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.

Comments

grap theory , brookes' law, spherical chickens

[fermion]

One thing that people tend to do is take first approximations and limited domain fits and try to expand them to be a rule of life, the universe, and everything. Then when you try to explain that the chicken is not in fact spherical, they get really mad and call you a liar.

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 non-productive 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.

In defense of n log(n)

[E 99]

(Aside from the fact that 2^n and n^2 are both absurd in any kind of network I can think of), n log(n) has the advantage over all the other models mentioned in that it correctly gives a zero value for a network of one, which is not a network at all and obviously adds no value. Or if you want the combined value of the network and the networked, maybe it would be n + n log(n).