Duncan Watts

It’s A Small World After All

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Professor Duncan Watts
Associate Professor, Department of Sociology, Columbia University
Author, Six Degrees

One of the jokes that Professor David Goodstein at Caltech likes to tell his students goes like this: “It’s well known that the fundamental components of an atom are the electron, proton, and neutron. Similarly, scientists have discovered a fundamental unit in society, the person!” Since this realization, sociologists have been trying to understand and perhaps even enhance social networks and interactions. Dr. Duncan Watts (DW), Professor of Sociology at Columbia University, joins Frank Ling (FL) to talk about his research on using mathematical models to study social networks and his new book Six Degrees.

FL: Professor Watts, thanks for joining us today.

DW: Thanks, thanks.

FL: Many of us are probably aware of the Six Degrees of Kevin Bacon, but not the science behind it. To begin with, perhaps you can tell us what exactly this Six Degrees phenomenon is.

DW: Well, that’s generally true. When I first heard about the idea that everybody can be connected to everybody else through only six handshakes, as some people would say, I assume like many people do that it’s just an urban myth, but I got interested in it and several years later, it’s clear that this is an idea that’s been around for long, long time. Almost a hundred years as far as we can tell and has been a subject of academic inquiry for at least fifty years and lot’s of different people from sociologists and political scientists and mathematicians have thought about it.

FL: So is there are special significance to the value of six or is it just an average?

DW: The origin of the number six is unclear. The short answer is no. It doesn’t matter that it’s six. The real point is that it’s a small number, so not a thousand, it’s not a million, maybe it’s six, eight, five. The people who think about these problems, it’s not really that important as long as it’s a small number. The number six, it’s not clear where that comes from, but there was an experiment done in the 1960s by the social psychologist Stanley Milgram and this is the experiment that wasn’t the first time people had thought about the small world problem as it’s called in sociology, but it was the first experiment that anyone had ever done. It certainly captured a lot of people’s attention and Milgram, the way he tested this idea is he picked a single person who was a stockbroker in Boston and he picked about 300 people from Boston and Omaha, Nebraska whose job it was to try and reach this target person, the stockbroker. And they were given a set of instructions that they had to reach this person and they were given a lot of information about him, that they were told they could only send the message to someone who they knew personally. They didn’t know the stockbroker personally, which is of course unlikely. They had to pick someone else who they knew personally who they thought was closer to the stock broker than they were and then these people got the same set of instructions and they passed it on to another person and so on. And so he created these message chains that converged from around the country onto the stockbroker. And about 60 odd or about 20% of the chains actually made it. Of those, the average length was about six and that’s where I think at least the phrase six degrees of separation came from was from this first ever experiment. Oddly enough, the person who made the phrase six degrees of separation famous was not a scientist at all, but a playwright, John Guare who wrote the play Six Degrees of Separation in 1990 and later on into a movie. It’s interesting because in this topic, there is continual interplay between the science and popular culture and each one has inspired the other in its turn so it’s a fun topic.

FL: Right, that’s very fascinating. You were originally trained as a physicist and you’ve observed as some others have the similarities between physical models and sociological models. Perhaps you can talk about some of them.

DW: Yeah, I did get into sociology in a sort of roundabout way. I started off studying physics and got very interested in college in what people call chaos theory but the more technical name for this is non-linear dynamics and then I went on to graduate school at Cornell to study non-linear dynamics in the engineering school there. And in the process of doing that, got interested in the behavior of very large connected systems. The very general idea is that you take a bunch of objects, things, entities and maybe the entities are people, maybe they are computers in the internet, or airplanes in a air traffic control system or biological organisms in a ecosystem and you let them interact with each other. This is what things do in the world, they interact. But the result of those interactions is that the system can do as a whole can do some really unexpected things, so we have a very good understanding, for example, of how airplanes fly and we can predict relatively accurately how long it’s going to take for an airplane to fly from point A to point B. But when you put a lot of airplanes in the sky together and you make them all go through airports, then a little disturbance at one place can result in congestion that spreads all over the country.

