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Bottlenecks pp 235-248 | Cite as

Six Degrees of Recommendation

  • David C. Evans
Chapter

Abstract

So let's say you've achieved perfect alignment between the design of your digital innovation and our psychological bottlenecks, and in that way, our receptivity is maximized. Just how many recommendations would it take to reach everyone?

Keywords

Small World Target Person Social Graph Digital Innovation Great Social Distance 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

So let’s say you’ve achieved perfect alignment between the design of your digital innovation and our psychological bottlenecks, and in that way, our receptivity is maximized. Just how many recommendations would it take to reach everyone?

Did we just say everyone? Believe we did. And we meant everyone. On planet Earth.

By 2015, Microsoft Office was used by 1.2 billion people in 107 languages; Google search by at least 1.2 billion in 130 languages; and Facebook by at least 1.6 billion in 142 languages. i Each of those companies spread faster than the last, albeit only to one or two sevenths of the world population. How long would it take your (perfected) meme to reach everyone? Microsoft’s CEO Satya Nadella challenged his company to empower everyone on the planet to achieve more. Can that be done in a reasonable amount of time?

We will close out this discussion with a consideration of the speed by which a meme with peak memetic fitness could spread throughout the global meme pool, and the science that had to be invented to assess that. To answer the question of how long might it take a meme to reach 100% of us, scientists needed to understand the shape of humanity, the architecture of the global human network.

Key Point

How many “degrees” of recommendations would it take for your meme to reach everyone on Earth?

Yes, the final question we’re asking you to consider is how many “degrees” of recommendations would it take for your meme to reach everyone. One of us tells someone who tells someone…that’s three. To reach 100% of us, would it take far too many recommendations to happen in your lifetime? Or is it some number that is still huge, but small enough to reasonably strive for?

Or is it six?

Six degrees of recommendation to achieve total memetic fitness, to spread to the entire human population? That…that could conceivably happen between now and your next cup of coffee. Between the launch of your meme and the end of the launch party. That would smoke Gangnam Style . The South Korean rapper Psy, who in 2013 put out an irreverent song making fun of the rich part of town, earned 2.4 billion views on YouTube in less than three years. So is it actually possible to get 7 billion users in less than an hour? That is, in less than six recommendations?

To measure whether that is possible with any degree of reliability, the world needed a new science.

That new discipline, alluded to in the previous chapter, is called network science , and although it has as many origins as it has applications, it is not too great a stretch to say it was social psychologist Stanley Milgram who, in the late 1960s, first encouraged it to take itself seriously. He did that by embracing the mind-trip now known as six degrees of separation , which had been smoldering in literature for several decades but was impossible to test rigorously. Understanding that history will not only reveal whether six recommendations could spread your meme to everyone, it will also show you what kind of courage is needed to spread a really big meme like a brand new science. Or the internet itself.

Six degrees of separation . We’re guessing you’ve heard of this meme, or perhaps already accept is as axiomatic. The claim is that any two people on planet Earth, chosen at random, can be connected through a chain of six acquaintances (or five links or hops). Any two people, and every two people, not just celebrities, and not just Kevin Bacon. Choose even the most obscure, everyday two of us from the most distant corners of the globe, and we could recommend an idea to each other through only four intermediate acquaintances whom we know on a first-name basis. That’s the claim.

Mind you, no telecommunications network comes anywhere close to reaching everyone. No internet. No electrical grid. No airline network. Not even the worst diseases like AIDS or SARS. The network we’re talking about is the network of human acquaintances. Our relationships. “Do I know Peggy? Why, sure I do. She was the one who introduced me to sushi.” That network. The social network sans social media.

The six-degrees claim is provocative because it’s shocking—shockingly low. Regardless whether one argues that six is the longest path needed to connect any two people on Earth (the diameter in the terminology of network science) or the shortest path (the radius ), or the mean path length, or the median—there were 2 billion people on Earth when this idea was hatched and 7 billion now, so six just seems preposterous. If true, this would mean that if a native of Jakarta, Indonesia recommends the smartphone app that you invented to a friend, it would take only four more recommendations to reach people in Jackson, Wyoming, Jabalpur, India, Joal-Fadiouth, Senegal, Juliaca, Peru, Jastrzębie Zdrój, Poland, and every other corner of the globe.

