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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."
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...
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"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.
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?
The government has a defect: it's potentially democratic. Corporations have no defect: they're pure tyrannies. -Chomsky
See, these "laws" aren't all that significant. They are more like "rules of thumb." These laws try to put qualitative values by using quantitative theories or computations. It's ridiculous.
For example, Moore's law means almost nothing now. Processor clock speed is only one aspect of the speed of a computer. It's still useful to gauge this as over all computer process speed, but soon that won't matter as much either. Even still, can you measure to the exact mhz that processing speed has exactly doubled in the past 18 months?
All these "laws" have no proof to begin with so how can one refute them? It's marketing and CEO level philosophy which exists in a world far outside of reality.
Metcalfe's law and this new law are both trying to measure how valuable a network node is. Hell, the value could be ZERO; for example, a pr0n leecher. Or it could be extremely valuable, like wikipedia. And to confuse it more, is citibank.com more valuable than walmart.com, and are both of them more valuable than whitehouse.gov or unicef.org? How does one measure value. And if myblog.com has a low value, but slashdot.org has a high value, don't these nodes offset each other and potentially refute the refutal?
But who really cares? I mean cmon... this is a stupid little law trying to be big and important when there's no need for a "law." It's marketing spin trying to make something more important than it really is. I would agree that the value of a network is more than the sum of it's parts, but trying to put a number to it is pretty stupid.
"All great wisdom is contained in .signature files"
It sounds like people are trying to use math where what they really want is economics. The value of a network is easily measured as what people are willing to pay for it and since this is governed by market forces which are complex and not necessarily "rational" there is no "law" for it.
If, and only if, you assign a mathematical meaning to "value" can you have any hope of coming up with a real answer.
For all intensive purposes, "whom" is no longer a word. That begs the question, "who cares"?
Actually, the original form of Murphy's law was something along the lines of "If it is possible to connect it backwards, eventually some stupid technician will." This was generalized into "Anything that can go wrong, will go wrong." The final word "eventually" was merely implied and not generally understood.
I have always been more impressed with a variant of Murphy's law that I attribute to Douglas Adams, but he didn't spell it out explicitly. "Anything that CAN'T go wrong is impossible to fix when it DOES go wrong." I first became convinced of the absolute truth of this when dealing with Plug'n'Play in Windows 95.
Maybe this is why the GP had to "study" this "law", as in, produce some intuitive definition of "the value of a network" and see if the "law" holds with this definition when N increases (and for what range of N). Then produce another "definition of value" (maybe for the different customer/situation/etc.). Rinse and repeat...
Paul B.
Except the "value" of a node is necesarily an average. Of the value of a given node to all of the other nodes, across all of the states a node will be in during the lifetime of the network. These networks' values are transmitted, changing each node's state (and value) over time. So the value proposition is necessarily dynamic. Metcalfe's n(n-1)/2 relationship still applies; the difference is that the value is really (n(n-1)/2)v where v is the node value. Call this "Ruby's Clause" to Metcalfe's Law: the law is still valid; this new research really just quibbles with the non-unity value of "v".
--
make install -not war
At best one would find an^2 to be valid, where a1, or perhaps some function with an asymptote. What is sure is that double the people with not produce four times as much work. Again, just reference the mythical man month.
"She's a scientist and a lesbian. She's not going to let it slide." Orphan Black
The reason this conclusion is significant is that Metcalfe's Law has been trotted out countless times to hype the capabilities of the internet. Given the result in the referenced paper, Metcalfe's law is meaningless with respect to the internet. As you point out, there are nodes of widely varying capability connected to the internet and so you can't use Metcalfe's Law to make any predictions/calculations about the value of it.
"Lack of technical competence coupled with the arrogance of power, as usual, leads to no good end."