it, none too flatteringly, "slime mold." In spite of their unglamorous name, the hundreds of species of slime mold lead fascinating and mysterious lives.

All slime molds start life as a single, microscopic cell, and eventually end up as that puddle of goo. A plasmodial slime mold, like the one that researcher Toshiyuki Nakagaki coaxed through a maze (see article), constantly grows and divides. But instead of breaking itself into two new cells, it divides only its nucleus, becoming one larger cell with two nuclei. This process repeats until the plasmodium is a giant cell, like a sac of jelly, filled with thousands of nuclei. Ever so slowly, the plasmodium creeps across the forest floor, eating the tiny bacteria and yeast it finds there.

A different group, called the cellular slime molds, stay microscopic for most of their lives. They, too, live and feed in damp soil. When food gets scarce, though, these slime molds have an amazing trick for survival. Each individual sends out a chemical signal, allowing the slime mold cells to find each other. Then they aggregate, or stick together, until they have formed a giant roaming blob. This blob looks and acts like one creature, even though it is really thousands of individuals oozing along together.

Despite these differences, both kinds of slime molds complete their lives with an amazing final transformation. Either slime mold (plasmodial or cellular) keeps crawling along until it reaches a drier spot. There, it stops and metamorphoses into a sporangium: a tall, thin stalk with a sac on top, similar to a mushroom. The slime mold cells turn into stalk cells, or sac cells, or spores. Finally, the cells that have become spores burst out of the top of the sporangium and are blown away by the wind. Where they land, they will start their life cycle over, invisible-and individual-once again.

-E.P.

An ant colony is highly organized. Yet individual ants have no way to see or think about the whole colony at once. Instead, they follow simple rules, and act on signals they get from their neighbors.

Deborah Gordon, a scientist at Stanford University, studies how the individual behaviors of ants create the complex organization of an ant colony. For example, different ants in the colony will perform different roles (such as foraging or tending the nursery) depending on what is needed, though no one gives them this command.

Ant behavior is influenced by the signals ants give each other: chemical signs from one ant to its neighbor that say "Danger, run away!" or "Food over here!" When a group of relatively unintelligent individuals forms a highly functioning, complex society, the way ants do, these five principles are being followed:

1. "More" makes "different." A colony often ants wouldn't run into each other often enough to exchange information. But in a colony of thousands of ants, enough information can be shared, often enough, to produce emergent behavior-something different from the behavior of the individuals.

2. Ignorance is useful. The ants' set of rules needs to be simple; if some ants have too much information, the system will break down.

3. Random encounters are necessary. The more often ants bump into their neighbors and share information, the better.

4. Individuals detect patterns. An ant perceives simple kinds of information: "This neighbor is foraging." But if an ant crosses paths with 50 foragers and only one nest-builder, this pattern should cause her to switch her own task to nest-building.

5. Pay attention to your neighbors. This is the most crucial rule. If neighboring ants do not interact with each other, they will remain simple parts; the colony cannot become a complex whole.

-E.P.

Alan Turing, in his 1954 paper "Morphogenesis," raised a question that today's biologists are still trying to answer: how does a single-celled embryo develop into a many-celled organism? At first glance, this might not seem like a problem of emergence, because our bodies do follow the orders of a leader-our DNA. But in fact, every one of our cells contains an entire copy of our genetic code. This means that no one cell has more information than any other cell; they are all working from the same instruction book. Each cell must somehow determine which chapter of instructions from the genetic code it must read. Is it a muscle cell? A skin cell? A neuron?

We all begin life as a one-celled embryo. As soon as that cell divides, the embryo begins to make itself into different parts. There must be a top and a bottom, a front and a back. As the cells keep multiplying, they continue to fill more specific roles, or differentiate. Some areas of the embryo will become arms and legs; some will be intestines and some will be skin. The developing embryo can't afford to make any mistakes in this process.

The cells differentiate by narrowing down which chapter of the genetic instructions they are to read. And how they find the right page is determined not by a leader, but by interactions between neighboring cells. Just like ants in a colony, cells in an organism get information from the other individuals around them. Scientists are only beginning to understand how the cells pass these signals to each other. The result is that many individual cells, working without knowledge of the whole body, produce an organism that is both organized and amazingly complex.

-E.P.

