Duncan J. Watts
Professor
Columbia University

"Six Degrees: The Science of a Connected Age"

In my talk today, I will start with a brief history of the "Six Degrees" idea. I will talk about how this idea has evolved over the last few years into a question that has much broader significance than was originally believed. Then I will generalize the Six Degrees idea into a discussion of the "Science of Networks". This may sound a little pretentious - that's why I put it in quotes. People are coming up with new "sciences" all the time, which after a few years look like stock market bubbles. Hopefully this won't be one of them. To convince you of this, I will talk through a couple of specific problems in which thinking about networks can help us understand the problem better.

What is "Six Degrees"? If you're like me, when you first heard about the concept of "six degrees of separation" you probably assumed it was an urban myth. The first time I heard about it, I was in grad school at Cornell studying something completely different. My father asked if I had ever heard of the concept that I was only six handshakes away from the President of the United States. I thought it was a cute idea and wondered if it was true. Ten years later, I'm still thinking about the problem.

The phrase comes from a playwright named John Guare who wrote a play called "Six Degrees of Separation." This was also a movie starring Will Smith. If you've seen this movie, you will be aware that it doesn't really have anything to do with six degrees of separation at all. It did, however, make the phrase famous. So thank you, John Guare!

The idea has been around for a long time, but we don't know exactly how long. The first mention that we have been able to discover is in a short story called "Chains", written in the 1920's by the Hungarian Frigyes Karinthy. The protagonist in the story boasts that he can connect himself to different powerful people. He makes up stories about how he knows someone who knows someone who knows someone and he connects himself through these chains.

All of the chains happen to be six links long, which I believe must be coincidence because he's never heard of the concept of Six Degrees. The author is only speculating on how these chains can grow. Furthermore, this story was only translated into English last year, and this only happened because we wanted to include it in an edited volume. One of my colleagues on the project is Hungarian, and he is always keen to promote Hungarian contributions to world science.

It was not until 30 years later that this idea became a formal research problem. Even then, it was an interdisciplinary research problem. It began in a 1950's collaboration between Ithiel de Sola Pool (a political scientist) and Manfred Kochen (a mathematician). Pool was interested in chains of political influence. For example, if you are not an elected official, do you know someone who is? Can you exert some kind of influence over the political process if you know someone who is in politics or if you do not? How long do these chains have to get before your influence is dissipated? Given that length, how many people in the world are included in this invisible pool of people who can influence the political process? He was not a mathematician, but he recognized that a math problem was buried inside of this political science question. So he started to collaborate with Kochen.

Their first question was, "what's the likelihood that two strangers who meet at a cocktail party have an acquaintance in common?" This happens a lot at cocktail parties, and the people for whom this happens invariably look at each other and say, "It's a small world!" This is why I never do that - I just say, "That's interesting." When someone else says that, most of my friends snicker and hopefully that's the end of it.

This behavior was apparently as common in the 1950's as it is today. This behavior is why they called it the "small world problem". They were also very interested, however, in all of those times when you meet a stranger at a party and you do not have a mutual friend in common. In those situations, you may still be connected, but you may have two or more intermediaries between you instead of just one. How long do these chains get before everyone in a large community (like the United States) before everyone is connected to everyone else? That is the more difficult question.

If you want to make the question more difficult still, then you must take into account that real world social networks have a lot of structure to them. In social networks you see a lot of clustering - if A knows B and A knows C, then there is a much higher probability that B knows C. Your friends tend to be friends with each other.

There are lots of reasons for this. One reason for this is homophily - the tendency for people to associate with other people like themselves. You will notice that your friends and colleagues probably all grew up in similar neighborhoods, went to similar schools, belong to the same race, and are probably of the same gender. There are lots of different ways in which we flock together, the result of which is that there is a lot more clustering in our social networks than in the world at large.

The other reason for clustering is that social networks tend to grow over time through the brokering of mutual friends. The people you know today will heavily bias the people that you will know tomorrow. The result of this is that you keep closing these social triangles.

