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## Metcalfe's Law Refuted225

Posted by Zonk
pdp0x14 writes "Cnet News reports on a powerful refutation of Metcalfe's Law (that the value of a network goes up with n^2 in the number of members). The academic paper is available at Southwest Missouri State University. Basically, the thesis is that not all the links in a network are equally valuable, so Metcalfe's argument that everyone can connect to everyone (n(n-1)/2 links, roughly n^2) is irrelevant. The authors propose nlog(n) instead, a much smaller increase."
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## Metcalfe's Law Refuted

• #### Figures. (Score:4, Funny)

on Tuesday March 15, 2005 @04:58PM (#11946705)
Anything that can be refuted...will.
• #### Re:Figures. (Score:5, Funny)

on Tuesday March 15, 2005 @04:59PM (#11946718)
That's a lie and you know it!
• #### Re:Figures. (Score:4, Insightful)

on Tuesday March 15, 2005 @05:14PM (#11946877)
That's a lie and you know it!

Yeah, I think we all do. CS theory is just like math or logic theories. You start with a set of reasonable assumptions and then try to deduce a theorem. It's perfectly correct to say the value of the network increases at C*(node)^2 provided that you're talking about generic nodes. I.e. they are the same.

If you're folding or SETI'ing, the nodes with water-cooled FX-55s will obviously outperform the P3-700 nodes. Or in the case of data-sharing the 100mbps connected nodes(the link between the main ISP hub and all customer hub would be considered a node) will clearly outperform the 1.5mbps nodes. But nodes of variable value were not in Metcalfe's list of assumptions, so why argue about his theorem in cases like these?
• #### Re:Figures. (Score:3, Insightful)

The reason this conclusion is significant is that Metcalfe's Law has been trotted out countless times to hype the capabilities of the internet. Given the result in the referenced paper, Metcalfe's law is meaningless with respect to the internet. As you point out, there are nodes of widely varying capability connected to the internet and so you can't use Metcalfe's Law to make any predictions/calculations about the value of it.

• #### Re:Figures. (Score:5, Funny)

on Tuesday March 15, 2005 @05:00PM (#11946720) Homepage
Anything that can be refuted...will.

I think that opinion has been refuted.

• #### Re:Figures. (Score:2, Funny)

Clearly false, because all broad generalizations are wrong.
• #### Use it for what (Score:3, Interesting)

on Tuesday March 15, 2005 @05:00PM (#11946723) Homepage
For what do they use this formula.
• #### Re:Use it for what (Score:2)

For arguing with others.

Might as well make it:
http://getfirefox.com/ [getfirefox.com]
• #### Re:Use it for what (Score:2)

For promoting doing things by committee that would better be done by one or two people.
• #### Erdos-Bacon numbers, for example. (Score:5, Funny)

on Tuesday March 15, 2005 @05:00PM (#11946724)
Everyone knows that having a low Erdos-Bacon number [simonsingh.com] is more valuable than having a high one, so the proof of this is trivial. Oh, wait, computer networks? Never mind.
• #### Re:Erdos-Bacon numbers, for example. (Score:2)

I'm a geek. When I read this I thought to myself, "I know what an Erdos number is, but what does Francis Bacon have to do with it?"

It wasn't until I followed the link that I realized that it might have something to do with Kevin Bacon and the whole "degrees of separation" thing.
• #### "Refuted"? (Score:4, Insightful)

by Anonymous Coward on Tuesday March 15, 2005 @05:00PM (#11946727)
"Refutation" seems like almost as big an overstatement in this context as is the use of "law" to describe some wild-ass aphorism or a disagreement with it.

It's not like "value of a network" is some precisely measurable quantity.

• #### Re:"Refuted"? (Score:4, Informative)

on Tuesday March 15, 2005 @05:07PM (#11946805) Homepage Journal
The article is misquoting. Metcalfe said something like "usefulness" of a network. The squared term is because there are two endpoints to each connection, so it makes sense that the usefulness goes up as the number of possible connections.
• #### Re:"Refuted"? (Score:2)

From the article ...

the thesis is that not all the links in a network are equally valuable

... obvious ...

from the parent poster:

so it makes sense that the usefulness goes up as the number of possible connections.

The usefulness goes DOWN [tt] with the number of possible connections, when more and more of those connections are low-quality.