In August of 2000, a Japanese scientist named Toshiyuki Nakagaki announced that he had trained an amoebalike organism called slime mold to find the shortest route through a maze. Nakagaki had placed the mold in a small maze with four possible routes and planted pieces of food at two of the exits. Despite its being an incredibly primitive organism with no centralized brain whatsoever, the slime mold managed to plot the most efficient route to the food, stretching its body through the maze so that it connected directly to the two food sources. The slime mold had "solved" the maze puzzle.

For such a simple organism, the slime mold has an impressive intellectual pedigree. Nakagaki's announcement was only the latest in a long chain of investigations into the subtleties of slime mold behavior. For scientists trying to understand systems that use relatively simple components to build higher-level intelligence, the slime mold may someday be seen as the equivalent of the finches and tortoises that Darwin observed on the Galapagos Islands. In other words, the slime mold is an organism that brought on a scientist's breakthrough, a major enough breakthrough to cross areas of scientific study with its important implications.

How did such a lowly organism come to play such an important scientific role? That story begins in the late sixties in New York City, with a scientist named Evelyn Fox Keller. Though a student of physics, Keller had written her PhD dissertation in molecular biology, and she had spent some time exploring the new field of study of "nonequilibrium dynamics," which later became associated with complexity theory. By 1968, she was working as a mathematician and thinking about the application of mathematics to biological problems. Mathematics has played a tremendous role in expanding our understanding of physics-so Keller thought it might perhaps also be useful for understanding living systems.

In the spring of 1968, Keller met Lee Segel, an applied mathematician who shared her interests. It was Segel who first introduced her to the bizarre conduct of the slime mold, and together they began a series of investigations that would help transform not just our understanding of biological development but also the disparate worlds of brain science, software design, and urban studies.

While slime mold cells are relatively simple, they have attracted a disproportionate amount of attention from a number of different disciplines-embryology, mathematics, computer science-because they display such an intriguing example of coordinated group behavior. Anyone who has ever contemplated the great mystery of human physiology-how do all my cells manage to work so well together?-will find something resonant in the slime mold's swarm. If we could only figure out how the Dictyostelium pull it off, maybe we would gain some insight into our own baffling togetherness?

Anywhere in the world during the summer you can start your own investigation into slime mold life. Walk through a normally cool, damp section of a forest on a dry and sunny day, or sift through the bark mulch that lies on a garden floor, and you may find a grotesque substance coating a few inches of rotting wood. On first inspection, the reddish orange mass suggests that the neighbor's dog has eaten something disagreeable, but if you observe the slime mold over several days-or, even better, capture it with time-lapse photography-you'll discover that it moves, ever so slowly, across the soil. It grows larger, more and more cells coming together, or aggregating. And it seems to be going somewhere. If the weather conditions grow wetter and cooler, you may return to the same spot and find the mass missing altogether. Has it wandered off to some other part of the forest? Or somehow vanished into air?

As it turns out, the slime mold has done something far more mysterious, a trick of biology that confounded scientists for centuries. That is, before Keller and Segel began their collaboration. The slime mold behavior is so odd that understanding it required thinking outside the boundaries of traditional disciplines-which may be why it took the instincts of a molecular biologist with a degree in physics to unravel its mystery.

"I was working in a biomath department-and it was a very small department," Keller says today, laughing. While the field of mathematical biology was relatively new in the late sixties, it had a fascinating, if enigmatic, precedent in a then-little-known essay written by Alan Turing, the brilliant English code-breaker from World War II who also helped invent the digital computer. One of Turing's last published papers, before his death in 1954, studied the riddle of "morphogenesis"-the capacity of all life-forms to develop ever more complex bodies out of impossibly simple beginnings. Turing's paper had focused more on the recurring numerical patterns of flowers, but it demonstrated-using mathematical tools-how a complex organism could assemble itself without any master planner calling the shorts.

"I was thinking about slime mold aggregation as a model for biological development," Keller says, "and I came across Turing's paper." Bingo!

For some time, researchers had understood that slime mold cells emitted a common substance called cyclic AMP, which was somehow involved in aggregation (the coming-together process). But until Keller began her investigations, the common belief had been that slime mold swarms formed at the command of "pacemaker" cells that ordered the other cells to begin aggregating and led the process. In 1962, Harvard's B. M. Shafer showed how such pacemaker cells could use cyclic AMP as a signal to "rally the troops." The slime mold's "generals" would release cyclic AMP first, triggering waves of the chemical that washed through the entire community, as each isolated cell relayed the signal to its neighbors, like a relay of semaphores. Or like a giant game of "Telephone."

