Metcalfe's Law Refuted

pdp0x14 writes "Cnet News reports on a powerful refutation of Metcalfe's Law (that the value of a network goes up with n^2 in the number of members). The academic paper is available at Southwest Missouri State University. Basically, the thesis is that not all the links in a network are equally valuable, so Metcalfe's argument that everyone can connect to everyone (n(n-1)/2 links, roughly n^2) is irrelevant. The authors propose nlog(n) instead, a much smaller increase."

Comments

"Refuted"?

[Anonymous Coward]

"Refutation" seems like almost as big an overstatement in this context as is the use of "law" to describe some wild-ass aphorism or a disagreement with it.

It's not like "value of a network" is some precisely measurable quantity.

Re:"Refuted"?

[susano_otter]

Not only that, but isn't this actually a case of "potential value" (not greater than the total number of possible connections inherent to the network - Metcalfe's Law) versus "typical usaage patterns"?

Networks are just like anything else in life. They have a maximal or optimal value, but most people don't bother trying to get full value out of them.

If Metcalfe were to say "the average mid-sized sedan seats up to five people, for which reason I value it as a five-person car", these guys would reply "yeah, but most people don't fill all five seats in their mid-sized sedans, therefore mid-sized sedans don't really seat five people after all... pwn3d!"

It's stupid. Metcalfe is talking about potential value. These guys are talking about typical utilization.

Andrew Odlyzko is godlike

[Paul Crowley]

It's a shame the summary didn't say who the authors are. Odlyzko is a Very Good Thing - he writes intelligently about everything from cryptographic number theory to making academic papers freely available online. I've long thought that n^2 was too high - though n log(n) sounds a little low...

Why call it a law, exactly?

[Gothic_Walrus]

I was a bit confused about the story at first, and a quick Google define proved that I had reason:

"A statement that summarizes the results observed in an experiment that is repeated many times by many different scientists. A scientific law is widely accepted as true or as a fact." -- Source

"A general principle or rule that is assumed or that has been proven to hold between expressions." -- Source

This can't be a law. It's been proven wrong, and unless I'm mistaken, it was never proven to be correct in the first place.

Why use the word law, then? Is it a misuse of the word? Generalizing? An attempt to confuse stupid Slashdotters like me? :)

Isn't this the same Metcalfe...

[Slartibartfast]

- who said that Linux sucks, and would die years ago
- who predicted the Internet would implode... years ago
- whose ego far outpaces his abilities?

[Check old columns in InfoWorld, c. 2000, for details.]

Granted -- he did some good stuff. But the truly good stuff he's done was so long ago that the only meaning it has in contemporary terms is a resume line item. Now he's just another VC talking head, with ego to match; to find that one of his "laws" doesn't hold water is about the same as saying that SCO's legal team isn't always on the level.

Re:Figures.

[grumpygrodyguy]

That's a lie and you know it!

Yeah, I think we all do. CS theory is just like math or logic theories. You start with a set of reasonable assumptions and then try to deduce a theorem. It's perfectly correct to say the value of the network increases at C*(node)^2 provided that you're talking about generic nodes. I.e. they are the same.

If you're folding or SETI'ing, the nodes with water-cooled FX-55s will obviously outperform the P3-700 nodes. Or in the case of data-sharing the 100mbps connected nodes(the link between the main ISP hub and all customer hub would be considered a node) will clearly outperform the 1.5mbps nodes. But nodes of variable value were not in Metcalfe's list of assumptions, so why argue about his theorem in cases like these?