Culture Dish

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Every time I see that someone has joined the Six Degrees of Separation experiment group on Facebook (which now has more than 2.5 million people in it), I think about something I posted about on Culture Dish a few years ago: At this point, pretty much everyone knows the theory of Six Degrees of Separation:
That everyone in the world somehow connected through a chain of six
people. What most people don’t know is, the results from the study that supposedly
proved the theory were seriously flawed …


The phrase “Six Degrees of Separation” was coined by inspired by a study by Stanley Milgram
– the famous and controversial social psychologist who
originally conducted the Milgram Shock Experiment, examining people’s obedience to authority by testing
how many would administer potentially lethal electric shocks to
screaming victims (a study that was oddly just repeated).

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For his study,
Milgram asked people to give a letter to other people they knew by
name, then he tracked how long it took for each letter to end up in the
hands of a person the original sender didn’t know in another city. He
reported that the average number of people it took to get from the
sender to an unknown person was six. Hence, the phrase “six degrees of
separation.” But recently, someone looked into his data and didn’t like what she saw:

Judith
Kleinfeld, a professor psychology at Alaska Fairbanks University, went
back to Milgram’s original research notes and found something
surprising. It turned out, she told us, that 95% of the letters sent
out had failed to reach the target. Not only did they fail to get there
in six steps, they failed to get there at all. Milgram was a giant
figure in his world of research, but here was evidence that the claim
he was famously associated with was not supported by his experiments.

Which
if true would mean the whole Six Degrees of Separation thing is more fiction
than solid statistics (much to the dismay of the many the films, plays
and books written using Six Degrees as their driving force).  According to the BBC, several researchers apparently did similar studies to Milgram’s, but those studies all had the same
problem:

In the most recent, two years ago, only 3% of letters reached their target. “If 95 or 97 letters out of 100 never reached their
target, would you say it was proof of six degrees of separation? So why
do we want to believe this?” …”The pleasing idea that we live in a ‘small world’ where
people are connected by ‘six degrees of separation’ may be the academic
equivalent of an urban myth,” she says.

Kleinfeld has her journal article detailing the backstory of Milgram’s study and her findings about his research here.  It’s fascinating stuff (she’s also posted a shorter follow up here).

Comments

  1. #1 Stephen Downes
    January 15, 2009

    Actually, the people who write about it – like Watt and Barabasi – are pretty upfront about the flaws in the original study.

  2. #2 Joshua Zelinsky
    January 15, 2009

    The original study was hopelessly flawed but it is inaccurate to call it “fraud.” There’s a serious issue here; if a letter fails to arrive one doesn’t know if it failed because there was no connection or if it failed because the letter become possessed by someone who was lazy or misplaced it or something similar. It is unfair to Milgram to call the result “fraud.”

  3. #3 Christie
    January 15, 2009

    OK, but it’s also unfair to call it “six degrees of separation” when the reason the letter might not have gotten there was that it took 10,000 people, had absolutely no connection, or got lost along the way. That’s some pretty big misrepresentation of the study’s data.

  4. #4 The Science Pundit
    January 15, 2009

    Perhaps the more accurate interpretation of the data is to say that the probability of the letter ever reaching its intended destination drops off precipitously if it hasn’t arrived after six people. Then again, I have no way of knowing how many of the ones that didn’t make it ever made it to the sixth person.

  5. #5 John Scanlon FCD
    January 16, 2009

    How about “354 degrees of apathy”?
    (did you see I used polysemy there?)

    There’d be ways of tracking the package with wireless technology these days, and the apathy problem could be reduced with rewards for successful transmission, but how do you stop people surreptitiously Googling the target or calling directory assistance?

    In any case, the study may be hopelessly and irrecoverably flawed but has still had a huge influence on network theory and popular culture. That may be enough.

  6. #6 Martin
    January 16, 2009

    I’m sorry, but a number of the claims in this blog entry are simply wrong, and to quite a spectacular degree.

    “The phrase “Six Degrees of Separation” was coined by Stanley Milgram” – Actually it’s been associated with several people, most likely John Guare. It certainly has nothing to do with Milgram’s Small World Experiment. In fact, I challenge you to find me one single instance of Milgram using this phrase anywhere.

