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Is Metcalfe's Law Wrong?

In a recent issue of IEEE Spectrum magazine Bob Briscoe, Andrew Odlyzko, and Benjamin Tilly, three respected academics argued that the Metcalfe's Law - which states that the value of the network is proportional to the square of the number of users of the system - is wrong and dangerous.

Bob Metcalfe doesn't think so, and defends the Law and in a long chat argues that as the networks evolve, so does the law. Download the 26-minute interview here, and the transcript is available after the turn.

Transcript

Om Malik:

This is Om Malik from gigaom.com, talking to Bob Metcalfe, the inventor of Ethernet and the author of "Metcalfe's Law." We are talking today about the relevance of Metcalfe's Law in the age of social networking and what people are beginning to call "the long tail." Hi, Bob, how are you?

Robert Metcalfe:

I'm great, good to hear from you.

Om:

Nice to talk to you again. It's been a while, we haven't been in touch, but there seems to have been some controversy around Metcalfe's Law and how relevant it is. You're no stranger to controversy, but you've always been proven right. What do you think? What's going on this time around?

Robert:

I haven't always been proven right.

Om:

Okay. 80% batting average is pretty good. You've got David Ortiz kind of numbers there.

Robert:

[laughs] I'll take 80% then. Well, it is surprising, Metcalf's Law is about 25 years old, and there's an article currently appearing as a cover story in IEEE-Spectrum Magazine, that has about 385,000 readers. And the title of that article is "Metcalfe's Law Is Wrong." Every few years there seems to be an attack on my law and I feel obligated to defend my law. And, as you've guessed, the current context is social networking, where there's a suspicion that there's a network effect working to drive the proliferation of these social networks.

Om:

As somebody who's covered telecom for a long time I've always seen Metcalfe's Law as a purely telecom/networking phenomenon. How does it really relate to social networks like MySpace and how does it become irrelevant in this age of social networking? We've been social networkers since Adam said hello to Eve. That was social networking, right?

Robert:

That's right.

Om:

So what's the story here?

Robert:

Well let's go back 20 years to the humble beginnings of what much later became Metcalfe's Law, where I was trying to sell people on Ethernet. And I was selling these kits of three Ethernet cards, and some software where they can share disks, printers and exchange email. And after a few months of this, many of my customers reported that the little networks that they'd set up weren't very useful.

So I made up this slide, after some thought, which communicated that the cost of the network grew linearly, that is the cost was $1,000 to buy an Ethernet card in those days, but the value of the network grew as the square of the number of users. So that at some point, the critical mass point, the value of the network would exceed cost. And three nodes was not a big enough network, and they should try, say, 30 and see if that worked. And it did work, and Ethernet caught on. And a quarter-billion Ethernet switch boards were sold last year.

So that's where Metcalfe's Law came from. The value of a network grows as a square of the number of users and the way that that sort of gets applied in social networking is: you have a group of people who get connected and the more of them that get connected, the better. Can you quantify that? The Metcalfe Law is a vague attempt to quantify the benefits of hooking more and more people together.

Om:

OK. So, connecting devices, computers, nodes on the network which, as you had originally outlined, that makes a lot of sense to me. But how does it pertain to people? Now, let me actually expand on this. I had written a piece -- about two years ago -- basically saying Metcalfe's Law meets market reality. And I looked at eBay, because at certain points, you keep adding nodes. Or in the case of eBay, sellers, or the buyers for that matter, the value of that network started to degrade because there was too much crap coming online. And the network was beginning to get a lot of static, so to speak. There was a lot of static... so it didn't make a lot of sense. But in this case, in the social networks, isn't that what you're talking about? In Metcalfe's Law, you can only go up to a certain point and after that the social networks start to degrade. I mean, I can just sit here and say "There are six billion people on the planet, that's my social network because I'm a human being." Just trying to use your law into what are the online equivalent of off-line relationships, that just doesn't make sense to me.

Robert:

Well, the current attack on Metcalfe's Law in IEEE Spectrum, actually they call the law in that little article, which I recommend, they call my law "dangerous." Because apparently they're afraid that just the way Metcalfe's Law was used to inflate the internet bubble, the first internet bubble, that now suddenly with some connection to social networks it's being used to inflate the social networking bubble. And the authors re-argue the case and say that Metcalfe's Law overstates the value of a network and that in fact, in their case, the value only grows as n-log-n, instead of n squared. N times the logarithm of n instead of n squared, which is slower.