You get the dregs, like AO-Hell users who click on spam, windows lusers whose boxes breed viruses, etc.

We may have passed the optimal size for the current breed of n

• #### Re:"Refuted"? (Score:2, Interesting)

The usefulness goes DOWN [tt] with the number of possible connections, when more and more of those connections are low-quality.

I would argue that the utility does not go down with the number of possible connections. It is more likely that the extremely low learning curve for user-friendly aol-type connections has removed knowledge barriers that perhaps aught to have been left in place.

You get the dregs, like AO-Hell users who click on spam, windows lusers whose boxes breed viruses, etc

Wasn't AO-Hel

• #### Re:"Refuted"? (Score:4, Funny)

on Tuesday March 15, 2005 @05:15PM (#11946895)
But MS says I can increase my ROI on my network infrastructure by using their software.

And Sun tells me that the Network is the computer!
• #### Re:"Refuted"? (Score:2)

Please don't make uninformed comments. It doesn't make you look smart (hopefully).
• #### Re:"Refuted"? (Score:2)

Please don't make uninformed comments. It doesn't make you look smart (hopefully).

You're new to Slashdot, aren't you?
• #### Re:"Refuted"? (Score:5, Insightful)

on Tuesday March 15, 2005 @05:23PM (#11946982) Homepage
Not only that, but isn't this actually a case of "potential value" (not greater than the total number of possible connections inherent to the network - Metcalfe's Law) versus "typical usaage patterns"?

Networks are just like anything else in life. They have a maximal or optimal value, but most people don't bother trying to get full value out of them.

If Metcalfe were to say "the average mid-sized sedan seats up to five people, for which reason I value it as a five-person car", these guys would reply "yeah, but most people don't fill all five seats in their mid-sized sedans, therefore mid-sized sedans don't really seat five people after all... pwn3d!"

It's stupid. Metcalfe is talking about potential value. These guys are talking about typical utilization.
• #### Re:"Refuted"? (Score:2)

It's not like "value of a network" is some precisely measurable quantity.

Working in the realm of psychology, I tend to be more of the opinion that it may be assessed (you of course will have an error - I dimly recall LORD&NOVICK 1968, Statistical theories of mental test scores - may fit here) if you a priori go through the hassle of operationalization which, as a prerequisite (at least IMHO), needs a theory of how that value is established - which is the crucial point. Depending on this definition yo
• #### Andrew Odlyzko is godlike (Score:5, Insightful)

on Tuesday March 15, 2005 @05:01PM (#11946735) Homepage Journal
It's a shame the summary didn't say who the authors are. Odlyzko is a Very Good Thing - he writes intelligently about everything from cryptographic number theory to making academic papers freely available online. I've long thought that n^2 was too high - though n log(n) sounds a little low...
• #### Re:Andrew Odlyzko is godlike (Score:3, Interesting)

I've long thought that n^2 was too high - though n log(n) sounds a little low...

I always thought n log(n) sounded a little high neglecting the effects of noise and other costs of large networks. What's really the difference between being able to phone a million people compared to a billion people? I bet the jump from 100 to 1000 people is at least as big for most people.

You reach the point of diminishing returns even on the log scale. And if the value of the network to the average person doesn't even

• #### Re:Andrew Odlyzko is godlike (Score:5, Interesting)

<akrumbach@gmail.com> on Tuesday March 15, 2005 @05:32PM (#11947055) Homepage Journal
No, I don't think the log scale wears down.

After all, it's the high end of that curve -- e.g. the anybody-to-anybody connection of the 'net -- that brings us things like wikipedia [wikipedia.org] and Linux [kernel.org]. IMO, when you start reaching scales "beyond mortal comprehension" (or at least everyday life) the growth isn't as much being able to connect to more individuals, but being able to have more specialized groupings and network those.

Even if the average person doesn't get very connected into the network, the value can still be quite high. Never forget the "Kevin Bacon" effect [virginia.edu].
• #### Re:Andrew Odlyzko is godlike (Score:2)

What's really the difference between being able to phone a million people compared to a billion people?

Not the best choice of example, IMO. For the phone network, a million people doesn't even cover my local-distance landline region, which might be enough to order pizza but useless if I travel much. A billion people, OTOH, covers most if not all of the phones in the world.