So, is it true? Is it possible?

Well, testing this claim remained something of an unreachable intellectual opiate for almost a century. Scientists had neither the mathematics to formalize the question nor the infrastructure to test it empirically.

The first person to describe the six-degrees question was Hungarian writer Frigyes Karinthy in a piece called “Chain-Links ” published in 1929. ii In a Socratic-style dialogue between a character called Chesterton and the narrator, Karinthy wrote:
  • “One of us suggested performing the following experiment to prove that the population of the Earth is closer together now than it has ever been before. We should select any person from the 1.5 billion inhabitants of the Earth - anyone, anywhere at all. He bet us that, using no more than five individuals, one of whom is a personal acquaintance, he could contact the selected individual using nothing except the network of personal acquaintances. For example, ’Look, you know Mr. X.Y., please ask him to contact his friend Mr. Q.Z., whom he knows, and so forth.’”

Karinthy then tried to trace acquaintance-chains between himself, Nobel Laureates, and even “an anonymous riveter at the Ford Motor Company,” whom he believed he could reach in four jumps.

The six-degrees meme then split and went two separate directions, one in mathematics and one in literature. Both were slow-burning and murky. In mathematics, the idea was termed “the small world problem ” after the outburst we make when we discover a completed acquaintance chain. (“Wow, what a small world!”). In literature, a much more artful phrase was born in the title of a 1990 play by John Guare, titled “Six Degrees of Separation .” iii
  • I read somewhere that everybody on this planet is separated by only six other people. Six degrees of separation. Between us and everybody else on this planet. The president of the United States. A gondolier in Venice. Fill in the names. I find that a) tremendously comforting that we’re so close and b) like Chinese water torture that we’re so close. Because you have to find the right six people to make the connection…I am bound to everyone on this planet by a trail of six people. It’s a profound thought.

Bound to everyone on this planet by a trail of six people. A profound thought indeed. Although Guare’s work inspired a motion picture, a breakthrough online social network called SixDegrees.com , and later even a TV series directed by J. J. Abrams, he inadvertently threw off the emerging scientists of network theory by attributing his idea to the wrong source. Instead of citing Karinthy or others in the humanities, he attributed it as late as 1999 to Guglielmo Marconi, iv who with Karl Braun won a 1909 Nobel prize in physics for their work on wireless telegraphs. Unfortunately, Marconi did not in fact, propose a network theory in his Nobel acceptance speech v or anywhere else. By 2010, Guare began attributing his idea more appropriately to Stanley Milgram, vi but that’s getting ahead of the story.

Guare could be forgiven, in a sense, because the mathematicians who were in fact tackling the six-degrees prediction stayed underground with their work for, incredibly, over 20 years. Those scholars were Ithiel de Sola Pool and Manfred Kochen from the University of Paris. Around 1958, they had begun a manuscript that just seemed to raise more questions than it answered. Thus it stayed under the table in unpublished form. De Sola Pool took a job at MIT and convinced young Michael Gurevich to do his dissertation on the topic in 1961, vii but it would still be until 1978 before they published “Contacts and Influence” in the inaugural issue of Social Networks , and even then with some pretty strong reservations. viii

Here are the essential aspects of their mathematical claim. Supporting the idea that all humans are connected in six jumps starts easily enough: if we each have 1,000 friends, then we have a million friends-of-friends, a billion friends-of-friends-of-friends, and a trillion people “with three intermediaries.” The entire human population must necessarily be connected to us with plenty of jumps to spare.

But de Sola Pool’s team had no empirical data on how many acquaintances we in fact have. The only sociometric studies available at this time had been done on kids in preschools. So they imputed the 200 number that Gurevich estimated (history ultimately proving him not too far off), and the prediction of six jumps held up, but they felt like this was a pretty big assumption.