Of course they missed the opportunity to catch the point you just raised, which is it's possible there's a point after which the network's value starts going down, let alone going up more slowly. They argue that it just goes up more slowly than n squared. But one could -- and I haven't yet -- but one could look for ways in which at some point a network reaches and not only passes critical mass but at some point reaches a point of not only diminishing returns, but actually negative returns. Where spam, too much spam, too much e-mail makes it less valuable for its size. I think that would be a direction to go if one wanted to properly refine Metcalfe's Law.

Om:

Right. I mean, do you actually even look at it and say, "How are people applying a law that more pertains to actual, physical networks?" You know, as you defined them back in the day, being applied to something like MySpace or Bebo or one of these social networks. Where does the correlation come from? I don't even understand. Why are they wasting their cycles comparing those two things? You know, Andrew is a good friend. I don't know why he is spending time on equating these two things.

Robert:

Well, the trends...Metcalfe's Law is old now. So, it's been modified several times. So, you're right. The original 35mm slide which is in Andrew's article...which, but the way, it was George Gilder in 1993 in Forbes Magazine who called that slide Metcalfe's Law. But along the way the law changed to be the value of a network grew to be a square of the number of users. And you're right. It started as devices, then over the 25 years transmogrified into users.

So, it's valuable to you and me, I hope, that we're talking by phone. And this little phone I've got here would be more valuable if I could talk to two people or three people or four people. So, I don't agree with you that it would be inapplicable to social networks. That if a group of us have an affinity...some sort of affinity like we like the same book, the same candidate, the same idea, the same product... If we can be connected, that's valuable to us. And the more of us that can be connected, the more valuable it is. So, for example, in the eBay case, the more buyers and the more sellers that can be connected, the lower the frictions and the higher the economic activity, the more value generated by the lowering the frictions of us finding each other.

This, then, eventually leads to Chris Anderson's great book "The Long Tail" which is now out and I recommend highly. My argument would be that there has been a latent "long tail" of various affinities for a very long time. But thanks to the internet and then the world wide web on top of that, the cost of getting connected has gone down and more of these affinities have gone from latent to actual. That is, the cost of connecting has become low enough that the values have exceeded them. The critical mass has been achieved, so that's why you see this power "long tail" forming, because now those tiny little networks are now economic, or valuable, or their value exceeds their costs, where in the past they didn't, so those networks didn't form.

Om:

Right. So, here is one rub, though, that you didn't think about. Your version of the world, which is the Metcalfe's Law and the "long tail" are actually coming at...are polar opposites, right? The "long tail" is about a very finite network that works...I mean, it's looking at niches which work. So isn't that what...it's the exact opposite of Metcalfe's Law in a sense, that you're saying the more nodes we have on the network, the better we are. The network is better and more efficient whereas "long tail" is about having very defined, small communities or very small networks like micro networks, which add up to become one mega-network. So, can you explain a little bit about that? How do these...

Robert:

You can look at Metcalfe's Law in two ways. The original way of looking at it, and the way I'm now returning to look at it, it mostly applied to networks. Remember, I was selling Ethernets that were too small and having trouble. So I cam up with this concept which argued for getting above critical mass. So, the way I'm looking at this little law now is we're talking about when does the network achieve critical mass? When is it useful to have the network? When does the network pay off? And if you look at my little formula there -- the value growing as a square, the cost going linear -- there is a critical mass point. That is the number of users at which the network becomes viable. That critical mass number, I claim, is going down, which explains why the "long tail" is growing out. That is, increasing numbers of the smaller networks are becoming viable.

Om:

So, you're saying there are many Metcalfe's Laws at work in this world we live in, right now. Instead of there was one network and one network grows and now there are smaller and smaller networks, and they're being guided by the same principle as the original Metcalfe's Law.

Robert:

Yes, in an obvious desperate attempt to prolong the life of my law, I've now declared it to be recursive, which is to say there is a certain network value, associated with being on the internet, but then above that at a higher level, associated with each of the affinities that we might have, there's another opportunity for a higher level network to form, and there Metcalfe's Law is reapplied with a different set of coefficients.

