Six n+1 degrees of separation.
September 12, 2006 12:41 PM   Subscribe

 
Judith Kleinfeld! I think I have a friend who knows her.
posted by Iridic at 12:49 PM on September 12, 2006


I think my friend knows your friend.
posted by ericb at 12:53 PM on September 12, 2006


I may be misunderstanding the article, but it seems like Kleinfeld is nuts.

Surely Milgram never said "if you send a letter to someone you don't know, it only takes six steps to get there." I interpreted it as "if you send lots of letters (most of which will never reach their destination), at least one of them will take only 6 steps."

Of course it's phenomenally unlikely that the first letter you send would reach the recepient in six steps; but to prove the whole "six degrees" thing all that would have to happen is for one letter to arrive in 6°.
posted by matthewr at 12:53 PM on September 12, 2006 [1 favorite]


Just because the experiment didn't work doesn't mean he was wrong in fact I don't see how it can work. You need a player who can see the big picture and all possible connections in order to create the chain. Just asking someone to forward a folder to someone geographically closer to the target is different from someone knowing that Bob who lives next doors neighbor is the uncle of the person in question. I ramble.
posted by zeoslap at 12:53 PM on September 12, 2006


What MatthewR said.
posted by zeoslap at 12:56 PM on September 12, 2006


He faked that experiment where he measured the charge of an electron too.
posted by GuyZero at 12:57 PM on September 12, 2006


Is Kleinfeld's source of contention the low response rate?

I'd be interested in knowing what sample size is required for Milgram to make his claim. I didn't see much about this in Kleinfeld's Society (2002) paper

In general, statistics doesn't require enormously large sample sizes if significance can be established (mathematically) within 95% or 99% certainty.
posted by Blazecock Pileon at 12:57 PM on September 12, 2006


A fraud? Hardly. That some of Milgram's letters failed to reach their target was simply a condition of the experiment's methodology. Of the letters that did reach their target, the characteristic path length was something less than 6, IIRC.

The BBC article is fundamentally confused. Milgram's experiment does not measure how well people forward letters (as the BBC seems to equate).

See updates to this research by Duncan Watts (Six Degrees) and Albert Laslo Barabasi. These physicists use large, testable network models to prove the basic discovered hypothesis of Milgram's research.

BBC got conned on this one.
posted by fstutzman at 1:03 PM on September 12, 2006


+1 to MatthewR as well.
posted by fstutzman at 1:04 PM on September 12, 2006


matthewr: I think Kleinfeld's argument is that "Six degrees" has reached the status of urban legend, and most people do understand it to mean "You are connected to everyone else by no more than six personal connections." That, obviously, doesn't square at all with the idea that if you send a lot of letters, one of them might go through only six intermediaries.

You said: "to prove the whole "six degrees" thing all that would have to happen is for one letter to arrive in 6°" What that proves is the assertion that "At least one pair of random people is connected by six degrees." If that's all the experiment shows, then how is it not completely worthless?
posted by rusty at 1:05 PM on September 12, 2006


From the last link:

In my view, the research on the small world problem suggests not a counter-intuitive triumph of social research but an all-too-familiar pattern: We live in a world where social capital, the ability to make personal connections, is not wide-spread and more apt to be a possession of high-income, white people or people with exceptional social intelligence. Certainly some people operate in small worlds, such as scientists with worldwide connections or university administrators (Garfield, 1979; Shotland, 1976). But many low-income people or minority people do not seem to. What the empirical evidence suggests is that l some people are well-connected and others are not, a world not of elegant mathematical patterns where a random connector can zap us together but a more prosaic world, a lot like a bowl of lumpy oatmeal.

posted by mecran01 at 1:06 PM on September 12, 2006


Whatever you do, Ms. Klien, do not let this man sleep in your guest bedroom:


posted by thanotopsis at 1:09 PM on September 12, 2006


From the Wikipedia entry:

Although the participants expected the chain to include at least a hundred intermediaries, 80% of the successfully delivered packages were delivered after four or fewer steps.

That's 80% of the successfully delivered packages, now. There's no indication in the article of what the overall failure rates were, but it seems like Milgram wasn't so concerned with those. A clarified restatement of the "Six Degrees" theory might go something like, "although the chances of initiating a successful letter chain are very small, the successful chains that do occur tend to be unusually short in length."