Next, they realized they didn’t know how social classes and cliques might throw off their models. Class was hard to ignore here. In all likelihood, the six-degrees prediction struck so many as shockingly low (including Ouisa in Guare’s play) because it meant the lowest classes were only a few friends removed from the highest—despite all erstwhile efforts at segregation. Even if the poor and the rich weren’t completely cut off from each other, it seemed like their acquaintance chains should at least be longer than those from poor to poor or rich to rich. De Sola Pool’s model had to account for this. And it had to account for all the other cliques formed by race, ethnicities, neighborhoods, workplaces, schools, and fans of sports teams mingling in the same stadiums. In all, you see why De Sola Pool wrote, “The central problem that prevents an entirely satisfactory model is that we do not know how to deal with the structuredness of the population.”

They adjusted their models to account for structuredness best they could, but once again only with big assumptions about the number, size, and nature of classes and cliques. The biggest assumption of all was that they treated all of these social groupings exactly alike. Agonizing over these problems took years.

But the delay may have been fortuitous, because in the late 1950s, psychologist Stanley Milgram had visited de Sola Pool and Kochen in Paris and told them of a way they might test the six-degrees prediction by sending letters.

Milgram, the genius 1960s-era experimentalist, influenced all aspects of social psychology with a fearlessness inspired by trying to prevent another Holocaust. Around that time, Milgram had been tinkering with a lost letter technique in which he essentially hacked the postal service to assess prejudice. ix That story is for another day, but Milgram was emboldened to try to test the six-degrees prediction with real letters. (Milgram himself never used the term “six degrees of separation ,” preferring the term used by the mathematicians and network scientists to this day, “the small world problem.”) Rather than send letters through the postal service, Milgram’s idea was to send letters through the still undigitized network of social acquaintances.

So in 1969, Jeffrey Travers and Milgram made 296 letters. x They fully explained the purpose of the study on the outside of the envelopes: to see if the letters would get to an arbitrarily chosen target person, and to measure how many friends it took to get there. Anyone who got the letter was instructed to mail it directly only if they “previously met the target person and know each other on a first name basis.” Otherwise, they should mail the letters “to a friend, relative, or acquaintance,” whom they felt could get it closer, “but it must be someone you know personally.”

The target person was a stockholder living in Sharon, Massachusetts, whose name, address, employer, college, military service, and wife’s maiden name and hometown were disclosed in the document. In terms of network science , these details meant that the target was not a node, but instead a little weblet in a larger social graph.

Travers and Milgram started the letters with 100 Nebraskans who were stockholders just like the target, 96 additional Nebraskans recruited via the newspaper, and 100 Bostonians also recruited via a newspaper. You see what Milgram was doing here: he was trying to test how class and geography might affect the length of the acquaintance chains. But he and Travers already began to worry about the receptivity of people who were drawn into the study. The fate of many of the letters would be scientific black holes caused by apathy: abandoned file drawers, trash cans, or landfills. Bottlenecked and forgotten. So they instructed every participant who sent the letter on to also mail an enclosed postcard back to Milgram’s lab. Worse, they realized that incomplete chains were ambiguous in their interpretation: did they mean that no acquaintance chain existed to connect the two people? Or that it was too weak to pass a meme through? Or did incomplete chains mean that an acquaintance chain existed but was simply unknown to the people in it?

This bold first study itself limped into publication with imperfect results and Milgram’s frustrations. Seventy-nine letters never even got started, and two hundred thirty-two didn’t make it to the end. But of those that did, Milgram wrote, “The mean distribution is 5.2 links.”

Five point two. Shockingly low. And under six. The maximum length of completed chains was 11 jumps—still shockingly low. And the letters that didn’t arrive seemed to be killed by a lack of motivation to take part in the study, rather than be passed around in long chains or endless loops. In fact, incomplete chains had an average of only 2.6 jumps and a maximum of 14. There was no data here to suggest that the world wasn’t small, at least the small world of the American population. Karinthy wasn’t wrong. But Milgram’s study wasn’t enough to prove that he was right. Surely the next study came out soon after? No. Another 30 years would pass before anyone published a new mathematical model and tried to replicate this study.