    “95% of the letters sent out had failed to reach the target” – Again not true. If you actually read the paper in Sociometry, the success rate was 64 / 296 papers, or 21%. The 95% figure is either a fantasy, or perhaps came from Milgram’s earlier, non peer-reviewed attempts.

    But the worst mistake by far is this claim: “What’s interesting is that several researchers did follow up studies and claimed to find similar results, but those studies all had the same problem as Miilgram’s.”

    Utter nonsense. The study has been replicated many times in social networks, often using complete sets of data – for example actors in the IMDB, links between websites, academic papers, friendships on social networking sites, and all find the same network characteristics, and similar degrees of separation. To claim that the small world theory is a “myth” and unsupported by evidence is simply wrong. It’s junk science of the worst kind.

    And Kleinfeld doesn’t seem to understand the theory anyway. The comment, “not only did they fail to get there in six steps”, seems to confuse average path length by network diameter. I’m pretty sure Milgram never claimed that you could get from anyone to anywhere else in six steps. Clearly the diameter of a social network (the longest possible path) is likely to be substantially larger than the average path length.

    Fair enough, I accept that the research was limited, but in fact a 21% response rate is fairly substantial in comparison with other forms of survey like opinion polls, certainly much more substantial than the nonsense 3-5% figure that Kleinfeld invented, and the findings are accepted because they have been backed up again and again and again by solid evidence, often with complete data.

    If you’re going to make such a strong claim as saying that one of the most well-known theories in complexity science is a “fraud”, then you really ought to research your topic and make sure that you know what you’re talking about beforehand.

  7. #7 Skloot
    January 16, 2009

    Martin: You’re right that Milgram didn’t actually coin the phrase — it was just based on his work. I’ve corrected that above. But you’ll have to take up the rest of your complaints with Kleinfeld — those are her claims and quotes you’re criticizing. I know that plenty of people have stood up for the Milgram study in the past, but the numbers Kleinfeld cites make it hard to imagine why.

    I’m on the road right now, as I said in my last post, so this and other posts that are going up while I’m gone are old archival posts I wrote years ago. I may look into your criticisms of her work to see what’s behind them when I’m back from my travels. But the flaws in the original study seem to be widely accepted at this point — as another commenter pointed out above.

  8. #8 Me
    January 16, 2009

    Well if one of you lot happen to stumble across my wheelie bin that was pinched in the night do let me know.

    Someone is bound to know someone who probably knows someone and eventually someone will know who the chuff took it.

  9. #9 Christie
    January 16, 2009

    Still, as a molecular biologist, if I simply excluded 79% of my data in the analysis I’d never be published. How is that not a really, really big deal?

  10. #10 Coriolis
    January 16, 2009

    The % of data excluded by itself doesn’t necessarily mean anything across fields. If you were a particle physicist and you included 21% of your data in a paper it would be (several) very thick books. In practice they use a very small amount from the vast amount of data collected.

    In any case there is a whole field of network/complexity science dealing with these subjects and the “6 degrees separation” thing is mostly just the popular face of it. Many different networks have been examined and the fact that for real systems there is a shorter average distance between nodes (nodes=people in this case) in the network than one would have in a random system has been shown repeatedly.

    I personally don’t have a very high opinion of the long-term utility of the whole network/complexity thing, but whatever issues there are in Milgram’s old work wouldn’t change any of that.

  11. #11 Phil Goetz
    January 16, 2009

    Martin, your observations may be right, but you could have made them without being so rude.

  12. #12 Mark P
    January 16, 2009

    Not my field, and who cares anyway, but people seem to be conflating the popular idea that everyone in the country (world? universe?) is separated by an average of six people, and an entire area of research called “network/complexity science”. Saying that the first is not true is not saying that the second is not true (or is invalid).

  13. #13 laurawallace
    January 16, 2009

    Six degrees of separation is an idea. It has been used as a theory and in literature especially with John Guare’s book Six Degrees of Separation.

    The funniest treatment of this idea is the Kevin Bacon book , tying Bacon in with all these actors ,in 3-6 steps usually .

    It is not a scientific theory, by any stretch. It is an idea that can be used creatively to connect people in a positive way.

  14. #14 Martin
    January 16, 2009

    I’m not entirely sure why the last comment I left was deleted, particularly since I linked back to the original paper.

