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Metcalfe's Law Refuted
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."
Anything that can be refuted...will.
For what do they use this formula.
If you mod this up, your slashdot background will turn into a beautiful sunset!
Everyone knows that having a low Erdos-Bacon number is more valuable than having a high one, so the proof of this is trivial. Oh, wait, computer networks? Never mind.
---------The early bird gets the worm, but the second mouse gets the cheese.
It's not like "value of a network" is some precisely measurable quantity.
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...
Xenu loves you!
More like (n-k)log(n-k) where k is the frequency coefficient of That Big Dumb Guy Who Has Nothing Useful to Say.
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.
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..."
"A door is what a dog is perpetually on the wrong side of" - Ogden Nash
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.
Number of members: Millions
Value: Debatable
suso.org website/email hosting, no disk space quotas and personalized support.
For every link to Goatse, the value of the network has an absolute drop of 225.2.
It's common sense, of course, but worth taking note of.
-dave
http://millionnumbers.com/ - own the number of your dreams
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.
Slashdot itself is a good counter-example.
"I'm not impatient. I just hate waiting." - My Dad
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.
Will we see Moore's law reduced to a log-based function as well? Will Brooks' Law be shown to be fallacious, leading to a large upsurge of temporary IT jobs? And how about Godwin's Law. 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!
We are the Music Makers, and We are the Dreamers of Dreams...
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.
"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
"A general principle or rule that is assumed or that has been proven to hold between expressions." -- Source
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? :)
Goo goo g'joob.
- 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.
Links in social networks are also of variable quality; so does this mean that the "six degrees" meme is merely wishful thinking?
but i don't think it takes a genious to apply a little logic to it and realise that it has very little application in real life.
Met any Token Ring salesmen lately?
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.
I Want To Believe
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.
"All great wisdom is contained in .signature files"
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.
Freedom = (Meaningful - Coerced) Choice != (Speech | Beer^2), and sad sock puppets' bad mods avail them naught.
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.
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.
For all intensive purposes, "whom" is no longer a word. That begs the question, "who cares"?
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 sorting out useful nodes on the network from useless nodes becomes harder. So once this limit is reached, the more nodes you add, the more useless the network becomes.
For example, look at the web in 1990 versus what we have today. Back then, you could do a search on Lycos or Yahoo and most of the time you could find what you were looking for, but nowadays search engines are glorified phone books where the way documents/web sites get to the top of a search list has little to do with the usefulness of the content, but rather how much money they pay to web site portals to have their site ranked above others for any given topic. Furthermore, due to keyword stuffing from porn sites, blogs, and other irrelevant content web crawlers scan for web page indexing, sites like google are becoming less and less useful over time.
In the internet/cell phone/ANYONE CAN ANNOY ANYONE ELSE THEY FRIGGING WANT AT ANY GIVEN TIME culture we now live in, sometimes it is damned near impossible to get any real work done, or more importantly just be able to relax at the end of the day when a bunch of people who are addicted to communicating with others for no good reason feel the need to bother you just because they can.
I think Donald Knuth's solution of just pulling the plug on all communication devices is about the only option some of us have because like most things in science, if you give the average person a little bit of scientific rope, they will surely find a way to hang themselves.
And yah, yah, yah you can say you can just tell people who may be friends, family members, business associates, or whatever not to bug you for certain activities during certain hours (i.e. don't bug me at work about personal stuff and at home don't bug me about work, just because you know how to reach me on my cell phone or computer 24/7), but that is easier said than done without pissing a lot of people off you don't want to piss off for other reasons.
And when it comes to a network, the more nodes you add the more potential there is for people to waste your time and therefore less gets done and the network becomes useless.
Metcalf's law is good in theory, but in practice people sometimes don't realize how much of their life they waste getting interrupted by people who think that just because cell phone minutes are cheap nowadays, that it means your line is always intended to be open for any random topic of discussion as opposed to the good purpose of leaving it open for emergencies and truly important business.
In the old days, when someone wanted to discuss something with another person they physically had to make the effort to get off their lazy arse and meet that person somewhere. Nowadays, you just have to hit a number on speed dial or double click on someone in your buddy list to be able to "reach out and annoy someone".
If time is money, then the abuses many common folk make with the internet is costing the world trillions of dollars in lost productivity.
Which says: You Make HULK AnnnnnGRRyyyyyy!!!!!! ARRRRRRRRGGGGG!!!!!
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".
--
make install -not war
A 'law' is not stronger than a 'theory'. A 'law' is a 'theory' which can be briefy stated. It's a common misperception.
Socialism: a lie told by totalitarians and believed by fools.