But by that point, we had email.

Working at Cornell University in New York in 1998, Duncan Watts and Steven Strogatz (Figure 23-1) had figured out the math xi and a way to test all this online. The divergent backgrounds of these two scholars cast them perfectly in this tale of connection. Strogatz was a brilliant mild-mannered math student from Connecticut who, by his own admission, had more in common with his calculus teachers growing up than with girls. He was a tenured professor at the time he met Watts, who was a former Australian naval cadet just as comfortable sharp-shooting, rock climbing, and extreme skiing as he was building algorithmic models. Watts later worked at Yahoo! and at Microsoft. Strogatz would often marvel at the serendipity of global networks that even brought them together. xii
Figure 23-1.

Founding network scientists Steven Strogatz (left) and Duncan Watts (right).

Together, they had hit upon an elegant way to take into consideration both the “structuredness ” of our relationships (that greater likelihood of forming acquaintance-chains between “nearby” others in both the physical and social-stratification senses) as well as the many odd, unlikely connections we make in our winding travels. Their model started with the most structured network possible, a nightmare of insular provincialism really, in which we are connected to only a few nearby neighbors. These lattice networks are neat and comforting to look upon when they are drawn (Figure 23-2), but notice what happens when you try to pass a meme between any two points: it must traverse every link and node in between them in a long, laborious chain. This is not a small world, quite the opposite. When we only connect locally, we make the rest of the world more distant.
Figure 23-2.

Lattice networks in which each node is only connected to nearby neighbors. For (a), six jumps are needed to connect the most distant nodes; for (b), four are needed.

So Watts and Strogatz measured what happens when a few random, distant friendships are mixed in with these locals-only webs. They programmed their models to connect random pairs of people, just like what happens when we meet others in university dormitories or on business trips or sitting next to us at concerts, or soccer matches, or on ski lifts (Figure 23-3).
Figure 23-3.

A lattice network with the addition of a few random “small world” connections between nodes. The number of jumps needed to connect the most distant nodes is reduced to three.

Essentially, they took the opposite approach from de Sola Pool and Kochen, who assumed a globally-connected world and made exceptions for cliques. Watts and Strogatz assumed a world of cliques and made exceptions for globe-bridging friendships.

They got the idea from Mark Granovetter, who coined the phrase the strength of weak ties in 1973. xiii Granovetter argued that ideas will “traverse greater social distance (i.e., path length) when passed through weak ties rather than strong.” Insular groups of strongly-tied people can only share the same ideas over and over (even jokes). For a meme to travel, it needs those weaker, more fleeting connections that bridge distant sectors of the larger network. The formation of enough random ties eventually produces networks that look more like real life. They are the scale-free networks we talked about last chapter in which there is a huge range in the number of connections each of us has (Figure 23-4). Some of us remain connected to only a few local contacts, while others are hubs connected to hundreds of others, near and far.
Figure 23-4.

A scale-free network.

Watts and Strogatz immediately saw that the result of infusing a few random, weak-tie bridges into a lattice network was dramatic: those long chains that formerly connected any two nodes were now vastly shortened by these interpersonal shortcuts. This held true even with billions of nodes the size of the human grid. With relatively few of these bridges, they reaffirmed that the six-degrees claim was still mathematically plausible.

The key thing that shrinks the world is those random connections. Immediately, this tells you that if you want to go viral, look for ways to launch your meme to distant hot-spots. Tell the person sitting next to you on flights about it. Give talks at conferences in distant countries and semi-related fields. Set up satellite headquarters around the globe. The results could be dramatic. For example, Brazil turned out to be a huge hub for both Microsoft’s Hotmail and Google’s social network Orkut. Was that foreseen, or just fortunate?

Key Point

Recommendations of your memes to distant, random others in the social graph dramatically improve their chances of a viral cascade.

But the six-degrees myth really entered the global digital age when Watts went on to test it in email, working with colleagues Peter Dodds and Roby Muhamad. xiv Participants joined a web site where they were randomly assigned to one of 18 target persons spread across 13 countries. Some of the most notable targets were “a professor at an Ivy League university, an archival inspector in Estonia, a technology consultant in India, a policeman in Australia, and a veterinarian in the Norwegian army.” Using email, participants in the study were asked to pass a message closer to the target.