    @Laura: I was referring more to the theory that social networks exhibit small-world characteristics.

    @Mark: Exactly.

    @Coriolis & Christie: I’m not particularly defending the 21%. What I’m pointing out is that a) Milgram identified this problem is his original paper, and explained his approach to it, and it would be fair to at least mention this in a blog post that all but accuses him of fraud, b) other research used much more complete data, and c) it’s dodgy to cite somebody using the wrong figures without checking the primary source.

    @Phil: Sorry, but it’s annoying to see work in my field misrepresented, and it’s especially annoying to see it happen on ScienceBlogs.

  15. #15 Sandra_r
    January 16, 2009

    Panic over. My bin turned up. I knew this 6 degrees of seperation was bollocks, it was hidden in the next street.

    O/T ohh isnt she pretty!?

  16. #16 William O'Connor
    January 17, 2009

    People simply are not connected to each other closely. The reason such myths as “six degrees” occur is because of the basic need in the human psyche to establish connectivity, and the elementary desire for closeness. But that close connection doesn’t really exist, and although a certain few needs are universal—like the need for belonging to a harmonious community and communication, the majority of needs and wants are not universally shared—they are special to distinct groups. We have become different due to genetic drift and we will become even more so in the future.

  17. #17 Calton Bolick
    January 18, 2009

    But you’ll have to take up the rest of your complaints with Kleinfeld

    Actually, given that you chose to write about it approvingly, you can’t dodge responsibility for your own words. Even worse, I can’t find the word “fraud” anywhere in the links you provided, and yet it’s the word you chose for your headline. “Fraud” is your characterization, and you’re the one who needs to stand by it.

  18. #18 Ken T
    January 18, 2009

    I don’t understand some of the responses here. Clearly if the majority of the letters didn’t make it to the intended target, the results simply don’t mean much.

    Maybe this kind of result has been duplicated in other media, but somehow I doubt it happened unless the results were sought out before hand.

    People’s relationships just aren’t neatly organized. We break into islands and share very little with those outside our subgroup. At least that’s my uninformed opinion.

  19. #19 idlemind
    January 18, 2009

    Utter nonsense. The study has been replicated many times in social networks, often using complete sets of data …

    And not a link in sight. Or a cite in sight, for that matter.

    I can’t find the word “fraud” anywhere in the links you provided, and yet it’s the word you chose for your headline.

    OK, what would you call it?

  20. #20 Ed Yong
    January 20, 2009

    Rebecca, you might get a kick out of Richard Wiseman’s modern take on Milgram’s experiment. He talks about it in his book Quirkology.

  21. #21 Atticus
    April 3, 2009

    If someone were to send a chain mail letter out to fifteen people, and each of those people were to send it to fifteen people, it would only take 8 round of those people to reach everyone in the entire world. Most people know more than fifteen people, and certainly have walked past more than just that. This means that, though the chain is weak, it’s more likely than not that everyone knows everyone.

  22. #22 patrick
    April 21, 2009

    It’s actually 6.6. Microsoft studied 30 Billion (with a B) instant messages and found that we are all only 6.6 degrees separated from each other.

    more info:
    http://www.dailygalaxy.com/my_weblog/2009/04/are-we-really-s.html

    Also, it would be good to learn the definition of fraud before declaring it.

  23. #23 Fred S
    April 30, 2009

    Ok my take on this 6 degrees of separation I belive in it more and more each day or aleast it might not be to far off cause of the people I know and have met in the music industry alone. Just to name a few countries from which these bands are from Japan, Holland, Canada, Austraila, Columbia, and Malta. Then with people I know that they know like I went to grade school with someone that is related to Katie holmes, my best friend’s brother was in Megadeth and played with Kerry King of Slayer. Just that right there probly covers most of the world but I know so many others that I do belive it is not to far off for the 6 degrees of separation. So if it is not true its pretty damn close if nothing else a very very small world after all.

  24. #24 Max
    May 21, 2009

    If you really think about it, this “theory” could be true. Maybe the number of “chains” is off, but everyone knows each other in directly. You can use a High School as an example. There is no one kid in that school that no body knows about. Every one is connected by the common fact they all go to that school. Now if you put that on a larger scale, Earth, there doesn’t seem to be a reason why it wouldn’t work.