The value of a network (telcom, social, or otherwise) is not just the connections that you directly use, but the ones that you know yo
• #### Re:Andrew Odlyzko is godlike (Score:2)

The value of a network (telcom, social, or otherwise) is not just the connections that you directly use, but the ones that you know you COULD use if it were necessary.

Well, the point of the article was that the reverse is true, roughy because a small network gets you the ones you *actually* use, but I'm not sure I buy that.

I guess it's the difference between a network built from random endpoints, and a network built from chosen endpoints. This may be a very good objection to the claims in the article -
• #### Re:Andrew Odlyzko is godlike (Score:2)

What's really the difference between being able to phone a million people compared to a billion people?

I guess telemarketers could tell VOLUMES about it...
• #### Re:Andrew Odlyzko is godlike (Score:4, Interesting)

on Tuesday March 15, 2005 @08:20PM (#11948689) Homepage Journal
His economic arguments seem to neglect a number of factors in coming to the conclusion that large networks would always merge.

The first is that a single user may be a user of multiple networks; obviously, little value is created on account of a user of both networks when they merge, since the user could already communicate with all of the users. This effect can mean that two networks combined can simply cause the two network owners to share the value each of them had before (for example, the advent of VoIP means that people no longer need POTS lines, so the amount of money that can be extracted from consumers drops).

The second is that the communication value of a network may not be the reason for having it. For example, in the US, cell phones often have SMS, but it's a fragmented network. The networks don't merge, however, because SMS isn't widely used in comparison to voice service. The companies derive the greatest benefit from people paying a bit extra to get a SMS-capable phone, but using voice instead. Merging the SMS networks would increase their value greatly, but still wouldn't compare to the value of the existing universal network.

Between these two effects, the dot-com bust is predictable, especially when you realize that it happened among a userbase who could already call each other on the phone. Even if the value of a global network is huge, the ability of companies to extract that value in revenue is very limited.

The effect of spam can be seen as changing the nature of the network to a broadcast network, generally acknowledged to be worth O(n). The change is value from adding users is negated if they communicate with the network as a whole rather than individually with each (or some) of the members.

The argument based on Zipf's Law makes sense as a general rule, because an individual gets 1/k value from the kth most valuable user. On the other hand, this misses two points.

The links which would be most valuable may not be in the network yet. Adding user k+1 doesn't give only value 1/(k+1) to each user, because the new user is probably not less valuable than all of the existing users to each of the existing users. If the network already included everyone, Zipf's law would apply directly. But the total value to a user of n users out of a world of m users is (n log m)/m. If we assume that there is a constant number of people in the world and that the users of a network are randomly chosen from that pool, then the total value to any given user of that user's links is O(n), and the value of the network is O(n^2). We just have to remember that we hit a wall at the point where practically everyone is connected, and growing the population is only worth O(m log m).

The basic insight is that, if your friends are split across two SMS networks, there is a large value to you in them joining. If your friends picked SMS networks at random (or based on some unrelated consideration), this is likely to happen.

On the other hand, a network constructed by value (that is, if new users are chosen to be of high value to the existing users) is going to extract the value of a larger network at a smaller size and then grow at the O(n log n) rate in a merger. This is why AOL was of high value by itself (lots of friends and family) and the internet was of high value by itself (lots of people who collaborated), but the connection did not add all that much to either (with the primary exception of AOL users going off to college). Opposed to this is the fact that a user may get a different set of high-value links by having new needs; picking up a new hobby will radically improve the values of a set of previously low-valued links, and, to a certain extent, reshuffle the selection of users on the network.

So my estimation is that there are several flaws with the essentially correct O(n^2) idea: separate networks get extra total value out of duplication, at the expense of the users; all networks, even with different properties, compete with each other; it's limited and
• #### It's harder than that... (Score:5, Funny)

on Tuesday March 15, 2005 @05:01PM (#11946743)
More like (n-k)log(n-k) where k is the frequency coefficient of That Big Dumb Guy Who Has Nothing Useful to Say.
• #### Re:It's harder than that... (Score:5, Funny)

on Tuesday March 15, 2005 @05:04PM (#11946775) Homepage
More like (n-k)log(n-k) where k is the frequency coefficient of That Big Dumb Guy Who Has Nothing Useful to Say.