Think back to when you moved to college or to a new city. You can probably trace several steps forward from the original few people that you knew into a tree of friends that eventually grew. All of this generates more clustering. This is a very important feature of social networks, and has some very important implications for things like solidarity and other aspects that make us feel part of a group.

On the other hand, clustering makes it extremely difficult to do any mathematical analysis. The interdependence of links makes the mathematics extremely difficult. This is what Pool and Kochen discovered. Because the math was so hard, the theoretical work on this problem stalled in the 1950's.

Their paper, however, triggered a very interesting experiment by Stanley Milgram. Most people who talk about the Small World Problem, in fact, tend to think that it started with Milgram. It had started earlier, but this is where it became famous. Milgram was a sort of psychologist. He is more infamous for a series of experiments he did on people to test their responses to authority - this one involved electric shocks. To do any kind of experiment with human subjects these days, you have to fill out all kinds of paperwork. When you mention Milgram and "human subjects" in your applications these days, people get very nervous!

He ran his small world experiment in 1967. He chose a single person in Boston as a "target" - he was a stockbroker who lived outside of Boston. He then chose another 300 individuals who he nominated as senders. Some of them lived in Boston and about two thirds of them lived in Omaha, Nebraska. He chose Omaha because it was the farthest away from Boston socially (if not geographically). It is interesting to note that both Milgram and Warren Buffett have benefited from these same characteristics of Omaha. I have been to Omaha, and it really is… distant.

Each of the 300 "senders" received a packet, and were given an assignment to get the packet to the target in Boston. They were given a detailed description of this person - his name, profession, address, years of military service, etc. However, if you are not a personal friend of this person, you cannot send the package directly to him. You must send it to someone who is a personal friend of this person, or at least to someone who you think is closer to this person than you are. He was deliberately vague about what he meant by "closer".

Many of these people cooperated and sent the packages onward. It is remarkable that 75% of the people actually sent the packages onward - it is probably a testament to how little junk mail people received in the 1960's. It is much more difficult to do these experiments these days. In the end, Migram generated a series of chain letters that made their way across the country to the target in Boston. Of the 300 chains that started, about 64 reached the target. This is a remarkable completion rate - about 20%.

The famous result of this experiment was that the average number of links in the successful chains was about six. Milgram never used the phrase "six degrees". He always talked about "the small world problem". However, we assume that this result is the source of "six degrees". Interestingly, Milgram himself believes that the phrase comes from something that Marconi said about the telegraph, but there is no record that Marconi ever actually said that. This problem has been part of a constant flow between social science and popular culture.

After Milgram, there was another lapse in this research for several decades. This experiment was replicated a few times with similar results, but nothing was ever done on a larger scale than the first one. These experiments are extremely difficult to run, network data is extremely hard to collect, and the mathematics on a large scale are very difficult. Some work has been done on small networks, like within a company. But imagine the difficulty of mapping the friendship networks of a small city. It would be completely unfeasible. Large-scale network analysis did not go very far for about three decades.

In the mid-1990's, I worked as a grad student in the engineering department on a completely different problem. Steve Strogatz, my advisor and applied mathematician, and I decided to look at this as a math problem. We wondered how the interconnections of people in social networks influence their behaviors. We had three advantages over our predecessors in this work. The first advantage, oddly enough, was that we didn't know anything about the problem or the previous work that had been done. Normally, grad students are supposed to read all of the literature on the subject, and the usual result of that is that you get really depressed. You think that so much has already been done. You also start to think about the problem in the same ways that your predecessors did. This is not quite groupthink, but it has a similar consequence. When you read about ten different people who have approached the problem in the same way, your mind starts tracking onto the same path. We didn't do this, deliberately. We tried to remain ignorant as long as possible.

Our second advantage was that while we knew this was a math problem, we didn't think it was a pencil-and-paper math problem. This was a problem that computers would be good at solving, and we had much faster computers than Milgram had had in the 1960's. We relied heavily on computer simulation in our experiments.

