Do you know my friend?

April 1, 2008 1:37 PM

Mathematics filter: What are the odds of a pair of my friends meeting another couple who are also my friends, but they have never met before? Bonus. This happened on vacation in another city where neither of them, nor I, have ever lived... Is this an example of six degrees of separation?
posted by Gungho to grab bag (16 comments total)

It's difficult to determine the odds of a pair of strangers meeting since this happens every day all over the world. Maybe we should try to figure out what the odds are of you having more than two friends, but in order to do that we'd need to know more about you. ;)
Seriously, though, I believe in order to calculate the odds we'd need to have more of a finite set.
posted by mcarthey at 1:44 PM on April 1

I don't think this is particularly mind blowing, given that you and your friends presumably have some social strata in common, and even if none of you live in that vacation city, you probably have some shared propensity to visit there.

I'm not a math guy, and I don't think there's enough in your question to actually do any math, but if you think the inputs into this calculation include all the people in the world, and all the cities in the world, my guess is the pools are much smaller than that, based on these shared characterstics (and others, such as the inclination to "meet" other couples on vacation).

I'm always surprised not these kinds of things happen, but by how much more likely they are to happen than one would intuit.
posted by stupidsexyFlanders at 1:46 PM on April 1 [1 favorite]

There is no way to calculate the odds you're asking for mathematically. Too many variables, too many of those variables are unknown.

But I think it's less unlikely than you'd think. For example; when I was 11 or 12 years old my brother and I were vacationing at Disneyland and would take the monorail over to the Contemporary Resort and play Gauntlet II for hours. So one day a pair of guys starts playing with us and they're talking to eachother about playing Gauntlet up at the 7-11 by King Street. My brother and I blink at eachother because we play Gauntlet too. At a 7-11. Near the entrance to a road named King Street. In Connecticut, 2000 miles away.

Turns out these guys live about a mile and a half from my brother and I and spend a lot of time playing the same Gauntlet machine in the same 7-11 that my brother and I play at, a couple thousand miles away.

Stuff like this happens.
posted by Justinian at 1:49 PM on April 1

This is correct:
I don't think there's enough in your question to actually do any math

This is not a valid argument:
But I think it's less unlikely than you'd think. For example...

Think about it this way.
Question: What are my odds of winning the lottery?
Answer: Less unlikely than you think! My aunt won the lottery!

All this argument really demonstrates is that unlikely things (winning the lottery, meeting somebody you know halfway across the earth, etc) actually do happen sometimes. One data point gives you no information about overall probabilities.
posted by number9dream at 2:01 PM on April 1

Justinian, In your example A meets B. In my example A meets B and through random discussion discover that they both know C.

I once heard an analysys of the Kevin Bacon effect where they assumed that people know somewhere around 100 people close enough that they may include them in random discussions etc., and that the original six degrees experiment only included about 45 people... IIRC. So given those numbers: That I know 100 people who know 100 people etc. Can the odds be calculated?
posted by Gungho at 2:04 PM on April 1

It's more common than you'd think.

When I was in my teens, I went to the Smithsonian Institution. In wandering around the Air and Space Museum, I got into a dusty area that was under construction, and found a small bookstore that was still open underneath all the plywood and plastic. You wouldn't think there was anything there. There was one other patron, and we struck up a conversation about how we'd lucked into the rather nice little store.

Turns out this guy not only lived in my state.... but also in my home town. After a bit more discussion, we realized that we lived about two miles apart, and that I had probably walked past his house on my way to school hundreds of times. But I met him only in the Smithsonian Institution in Washington DC, all the way across the country, in a nearly empty bookstore in a seemingly-empty wing... and never saw him again.

on preview: as number9 is saying, indirectly, the plural of anecdote is not data. Yet, the fact that two people in the thread have already posted similar experiences tends to be an indicator that it's not staggeringly unlikely, like quintillions to one or something. Nobody can give you a truly meaningful or precise answer. In the absence of hard mathematical fact, about all we can fall back on is handwavy guessing, and anecdotes may help us shave a few zeroes off the end of our imaginary large number. :)
posted by Malor at 2:07 PM on April 1

This thread has a bunch of info on the six degrees thing, including the original studies.
posted by thrako at 2:12 PM on April 1

We have an entire branch of our family that travels just to meet other members of the family under bizzare circumstances...like my cousin and I running into each other in an airport bathroom in SFO when we both lived in NYC. Or my uncle and sister running into each other in Quebec when neither knew the other was going to be up there (and we don't have relatives that they could have been visting up there either). Or my other sister running into the same Uncleand Aunt in Romania someplace while my sister was living in Paris and my Aunt and Uncle lived in NYC.

