[dleslie]

They're talking about relations with one or more degrees of separation. A coworker's kid and an instructor of their own kids.

Including several degrees of separation allows one to find matches much more readily.

Perhaps you've played six degrees of Kevin Bacon?

[darkpuma]

If all the world is six degrees or less from everybody else, then we could perhaps say people have an average of 45 or so first degree connections to other people (45^6 == population of the world, approximately.) So at two degrees, there 45^2 = 2,025 people. That passes my sanity check.

So you've got less than 30 people in this thread accounting for let's call it 60,000 second degree connections in a world with 7,700,000,000 people and less than 300 people world-wide with the illness.

I don't know, even with birthday paradox stuff it still seems pretty unlikely to me. Even if we say half the population are losers with no friends and should be excluded from the calculation and therefore bump that 45 figure to 90, 90^2*30 is still a mere 243,000. If you knock it up to three degrees of separation with 90 first degree connections per person, then for 30 people you're passed 21 million which is getting somewhere I guess.

The numbers in the Kevin Bacon game grow very fast, but they still start out relatively small. And two degrees is relatively small.

[feral]

> If all the world is six degrees or less from everybody else, then we could perhaps say people have an average of 45 or so first degree connections to other people (45^6 == population of the world, approximately.) So at two degrees, there 45^2 = 2,025 people. That passes my sanity check.

45 is probably much too low.

Your model there doesn't take into account any clustering which is really important.

You want to think of a higher number of first degree connections (higher average node degree), but where there's a large overlap in the second degree connections each first degree connection provides (so you can't just do N^6).

[Cass]

On the web, there's usually a ratio of readers/lurkers to commenters of somewhere between 100 to 1 and 1000 to 1. So if 30 people comment on this article, that means 300 to 3000 are reading it. That means your second degree connections need to be two or three orders of magnitude higher.

[Retra]

They're not only checking two degrees though, they're checking as far as they can and just happen to find them within two degrees. So it's not "how likely are they to find them in two degrees", but "how likely are they to find them at any depth, and then given that they've found them, how likely are they to lie with two degrees."