Actually, would't that be (n-2k)log(n-2k)? Each big dumb guy who has nothing useful to say has to be talking to someone who would otherwise be productive.
• #### Re:It's harder than that... (Score:2, Funny)

And you guys have now successfully proven that k >= 2 for Slashdot.

(yes, it's a joke)
• #### Re:It's harder than that... (Score:2, Funny)

That should be (n-2k+2a)log(n-2k+2a). Where a is the Auto-Dumbness coefficient.(Some dumb guys talk to each other, not wasting any useful time)
• #### Re:It's harder than that... (Score:2)

Actually, would't that be (n-2k)log(n-2k)? Each big dumb guy who has nothing useful to say has to be talking to someone who would otherwise be productive.

Nah, sales conferences and slashdot have a lot of peer-chatter covered by that case for instance.
• #### Re:It's harder than that... (Score:2)

The true answer is 0. As n->infinity, k->n.
• #### Interesting. (Score:2, Interesting)

by Anonymous Coward
My firm has done some serious studying of Metcalfe's law. Our general conclusion was that even though there are cases where it absolutely does not apply, for the most part it is pretty consistent.
I don't know, since when has any computer-related "law" really been a law.
• #### Re:Interesting. (Score:2)

I don't know, since when has any computer-related "law" really been a law.

Murphy's Law?

While not a "computer-related" law, whenever it is related to computers, it seems to hold true :)

• #### Re:Interesting. (Score:2)

What kind of value is there is "studying" a law of this kind. I don't see how you can study a concept as vague as "the value of a network" expressed in some kind of abstract numbers that have no bearing on anything.
• #### Re:Interesting. (Score:3, Insightful)

Maybe this is why the GP had to "study" this "law", as in, produce some intuitive definition of "the value of a network" and see if the "law" holds with this definition when N increases (and for what range of N). Then produce another "definition of value" (maybe for the different customer/situation/etc.). Rinse and repeat...

Paul B.
• #### The real Metcalfe law (Score:5, Funny)

on Tuesday March 15, 2005 @05:02PM (#11946750)
You can read this law like this:

"hello, I'm Robert Metcalfe. I state that the value of a network grows exponentially to the number of nodes present in it. So the more nodes you have, the better your network. Oh, and incidentally, I'm the CEO of 3Com, a company that sells network cards..."
• #### Re:The real Metcalfe law (Score:2, Interesting)

Along the same lines, I wonder if the RIAA uses Metcalfe's Law in any way to establish the value of a file shared on a p2p network?
• #### Re:The real Metcalfe law (Score:2)

According to latest RIAA calculations, a single file on a p2p network has the value of: hojillion blazillion kadillion dollars

Actually, in a post-scarcity economy, if we attribute value by how-much-it-has-been-duplicated, the vast majority of files are probably worthless.

by Anonymous Coward on Tuesday March 15, 2005 @05:03PM (#11946753)
The link that the submission attributes to Southwest Missouri State University is actually at the University of Minnesota... (Not terribly surprising, given that Odlyzko is at the University of Minnesota!) Please correct the article accordingly.
• #### Example: AOL (Score:5, Funny)

on Tuesday March 15, 2005 @05:03PM (#11946754) Homepage Journal
Number of members: Millions
Value: Debatable

suso.org website/email hosting [suso.org], no disk space quotas and personalized support.
• #### No need to go that far. (Score:5, Informative)

on Tuesday March 15, 2005 @05:06PM (#11946791) Homepage
Slashdot itself is a good counter-example.
• #### Re:No need to go that far. (Score:2)

What in the hell do you mean?
• #### In addition... (Score:2, Funny)

For every link to Goatse, the value of the network has an absolute drop of 225.2.
• #### Smaller Networks Win Out (Score:5, Interesting)

on Tuesday March 15, 2005 @05:04PM (#11946766) Homepage
The last paragraph makes a very interesting point:
When two networks merge, "the smaller network gains considerably more than the larger one. This produces an incentive for larger networks to refuse to interconnect without payment, a very common phenomenon in the real economy," the researchers conclude.
Assuming their research holds true, adding 100 computers to 100,000 computers is pretty worthless for a big network - they get only a small gain compared to their starting value. The small network, on the other hand, has huge amounts compared to where they started.

