October 21, 2003

"Cites & Insights" November 2003, and math of six degrees of separation

Walt Crawford just published the November 2003 edition of his library 'zine (not blog) "Cites & Insights". It's excellent reading over many topics. More excellent, to me :-), is that I'm mentioned in three different places, in discussions of censorware, copyright, and perspectives on legal risks. I sent a few clarifications, though I don't think it's worth the space of going through the items for a post.

Rather, to do a change of pace, the discussion of the "Six Degrees Of Separation" idea caught my eye:

Once you leave a field, you need to look for other communities--and lots of us don't belong to that many communities. I'd be astonished if "six degrees of separation" for the world as a whole, or even for the United States, worked out in practice. It's a community thing. I'd be astonished if "six degrees of separation" for the world as a whole, or even for the United States, worked out in practice. It's a community thing.

The result is right. Formally, it's a graph-theory mathematical result. Given a graph of 6 billion nodes, and each node connected to (a few hundred? a thousand?) or so total other nodes, what's the average length of the smallest path between two nodes? I don't have a reference to the exact answer, but it's low.

The interesting experimental result of these studies is that estimating a good path in the real-world is actually practical. The key is that, while there's community clustering, people can figure out how to "route" a message across communities, if they want. The critical factor is figuring out the maximal jump per each link. As the results show, it's do-able.

Note asking "What's the number of hops for a connection"? is very different from "How many connections are made, versus die of disinterest?". That's akin to the issue of average life expectancy, where historically, there's a big difference between "Average everyone's lifespans, from 0 to 100", versus "If you survive childhood, how much longer do you live?" - because many people used to die around "0". And many message chains die around "0" too.

That is, overall, very few people may be interested in being routers (there's a lot of dropped packets). So if a path completes (every person is being a router), it has only a few hops necessary. But don't expect many paths to complete. Two different ideas.

By Seth Finkelstein | posted in infothought | on October 21, 2003 11:59 PM (Infothought permalink) | Followups
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An even better explication than in your email to me. "Two different ideas" indeed: just as the lead perspective in the issue was about the difference between provable availability of institutionally-archived papers and effective availability for non-specialist. Thanks: You're encouraging me (and others) to think more carefully, always a good thing.

Posted by: walt crawford at October 22, 2003 12:23 PM