Our third advantage was our backgrounds in physics and mathematics. There is a way of thinking about problems in physics and mathematics, which is very different than the training that you receive in the social sciences. We never tried to solve the problem in the same way that our predecessors had. We asked a question that was much more difficult than the original question, but turned out to be easier in some ways as well.

The original question was "How small is the world?" We realized that it was impossible to calculate in the real world. Instead we asked as different question. Imagine all possible worlds and all possible ways of connecting people together under some constraints. For example, it is only possible for an individual to know a tiny proportion of the entire population. If you can configure worlds in any way you like, how difficult would it be for one of those worlds to be a "small world"? In the universe of possible worlds, what portion of those worlds has locally dense connections and still manages to have relatively short chains connecting people globally?

There are three possible answers to this question. The first is that it is simply not possible - the clustering forces and the global connectivity forces simply cannot coexist. If this is the answer, then "six degrees" really is an urban myth. The second possible answer is that it is possible, but it requires a tightly adjusted set of conditions. There are a lot of optimization problems like this - the solution only works when all of the parameters are just right. This would not be a very promising answer because there is no optimization or selection force going on in the real world that drives it to be small. The third possible answer - the one that we're hoping for - is that almost all possible worlds behave like small worlds. This is indeed the way it is, and we were able to show that most worlds are small worlds. This can be any network, not just social networks. As long as there is some source of order (associating with friends) and some small source of disorder or randomness (going to cocktail parties, going away to college, etc.), we will create small world property. That is all that is required. The prediction, then, is that small world networks should be everywhere.

So we started to look for small world networks in all kinds of different data sets. They have been found all over the place. You can find them in social networks online, you can find them in the Internet (CAIDA), you can find them in power transmission grids, and you can find them in the neural network of the C. Elegans (a worm). When you do network analysis, you quickly discover that pictures are almost useless - all networks look like a really big mess. That's why we have statistical and computational ways to think about networks. For various reasons, though, we still like to see pictures.

Over the last several years, many people have been working on these problems. Collectively, we have a pretty good understanding of the conditions that make the small world phenomenon work. We are also starting to understand other aspects of large-scale networks. There has been a tremendous amount of work theoretically, analytically and with mathematical modeling, all facilitated by the growing speed of computers, the dramatic increase in the availability of electronic data, and new combinations of different theories from different disciplines. There is a lot going on, but it does not yet make the case for networks as a convincing science.

I would like to convince you that all of this is going somewhere. This is not just navel-gazing. It is important to ask the "so what" question. Where do these networks arise and why do they matter? Networks arise everywhere. Once I started to think about network problems, I started to see them everywhere. The reason is that any system consists of discrete (separate) objects (like the people in this room), where you can define relations between the objects.

The relationships can be very tangible and physical (like a cable connecting two computers) or it can be less physical (like friendship), or it can be abstract (like the relationship between two words). This is a very general way to think about the world, and one result is that networks appear to be ubiquitous. Here are some examples - the September 11 hijackers and their associates, syphilis transmission network in Georgia, and corporate partnerships and other relationships.

Network approaches are becoming very popular in epidemiology. People really do interact in social networks, and this is very important for understanding disease outbreaks and possible prevention strategies for those outbreaks. Corporate networks are becoming of much more interest - co-ownership networks, people sitting on different boards with different people, CEO's belonging to the same golf clubs. How are these organizations connected in ways that may be invisible to the public?

So what? If everything can be mapped as a network, then why is that a useful tool anymore? Someone once asked me what network science was good for? I responded by asking, "Well, what is math good for?" Network science is not an answer to a question. It is a way to think about problems. You learn differential equations when you learn calculus. There is a lot of power in the ability to analyze differential equations, but only if it is appropriate to the problem. Just because you could make up an equation about a problem, it does not mean that that equation will be informative. By the same token, just because you can represent a problem as a network, it does not mean that that representation will be informative. I have to say that there is a lot of uninformative research going on right now.