It's common sense, of course, but worth taking note of.
• #### Also... (Score:2)

Note that this is an average. A small but valuable network is still, well, valuable. i.e. Google's size when compared to the internet as a whole is nothing, but they still add an immense amount to it. nLog(n) is only an approximation.
• #### Re:Smaller Networks Win Out (Score:4, Interesting)

on Tuesday March 15, 2005 @05:41PM (#11947174) Homepage
While it's true that an individual user of the smaller network sees a bigger increase than a user on the larger network,
the total value of the larger network increases more.

Assuming a value of N log(N);

Value of 100,000 is 500,000
Value of 100 is 200
The value of 100,100 (the two together) 500,543

Increase in value per node for larger; 0.00543
Increase in value per node for smaller; 3.00543

Total increase across larger network 543
Total increase across smaller network 300

-- Should you believe authority without question?
• #### Re:Smaller Networks Win Out (Score:2)

Exactly what the article and I were pointing out. The value increase for large networks is, on average, worthless.
• #### Re:Smaller Networks Win Out (Score:3, Interesting)

This has been the general thought on "peering" relationships between ISPs. Don't peer with smaller networks, let them buy your connectivity.
• #### Re:Smaller Networks Win Out (Score:3, Interesting)

When two networks merge, "the smaller network gains considerably more than the larger one. This produces an incentive for larger networks to refuse to interconnect without payment, a very common phenomenon in the real economy," the researchers conclude.

Well, it is mostly a question of who sits on the backbone, otherwise networks would merge to provide competitiveness. Imagine the small network peering with another 100 person network. Now that 200 person network enters peering with some 200 person network.
• #### In other news... (Score:5, Funny)

on Tuesday March 15, 2005 @05:05PM (#11946787)
Powerful refutation of Murphy's Law! It has been determined that not everything thing that *can* go wrong *does* go wrong. Using the Apollo 13 mission as a case study, it has indeed been shown that only a small fraction of the things that could have gone wrong indeed did go wrong.

NASA Scientists have now recast murphy law as, "There are a lot of things that can go wrong. Some of them might happen." Which, of course, shows that far fewer things go wrong than previously thought.

Scientists predict that this will have no effect on the size or scope of any government project or agency.
• #### Re:In other news... (Score:3, Insightful)

Actually, the original form of Murphy's law was something along the lines of "If it is possible to connect it backwards, eventually some stupid technician will." This was generalized into "Anything that can go wrong, will go wrong." The final word "eventually" was merely implied and not generally understood.

I have always been more impressed with a variant of Murphy's law that I attribute to Douglas Adams, but he didn't spell it out explicitly. "Anything that CAN'T go wrong is impossible to fix when it DOES
• #### finding nodes (Score:3, Interesting)

<lkcl@lkcl.net> on Tuesday March 15, 2005 @05:08PM (#11946820) Homepage
the ability to _find_ useful nodes decreases with the quantity of nodes.

that's what makes google so valuable: the ability to provide a "meta" node-set.
• #### Re:finding nodes (Score:2)

Perhaps more specifically the overhead associated with finding them goes up.
• #### And what other "laws" will be changing? (Score:5, Funny)

<brendt.hess@motospo[ ]com ['rt.' in gap]> on Tuesday March 15, 2005 @05:09PM (#11946829)
Now that researchers realize that the so-called laws of computing are not rigorously formed, what else will be subject to attack?

Will we see Moore's law [wikipedia.org] reduced to a log-based function as well? Will Brooks' Law [wikipedia.org] be shown to be fallacious, leading to a large upsurge of temporary IT jobs? And how about Godwin's Law [wikipedia.org]. Will we no longer have to fear the inevitability of Nazis or Hitler?

What will this all lead to... nothing but anarchy. Anarchy, I tell you!