Same branch of the family, one of the cousins was living on a kibbutz in Israel and met a guy who lived around the corner from her, they'd never met before. Their wedding was beautiful.

We thought it was just us :)
posted by legotech at 2:29 PM on April 1

This is not a valid argument:
But I think it's less unlikely than you'd think. For example...

"I think" isn't an argument at all. If I was making an argument, I'd have done so.

That I know 100 people who know 100 people etc. Can the odds be calculated?

What odds are you looking for, precisely? How you ask the question is important; to me, the unlikely appearing part wasn't that two couples both happened to know you but that they met each other in a far away city. But I don't think you've defined the question very well.
posted by Justinian at 2:34 PM on April 1

This is bound to happen to each of us eventually, assuming we live long enough.
posted by toomuchpete at 3:02 PM on April 1

the chances of sitting beside a stranger on the plane who knows someone that you know are better than 50%... i read this in some math book as a kid and was always fascinated by the statement and wondered how they came up with that number...

having said that, i'm on about 10 to 50 flights a month and have never tested the theory...

hmm... i'll report back here next month and let ask.mefi know...
posted by dawdle at 3:47 PM on April 1

There's a great book called *Struck by Lightning* by a university of Toronto math prof named Rosenthal that discusses something quite a bit like your question, among other issues related to probabilities. His version is slightly different. He figures out the probability of running into a friend at Disney World when neither you nor the friend knew the other would be there. I don't recall the exact probabilities, but they weren't nearly as high as you might expect.
posted by trigger at 4:24 PM on April 1

Stop the World! I've been to DisneyWorld once, and I ran into a neighbor. Neither one of us knew the other was going. OK this is freaking me out.
posted by Gungho at 5:03 PM on April 1

The Odds of That is a fantastic (and quite lengthy, but in a good way) NYTimes piece that deals with coincidences. Covers everything from a suspiciously long list of dead/missing biochemists to situations like the one you describe.
posted by yellowbinder at 5:14 PM on April 1

"What are the odds? The mathematician will answer that even in the most unbelievable situations, the odds are actually very good. The law of large numbers says that with a large enough denominator -- in other words, in a big wide world -- stuff will happen, even very weird stuff. ''The really unusual day would be one where nothing unusual happens,'' explains Persi Diaconis, a Stanford statistician who has spent his career collecting and studying examples of coincidence. Given that there are 280 million people in the United States, he says, ''280 times a day, a one-in-a-million shot is going to occur.''

Throw your best story at him -- the one about running into your childhood playmate on a street corner in Azerbaijan or marrying a woman who has a birthmark shaped like a shooting star that is a perfect match for your own or dreaming that your great-aunt Lucy would break her collarbone hours before she actually does -- and he will nod politely and answer that such things happen all the time. In fact, he and his colleagues also warn me that although I pulled all examples in the prior sentence from thin air, I will probably get letters from readers saying one of those things actually happened to them. " - From the article I linked above
posted by yellowbinder at 5:20 PM on April 1

FWIW, I like to think about it like this, without specifically getting into numbers: if, before going on vacation you had said "Imagine I run into Juan's friend Pierre on April 4th at 3pm while on vacation in Vancouver. I've never met Pierre, heard of Pierre, and didn't know Juan had any friends on vacation in Vancouver." The odds of that happening are minuscule.

However, if you had simply said "Imagine I run into someone that knows someone I know", think about how large that pool of people would be, and therefore how much more likely it is to have happened.
posted by inigo2 at 5:48 AM on April 2