And then, returning to this "long tail" concept, at say, this higher level. All of us interested in islands in Maine, for example. There must be a million of us and previously we could never find each other and it wasn't really worth being connected. But now we can form a blog about islands in Maine and be connected, and the cost of being connected is so low that now there can be this little network. And so Metcalfe's Law is reapplied at a higher level. And you can imagine it recurring again around a particular island in Maine, for those of us who are interested in these islands. We're in the community of Maine Island People, and now we're in a sub-community. And that network is now viable because of the decreasing cost and higher value of networking.

Have I made the point about this recursion of Metcalfe's Law?

Om:

Yes, I understand that. But there is one little thing which I am trying to... maybe in my puny little brain, it's not clicking... So, you're saying what used to be, in the old world, and you were talking about Metcalfe's Law, that the devices on the network, which were the PCs and the workstations, and then there was the network. Now, network, as it becomes the device, the Metcalfe's Law, its value has moved up the stack into the affinity groups, popularly called social networks, right now. Am I understanding? Is that what you're trying to explain to me, sir?

Robert:

Yes. There's a sort of a base-level network of being on the internet, then there's being a member of MySpace, a social network.

Om:

Right.

Robert:

So, when there were 11 people that were members of MySpace, apparently that network, whenever the hell it started, at some point MySpace achieved critical mass. It became viral and grew and it was worth it. It was worth going to MySpace, worth uploading your picture and your vital statistics. It's worth it for you do to that, because of all the other people you can now network with in the MySpace network. And my argument is that's a new occurrence, a new opportunity to apply the general notion of Metcalfe's Law, using MySpace as a network, rather than the whole world wide web, rather than the whole internet as a network.

Om:

So, there is the Metcalfe's Law, layer one and then there's Metcalfe's Law, layer two, and upon network upon network upon network. So as we grow, the pyramid grows. You're saying Metcalfe's Law actually mutates and adapts to that finite number of people in an affinity group or have similar social interest or whatever.

Robert:

Exactly. And that's why I wrote this little piece that I sent you, whose title is "Metcalfe's Law Recurses Down the Long Tail of Social Networks." That's sort of a recasting in this lame attempt to extend the life of my pitiful law. Sort of the modern version of it recursing. And social networks is a bit more than MySpace. I mean, a blog is a social network in a way. Are you using the term very specifically? Would a blog be a social network?

Om:

I think a blog is a social network. All of my friends in recent times, some of my newer friends, including folks like Mike Hirschland, I met through the blog. They were not introductions by other people. They were through the blog and that's my network. They are the people and they feel happy for me and they feel sad for me. So, that's my social network of sorts. So, yeah, I'm with you on the whole concept of affinity groups or social networks, and not confusing MySpace as the social network.

Robert:

Well, The New York Times used to be a -- well, still is -- a social network. But it was among very few big social networks because the cost of social networking, to be The New York Times -- was you had to have a printing press and you had to cut down trees and you had to have editors and you had to have truck to deliver the newspapers. And the cost of social networking was extraordinarily high, so you had very few newspapers. But since about 1994, when the internet kicked in, now you've got millions of newspapers. Every blog, I think of as a newspaper, with its own little community, its own little circulation, its own little audience. And why are there millions of blogs? Because the cost of creating that publication had gone to zero. You don't need to cut down trees, you don't need to have trucks, you don't need buildings and bureaus. You can just go to wordpress.com and set up your own blog and you're in business.

The cost of that network has come down, therefore the critical mass has come way, way down, so now there are many, many more publication networks that are viable, hence the blogosphere.

Om:

Right. So, why do you think this piece is saying that your law is wrong? You've talked about the relevance of Metcalfe's Law in our ever-changing world. What do you make of their contention that it's wrong? What's your thought on that?

Robert:

Well, I sort of have two thoughts. At one level I think they're wrong, and at another level, I think that the direction they're going.... I mean, I'm flattered that they would revise the law and accuse it of being wrong and even dangerous. That, I like. My law is "dangerous." So, I'm grateful for the attention. The reasons they give are weak. So, for example, by refining... you know the law states v as approximately n squared, but "No, no, no," they say. V is approximately n-log-n. Well, you know Metcalfe's Law has never been numerically evaluated. Nobody has ever taken a bunch of v's and n's and attempted to fit them with a curve or assess the content of apportionality on the law.

