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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."
Anything that can be refuted...will.
Everyone knows that having a low Erdos-Bacon number is more valuable than having a high one, so the proof of this is trivial. Oh, wait, computer networks? Never mind.
---------The early bird gets the worm, but the second mouse gets the cheese.
It's not like "value of a network" is some precisely measurable quantity.
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...
Xenu loves you!
More like (n-k)log(n-k) where k is the frequency coefficient of That Big Dumb Guy Who Has Nothing Useful to Say.
You can read this law like this:
"hello, I'm Robert Metcalfe. I state that the value of a network grows exponentially to the number of nodes present in it. So the more nodes you have, the better your network. Oh, and incidentally, I'm the CEO of 3Com, a company that sells network cards..."
"A door is what a dog is perpetually on the wrong side of" - Ogden Nash
The link that the submission attributes to Southwest Missouri State University is actually at the University of Minnesota... (Not terribly surprising, given that Odlyzko is at the University of Minnesota!) Please correct the article accordingly.
Number of members: Millions
Value: Debatable
suso.org website/email hosting, no disk space quotas and personalized support.
It's common sense, of course, but worth taking note of.
-dave
http://millionnumbers.com/ - own the number of your dreams
Powerful refutation of Murphy's Law! It has been determined that not everything thing that *can* go wrong *does* go wrong. Using the Apollo 13 mission as a case study, it has indeed been shown that only a small fraction of the things that could have gone wrong indeed did go wrong.
NASA Scientists have now recast murphy law as, "There are a lot of things that can go wrong. Some of them might happen." Which, of course, shows that far fewer things go wrong than previously thought.
Scientists predict that this will have no effect on the size or scope of any government project or agency.
Slashdot itself is a good counter-example.
"I'm not impatient. I just hate waiting." - My Dad
Will we see Moore's law reduced to a log-based function as well? Will Brooks' Law be shown to be fallacious, leading to a large upsurge of temporary IT jobs? And how about Godwin's Law. Will we no longer have to fear the inevitability of Nazis or Hitler?
What will this all lead to... nothing but anarchy. Anarchy, I tell you!
We are the Music Makers, and We are the Dreamers of Dreams...
I was happily working on a project when my manager assigned two more people to the team, making us three in number. I'm John, I've got it all figurted out and would have finished the product. I now work with Bob. Bob talks too much. Always coming to me with silly questions and he never seems to quite "get it". I also now work with Tom. Tom is never available, he never answers his phone, and I swear he's cutting out at three on Fridays. I know you've been in this situation as well. We're a network, which I'd hardly refer to as peer-ro-peer. Our bandwidth may not be comparable to the study, but the general theorem is the same.
"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? :)
Goo goo g'joob.
- 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.
Especially the section on Zipf's Law.
Where I think Metcalf's Laws does apply is in an information network where no proprietary secrets exist. For instance, searching for technical documentation or a movie star's biography. In these instances, the value of the network, as measured by the immediacy with which one could obtain useful information by asking a question, is proportional to something on the order of n*n for n nodes.
Consider the network the top 10 search results in Google for all possible queries. Let's pretend for a moment that Google wasn't polluted with Spam. In this case, each node (search result) is providing a substantial amount of value to the network, although no matter how small or targeted the group, Zipf's Law will be observable to a degree.
Or consider if you had personal tele-access to every person on the planet and could ask any one of them a question at any time. Clearly here the value of the network is something on the order of n*n.
Most or all of Odlyzko's examples presupposed economic interests or constraints.
I Want To Believe