FL: The so-called butterfly effect.

DW: That’s right. The butterfly effect is sort of an example of a whole set of phenomena that occur in these big, complex non-linear systems where a small disturbance in one place can propagate in sort of unpredictable ways and manifest itself as a very different kind of effect somewhere else at some later point in time. And so the transition stage that I went through when I was doing the mathematics of these big coupled systems, is that I got very interested in the connectivity. My reasoning was if it’s true, these interactions between the parts are what really making them different. This expression the whole is different from the sum of its parts. If it’s true that what is making the whole different from the sum of its parts is the interactions between them, then that’s the thing we really need to understand and one way to think about that is in terms of the network. The network is the whole pattern of interactions or links or relationships that connect up the different bits and pieces and so once you start to think of the problem from that perspective, then you start to see networks all over the place. You see them in biology, you see them in engineering, in power grids, in airline systems, and most of all you see them in social systems. You see them in economies, markets, firms, and you see them in communities, organizations, and friendship networks. And this is something we are starting to see more and more of in the world of the internet that everybody, scientists and non-scientists alike, have started to think more about connectivity between people and we have these popular companies now like Friendster, Spoke, and Orkut that explicitly show you the links between many, many people. And so, I started to get interested in these problems and decided that I was less interested in studying the mathematics of biological systems or engineering systems and more interested in studying the mathematics of social systems. It took a few years but as a result of that transition, I became a mathematical sociologist.

FL: I’m just curious here. In these models, do you treat the people as discreet units or part of a continuum or field?

DW: That’s an interesting question because the answer is yes and no. The way that the models is written down is in terms of discreet entities. You start off by buying into the typical assumption that people are self-contained units and they have rules or behavior and they respond to input, signals, influences that come from their environment. And part of that environment is the other people they are connected to. Your friends or your business partners or whoever you pay attention to or you use for resource or support. And so you define a population of individuals and you define the rules that they follow and then you define this network as interactions and there are lots of way to do that. But then, the interesting thing is that once everybody starts interacting in this way, the behavior that they exhibit subsequently is very hard to trace back to these original characteristics. In another words, if someone does something, if someone buys a product, or someone adopts a new fashion, the standard view from economics says that you can infer that they must have wanted that product, that they must have liked it, that particular fashion. This is an external expression of some internal preference. This is what economist call revealed preferences. Once you start to think about networks and networks of influences, it becomes very difficult to make that association because maybe you wanted this thing before you bought it or maybe you just had no idea you wanted and you friend told you that this was a good thing to get and so you got it. So we have lots of examples of this. You are making decisions about which cell phones to get. It’s complicated to think about all the cell phone plans that are available and your friend says I have AT&T and it works great. So, you know, your decision is being simplified for you. So, you go and you get AT&T. An economist would say, “Aha! Listen, AT&T’s marketshare just went up. That means it is a superior product to the opposition.” In fact, it may not be the case. It’s just that your friend told you to get and may be your friend didn’t know anything either. Once you start to take into account all these interactions between people, it becomes much more difficult to say what processing is going on within in the person and what processing is going on in the network. And so, even though you start off with this population of discreet entities, the behavior that gets exhibited is very hard to pin down to these entities. In a sense, the barrier between internal and external disappears to some extent. Individuals are unpredictable. This is one of the objections that many people have to mathematical sociology. They say how can you make simple models about people because people are very complicated and they have lots of reasons for doing whatever there is that they have to do. And that’s true. It’s very hard to use these sorts of models to influence a person. When you put lots and lots of people together, rather than increasing complexity, you often see decreasing complexity. So, this is why it’s possible to do science in social systems because you take lots of very complicated nuanced individuals and you put them together and they behave in occasionally predictable ways and that’s the kind of outcome that we are interested in understanding, collective behavior and collective dynamics. That’s not something you can really use in a day to day basis in your own lives.

