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Metcalfe's Law Refutation Explained
sdpinpdx writes "According to this article in the July 2006 IEEE Spectrum Metcalfe's Law (that the value of a network is n^2) is wrong (it's probably only n log(n)). The authors speculate this had something to do with the .com bubble, and that their more conservative model might help alleviate the next one. The article includes an interesting quote from Metcalfe: 'The original point of my law (a 35mm slide circa 1980, way before George Gilder named it...) was to establish the existence of a cost-value crossover point--critical mass--before which networks don't pay. The trick is to get past that point, to establish critical mass.'" This would seem to be an update to a story we ran more than a year ago.
That law treats a network as if its only value is its interconnectedness. Especially while some nodes send more info than they receive, some nodes are more valuable, and some connections are more valuable. Unless the actual information transmitted has no value to the network.
Which is what I've gathered from Metcalfe's InfoWorld columns since then.
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make install -not war
Depending upon the uniqueness of each node.
Having two different Legal dictionaries offers less definitions than having both a Legal and a Medical dictionary.
Two bricklayers or two Carpenters may build a house slower than one carpenter and one bricklayer.
And a car wouldn't get very far if all it's wheels spun clockwise.
Back when computers were more specific purpose (This one is for Payroll, this one for Budget, this one for Customer tracking, this one for the actual Job...) linking them together had amazing potential, but now when an entire operation could be run off one machine (Quickbooks, Photoshop, Coreldraw, Web Browser, Fax server were all together one one machine I know of, and all critical for the business) there's not that much data that needs to move over a network to run the business.
Wikipedia, for example, would still be very useful even if it had zero links to external sites, because in itself it encompasses so much. Amazon does not need to offer links to other retailers, because they sell near everything.
Either I don't get it or this is virtual dick-waving. For what I'd say, it's not size that matters, it's how you use it.
It's not the number of connected hosts that tell you about the value or quality of a network, or how much can be accomplished with it. You can network the biggest LAN in the world and have it play Quake all day, I'd put my money on the 5 computers calculating some more primes back in the basement.
The value of a network lies in what it connects. Not in its size.
We used to have a Bill of Rights. Now, with the rights gone, all we have left is the bill.
According to the article (and common sense, because Metcalfe is not a short-sighted fool), Metcalfe acknowledges that his original reason for stating his "law" was simply to illustrate that even though small networks might not be interesting, once a certain size was reached, they would become compelling. For this, the distinction between n^2 and n.log(n) is pretty irrelevant -- the significant feature is that both are superlinear (as the article notes). Metcalfe was absolutely correct.
This is not to say he was unique in recognizing this, or that it'd be surprising for someone invested in selling networks to claim they'll become important. The point is he was not attempting to carefully quantify the scaling effects of networking. Rather, he had an instinct that said networks will be big when they get big. The quickest back-of-the-envelope estimate of the scaling law says n.(n-1)~n^2, so he used that for his talk.
When networks started to catch on, someone (the name is in the article but I'm too lazy to go back and look it up) grabbed ahold of this tidbit and named it Metcalfe's Law. Doing anything quantitative with this is ridiculous. It's obvious to everyone involved, Metcalfe included, that his "law" was just the simplest superlinear curve, not some carefully constructed value function. Even the new estimate -- n.log(n) -- is on pretty crude footing. I'm sure you can find a good analysis that gives this result, but there is so much ambiguity in what the value function should actually measure that it's hard to know you're doing the right thing.
Basically, Metcalfe was right. Networks grow in value faster than they grow in node size. His "Law" may be wrong, but it was just a heuristic to begin with. Anyone basing a business model on the details of that law deserved to have their bubble burst.