What most social and network scientists actually care about is not networks, but behavior. Why do groups, organizations, societies and economies behave the ways that they do? To the extent that we can understand how network structure can influence behavior, then network science will be a useful tool. To the extent that it is merely a different representation of something that we already know, then it won't be very useful.

What can networks tell us about behavior and collective behavior in particular? We need to understand how we behave as individuals, and we need to understand the other things that happen when we get together in groups. Behaviors emerge, norms emerge, and exchange economies evolve.

Let's talk through a couple of examples. In New York City, many apartment buildings have doormen. My advisor had moved from North Carolina and was puzzled by this phenomenon and its effects. He developed a hypothesis that he wanted to test - that having someone opening the doors and being deferential every day had made Columbia University faculty more arrogant than other faculty. As he studied them, however, he discovered a lot of other interesting things about them. One of these interesting items is that there does not appear to be a labor market for doormen. If you move to New York, you can become a waiter, an actor (what's the difference?), or you can apply for most any job. But you cannot apply to be a doorman. If you don't have the job, you can't get it. The only way to get the job is if you know someone else who has it. Recruiting for the position of doorman happens through social ties.

This is especially interesting in New York. We think that social networks are important in Third World countries because they do not have well-developed social institutions, and they can only establish enforceable contracts using other kinds of relationships like family and social ties. But New York is the heart of capitalism. There are loads of financial institutions in New York. And yet, there exists a labor market in New York that does not behave like a labor market. There are a lot of other examples out there where recruitment really works through social ties, even if there is a well-functioning labor market. If there are too many applicants for a job, then an applicant with social ties will dramatically improve their chances of being hired.

Mark Granovetter pointed this out many years ago. The most important relationships for this type of activity is not your closest friends (your "strong ties"), but your "weak ties" - your friends-of-friends and acquaintances. Because of homophily, your closest friends are probably a lot like you are, and they will have the same information that you do. Your acquaintances, however, are more likely to have information that you do not.

The previous example is only two degrees. Six degrees sounds like a small number but it is actually quite large. Who do we really care about in the world? We mostly care about ourselves. If you stub your toe in the morning, you'll be in a bad mood for the rest of the day. It's not a significant event in the history of the world, but it matters to you. You also care about your friends, family and loved ones - your one-degrees. You are curious about your friends-of-friends, some of the time. If one of your good friends is upset because one of her friends has just had a bad breakup or a tragedy, then you will feel bad for that two-degree friend, but you're not really feeling bad. You're feeling some empathy.

At three degrees, you couldn't care less. A friend of a friend of a friend is a stranger - just one of the masses out there. Our social horizon ends at two degrees. Almost everyone is outside of our social horizons. So what if everyone is only six degrees away from us? That's still everyone! If we cared about everyone, we couldn't get out of bed in the morning. We have to ignore these things - this is an adaptive response. Maybe six degrees doesn't matter. Maybe you can't call up a friend of a friend of a friend of a friend, and ask for a job.

This was a problem that a company called sixdegrees.com did not understand a few years ago. This company was the original "Friendster". It was more slanted towards the job market rather than friendships, but the problem was that no one could figure out what to do with it. If someone was five degrees away from you and wanted something from you, the relationship meant nothing. So maybe anything beyond two degrees doesn't matter.

That might be true if networks were static, but social networks are always changing as we meet new people. As you do this strategically, you meet new friends and their colleagues and their friends and their colleagues. Over a period of two or three years, you can advance many links through the network. If networks are indeed small worlds, and if search patterns like Milgram's do indeed work, then over time we can navigate our way out to six degrees and find what we're looking for. This does have important consequences for how we as individuals can solve problems and find information.

We did an experiment motivated by this concept and some doubts that had been raised about the original Milgram experiment. We did exactly the same experiment as Milgram, but on a much much larger scale. We used 18 different targets instead of one, and we included over 21,000 chains and over 60,000 people from 170 countries. It starts to sound like a global experiment. The results mostly validated those of Milgram, except one. Milgram highlighted the role of particular individuals who were highly connected. He believed that these people were hubs, like O'Hare in the airport network. Milgram found some evidence for this in his original experiment - he called them "sociometric stars". I don't think these people exist. I believe that these problems work in a much more egalitarian fashion.

