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March 30, 2005
Meet My Mind, Metcalf
Interesting paper on why the value of networks is only n log n, instead of n^2 (Metcalf) or 2^n.
Their point is taken, but the example given is that n log n applies to the union of two networks of equal size n. It seems in that case that lots of new connections may be formed, more so than if each network grew on its own. I can agree to n log n in that case, but a large union seems to create more opportunities, but only in cases where there are chances at intercommunication.
In their Thoreau example, Maine may not have anything to say to Texas. But a large union of two networks makes this example brittle. It's as if Maine was suddenly moved next door to Texas. Then Maine has a lot more interest in what's going on in Texas, and vice-versa. Not only that, they find out that there's more in common between this Red state and Blue state than they thought. And then they form the MTFTA (Main-Texas Free Trade Agreement), and suddenly there's even more connections, more so than if Maine had never left the cold Northeast.
Of course, a network of earthworms, no matter how large (well, within reason here...), will probably not have much to say to Texas, regardless. Merge those two networks, and not much happens. So I believe, on average, that networks do grow n log n, but there seems to be edge cases where growth is greater. Early internet, blogs, usenet, etc. Not just merging two networks, but moving networks closer to each other.
That's hand-wavy discourse. To tighten things up a bit, I will say that networks grow faster if they share similar properties and the exposed/addressable surface area is increasing. Which explains my previously-stated cases of usenet, bbs, blogs, etc. New technology increased surface area of network that users/computers could address. Boom, n^2 growth for the network.
Sounds like arguments for open-ness and transparency too, then, huh?
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Posted by Noel at 08:18 AM
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