Despite the global scope, the average number of links was 4.05 for completed chains, and about 7 for uncompleted chains. Close enough to declare Karinthy and Guare correct. We are bound to everyone on this planet by a trail of six people.

Since then, a variety of other social media networks have been analyzed. Looking at the Windows Messenger network in 2007 (before Microsoft rebranded it Skype), Jure Leskovec and Eric Horvitz found that “A random pair of nodes in the Messenger network is 6.6 hops apart on the average.” xv

Then in 2011, Facebook data scientists analyzed their network of 721 million active users, reporting that, “as Facebook has grown over the years, representing an ever larger fraction of the global population, it has become steadily more connected. The average distance in 2008 was 5.28 hops, while now it is 4.74.” xvi

We can finally say with confidence that there is unlikely to be much more than six degrees of separation connecting everyone on Earth. The world’s foremost mathematicians and the world’s largest digitized social networks converge on the same truth. A shockingly low number of acquaintances connects us all.

Key Point

Your meme could be exposed to everyone on Earth, whether online or not, in as few as six degrees of recommendations.

So we give you the happiest possible bedtime story for an ardent innovator like yourself: it is mathematically and sociologically confirmed that you could invent a digital meme that spreads to 100% of the online population in the time it takes for six of us to make a recommendation. That absolutely could happen in less than an hour.

Why then, you ask, in the history of technology, have the fastest-spreading memes gotten to only 2 billion (out of 7) over a year or two? The main factor is our psychological receptivity to the acts of recommending and accepting the recommendations of memes. Memes come in all the time, but as you’ve seen, most get bottlenecked. On that point, the Facebook and Windows Messenger studies we’ve reviewed only look at networks of attentional channels in which memes could be recommended, not necessarily instances in which memes actually were.

Before we accept that Facebook has shrunk the world from six degrees of separation to five or four, xvii we’d like to see more studies of networks of people who influenced each other to spread an actual invention. Milgram was clear, you would only “become a participant in the study by sending the document on.” Acquaintance chains for him were comprised of people who would get a letter in the mail, actually read it, and actually send it on to someone who actually would too, despite how odd the letter appeared. Fully 22% of the chains were completed thus in his study, which Milgram viewed as a failure, although only 2% of the chains were completed in Watts’ email study. How many recommendation chains would be completed in a study of Facebook?

In short, we’d like to see more studies not of six degrees of separation , but six degrees of recommendation . By analogy, dropping the criteria that people influence each other might be about as undermining to this myth as dropping the criteria that actors appear in the same movie as Kevin Bacon in the game “Six Degrees of Kevin Bacon .” Just driving by his house in Hollywood doesn’t count. Any tourist can do that. In network terms, your models cannot just look at the presence of links (or edges), but they must account for the strength of those links and the receptivity thresholds of the nodes, and ultimately, networks in which a signal is known to have passed. The point is, relaxing the definition of an acquaintance might make the world more connected only because the people are less so. If Milgram’s and Watts’ studies are still the best we have, let’s do better.

But the possibility of a total global cascade is there. Now it’s up to you to get to work to take advantage of it. Perhaps the rapidity and reach of “trending” memes will decrease in the manner of Moore’s law. Justin Bieber’s “Sorry” video reached 2 billion views far more quickly than Psy’s “Gangnam Style ” did. Pokémon Go had a good run in 2016. But one day all that will be long ago, and perhaps, seemingly very slow. And perhaps there should be two awards given, the Dawkins award for the meme that spreads the fastest and the furthest, and the Maslow award for the top-trending meme that people, on some level, actually need (Chapter  13).

To get there, you’ll need to get serious about aligning your innovation with user psychology and increasing your memetic fitness and our receptivity. You’ll need to hire memetic engineers. The tantalizing truth of the small world is that global cascades are possible in theory, but still quite challenging in practice. Network science sets the stage, but psychology is still needed for you to see how the play ends.