If it is true that individuals can solve these complex search problems using simple heuristics, then this is relevant to the way in which collectives solve certain kinds of problems. I would like to make a distinction between these collective problems and the kinds of problems that Jim Surowiecki talks about. It has to do with the aggregation mechanisms that he alluded to. These aggregators are as important as the condition of independence. In the case of Frances Galton, the aggregation mechanism was very clear - you can put all of the answers in your pockets and average them.

Design challenges are quite different - you cannot ask everyone to submit a design and then average together all the parts. This is a kind of problem that requires intense collaboration. There are a lot of problems in industry and business related to design and innovation that require collaboration. No one knows more than a tiny part of the problem. No one even knows exactly what they're supposed to be doing, and nobody else does either. There is no overall architect or master planner to allocate pieces of the work to different people. Instead, there is some kind of collective problem-solving activity in which people perform these kinds of social searches looking for information they don't have and the people who do have it. Together they are able to solve problems that not only could they not solve alone, but they also could not even understand how they did it after the fact.

I remember sitting in a roundtable discussion with some executives whose firms were in the World Trade Center when it collapsed, including people from Merrill Lynch, Deutsche Bank, Cantor Fitzgerald. The remarkable thing about this discussion was that they all remembered the estimates that they made on the day of the event for how long it would take for them to get back into the markets. All of them thought that it would take them weeks or months, and all of them were back within days. There are occasions in which firms (in my book I talk about a supply chain disaster at Toyota) solve complex problems without ever being able to understand how it happened. There is clearly a relationship between collectives being able to solve these difficult, ambiguous problems, and the ability of individuals to perform these social network searches.

The last example is about making decisions. The standard model of microeconomics is a strong reflection of the Enlightenment. It states that individuals are rational, have clearly defined preferences, know what they want, that the preferences remain constant, and that the decisions do not affect the preferences that they have. Most economics plays around the edges of these assumptions - they argue whether people have bounded rationality or not. Fundamentally, though, classical economics accepts the assumption that people know what they want.

In most situations, that's just not true. Very often, even in simple situations like choosing a restaurant, we simply do not have enough information. This gets even harder with a more complicated decision like what career to pursue, whom to marry, which project to invest it, etc. We almost never have enough information to make a truly rational decision. Furthermore, when we do have more information, we cannot understand the logical consequences of that information. The stock market is a good example - there is plenty of information out there, but what does it all mean?

Finally, it is not just that problem solving is difficult for individuals, it sometimes doesn't make sense to solve problems individually. Who wants to watch a reality TV show that no one else is watching? They're not very good. The only reason to watch them is to make fun of them. You get to talk with your friends about them the next day. If no one cared what Nicole Kidman was wearing, would you? (This is a weird thing for me.) How many pictures of her do we need? How many times does she need to be on the cover of magazines?

The only reason that people care about celebrities is that other people care about celebrities. That is not an unreasonable thing. In many situations, there is a tremendous premium on coordinated responses. We want to do the things that other people are doing. In some circumstances, it is psycho-sociological - there are lots of different explanations for why individuals want to succumb to group pressure and why we want to be part of a group.

There are also quite rational reasons for conforming. If you are the only person to buy a fax machine, it won't be worth anything. The value of many technology-related decisions is an explicit function of the number of other people making that decision. There are lots of reasons why we don't behave in an individualistic manner. The typical response to a challenge is to look around to see what other people are doing - this is social decision-making. If we do the same things as our neighbors, then we cannot do worse than them - there is only one thing worse than doing badly; it's doing badly when your friends do well. We are very competitive with our friends.