• #### Re:And what other "laws" will be changing? (Score:2)

Ah, it's not so bad. The herds of temporary IT workers will still have enough computer resources to Godwinate forum threads, the aggregate value of which will remain O(0). :)
• #### Re:And what other "laws" will be changing? (Score:2, Funny)

Laws are for facists, you fucking nazi. ;-)
• #### Re:And what other "laws" will be changing? (Score:2, Funny)

Did you just say that adding Nazis to a project every 18 months will delay the delivery date?
• #### Annecdotal Support (Score:5, Funny)

on Tuesday March 15, 2005 @05:10PM (#11946834)
I was happily working on a project when my manager assigned two more people to the team, making us three in number. I'm John, I've got it all figurted out and would have finished the product. I now work with Bob. Bob talks too much. Always coming to me with silly questions and he never seems to quite "get it". I also now work with Tom. Tom is never available, he never answers his phone, and I swear he's cutting out at three on Fridays. I know you've been in this situation as well. We're a network, which I'd hardly refer to as peer-ro-peer. Our bandwidth may not be comparable to the study, but the general theorem is the same.
• #### Re:Annecdotal Support (Score:3, Funny)

I'm your boss. I know you were working on the project happily. I added Tom and Bob because you were finishing the product too quick. You shouldn't finish the product quick because then we're underbudget. We can't afford to be underbudget otherwise our next quarter's funding will be cut.

Oh btw, stop wasting time posting on Slashdot.
• #### Why call it a law, exactly? (Score:5, Insightful)

on Tuesday March 15, 2005 @05:11PM (#11946844) Journal
I was a bit confused about the story at first, and a quick Google define proved that I had reason:

"A statement that summarizes the results observed in an experiment that is repeated many times by many different scientists. A scientific law is widely accepted as true or as a fact." -- Source [ucar.edu]

"A general principle or rule that is assumed or that has been proven to hold between expressions." -- Source [slashdot.org]

This can't be a law. It's been proven wrong, and unless I'm mistaken, it was never proven to be correct in the first place.

Why use the word law, then? Is it a misuse of the word? Generalizing? An attempt to confuse stupid Slashdotters like me? :)

• #### Re:Why call it a law, exactly? (Score:2)

Second link is screwed up. This [reference.com] is where I intended it to go. And this, children, is why you preview your post. :)
• #### Re:Why call it a law, exactly? (Score:2)

Standardized and accepted behavior, maybe?
Proof of the behavior: Moore's Law

Are you confused by that one? Have you not heard of it before?
• #### "Laws," "theories," "postulates," etc. (Score:2)

The bottom line, from an etymological standpoint, is that all of these are relatively arbitrary assignations. Why is it still the "Theory of Relativity," when it's "Moore's Law"? Bottom line: I think that "law," when used in a context such as this, is used with a bit of ironic tongue-in-cheek. The person making the designation *knows* it's not a law in the strict sense; but, instead of watering it down with other more mundane nomenclature, they go for the gusto, curious to see whether or not their theory
• #### Isn't this the same Metcalfe... (Score:5, Insightful)

<.ken. .at. .jots.org.> on Tuesday March 15, 2005 @05:11PM (#11946848) Homepage Journal
- who said that Linux sucks, and would die years ago
- who predicted the Internet would implode... years ago
- whose ego far outpaces his abilities?

[Check old columns in InfoWorld, c. 2000, for details.]

Granted -- he did some good stuff. But the truly good stuff he's done was so long ago that the only meaning it has in contemporary terms is a resume line item. Now he's just another VC talking head, with ego to match; to find that one of his "laws" doesn't hold water is about the same as saying that SCO's legal team isn't always on the level.
• #### does this debunk "six degrees of separation"? (Score:2, Interesting)

Links in social networks are also of variable quality; so does this mean that the "six degrees" meme is merely wishful thinking?
• #### Odlyzko's Arguments are Good (Score:5, Interesting)

on Tuesday March 15, 2005 @05:15PM (#11946894) Homepage
Especially the section on Zipf's Law.

Where I think Metcalf's Laws does apply is in an information network where no proprietary secrets exist. For instance, searching for technical documentation or a movie star's biography. In these instances, the value of the network, as measured by the immediacy with which one could obtain useful information by asking a question, is proportional to something on the order of n*n for n nodes.

Consider the network the top 10 search results in Google for all possible queries. Let's pretend for a moment that Google wasn't polluted with Spam. In this case, each node (search result) is providing a substantial amount of value to the network, although no matter how small or targeted the group, Zipf's Law will be observable to a degree.

Or consider if you had personal tele-access to every person on the planet and could ask any one of them a question at any time. Clearly here the value of the network is something on the order of n*n.