  25. #25 Joe Pessarra
    May 23, 2009

    From Wikipedia, the free encyclopedia.
    “Six degrees of separation is the theory that anyone on the planet can be connected to any other person on the planet through a chain of acquaintances that has no more than five intermediaries. The theory was first proposed in 1929 by the Hungarian writer, Frigyes Karinthy, in a short story called Chains.”

    ============================================================

    We have begun keeping track of those occasions when we meet people, discuss mutual items of interest, including friends, and finding we do know some of the same people.

    On a recent Danube cruise, we met four people from different parts of the USA, who knew people that we knew.

    One was a couple from St. Louis, whom we we dined with on the first evening. After they found where we were from in Texas, asked if we happened to know a certain family. We did; they lived 4 doors away from us.

    On another cruise to the Orient, we were randomly seated with a couple from England. They knew the owner of a pub in a very small town in Northumberland, where our distant cousins live, and who introduced us to the owner on one of our many trips there.

    Just two of many such occurences for us. The theory is interesting, even if unproven scientifically for those who worry about that. But, we are still keeping track, just for the fun of it.

    Joe in Georgetown, Texas

  26. #26 Helen Denvir
    July 1, 2009

    I TOTALLY believe in this philosophy – I don’t profess to be a philosopher; (however, I do have a 2nd stage connection to someone who works in an industry whereby he has links to several well known people in the public eye). By logical analysis, these already well known people (via my 2nd link) all have their own links with even better known people et al, et al (to infinity and beyond – to paraphrase). From my own (and I stress this is my own) layman’s analysis, this could mean links to almost anyone – in the world. I am strongly tempted to test this theory as a social experiment – if only to prove my husband wrong – he doesn’t believe it at all.

    Regarding the latest post from Joe (Georgetown, Texas), we had a similar encounter on a local level. We met some people on a flight home from Gran Canaria last year when my daughter had travel sickness. We recognised their accent and found we lived in the same town and had mutual friends -I found it bizarre but it seems to happen to people all the time. We have to realise that with all our different new methods of communication that it is, indeed, a very small world after all.

  27. #27 Jason Atkins
    July 4, 2009

    I think the easiest way to prove the theory is a mathmatical equation

    Take the total population of the world – 6,706,993,152
    Use the root number of 6 (to represent the degrees of separation) and you get 43.43

    That means if you know 44 people (lets round it up) that don’t know each other and each person on average knows the same then you could get to anyone in the world in 6 degrees

  28. #28 Daniel Solnit
    October 31, 2009

    The problem with most comments on the Milgram experiment is that they don’t differentiate between the shortest possible pathway, which could well be six links, and the random pathway taken by the letters. Only by working back from both beginning and endpoints (both people) through all their networks can you realistically establish the shortest number of links. The assertion that we are only six degrees apart is NOT the same as saying that any random six links will always get you to another specific person. We COULD test this if we worked from both ends, using two random people, and fan out three degrees into each of their networks searching for commonalities. Anyone know how to write a search app for facebook?

  29. #29 Anonymous
    November 10, 2009

    The main issue that often gets neglected is that every individual on earth would have to be reachable or “on the grid” so to speak in order to be able to truly quantify the otherwise correct mathematics behind this theory. There are still highly isolated peoples that because of geographic circumstances rarely if ever make contact with the outside world. Taking this into account, the results would most likely show a much higher average.

  30. #30 Dale Preece-Kelly
    April 14, 2010

    Boy you started a minefield with this one. I guess as I’m number 29 that i must be connected to at least 5 people in this list. Anyway, I have just researched this whole concept for an article for my website http://www.selfhope.co.uk and I think to call it fraud is just OTT. I agree with some of the other writers in that the perpetrators of the experiments (regardless of what their other experiments were) were very up front about the flaws contained there in. In essence this is an absolutely mind blowing concept that can only be proved I think by trying it ones self (something I intend to do). I write a self help web site and I felt that this concept would be a comfort to a lot of my readers in so far as they need never feel alone again, because they are only ever 6 steps away from company. I’m off to send my first 6 degrees email . . . .who knows one of you may receive it on the way to its end target! Take care all, i’ll be seeing 5 of you aroun!

  31. #31 sara
    May 2, 2010

    Now you can discover your degree of separation with everyone in the world at http://www.digrii.com

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