Metcalfe's Law Refutation Explained 79
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 costvalue crossover pointcritical massbefore 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.
Whoa. A year ago! (Score:4, Funny)
When do we get a refutation of Godwin's law? (Score:3, Funny)
Re:Linky... (Score:5, Informative)
http://en.wikipedia.org/wiki/Metcalfe's_Law [wikipedia.org]
Re:Linky... (Score:3, Funny)
Re:Linky... (Score:2)
And we've both lowered the value of the netowrk by posting offtopic comments.
I suspect this demostrates that the value of a network is closer to 1/n^2.
Hmm, so what if (Score:4, Funny)
So we get: (PESB ^ LEMI) / CY Patent total.
Can I get that formula named after me??
Re:Hmm, so what if (Score:2)
Re:Hmm, so what if (Score:2)
Re:Hmm, so what if (Score:1)
Re:Hmm, so what if (Score:1)
Re:Hmm, so what if (Score:1)
Just tell me... (Score:2)
Re:Just tell me... (Score:5, Funny)
Re:Just tell me... (Score:4, Funny)
Re:Just tell me... (Score:3, Funny)
Re:Just tell me... (Score:3, Funny)
 Tash
Vrooomm... [tashcorp.net]
Refutation? (Score:3, Funny)
Re:Refutation? (Score:3, Informative)
I'd say he's a pretty smart guy  I don't about practical or "street" smarts  but some smart people don't value money so highly.
Some Ns Are More Equal Than Others (Score:4, Insightful)
Which is what I've gathered from Metcalfe's InfoWorld columns since then.
Re:Some Ns Are More Equal Than Others (Score:1)
For example, email became less valuable when spammers discovered it.
Re:Some Ns Are More Equal Than Others (Score:2)
Re:Some Ns Are More Equal Than Others (Score:2)
Place a negitive value on some nodes, that a major spamming node may be worth a 10 on the network. It will soon me clear that Metcalfe's Law is an easy solution to the problem  neat, plausible, and wrong.
Re:Some Ns Are More Equal Than Others (Score:2)
Almost as insightful as TFA! (Score:2)
Now their assumed distribution might be a little naive, and certainly seems to have been chosen because it results in a relatively clean derived formula, but that's academic. This is a refinement of the orginal observation. A higherorder appro
Value could be variable. (Score:3, Insightful)
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.
Re:Value could be variable. (Score:1)
Yeah, but what if there were no incoming links  HTTP_REFERRER and HUMAN_EYE links? All of those links give Wikipedia its value. If there were no readers, there would be no value.
Re:Value could be variable. (Score:1)
Uh, they all DO spin in the same direction (unlike the other examples where things are actually different)  what changes is your point of reference, looking from a different side
Re:Value could be variable. (Score:1)
However, 27 carpenters and 46 bricklayers may build a house slower than one "special class" shop student who isn't allowed to handle anything "pointy."
Unless they "cooperate" by assigning 70 people to go for coffee and donuts, at which point the house may stall at the meeting stage when all the time available gets used up argueing over who gets to drive.
KFG
Re:Value could be variable. (Score:1)
Dixie express (Score:1)
And a car wouldn't get very far if all it's wheels spun clockwise.
It's called NASCAR, and you're right: the race tends to tend exactly where it began.
Re:Value could be variable. (Score:2)
grap theory , brookes' law, spherical chickens (Score:5, Interesting)
The thing we seem to know from things like process control, is that it takes a finite amount overhead to manage any group, and a very finite amount of resources to bring an outsider into a group. This is Brookes; Law, that says bringing more people onto a late project will only make it later. We see this action around us right now.
What I find most fascinating is how easily people will allow themselves to be deluded by a model, even though the reality is all around them. If we look at something like graph theory we see certain features. For instance, no one has an extremely large number of close friends. Most of us have what can be considered concentric circles of people we know, each group out is usually bigger, but more loosely connected. Communicating with the outer circles are very inefficient. Business are arranged the same way.I think what confused people is that the internet, like the telephone, made geographic distances less important, so it is easier to keep up communications with someone across the world, but that does not mean that the person's ability to relate has been increased.
Additionally, not everyone, or everything, can competently complete all tasks, and not all processes can be factored to take advantage of all resources. At some point one is paying for overhead that does not deliver any added efficiency. I think this is what we are seeing in many international corporations. The corporation supports nonproductive real estate, managers, IT, which forces the productive parts of the company to work harder and be less responsive to market forces.
I would say that that a network initially has a n^2 benefit, but quickly transitions to nlog(n). This is not so. If anything cause the dot com crash, it was not understanding that at some point the overhead begins to be the dominant factor, and efficiency is lost.
How is this supposed to say a thing about value? (Score:5, Insightful)
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.
Re:How is this supposed to say a thing about value (Score:2)
However the network that he is talking about is not analogous to a LAN. Think of it more as a social network, like the six degrees of separation thing. Who you know matters very little until your network of friends gets to a certain critical size.
What he was trying to say with algorithm is that you can measure how valuable a social network, not computer network, is.
Re:How is this supposed to say a thing about value (Score:2)
If your network consists of few people who are a source of tremenduous insight, every single one of them, your network is small but its
Re:How is this supposed to say a thing about value (Score:2)
You don't get it.
The point is not that 10 granny smith apples tied together with string form a more or less valuable network than 5 crays. The comparison is between different networks of the same thing but of different sizes. And it is about the value of the network itself, not what the networked things accomplish. There is an underlying assumption that the metric under consideration values the networking; it is irrelevant that one can always think of a task for which netw
Re:How is this supposed to say a thing about value (Score:5, Informative)
If the node cost, x, is $100 and there are 100 users, n, then the cost for the network is $10,000.