Most or all of Odlyzko's examples presupposed economic interests or constraints.
• #### Re:Odlyzko's Arguments are Good (Score:2)

Or consider if you had personal tele-access to every person on the planet and could ask any one of them a question at any time. Clearly here the value of the network is something on the order of n*n.

I disagree. When you consider that any other person on the planet can interrupt you with a question at any time (and presumably demand an answer), the utility to you is reduced. I would estimate the "value" of that network to society at large as being log(n) at best.

For instance, there are questions I would
• #### Re:Odlyzko's Arguments are Good (Score:2)

Right; I regret not having made explicit the assumption that everyone would be queriable without personal interruption. That is to say, instead of querying Hawking directly, imagine if you could query an AI agent that represented his knowledge. This same agent or network would also determine who's brain to pick for which question. This characterization essentially describes the founding goal of Google.
• #### These are just cutsey laws with no meaning (Score:3, Insightful)

<deviladvNO@SPAMgmail.com> on Tuesday March 15, 2005 @05:17PM (#11946923) Homepage
See, these "laws" aren't all that significant. They are more like "rules of thumb." These laws try to put qualitative values by using quantitative theories or computations. It's ridiculous.

For example, Moore's law means almost nothing now. Processor clock speed is only one aspect of the speed of a computer. It's still useful to gauge this as over all computer process speed, but soon that won't matter as much either. Even still, can you measure to the exact mhz that processing speed has exactly doubled in the past 18 months?

All these "laws" have no proof to begin with so how can one refute them? It's marketing and CEO level philosophy which exists in a world far outside of reality.

Metcalfe's law and this new law are both trying to measure how valuable a network node is. Hell, the value could be ZERO; for example, a pr0n leecher. Or it could be extremely valuable, like wikipedia. And to confuse it more, is citibank.com more valuable than walmart.com, and are both of them more valuable than whitehouse.gov or unicef.org? How does one measure value. And if myblog.com has a low value, but slashdot.org has a high value, don't these nodes offset each other and potentially refute the refutal?

But who really cares? I mean cmon... this is a stupid little law trying to be big and important when there's no need for a "law." It's marketing spin trying to make something more important than it really is. I would agree that the value of a network is more than the sum of it's parts, but trying to put a number to it is pretty stupid.
• #### Re:These are just cutsey laws with no meaning (Score:3, Informative)

For example, Moore's law means almost nothing now. Processor clock speed is only one aspect of the speed of a computer. It's still useful to gauge this as over all computer process speed, but soon that won't matter as much either. Even still, can you measure to the exact mhz that processing speed has exactly doubled in the past 18 months?

You're right to say that "Moore's law means almost nothing now." Especially since Moore's law is about transistor density in semi-conductors, not clock speed. The semi
• #### Lesson of usenet--Value? What value? (Score:4, Interesting)

on Tuesday March 15, 2005 @05:21PM (#11946956) Homepage Journal
Consider the usenet as a kind of asynchronous network. Consider the participants as nodes that connect and disconnect at random. Now consider the result. The value has *NOT* increased along with the number of nodes. Instead, the SNR became very small, and my belief is that the current SNR is negative, at least on average. There is still some good information to be found in pockets, but there is plenty of misinformation, too, and *LOTS* of noise.

I think the decisive factor is that the fanatical propagators of misinformation must be aware (at some level) that they are fighting against reality--but their response is to shout louder and more frequently, simply repeating their misinformation. Are they hoping that lies repeated enough times will somehow become true? Or they just hope to bury the truth they hate?

Scarcely matters. The result is obvious, and the same phenomenon seems to be overtaking the WWW, too. Doesn't do a lot of good to connect to the network when all the sites are basically put on the same level by the constraints of HTML, but most of them are full of propaganda of various stripes.

• #### Re:Lesson of usenet--Value? What value? (Score:2, Interesting)

Good post. Couldn't agree more.

Perhaps the formula is to simplistic. It needs to take into consideration AOL users, Virus writers, spyware, and bad porn as detriments.....

Maybe

( (n + #linux users) - ( AOLusers + Kv * #viri + Ks * #spywareAps + #aviAmatuerPr0nVideos) ) ^ 2

• #### Re:Lesson of usenet--Value? What value? (Score:2)

Instead, the SNR became very small, and my belief is that the current SNR is negative, at least on average.

Unless it actually sucks signal out of neighboring informational bodies, it can't be negative.