Now, Milgram could still have faked those results. But Kleinman's allegations of fraud--which seem to assume that Milgram's theory was about about the overall success rate of the letter chains--don't square with my interpretation of the theory. It seems to me that either Kleinman or the Wikipedia article (which is missing some citations) has a misunderstanding of Milgram's work.
posted by Iridic at 1:10 PM on September 12, 2006


Seems to me the experiment is actually testing people's abilities to find paths between their 6 (or whatever) connections, which is indeed an entirely different kettle of fish.
posted by MetaMonkey at 1:16 PM on September 12, 2006


if the average person knows 45 people by name then 6 degress is enough to (theoretically) reach everyone on the planet.
45^6=8,303,765,625 which is greater than the 6.5 billion current est. population of the planet.
Also, not that many people would be necessary to bridge groups.
posted by bashos_frog at 1:17 PM on September 12, 2006


just for info: Milgram gave 160 people who lived in Omaha Nebraska (which I thought was "en el quinto pino, in Spanish, but I digress!) a packet which contained the name of a stockbroker in Sharon, Mass., Each person was told to put their name on the package and forward it to someone they knew, who might be able to get the package closer to said stockbroker. So let's say you lived in Omaha but your cousin was in Uni in Boston, he might conceivably know people who might know the stockbroker.
Milgram found that most of the packets got to the stockbroker in 5 or 6 steps.

Sorry for stating the obvious but many people don't know the detail of the six degrees of separation experiment.

The most surprising thing, however, was that 16 of the packages were delivered by the same person (Milgram called him Mr Jacobs) to the stockbroker, while the balance were given to him by two other men, (Mr Brown and Mr Jones), showing that even when you select a random group, certain people are more "linked" than others.
So six degrees of separation does NOT mean we are ALL linked by six steps, it means that a very small number of people are linked to others in very few steps, and the rest of us are linked to the rest of the world through those special few.
posted by Wilder at 1:21 PM on September 12, 2006


Isn't this the Kevin Bacon appreciation thread?

No?
posted by QuarterlyProphet at 1:22 PM on September 12, 2006


commentary by Thomas Blass, University of Maryland.
posted by ikalliom at 1:27 PM on September 12, 2006


I was going to say what MathewR and Zeoslap said - although personally, I think the experiment would work much better if you sent letters to all of your acquaintances and they forwarded letters to all of their acquaintances and so on. Then you could measure how long it took those letters that reached the final destination. Of course, I am a lowly consultant and not a researcher, so what do I know?

Also, I checked once and I'm actually connected to Kevin Bacon by seven degrees. What does this mean?
posted by echo0720 at 1:32 PM on September 12, 2006


rusty: most people do understand it to mean "You are connected to everyone else by no more than six personal connections." That, obviously, doesn't square at all with the idea that if you send a lot of letters, one of them might go through only six intermediaries.

I don't agree.

I think semantics have confused your reply. The theory (as far as I can tell) is that everyone is connected to everyone else by no more than 6 degrees of seperation. That means that the optimal route has 6 steps or fewer. Of course there are millions of possible ways of connnecting Person A to Person B that take more than 6 steps, but that's got nothing to do with it. For example, you are connected to your best friend with 0 degrees of separation. The fact that you could construct a complex 7-step route of intermediate friends to get from you to him has nothing to do with it.

My take on this is:
The idea that everyone is separated by at most approximately six degrees predates Milgram. What Milgram tried to do was investigate the idea, in this case by using the idea of getting person A to contact person B by sending a letter through multiple intermediaries.

To show that Person A and Person B are connected by six degrees, Person A should send out an infinite* number of letters. If one or more of the letters reached Person B (to whom it is addressed) in fewer than six steps, then they are separated by six degrees.

If you tried this for every possible pair of people on the planet and found that one letter got through in < 6 steps for all of them, you would have conclusively proved the six degrees of separation. limited by resources, this is what milgram was trying to do (as far as i can tell). small>* Not strictly true, since the number of people on the planet (and hence the number of possible non-repeating connections, I assume) is finite. But the number must be really really big.
posted by matthewr at 1:37 PM on September 12, 2006


wilder: Milgram found that most of the [successful] packets got to the stockbroker in 5 or 6 steps.
posted by matthewr at 1:38 PM on September 12, 2006


It means you need to work in pictures, echo0720.
posted by cgc373 at 1:39 PM on September 12, 2006


Let's do our own 6. I know of a store in Harvard Square (MA, USA) that is called Ferranti-Dege Photography. It has been in business for 56 years. How many mefites have worked or shopped there?

So Why do I use F&D? Because I was once on top of Mount Vesuvious and was asked..Did you ever work at F&D?...No, but I shopped there.
posted by Gungho at 1:46 PM on September 12, 2006


Each person was told to put their name on the package and forward it to someone they knew, who might be able to get the package closer to said stockbroker.