Unlike Moore's Law, for example, which has been numerically true since 1965. Metcalfe's Law has never been numerically evaluated. So, whether it's n squared or n-log-n, who cares? I'll stick with n squared until I see some data points. I've never tried data points, and in their paper in IEEE-Spectrum, again, there are no data points, it's purely a conceptual argument.

One of their conceptual arguments is that Metcalfe's Law can't possibly be true because big networks rarely find it in their interests to merge with smaller ones. They seem to attribute that phenomenon, that empirical data... They attribute that to some defect in Metcalfe's Law, when I think that the reason why the big networks don't merge with the little networks is not that they don't see the value. They have it in their heads that they're going to conquer the little networks and they're going to capture those users and they don't have to buy them.

So, anyway, they use that argument very strongly. They have a sidebar in the piece about that. But I think it's a very lame argument that they make. So, anyway, I think they're wrong. I'm flattered at the attention. But I think a more fruitful direction if you want to refine Metcalfe's Law is to go in the time domain. Metcalfe's Law is not in the time domain. Moore's Law is. You may remember Moore's Law says basically that all semiconductors get half the price in two years. Two years in time.

If you apply Moore's Law to Metcalfe's Law, now you're talking. Now you're going in a fruitful direction. Because that critical mass point that I theorize exists for each little affinity network, that critical mass point is dependent on the cost of networking and Moore's law is halving that cost every two years. So, therefore, the critical mass is halving in size every two years. And that's what's making Chris Anderson write about the "long tail."

Om:

Well, you know, there's a lot of things we can talk about the "long tail." I have my opinions about that. I kind of feel that the "long tail" is good for the distribution channels and not necessarily so for the content creators, who actually have to make a living. And it doesn't take into account the nagging practicality of making money to live. But that's a topic for another whole conversation. I cover social networks and I cover all sorts of random stuff and I'm seeing the bubble 2.0 form right in front of my eyes. But I haven't seen the Metcalfe's Law being mentioned in any of the presentations made by some of the start-ups in this space or the social networking players. So, where is this coming from? It'll be interesting to kind of just figure out how did they even actually arrive at this one. This argument, I mean.

Robert:

I think that maybe the Spectrum article is alarming us unnecessarily and that Metcalfe's Law isn't going to be used, isn't being used at all to inflate the new internet bubble, the social-networking bubble.

Om:

You know, I have not come across anybody talking about Metcalfe's Law in direct relation.

Robert:

Oh, I have. Since reading the Spectrum piece. There's the Spectrum piece, right there. But then you take the Spectrum piece and you start using Google and you'll find, as I did, 30 or 40 pieces relating social networking and Metcalfe's Law. How does it work or if it does work. And then there's various blog entries. I'll have to send you some of them. I just found them by branching off of the Spectrum article and doing a little Google, and found lots and lots of mentions of it. And you can imagine...you know, these social networks clearly are deriving energy from network effects. And since Metcalfe's Law about as simple an explanation of network effects as you can find, it's not surprising that people would occasionally mention it. And when they do, I'm delighted.

Om:

I was mentioning more of when I meet social networking start-ups or that kind of stuff. I never hear them talk about Metcalfe's Law. I mean, I bet most of them don't even know what it is.

Robert:

Okay, then the Spectrum piece is inflating the danger. And that there really is no danger from Metcalfe's Law.

Om:

You know, I may be wrong. I may have limited information. I'm just saying my personal experience. Well, you know it's been great talking to you. I'm glad you've written this piece and you've shed some light on the whole issue. Hopefully we'll be re-introduced in a few months and see where we're at. Thank you, Bob, for your time today. I know you have a very busy day tomorrow, so I won't hold you up for very long.

Robert:

Well, thanks very much. I appreciate the attention. Be careful about that new bubble that's inflating.

Om:

Okay, sir, I will. Thank you.

Comments

As a social networking skeptic, it's great to see a serious discussion of the issues rather than the hyperbolic raving either for or against that tends to cloud the arena. Thanks for going to the source - I wish more people would.

Excellent interview. Metcalfe defends his "law" much better here than he did at vcmike.wordpress.com. His law makes sense to me now. Thanks!