Notes

  1. i.

    Microsoft Corp. (2016, Dec 4). Microsoft by the numbers. Retrieved from http://news.microsoft.com/bythenumbers/planet-office . Richter, F. (2013, February 12). 1.17 Billion People Use Google Search. Statista. Retrieved from https://www.statista.com/chart/899/unique-users-of-search-engines-in-december-2012/ . Facebook, (2016, September 30). Company info. Retrieved from http://newsroom.fb.com/company-info/ .

     
  2. ii.

    Karinthy, F. (1929). Chain-links. Everything is Different. Budapest: Athenaeum Press.

     
  3. iii.

    Guare, J. (1990). Six degrees of separation: A play. Vintage.

     
  4. iv.
     
  5. v.
     
  6. vi.
     
  7. vii.

    Gurevitch, M. (1961). The social structure of acquaintanceship networks Doctoral dissertation. Massachusetts Institute of Technology. Retrieved from http://dspace.mit.edu/bitstream/handle/1721.1/11312/33051044-MIT.pdf?sequence=2 .

     
  8. viii.

    de Sola Pool, I., & Kochen, M. (1978). Contacts and influence. Social Networks, 1(1), 5–51.

     
  9. ix.

    Milgram, S., Mann, L., & Harter, S. (1965). The lost-letter technique: A tool of social research. Public Opinion Quarterly, 29(3), 437.

     
  10. x.

    Travers, J., & Milgram, S. (1969). An experimental study of the small world problem. Sociometry, 425–443.

     
  11. xi.

    Watts, D. J., & Strogatz, S. H. (1998). Collective dynamics of ’small-world’ networks. nature, 393(6684), 440–442.

     
  12. xii.

    Connected: The Power of Six Degrees. (2008). TV movie. Retrieved from https://www.youtube.com/watch?v=2rzxAyY7D7k .

     
  13. xiii.

    Granovetter, M. S. (1973). The Strength of Weak Ties1. American Journal of Sociology, 78(6), 1360–1380.

     
  14. xiv.

    Dodds, P. S., Muhamad, R., & Watts, D. J. (2003). An experimental study of search in global social networks. Science, 301(5634), 827–829.

     
  15. xv.

    Leskovec, J., & Horvitz, E. (2007). Worldwide buzz: Planetary-scale views on an instant-messaging network (Vol. 60). Technical report, Microsoft Research. Retrieved from http://research.microsoft.com/en-us/um/people/horvitz/msn-paper.pdf?q=network-buzz .

     
  16. xvi.

    Backstrom, L. (2011, November 21). Anatomy of Facebook. Facebook. Retrieved from https://www.facebook.com/notes/facebook-data-science/anatomy-of-facebook/10150388519243859/ . See also Ugander, J., Karrer, B., Backstrom, L., & Marlow, C. (2011, November 18). The Anatomy of the Facebook Social Graph. Facebook. Retrieved from http://arxiv.org/abs/1111.4503 . See also Backstrom, L., Boldi, P., Rosa, M., Ugander, J., Vigna. S. (2011, November 19). Four Degrees of Separation. Facebook. Retrieved from http://arxiv.org/abs/1111.4570 .

     
  17. xvii.

    Bhagat, S., Diuk, C., Filiz, I.O., & Edunov, S. (2016, February 4). Three and a half degrees of separation. Facebook Research. Retrieved from https://research.fb.com/three-and-a-half-degrees-of-separation/ . Note: Facebook found their network shrink from 4.74 degrees of separation in 2011 to 4.57 in 2016. To wit, Facebook users in 2014 had an average of 338 connections, over twice as many as is invited to the average wedding, and far higher than the 140 that evolutionary psychologists like Robin Dunbar have argued our cerebral cortex has the capacity to track in a meaningful way. See also Dunbar, R. I. (1992). Neocortex size as a constraint on group size in primates. Journal of Human Evolution, 22(6), 469–493.

     

Copyright information

©  David C. Evans 2017

Authors and Affiliations

  • David C. Evans
    • 1
  1. 1.KenmoreUSA

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