Just a quibble.

• #### Brook's Law (Score:3, Interesting)

on Tuesday March 15, 2005 @05:22PM (#11946970)
In "The Mythical Man Month", Fredrick Brooks argues that the communciation complexity within a team follows rougly that same n**2 rule.

I wonder if this means that Brook's formalization of the team-size problem is somewhat overstated as well.
• #### clearly there is a limit to the value (Score:2)

Perhaps the value of a network goes up with n^2 in the number of members, but only to a point, the internet is a great example of this. The internet basically sucks now that everyone and their brother is on it, but clearly networks are better with more that say 10 people on them.
• #### Not quite disproven, only conditionally... (Score:2)

Basically, the thesis is that not all the links in a network are equally valuable

That "fact" results from two major problems, however, the solving of which would again make the "value" scale with O(N^2)...

First, legality. I have quite a lot of useful content on my computer, which I cannot legally share. I would say that the vast majority of us fall into that category. Thus, we have an artificial limitation on our value to a network.

Second, not everyone has broadband, and very very few people have
• #### Misapplied Math (Score:3, Insightful)

on Tuesday March 15, 2005 @05:33PM (#11947068) Journal

It sounds like people are trying to use math where what they really want is economics. The value of a network is easily measured as what people are willing to pay for it and since this is governed by market forces which are complex and not necessarily "rational" there is no "law" for it.

If, and only if, you assign a mathematical meaning to "value" can you have any hope of coming up with a real answer.

• #### Okay . . . (Score:2)

Basically, the thesis is that not all the links in a network are equally valuable, so Metcalfe's argument that everyone can connect to everyone (n(n-1)/2 links, roughly n^2) is irrelevant. The authors propose nlog(n) instead, a much smaller increase.

On behalf on many slashdotters, let me say:
Huh?

• #### Re:Okay . . . (Score:2)

"Basically, the thesis is that not all the links in a network are equally valuable, so Metcalfe's argument that everyone can connect to everyone (n(n-1)/2 links, roughly n^2) is irrelevant. The authors propose nlog(n) instead, a much smaller increase."

On behalf on many slashdotters, let me say: Huh?

That's kind of sad, you're saying 'Huh?' to very basic math stuff, but I guess maybe that's indicative of the /. crowd these days...

Really, this whole article is kind of a "duh", since, in what sort of netwo

• #### A network's usefulness reaches a limit (Score:2, Interesting)

once you get enough nodes on the network that any given node on the network can only make so much use of all of the other nodes based on one constant Metcalf's law seems to ignore and that is time.

Furthermore, as you increase noise on the network (i.e. spam, popup ads wasting your time from what you intend to use the network for, random people bugging you about things unimportant to you, but nevertheless important to them for whatever reason), the network becomes less and less useful and the difficulty in
• #### But you're forgetting Hulk's Law (Score:4, Funny)

on Tuesday March 15, 2005 @05:48PM (#11947246) Homepage Journal
Which says: You Make HULK AnnnnnGRRyyyyyy!!!!!! ARRRRRRRRGGGGG!!!!!
• #### no offense to the refuter (Score:2)

but I think most of us knew that already, based on the seeder/leecher ratio of most BitTorrent files.

And don't get me started on the "hit & run" non-sharers.
• #### Upper bound, since nodes are not all equal... duh? (Score:2)

Since when does anyone seriously assume that all nodes in a real-world network are of equal value?

Are there really people who look at basic graph theory stuff like this so-called "Metcalfe's law" and don't realize it's a theoretical upper bound?

I guess it's nice to see a better real-world approximation, which is, to me, the meat of the paper, but still... how is this a story again?

• #### Ruby's Clause (Score:3, Insightful)

on Tuesday March 15, 2005 @06:59PM (#11947907) Homepage Journal
Except the "value" of a node is necesarily an average. Of the value of a given node to all of the other nodes, across all of the states a node will be in during the lifetime of the network. These networks' values are transmitted, changing each node's state (and value) over time. So the value proposition is necessarily dynamic. Metcalfe's n(n-1)/2 relationship still applies; the difference is that the value is really (n(n-1)/2)v where v is the node value. Call this "Ruby's Clause" to Metcalfe's Law: the law is still valid; this new research really just quibbles with the non-unity value of "v".

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