Bucket Brigades and Telephone Trees
Imagine your house is on fire. Luckily, a cool river runs nearby. But you are all alone. You run back and forth to the river, bucket in hand, toting gallon after gallon of water to splash on your burning home. Unfortunately, your efforts are useless. Without some help, you will not be able to carry water fast enough to outpace the inferno.
Now suppose that you are not alone. You have one hundred neighbors, and, lucky for you, they all feel motivated to help. And each one just happens to have a bucket. If your neighbors are sufficiently strong, they can run back and forth to the river, haphazardly dumping buckets of water on the fire. A hundred people tossing water on your burning house is clearly better than you doing it by yourself. The problem is that once they get started your neighbors waste a lot of time running back and forth. Some of them tire easily; others are uncoordinated and spill a lot of water; one guy gets lost on his way back to your house. If each person acts independently, then your house will surely be destroyed.
Fortunately, this does not happen because a peculiar form of social organization is deployed: the bucket brigade. Your hundred neighbors form a line from the river to your house, passing full buckets of water toward your house and empty buckets toward the river. Not only does the bucket brigade arrangement mean that people do not have to spend time and energy walking back and forth to the river; it also means that weaker people who might not be able to walk or carry a heavy bucket long distances now have something to offer. A hundred people taking part in a bucket brigade might do the work of two hundred people running haphazardly.
But why exactly is a group of people arranged this way more effective than the same group of people—or even a larger group—working independently? If the whole is greater than the sum of its parts, how exactly does the whole come to be greater? Where does the “greater” part come from? It’s amazing to be able to increase the effectiveness of human beings by as much as an order of magnitude simply by arranging them differently. But what is it about combining people into groups with particular configurations that makes them able to do more things and different things than the individuals themselves?
To answer these questions, and before we get to the fun stuff, we first need to explain a few basic terms and ideas of network theory. These basic concepts set the stage for the individual stories and the more complicated ideas we will soon explore as we investigate the surprising power of social networks to affect the full spectrum of human experience.
We should first clarify what we mean by a group of people. A group can be defined by an attribute (for example, women, Democrats, lawyers, long-distance runners) or as a specific collection of individuals to whom we can literally point (“those people, right over there, waiting to get into the concert”). A social network is altogether different. While a network, like a group, is a collection of people, it includes something more: a specific set of connections between people in the group. These ties, and the particular pattern of these ties, are often more important than the individual people themselves. They allow groups to do things that a disconnected collection of individuals cannot. The ties explain why the whole is greater than the sum of its parts. And the specific pattern of the ties is crucial to understanding how networks function.
The bucket brigade that saves a house is a very simple social network. It is linear and has no branches: each person (except the first and last) is connected to two other people, the one in front and the one behind. For moving something like water long distances, this is a good way to be organized. But the optimal organization of one hundred people into a network depends very much on the task at hand. The best pattern of connections between a hundred people to put out a fire is different from the best pattern for, say, achieving a military objective. A company of one hundred soldiers is typically organized into ten tightly interconnected squads of ten. This allows each soldier to know all of his squad mates rather than just the grunt in front of him and the grunt behind him. The military goes to great lengths to help squad members know each other very well, so well in fact that they are willing to give their lives for one another.
Consider still another social network: the telephone tree. Suppose you need to contact a hundred people quickly to let them know that school is canceled. Before modern communications and the Internet, this was a challenge because there was no public source of up-to-the-minute information that everyone could access from their homes (though the ringing of church bells in the town square comes to mind). Instead, each person needed to be contacted directly. The telephone made this task much easier, but it was still a burden for one person to make all one hundred calls. And even if someone set out to do this, it might take quite a while to get to the people at the end of the list, by which time they may have already left home for school. Having a single person make all the calls is both inefficient and burdensome.
Ideally, one person would set off a chain reaction so that everyone could be reached as quickly as possible and with the least burden on any particular individual. One option is to create a list and have the person at the top of the list call the next person, the second person call the third, and so on until everyone gets the message, as in a bucket brigade. This would distribute the burden evenly, but it would still take a really long time for the hundredth person to be reached. Moreover, if someone in the sequence was not home when called, everyone later in the list would be left in the dark.
An alternative pattern of connections is a telephone tree. The first person calls two people, who each call two people, and so on until everyone is contacted. Unlike the bucket brigade, the telephone tree is designed to spread information to many people simultaneously, creating a cascade. The workload is distributed evenly among all group members, and the problem caused by one person not being home is limited. Moreover, with a single call, one person can set off a chain of events that could influence hundreds or thousands of other people—just as the person who donated the heart that was transplanted into John Lavis prompted another donation that saved eight more lives. The telephone tree also vastly reduces the number of steps it takes for information to flow among people in the group, minimizing the chance that the message will be degraded. This particular network structure thus helps to both amplify and preserve the message. In fact, within a few decades of the widespread deployment of home-based phones in the United States, telephone trees were used for all sorts of purposes. An article in the Los Angeles Times from 1957, for example, describes the use of a phone tree to mobilize amateur astronomers, as part of the “Moonwatch System” of the Smithsonian Astrophysical Observatory, to track American and Russian satellites.8
Alas, this same network structure also allows a single swindler to cheat thousands of people. In Ponzi schemes, money flows “up” a structure like a telephone tree. As new people are added to the network, they send money to the people “above” them and then new members are recruited “below” them to provide more money. As time passes, money is collected from more and more people. In what might be the biggest Ponzi scheme of all time, federal investigators discovered in 2008 that during the previous thirty years Bernie Madoff had swindled $50 billion from thousands of investors. Like the Corsican vendetta network we described earlier, Madoff’s investment network is the kind most of us would like to avoid.