FL: So, since these networks are self-emerging, you actually don’t get the specific insights into how individuals behave then right?

DW: You can, in the sense that the kind of insight you get is that our perceptions of why we do things we do are often really quite inaccurate. So, we have this belief that because we tend to perceive ourselves as atomized individuals, this is deeply buried in our culture, that everybody is independent and everybody does the thing they do because that’s what wanted to do and we often tell ourselves these stories after the fact that I did this because I wanted to be an individual, expressing myself and this is my preferences.

FL: I once read somewhere that in a crisis for example, in general, what we observe is that 10% of the people take decisive action which 80% follow these leaders. Can this be applied in a general way perhaps?

DW: I’m not sure where that statistic comes from. It may be the case but I think you would have a very tough time predicting ahead of time who those people would be. And this is another kind of insight we can get from studying systems is after the fact, if you look at the spread of an epidemic or the diffusion of an innovation or success of a particular product, it will often turn out that certain people were key players in that process and that they introduced it to new markets or convinced a lot of important people that it was a good idea and you can say a similar thing in crisis situations that somebody comes out after the fact to look like they were a key player and we often call these people opinion leaders and everybody is interested in figuring out who they are. It’s not so clear that before the fact, you could figure out who they are. It is often a consequence of all that is going around them as much as it is a consequence of their individual characteristics. And so once again, you get this weird distinction between the internal and the external and it becomes very hard to separate somebody’s behavior from the behavior of people around them. Just to back to the crisis situation, often the most unlikely people become critical and it’s not secretly, all along, they were raised for this task. They just did what the situation demanded of them in many cases. In slightly different circumstances, they would have behaved in a different way. I think that it’s very hard to see that in real life because in real life you just get this one set of events and that’s what happens and after the fact, it all seems clear. So, this person was important therefore it was something about them that made them important. Once you start to think about these processes in a mathematical sense and you start to understand the whole set of possible outcomes, it becomes more and more clear that there may not have been anything that special about them at all.

FL: So in your book, you mention that casual acquaintances may have a bigger potential for having life changing impacts rather than someone’s best friend. Could you elaborate on this a little bit?

DW: That comes from an old idea in sociology, a few decades old, that was proposed by a sociologist Mark Granovetter at Stanford University. It’s called the strength of weak ties. And the idea is that a weak tie is a relationship that is weak. It’s somebody who you don’t necessarily know that well. A strong tie is someone who is close friend. The idea is that people who are strong ties, your close friends, also tend to be connected to each other, whereas your weak ties tend to be people who are not so intimately embedded in your social network and the consequence of that your weak ties are more likely to know people and things that you don’t already know. So, your strong ties know many of the people you already know. They can’t really connect you to anyone you don’t know. Your weak ties are more likely to be able to do that. So Mark Granovetter, when he proposed this idea, was interested in people finding jobs and many of the people that he talked to when he asked them to did you get this job, they mentioned that they had had a referral. And he said a friend helped you get this job and they would always correct him and say I wasn’t really a friend, it was more of an acquaintance, so that’s how he came to this idea that it was acquaintances who maybe they don’t have much invested in you. It’s probably more complicated than that. The world is a complicated, but there does seem to be great deal in that idea and that is why it’s been around for so long.

FL: I guess we are running out of time here. Are there any last words you’d like to add about yourself or your book?

DW: One thing I can say about the book is it’s only partly about network, it’s partly about this idea of six degrees of separation and I think that is a fascinating idea, but I think more fascinating is what the consequences are with this idea and for networks in general and social processes that define our lives. And the sorts of things I am interested in these days are very much along those lines: How do epidemic diseases take off? How do cultural fads start off and why do some things become popular while other things fail. What can we learn about the world by thinking in these networklike terms?

FL: Professor Watts, thanks for your time. Thank you for joining us today.

DW: My pleasure.


  1. […] technical, and most of us don’t like reading academic papers, so here’s a brief summary from Duncan Watts: …your weak ties tend to be people who are not so intimately embedded in your social network […]

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