Setting The Record Straight About Metcalfe’s Law

One can have a lot of fun these days poking around Wikipedia, discovering various types of inaccuracies and, perhaps, fixing them. But how should one treat a case where Wikipedia accurately reports on an otherwise inaccurate statement?

This thought comes to mind following an exchange I had over the past few days with Jimmy Guterman, editor of Release 2.0. In the latest issue Jimmy correctly quoted the common statement of Metcalfe’s Law, which, according to Wikipedia amongst others, states that “the value of a network is proportional to the square of the number of users.” It turns out that’s not what Bob Metcalfe, inventor of Ethernet, founder of 3Com and my partner at Polaris Venture Partners, claimed. I pinged Jimmy about this and he was kind to blog about it and spread the word. I explain what I learned from Bob about Metcalfe’s Law here (a post which was triggered by an IEEE Spectrum article that Metcalfe’s Law was wrong). About the same time, Bob also did a guest post on my partner Mike’s blog.

Should the Wikipedia article be changed? Should the original image from Bob be included in the article?

Original Metcalfe's Law formulationOriginal Metcalfe's Law formulation

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6 Responses to Setting The Record Straight About Metcalfe’s Law

  1. This is a very important contribution to the correctness of our common knowledge. Thanks!

  2. No need to correct the Wikipedia entry, imho 🙂 Great to hear an accurate rendition ‘from the horses mouth’ (you’re blessed to work closely with the Godfather of Networking), but the Wiki inaccuracies – mostly linguistic (devices vs users) are perhaps less important than the underlying principles, or even the ‘counter laws’ by the likes of IEEE Spectrum.

    There is a somewhat philosophic (and quite rational) justification of the extrapolation from small networks to the entire Internet, and from machine exchanges to social interactions. Sociologists have postulated similarly to (and independently from) Metcalfe that the possible one-to-one interactions in a community of N members is N * (N-1). This is more accurate than N^2 but asymptotically close.

    Now, if we don’t limit ourselves to 1to1 connections (many-to-many or ‘any-to-any’ is more like real life), the curve easily becomes exponential (rather than logarithmic, as the Spectrum bunch suggests). Quite easy to see, mathematically, what the Long Tail is all about.

    The Cost, on the other hand (back from humans to devices) isn’t linear, either. With economies of scale it slows down – bringing the critical point closer.

    But we shouldn’t separate ‘devices’ and digital networks from humans and social networks: any device and electronic network only exists to serve human neeeds. For the notion of Value of networks we can go back to Adam Smith (‘Value is only augmented or created in the process of satisfying needs’) and look at things in the context of current Internet and social networking trends, as Mr (Dr?) Metcalfe tries in his response to the IEEE Spectrum claims.

    Speaking of the ‘danger’ of quadratic growth is sooo-o ‘2007, like the Bubble 2.0 itself 🙂


  3. Vlad, I don’t entirely agree with equating devices and users. Some non-user-centric devices, for example, talk primarily to other non-user-centric devices. These have economies of scale of their own.

    Also, the key subtlety in Bob’s formulation is not about devices vs. users. It is about “compatibly communicating”. It is the communication (the links) that adds value (except for the case of spam, which is another subject). Adding more nodes adds value to the extent that they communicate meaningfully with other nodes. It is not something that happens automatically.

  4. Vladimir Dimitroff says:

    Fully agree- I’ve just been taking ‘compatibly communicating’ for granted (otherwise, what kind of communication network is it?).

    As to ‘non-user-centric’ devices talking to each other, yes – but they hardly do it for their own sake, there is a human aspect behind them. We may have to go into philosophic definitions of ‘What is Value?’ (Can there be Value from devices for devices? Perhaps in some sci-fi world, an AI-based civilisation of machines…)

    The sole undisputed component in the Law (and its variations) is Value –


  5. Denver Fletcher says:

    The IEEE article makes 2 fundamental errors, in my view, that render it somewhat less than convincing. Firstly, they seem to deliberately misuse the term “proportional” as if it means “equal” … the value of a network’s being proportional to the square of the connected compatible devices does not tell you when the crossover point to profitability occurs simply by calclulating the square. There are different cost structures in every network, and different ARPU’s (Average Revenue Per User) … so that each network owner must calculate these numbers for themselves.

    But sometimes it is easier to illustrate by means of the obverse: imagine the catastrophic loss of value implicit in disconnecting your country’s plain old telephone system (POTS) network from the rest of the world. (The anti-globalisation crowd would do well to consider that human trade is a network of energy exchanges, and that the more people involved in the network, the more value accrues to everyone involved. Bastiat wrote on this over 150 years ago. Following their long disproven ideas about protectionism would be the same catastrophic loss as mentioned above. But I digress: this is not about deriding their beliefs – that’s just a bonus- but about widening the applicability of Metcalfe’s Insight to more than just telecommunications networks.)

    The second error in the IEEE article is even worse, for with all the talk of dot com madness and foolery it strongly implies that an idea is disreputable simply because some who’ve held it are. Metcalfe, to my knowledge, never asked George Gilder to publicise or perpetuate his mistatement of Metcalfe’s Law – George simply did it for his own purposes.

    Frankly, I’d expect rather more in the way of clear thinking, and concise expression of such thinking, from people who pretend to positions of authority on such matters.


  6. Thoughtful comment, Denver. Thanks for contributing to the discussion.

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