The whole thing seems like it could be short circuited by passing the letter off to Milgram, Milgram to whoever was the go between for the double blind and from them onto the stockbroker, no? Everyone should have got there in 3 steps.
posted by juv3nal at 1:54 PM on September 12, 2006


Here's my old post about how researchers at Columbia University attempted to replicate Milgram's original study using email forwarding and a list of global "targets," not just residents of the United States. I tried several times to reach people in other countries, but the forwards pooped out after one or two tries.
posted by jonp72 at 1:57 PM on September 12, 2006


My interpretation of Kleinfeld's article is that Milgram's experiments: a) did not convincingly show what he set out to show (e.g.: did not provide sufficient explanantion of the chains which petered out) and b) were flawed in their design (e.g.: in the less-than-random selection of the starters).

These alleged flaws might not be such big deals in the grand scheme of things since these studies were among the first of their kind. You would typically follow them up with more rigorous experiments and replications. However, the more disconcerting thing which Kleinfeld uncovered is that there have been very few follow-up studies. In particular, the few comparable studies have indicated that there might be significant "barrier" effects at race and class boundaries. If this is the case, it would be useful to know if this "six degrees of separation" still holds or if it turns into something like "six degrees within your socio-economic class, but ten degrees without". Yet, the lack of replication means that we still have this gap in our knowledge.

In fact, the mere fact that the main pillar of this theory -- particularly the magic number six -- is a forty-year-old study which hasn't (apparently) been replicated in the last forty years should at least give one pause. Why six? Why not sixteen? Or sixty? If this is an empirical fact, shouldn't it be empirically reproducible?
posted by mhum at 2:03 PM on September 12, 2006


I'll jump on the bandwagon of those who say that it's not at all clear what Milgram-like experiments prove.

Even if the path length of the received postcards indicates something about the average minimum path between people in two cities in the United States, the acquaintance-distance from Omaha to Chicago is probably smaller than the acquaintance-distance from Omaha to somewhere in Africa.

It also seems likely that the average physical distance of first-name-basis people is bigger now than it was 100 or 1000 years ago--there was a time when nobody in the Americas knew anyone in Europe! Six degrees is obviously not a timeless truth about humanity.

Arguments about how few people we each know on a first-name basis don't tell us much either (I did a calculation much like basho's frog did)---If you and all your friends each know 45 people on a first name basis, the total number of people known is likely to be many fewer than 45*45=2025. In fact, if the 46 of you only know each other--no-one outside the group--that condition is still true!

Here's what I want to know: have you ever gotten an internet chain letter where your own name appeared in one of the last 6 slots? If so, did Bill Gates ever give you that free trip to Disneyland that the chain letter promised?
posted by jepler at 2:08 PM on September 12, 2006



posted by Joeforking at 2:11 PM on September 12, 2006


> Judith Kleinfeld! I think I have a friend who knows her.

Hee hee. And this is just a note to let you know you have a mefi co-user-friend who was a friend of a friend of a friend of a friend of Chairman Mao.

> Ferranti-Dege Photography. It has been in business for 56 years. How many mefites
> have worked or shopped there?

Fuller raises hand. Shopped there.
posted by jfuller at 2:12 PM on September 12, 2006


I know Google by its first name. I'm one degree away from everybody.
posted by blacklite at 2:13 PM on September 12, 2006 [1 favorite]


it occurs to me that an e-mail provider for a large number of people could determine the maximum distance between two customers along the graph defined by "A has corresponded with B". Of course, then we'd find that we're all separated by 1 degree, a spammer who used a machine in china to send us all giavra spam.
posted by jepler at 2:15 PM on September 12, 2006


Even if you were able to say you could get to the Queen in three steps, it would tell you little about how well you are really connected with her.

Hey, I'm connected to the Queen in 3 steps (and I'm not even British!).
Actually, I think most people are. The problem is, she never passes on those letters.
posted by sour cream at 2:24 PM on September 12, 2006


Three steps to the Queen?

Oh, a sleeping drunkard up in Central Park,
And a lion-hunter in the jungle dark,
And a Chinese dentist,
And a British queen--
All fit together in the same machine.
Nice, nice, very nice;
Nice, nice, very nice;
Nice, nice, very nice--
So many different people
In the same device.


-Kurt Vonnegut Jr.
posted by Iridic at 2:33 PM on September 12, 2006


What fstutzman said above: Watts and Barabasi have done much more (reliable...) work on this and also addressed the fact that most of Milgrams' letters never reached their targets.

Barabasi's book "Linked" and Watts' book "Six Degrees" are both really good reads. I'm not a network scientist, and easily got through both, however some it was related to my work. I'd say that Linked is more accessible to the general public.

(And I'm 2 degrees from Barabasi and 3 degrees from Watts so obviously I totally know what I'm talking about.)
posted by easternblot at 2:54 PM on September 12, 2006


I'm less than six degrees of seperation from Kevin Bacon, so I'm pretty much connected to the entire world.
posted by Astro Zombie at 4:10 PM on September 12, 2006


Whoops. Here's the proof.
posted by Astro Zombie at 4:11 PM on September 12, 2006


Of course it's phenomenally unlikely that the first letter you send would reach the recepient in six steps; but to prove the whole "six degrees" thing all that would have to happen is for one letter to arrive in 6°.