It seemed like a perfectly reasonable explanation. Kings, dictators, and city councilmen have acted as the pacemaker cells of our social organizations for thousands of years. Our physical and emotional actions seem governed for the most part by the pacemaker cells in our brains. Why should it be any different for the slime molds? We humans are so predisposed to think in terms of pacemakers that this just seems natural.

But Shafer's theory had one small problem: no one could find the pacemakers. While all observers agreed that waves of cyclic AMP did indeed flow through the slime mold community before aggregation, no one could find a leader cell. All the cells were effectively interchangeable. That is, none of them possessed any distinguishing characteristics that might elevate them to pacemaker status. Shafer's theory has presumed the existence of a cellular "monarchy" or "command central" sending messages to the masses. But, as it turned out, all slime mold cells were created equal.

For the twenty years that followed the publication of Shafer's original essay, the slime mold scholars felt that their not being able to find pacemaker cells was a sign of insufficient data, or poorly-designed experiments. They claimed it was simply that they, the scientists, had not yet been able to find these special cells. The "generals" were there somewhere in the mix, they were sure-but they didn't yet know what these generals looked like.

But Keller and Segel took another, more radical approach. Turing's work on morphogenesis had sketched out a mathematical model wherein simple agents following simple rules could generate amazingly complex structures. Keller and Segel thought that the aggregations of slime mold cells might be a real-world example of that behavior. Turing had focused primarily on the interactions between cells in a single organism, but it was perfectly reasonable to assume that the math would work for aggregations of free-floating cells. And so Keller started to think: what if Shafer had it wrong? What if there were no pacemakers? What if the community of slime mold cells were organizing themselves?

Keller and Segels hunch paid off dramatically. Lacking the advanced visualization tools of today's computers, the two scratched out a series of equations using pen and paper. Their equations demonstrated how slime cells could trigger aggregation without following a leader, simply by altering the amount of cyclic AMP they released individually, then following trails of cyclic AMP that they encountered as they wandered through their environment. If the slime cells pumped out enough cyclic AMP, clusters of cells would start to form. Cells would begin following trails created by other cells, creating a positive feedback loop that encouraged more cells to join the cluster. If each solo cell was simply releasing cyclic AMP based on its own local assessment of the general conditions, Keller and Segel argued in a paper published in 1969, then the larger slime mold community might well be able to aggregate based on wider changes in the environment-all without a pacemaker cell calling the shots.

"The response was very interesting," Keller says now. "For anyone who understood applied mathematics, or had any experience in fluid dynamics, this was old hat to them. But to biologists, it didn't make any sense. I would give seminars, and the biologists would say, 'Where's the founder cell? Where's the pacemaker?' It didn't provide any satisfaction to them whatsoever." The pacemaker hypothesis persisted as the reigning model for another decade, until a series of experiments convincingly proved that the slime mold cells did not have a leader cell, but were organized from below. "It amazes me how difficult it is for people to think in terms of collective phenomena," says Keller.

Thirty years after the two researchers first sketched out their theory on paper, slime mold aggregation is recognized as a classic case study in "bottom-up" behavior.

Evelyn Fox Keller's colleague at MIT, Mitch Resnick, has developed a computer simulation of slime mold cells aggregating, allowing students to explore the eerie, invisible hand of self-organization as they alter the number of cells in the environment and the levels of cyclic AMP distributed. Firsttime users of Resnick's simulation invariably say that the on-screen images-brilliant clusters of red cells and green chemical trails-remind them of video games, and in fact the comparison reveals a secret lineage. Some of today's most popular computer games resemble slime mold cells because they are loosely based on the equations that Keller and Segel formulated by hand in the late sixties.

We like to talk about life on earth evolving out of the primordial soup. We could just as easily say that the most interesting digital life on our computer screens today evolved out of the slime mold.

Steven Johnson has written five books, including Emergence, from which this excerpt is taken. An excerpt from his book, The Ghost Map, about the London cholera epidemic, appeared in the July/August 2007 issue of Muse.

© 2008 Carus Publishing Company Provided by ProQuest LLC. All Rights Reserved.