There is a lot of information out there - Google is a great example of that. If you can find the right way to mine the information, you can do very well. This is "ecological rationality" - when simple heuristics (like "do what the other person is doing") can be quite effective. There is a lot of great research going on about this. One interesting idea is that of "recognition bias". We tend to select words and names that we recognize. This is not a rational process, but it often works quite well. For example, you would never send your kid to a college you had never heard of. If they get into the University of Chicago and University X, and you've heard all sorts of horror stories about the University of Chicago (it's in a slum, the weather stinks, the people are boring, etc.), you will still probably assume that X is going to be worse since you haven't even heard of it. And the thing is, you're probably right. These non-rational decision-making processes are actually quite adaptive. We can do quite well by paying attention to other people.

This can, however, create some very strange behavior - an information cascade. This happens when everyone is paying attention to everyone else, and everyone is doing the same thing. The aggregation that goes on in Jim's examples stops happening in this environment. Information is not aggregated. People are making decisions, but they are ignoring their private information. When this happens, you get an information cascade. We have done some work on the dynamics of information cascades, and they have some very weird problems.

Here are some examples of cascades. The dynamics of cascades are extremely hard to predict. Imagine a network of individuals listening to each other and making individual decisions about whether to do one thing or another. And the system is constantly being shocked by new ideas and new innovations that people are coming up with. Most of the time, nothing happens. When we think about crowds, we normally think about volatile behavior and riots. In truth, most of the time, nothing happens. We need to be able to explain not just the sudden changes, but the sudden changes in a life of great stability.

People go through their whole lives without making big changes, like religion. It does happen, but it is not terribly common. In many cases, they don't change their political beliefs, or they buy the same brand of car their whole lives. There is a lot of stability that can be reinforced by these externalities, but occasionally you get a massive information cascade.

One interesting property of these networks is that some individuals are more prone to changing their minds than others. If enough of those people are connected to each other, it creates what we call a "vulnerable cluster". When that cluster is big enough and a new idea gets into that cluster with enough influence, then it can topple that cluster. Once the vulnerable cluster goes, it takes down the entire network with it. That's the 30-second description of information cascades work.

What's interesting about this is that these vulnerable clusters are not the people that we're looking at. We pay far more attention to the "influential" people, the people with connections, the people with status, and the people with reputations. These are the people that we think drive cascades and the change of social mores. They are not. The people who set up the conditions for cascades to happen are the invisible people. They are the easily influenced people who are connected to other easily influenced people. Most of the dynamics that take place when a major change occurs take place invisibly. All of our focus is on the stars, but the stars have very little to do with it.

The second counter-intuitive result is that it does not seem to matter what the stimulus is. I will not say that quality doesn't matter. I will say that quality doesn't matter as much as we think it does, not nearly as much as we think it does. In our model, all of the shocks are the same (there is no difference in quality), but the difference in outcome is as large as it is possible to be. The same stimulus can create no effect or it can alter the entire world. There is precisely no relationship between input and output in our model. I don't think that's true in the real world, but the fact that it could be true in the real world should give one pause for thought.

If the outcome is unrelated either to the inherent preferences of individuals or the specific attributes of the thing that succeeds, then "learning from experience" is a problematic hypothesis. You cannot look at what succeeds and make inferences about relative quality. There is a notion of "revealed preferences" that is quite popular because it solves a lot of problems associated with actually looking inside people's brains. You can just look at what people buy, at what the market wants - but the problem is that the market does not know what it wants. After the market decides, however, it then decides that that is what it wanted. We are extremely good at doing this - at deciding after we've done something that it was the right thing to do and it was what we wanted to do. We are extremely good at rationalizing our behavior. We do this both at the individual and the collective levels. You can see where the idea of revealed preferences comes from, but it does not necessarily have any real explanatory power.

This presents us with some problems - how do we judge quality or assign credit? In what sense do people even behave as individuals? If it is true that people's decisions are affected by whom they are paying attention to, then we need to modify what we mean by "individuality". This is a culturally constructed idea (especially in this country) that the individual drives everything, everything can be attributed to the individual, and outcomes can be correlated with individual characteristics. If you're so smart, why aren't you rich? If your book is so good, why isn't it a best seller? That is how we think. The point that I would like to make is that all decisions are collective decisions, even the ones that we think are individual. The consequences of that statement are extremely difficult and often unwelcome, but we must take them seriously.