But that's a shit conclusion: "some people are connected to other people by 6 degrees or less". It doesn't even mean anything.
posted by cillit bang at 4:45 PM on September 12, 2006


cillit bang: The six degrees of separation thoery is:
"the hypothesis that anyone on Earth can be connected to any other person on the planet through a chain of acquaintances with no more than five intermediaries." [wp]

For any given pair of people, it may take several letters for the "right" five intermediaries to be found. What the theory posits it that, for any given pair, there exists at least one chain of five intermediaries who can connect them. The chances of finding a five-or-fewer-intermediate chain with the first letter you send is obviously pretty low.

What I was saying was that (if the theory is true): Everyone is connected to everyone else by six degrees of separation or fewer, but the chances of finding a chain of five or fewer intermediates with one letter (and a finite amount of time and other real-world constraints*) is very low.


* Assuming "No man is an island" and that no one kept the letter or received it twice, I suppose one letter would be guaranteed to find the intended recepient eventually. But it would take a very long time and sending lots of letters seems more sensible.

posted by matthewr at 5:12 PM on September 12, 2006


Judith Kleinfeld? Who does she think she is? I mean who does she know? She's an ill-bred lower-class nobody.

Not like that Milgram fellow. Clearly one of us. Enjoys his sherry, gives a firm & manly handshake, likes a bit of hide the sausage after dinner.

There's a man whose conclusions can be trusted! Here's to science!
posted by lalochezia at 5:42 PM on September 12, 2006


I'll second (or is it third) the recommendation to read Barabasi's booked "Linked" - it does a very good job of explaining the state of the art in network theory - the author of this article "debunking" Milgram might have done well to read it too.
posted by Zinger at 5:53 PM on September 12, 2006


matthewr, Milgram didn't send letters to all his friends to see how well he was connected. He gave them to strangers to see how well they were connected to the stockbroker guy. The "one letter getting through proves it" only works in the former case. One letter getting through in the latter doesn't prove a thing. At best, it doesn't disprove it.
posted by cillit bang at 6:23 PM on September 12, 2006


I watched a documentary a few years ago about a woman who somehow picked a random Mongolian herdsman, and then set out to find him to test the six degrees thing, all the way to Mongolia through random strangers. Pretty cool. Guardian story
posted by MetaMonkey at 7:10 PM on September 12, 2006


So how come Sars can't find Don?
posted by Biblio at 7:48 PM on September 12, 2006


Here's my old post about how researchers at Columbia University attempted to replicate Milgram's original study using email forwarding and a list of global "targets," not just residents of the United States. I tried several times to reach people in other countries, but the forwards pooped out after one or two tries.
I tried it too - all the people who I contacted initially deleted the messages because they thought they were spam.
posted by dg at 7:54 PM on September 12, 2006


This is a problem the Facebook can solve, almost certainly.
posted by rafter at 9:07 PM on September 12, 2006


From the Wikipedia entry: "The hypothesis was first proposed in 1929 by the Hungarian writer Karinthy Frigyes in a short story called Chains."
posted by semmi at 11:28 PM on September 12, 2006


I was always under the impression that 6 degrees was a mean, and not the upper limit. That is, I thought it meant that you could be associated on average with most everyone else in the world by 6 steps, but that it was understood that there would be outliers way above and way below this number. (Me and Kevin Bacon: 3 degrees)
posted by moonbiter at 12:03 AM on September 13, 2006


Hey, I'm connected to the Queen in 3 steps (and I'm not even British!).
Actually, I think most people are. The problem is, she never passes on those letters.


Just for fun I actually thought this through.

I know somebody who knows somebody who knows the queen of Denmark who knows the queen of England. That's 3 degrees, right?

I also know somebody who quite possibly knows somebody who knows the queen of England. I'm not 100 percent sure of this but I might be separated from her by two degrees.

Finally I know somebody who has spoken with the queen of England on at least one occasion and has had his picture taken with her. He probably wouldn't high-five her if he met her on the street, though, so I don't know if this counts. If it does, that's one degree.
posted by sveskemus at 2:51 AM on September 14, 2006


I rented a house from a man who runs part of one of the Queen's residences.

I slept with a man who slept with Douglas Adams. (Mr. Adams was drunk at the time).

I burned a hole in Ben Stiller's father's jacket (not really, he did it himself, but blamed me. At least his mom is nice.)
posted by Goofyy at 5:45 AM on September 14, 2006


In 1992, I had a beer with Kevin Bacon.

Damn, this game's no fun for me.
posted by bradth27 at 2:36 PM on September 14, 2006


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