If the single user business value, v, of the network is $10 for one user then the ROI for different valuation methods is:
Linear: vn = $1,000  no business case, don't even think about it
Metcalf's Law: (n(n1)=2)v = 49,500  winner
Metcalf's Law as misused by dotbombers: N^2 * V = 100,000  "Proves" selling frozen mud on the net is a winner
As restated by the authors: n long (n) * v = 2000  no business case, but better than a flat linear
There really are two problems here. The scaling formula and setting the business value. If you set the business value for a single connection greater than the cost of the network then it is a no brainer, but back when Metcalf as pushing networking that was a hard case to make and given how many people use /. at work that may still be the case.
you are deluded. (Score:2)
there is a difference in your numerical example only because it is misconceived.
Re:How is this supposed to say a thing about value (Score:2)
Um. That's not how BigO notation [wikipedia.org] works. O(n(n+1)/2) is the same as O(n^2). Constant terms don't matter. So your n log n might as well be 10n log n. Or n ln n. Or whatever. You can't plug in your n into the function and expect a useful number out of it.
A refutation of the Law, not of Metcalfe (Score:5, Insightful)
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 backoftheenvelope estimate of the scaling law says n.(n1)~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.
Re:A refutation of the Law, not of Metcalfe (Score:2)
Re:A refutation of the Law, not of Metcalfe (Score:1)
n.log(log(n))
In defense of n log(n) (Score:2, Interesting)
Re:In defense of n log(n) (Score:2)
Re:In defense of n log(n) (Score:1)
Re:In defense of n log(n) (Score:2)
Re:In defense of n log(n) (Score:2)
Re:In defense of n log(n) (Score:1)
Maybe because as n becomes large, a smaller percentage of those n(n1)/2 relationships are used in any reallife network. If you were going to start with n^2 there would have to be some inverse component added to the function to account for that.
With n^2, the nth user adds 2n1 value. That would mean that the next Internet user (the approx 1e9th)
Value? (Score:3, Funny)
Re:Value? (Score:2)
The same units as for ontological depth, by strange coincidence.
Re:Value? (Score:2)
Shit, I meant ontogenetic depth. Oops. :)
Re:Value? (Score:2)

Is it possible to refute such a hypothesis? (Score:2)
Different aspects of the network which have "value" scale different ways.
For example while the Internet has probably grown considerably since 1999, I don't really use more web sites regularly, or buy from more vendors than I used to. Yes there is Froogle and so on, but I'd
Re:Is it possible to refute such a hypothesis? (Score:2)
Let's consider two major online sales venues (The models will be idealized a bit, but...)
Amazon: Adding customers to Amazon does not really increase the value much to each customer, maybe Amazon is capable of getting better rates of bulk purchases from publishers, and is financially able to stock more books, but the growth of the value of Amazon is fairly linear with respect to number of users.
eBay: Adding users to eBay h
Does it really matter? (Score:1)
The REAL motive for the law... (Score:2)
authors' analysis doesn't just miss the boat... (Score:1)
That is: the authors' analysis is fundamentally flawed in a couple of different respects.
(1) They don't even attempt to establish an actual metric for the value of a network. Without that, any counterarguments to any previous assertions regarding network value that one might make are basically so much handwaving. (One can of course make the same objection to Metcalfe's Law, but saying "My handwavy claim is better than yours!" isn't much of an argument.)
On a
Re:authors' analysis doesn't just miss the boat... (Score:1)
Both models discussed are GROWTH models. You do not need a metric to model growth. If a child increases his height by 10% over the course of a year, he increases his height 10% in feet, meters, parsecs, lightyears, cubits. In
Re:authors' analysis doesn't just miss the boat... (Score:1)
Specifically:
(1) You do indeed need a metric to model growth, because unless you can agree on what you're measuring, you don't know how to tell whether (or how much) it's growing. That is: we know how fast the _network_ is growing; the question is how fast the _value_ is growing, and that's not meaningful unless you define "value". Your objection is not on point because you appear to implicitly assume that it's obvious what's being measured (which is true of a
I wonder if... (Score:1)
For example, does the community that forms around an open source project have n log(n) value where n is the number of members in that community?
What Metcalfe said a yearandahalf ago (Score:1)
http://www.networkworld.com/community/?q=node/635
That is so crappy (Score:1)
The inverse of Metcalfe's law (Score:2)
That's why may people prefer smaller mailing lists to larger communities, and in fact some topics simply can't be handled properly in large groups, even with moder
Well... (Score:2)
Kindergarten explanation (aka executive summary) (Score:1)
The number of lines to connect 3 dots = 3*(31)/2 = 3
The number of lines to connect 4 dots = 4*(41)/2 = 6
The number of lines to connect 5 dots = 5*(51)/2 = 10
The number of lines to connect n dots = n*(n1)/2 = Hey, let's just use an approximation this time.
Doing the math (Score:2)
So they were correct to pull a log function of of their ass, but they could have just as easily pulled out n*ln(n) or some other base. They made no attempt to "calibrate" th
Arguable better than N^2 (Score:2)
The option value of a network depends on how many groups can form using it. Every time a thousand specialized message boards like "people who audit for security in CUPS on Solaris" form, the network becomes more valuable. The number of possible groups is easy to calculate. A group can be represented as a bitmap with as many bits as there are endpoints, each bit representi
What ever happened to SCIENTISTS? (Score:1)