These are hard questions. Sometimes I feel hopeless about the prospects of finding any scientific progress on them. Maybe we should go back to getting up each day and seeing what happens. We have to try. There are a lot of people becoming interested in these problems - it is one of the most interdisciplinary efforts to have arisen in recent years. The jury is still out whether or not network science will be judged in ten years as the successor of chaos theory and catastrophe theory and complexity theory that came before it. Although they make valuable contributions to specific kinds of problems, they never really lived up to some of their own promises. Some people get very excited about networks and think that they will solve everything. Other people say, "Oh, we've heard that before!" I remain hopeful. If we ask the right sorts of questions, and if we remain realistic, then we might actually start to see something like the science of the 21st century.

Q: You made the comment that we are very good at rationalizing a decision as good after we've made the decision. Could you comment on the level of education and the level of cognitive dissonance and consonance that a person might have? Are less educated people happier with their post-decision conclusions? Are more educated people less happy? My observation is the educational pension plans (often supervised by Ph.D.'s) tend to have the most dissatisfaction associated with the decisions that they've made.

A: I don't know of a study that has addressed that particular question. I'm not sure that I would agree that levels of education necessarily help us maintain cognitive dissonance. In an ex ante sense, the levels of education or status might help people handle more complex choices. They might be more comfortable with complexity or uncertainly. That would be an interesting study to conduct. These people might be less inclined to use simple heuristics. However, in an ex post sense, these biases that we have are buried very deeply. Hindsight-wise is one example - this is the inability to correctly recall your ex ante prediction. This is where we tell ourselves "we knew it all along". We are very systematic at remembering that "back then" we predicted with certain probabilities that this was going to happen. Once we know the answer, it is very hard to take ourselves back to that time. This is an issue that the country has been struggling with in our intelligence analyses. It is difficult for everyone to do this.

There are other problems as well. Cognitive dissonance is one of them. It is just the stress resulting from the difference between your beliefs and your experiences or your beliefs and other people's beliefs. We try to reduce this stress by changing our behavior or by dissociating ourselves from the source of the difference or by changing our beliefs about what we believe. We can only speculate about whether different types of people would be more likely to select one of those options over another. I believe that we all do this, and we do it without realizing it. It is very hard to correct a problem that we are unaware of.

If you studied social psychology and probability theory, you might be able to be aware of some of these biases, but I would point out that scientists in general are not less religious than non-scientists. You would think that men of science would be less religious, but science gets quite religious at some point. A lot of science is very deterministic, and religion is very deterministic. Probabilists should not be religious - that is a theory that has not been tested. It is not just level of education or amount of science. It is very specific things that directly address some of these biases.

Q: You showed a lot of network mapping. There has been a lot of work done on who is in the network and how they are connected. Has there been any work done on the activity that takes place on that network?

A: There has been a lot of work done. If we content ourselves with relatively small groups, then people have done sociometric studies (using surveys about friends, information sources, etc.), and observational studies (where they sit and watch who talks with whom). People have collected this sort of data. There has not been a tremendous amount of work done using this information, in part because it is so difficult to collect. Right now we have a major ongoing study involving the email logs of an entire large university that will remain nameless. That has the advantage that (if you believe the email transmissions correlate at all with underlying social ties) we have time-stamps on every email sent between 40,000 people over about a year. We can measure all kinds of things about reciprocity, how many people we talk to, how much we talk to each one of them, and how these ties evolve over time. We can start to answer some of these questions now that we have huge amounts of electronic data. When you see the size of this data set, though, you realize just how much data you need to answer even the simplest questions. Bits and pieces of your question have been addressed by different studies, but I don't believe that anyone has taken a comprehensive look at the structure of a network, how it evolves over time, etc. This is something that remains to be done.

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