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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.
Hrm. The editors can't recognize that an article is a dupe of one submitted two days ago, but they can recognize that an article is related to one posted a year ago? Weird. :P
So what if I spend 10 minutes devising some silly and arbitrary, yet very simple formula to place value on something as subjective as the value of a network. But, I'll do one for patent lawsuits...though this formula will give the relative ignorance of the original patent, measured in PES-Bs (patent examiner smoke-breaks.) I think I will square it by LEMIs (Large Entity Monetary Incentives) and divide that by the total number of patents submitted in that CY (Calendar Year.)
So we get: (PES-B ^ LEMI) / CY Patent total.
Can I get that formula named after me??
Why go fast when you can go anywhere? O|||||||O
just kidding... try this one:
http://en.wikipedia.org/wiki/Metcalfe's_Law
It has been said that 63% of all statistics are made up
That law treats a network as if its only value is its interconnectedness. Especially while some nodes send more info than they receive, some nodes are more valuable, and some connections are more valuable. Unless the actual information transmitted has no value to the network.
Which is what I've gathered from Metcalfe's InfoWorld columns since then.
--
make install -not war
The internet isn't made of pipes you fool. It's made of tubes.
My only political goal is to see to it that no political party achieves its goals.
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.
"She's a scientist and a lesbian. She's not going to let it slide." Orphan Black
Either I don't get it or this is virtual dick-waving. For what I'd say, it's not size that matters, it's how you use it.
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.
We used to have a Bill of Rights. Now, with the rights gone, all we have left is the bill.
According to the article (and common sense, because Metcalfe is not a short-sighted fool), Metcalfe acknowledges that his original reason for stating his "law" was simply to illustrate that even though small networks might not be interesting, once a certain size was reached, they would become compelling. For this, the distinction between n^2 and n.log(n) is pretty irrelevant -- the significant feature is that both are superlinear (as the article notes). Metcalfe was absolutely correct.
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 back-of-the-envelope estimate of the scaling law says n.(n-1)~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.
So... what are the units of the result? Dollars? Web 2.0 beta credits?
Pipes, tubes, same difference. The real important thing is that we have those lottery balls to clean them out after the pocker chips get stuck.
Remember kids, tin foil doesn't work, so use LeadHat.
I don't know whether this post (+ the knowledge of the reference) or the fact that it was modded 'insightful' is funnier...
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(n-1)=2)v = 49,500 -- winner
Metcalf's Law as misused by dot-bombers: 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're probably right, but I thought I'd mention that one of the author's names I recognized as a top-notch mathematician: Andrew M. Odlyzko. I read about him in a book about the race to prove the Riemann Hypothesis.
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.
...the future crusty old bastards are already drinking the Kool-Aid.