The four different types of networks we have considered so far are shown in the illustration. First is a group of one hundred people (each represented by a circle, or node) among whom there are no ties. Next is a bucket brigade. Here, in addition to the one hundred people, there are a total of ninety-nine ties between the members of the group; every person (except the first and last) is connected to two other people by a mutual tie (meaning that full and empty buckets pass in both directions). In the telephone tree, there are one hundred people and again ninety-nine ties. But here, everyone, with the exception of the first and last people in the tree, is connected to three other people, with one inbound tie (the person they get the call from) and two outbound ties (the people they make calls to). There are no mutual ties; the flow of information is directional and so are the ties between people. In a company of one hundred soldiers, each member of each squad knows every other member of the squad very well; and each person has exactly nine ties. Here, there are one hundred people and 450 ties connecting them. (The reason there are not nine hundred ties is that each tie counts once for the two people it connects.) In the drawing, we imagine that there are no ties between squads or, at least, that the ties within squads are much tighter than the ties between squads. This is clearly an oversimplification, but it illustrates still another point about communities in social networks. A network community can be defined as a group of people who are much more connected to one another than they are to other groups of connected people found in other parts of the network. The communities are defined by structural connections, not necessarily by any particular shared traits.
Four different ways to connect one hundred people. Each circle (“node”) represents a person, and each line (“tie”) a relationship between two people. Lines with arrows indicate a directed relationship; in the telephone tree, one person calls another. Otherwise, ties are mutual: in the bucket brigade, full and empty buckets travel in both directions; in military squads, the connections between the soldiers are all two-way.
In a very basic sense, then, a social network is an organized set of people that consists of two kinds of elements: human beings and the connections between them. Unlike the bucket brigade, telephone tree, and military company, however, the organization of natural social networks is typically not imposed from the top. Real, everyday social networks evolve organically from the natural tendency of each person to seek out and make many or few friends, to have large or small families, to work in personable or anonymous workplaces.
For example, in the next illustration, we show a network of 105 students in a single dormitory at an American university and the friendship ties between them. On average, each student is connected to six other close friends, but some students have only one friend, and others have many. Moreover, some students are more embedded than others, meaning they have more connections to other people in the network via friends or friends of friends. In fact, network visualization software is designed to place those who are more interconnected in the center and those who are less interconnected at the periphery, helping us to see each person’s location in the network. When your friends and family become better connected, it increases your level of connection to the whole social network. We say it makes you more central because having better-connected friends literally moves you away from the edges and toward the center of a social network. And we can measure your centrality by counting not just the number of your friends and other contacts but also by counting your friends’ friends, and their friends, and so on. Unlike the bucket brigade where everyone feels his position to be the same (“there’s a guy on my left passing me buckets and a guy on my right to whom I give them—it doesn’t matter where in the line I am”), here, people are located in distinctly different kinds of places within the network.
In this natural network of close friendships among 105 college students living in the same dormitory, each circle represents a student, and each line a mutual friendship. Even though A and B both have four friends, A’s four friends are more likely to know one another (there are ties between them), whereas none of B’s friends know each other. A has greater transitivity than B. Also, even though C and D both have six friends, they have very different locations in the social network. C is much more central, and D is more peripheral; C’s friends have many friends themselves, whereas D’s friends tend to have few or no friends.
A network’s shape, also known as its structure or topology, is a basic property of the network. While the shape can be visualized, or represented, in different ways, the actual pattern of connections that determines the shape remains the same regardless of how the network is visualized. Imagine a set of five hundred buttons strewn on the floor. And imagine that there are two thousand strings we can use to connect the buttons. Next, imagine that we randomly select two buttons and connect them with a string, knotting each button at the end. Then we repeat this procedure, connecting random pairs of buttons one after another, until all the strings are used up. In the end, some buttons will have many strings attached to them, and others, by chance, will never have been picked and so will not be connected to another button. Perhaps some groups of buttons will be connected to each other but separated from other groups. These groups—even those that consist of a single unconnected button—are called components of the network; when we illustrate networks, we frequently represent only the largest component (in this case, the one with the most buttons).
If we were to select one button from one component and pick it up off the floor, all other buttons attached to it, directly or indirectly, would also be lifted into the air. And if we were to drop this mass of buttons onto another spot on the floor, it would look different than it did when we first picked it up. But the topology—which is a fundamental and intrinsic property of the network of buttons—would be exactly the same, no matter how many times we picked up and dropped the mass of connected buttons. Each button has the same relational position to other particular buttons that it had before; its location in the network has not changed. Visualization software tries to show this in two dimensions and to reveal the underlying topology by putting the most tangled buttons in the center and the least connected ones on the edges. It’s as if you were trying to untangle a gnarled set of Christmas-tree lights, and there were tendrils of the gnarled mess that you could pull out, and also a thicket of inter-knotted lights that remained in the center no matter how often you turned the tangle over on the floor.
For numerous reasons we will explore, people come to occupy particular spots in the naturally occurring and continuously evolving social networks that surround us. Organic networks have a structure, complexity, function, spontaneity, and sheer beauty not found in organized networks, and their existence provokes questions about how they arise, what rules they obey, and what purpose they serve.
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