# About Metcalfe's law

I sometimes use the Metcalfe Law in my work to describe how communication systems (mobile phones application, location-based services, etc.) have a value only if there is a critical mass of users. Being the only local boob with a fax machine does not allow you to go beyond showing off, it's actually like having one shoe. First formulated by Robert Metcalfe wrt to Ethernet, Metcalfe's law states that the value of a telecommunications network is proportional to the square of the number of users of the system(N2). It's then interesting to dig that stuff and see why very serious folks in IEEE Spectrum are pondering that argument. They actually critique how this "law" has been turned into a mantra during the Internet Boom (and now with the Web2.0 frenziness) and mostly focus on the correctness of its definition that sits in between linear and exponential growth:

"

If Metcalfe's mathematics were right, how can the law be wrong? Metcalfe was correct that the value of a network grows faster than its size in linear terms; the question is, how much faster? If there are n members on a network, Metcalfe said the value grows quadratically as the number of members grows.

We propose, instead, that the value of a network of size n grows in proportion to n log(n)."

(Taken from here)

But more importantly:

"

The fundamental flaw underlying both Metcalfe's and Reed's laws is in the assignment of equal value to all connections or all groups. (...) In general, connections are not all used with the same intensity. In fact, in large networks, such as the Internet, with millions and millions of potential connections between individuals, most are not used at all. So assigning equal value to all of them is not justified"

**Why do I blog this?** it's interesting to understand how such law can be criticized. I actually do think the cluster metaphor is still valid but one should be cautious about how to employ it (and take the limits they describe into account). Should there be a commonsensical use of that law and a more mathematical one (the latter.... to make quantitative forecast... which I am not into)?