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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!
Never did like that guy ever since he dissed Linux.
/. would I qualify this...]
[Hint for the humour impaired: I'm not being entirely serious here... Sigh, only on
Simon
Physicists get Hadrons!
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.
Mobile phone network grows much faster in utilization than a much more 'passive' network such as an art-network where most people will just watch and some will submit.
If you mod this up, your slashdot background will turn into a beautiful sunset!
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.
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. should have been called a 'theory' not a 'law'
Slashdot itself is a good counter-example.
"I'm not impatient. I just hate waiting." - My Dad
http://www.dtc.umn.edu/~odlyzko/doc/metcalfe.pdf
_NOT_ Southwest Missouri State U - UMN Digital Technology Center (400 feet away?).
Metcalfe's Law is at SMSU, not the refutation (we want the credit for the slashdot, thanks)
I'm thanking my lucky stars he didn't host the paper on his math account...
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?
I thought it said "Metallica's Law" which, says that you have to ROCK HARD and ROCK OFTEN !! Oh, and they'll sue you if you copy their CD's. Oh, and they're on VH1 now.
StupidChildren...the reason jesus is crying
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
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.
-dave
http://millionnumbers.com/ - own the number of your dreams
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"
Now it will come to be known as "Metcalfes Folly"
the speed of the network is limit 2^(1/n), as n-->infinity.
n(n-1)/2 is approximately equivalent to n^2? not really.
I forgot an important part, limit 2^(1/n)/n, as n-->infinity
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.
The pdf linked to in the article description is hosted by the University of Minnesota (umn.edu), not SMSU.
For every post on Slashdot there will be n^n dupe of that post.
There are 3 kinds of people in the world: Those that can count and those that cannot!
But seriously, who cares?
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.
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.
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 will weather examination.
But that's just my $.02. Call it "Slartibartfast's Law."
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 symmetrical connectivity. Thus, although we can download very fast, even if we could legally share, we cannot even come close to giving as much back as we take. I consider this a somewhat more natural limitation, though still partially artificial (we can, in theory, fork over the money for a symmetrical multi-megabit link, but very few of us can afford to).
So, do these limitations refute Metcalfe's law? I would say "no", because the second point above will eventually vanish, and we could get rid of the first problem if our laws didn't deny us access to the products of our own culture.
One final point that someone will probably scold me on - The existance of massively more valuable single nodes (such as Google, a sort of meta-contributer, or Sourceforge, a meta-meta contributer, or plain ol' collection sites such as Guttenberg, Internet Archive, the former MP3.com, and the like). These will of course contribute far more than the average member of a network. I see those as more of a bonus to the overall N^2 growth, rather than making everyone else less important. They do make everyone else appear like leeches by comparison, but all that material has to come from somewhere originally... Joe Brown of Sandusky, Ohio, may not have a fat pipe that thousands can download from, but if he can provide even a single unique or very rare file, he has helped make those collection-type sites more valuable. And, of course, for those collections without fat pipes, Joe running BitTorrent can help a resource he doesn't actually have share a resource he does have (ie, a mostly idle broadband connection) for the benefit of all.
Doesn't Metcalfe's Law still apply to spammers, who apparently do consider every link to be equally valuable? Or does the value to spammers only increase linearly with the number of potential spammees?
I've abandoned my search for truth; now I'm just looking for some useful delusions.
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"?
n(n-1)/2 links, roughly n^2 How is that roughly n^2? If anything, it's about (n^2)/2, but even then...
They value of any network goes -(n^2) after being linked to on slashdot.
On behalf on many slashdotters, let me say:
Huh?
Well, there's spam egg sausage and spam, that's not got much spam in it.
The laws of Celebrity Attack PR
1) Always attack.
People agreeing is boring.
2) Always attack someone famous.
Unknown people are boring.
3) Only attack ideas that were put forth originally only to get press.
We want a media fight not a real fight.*
4) Use over generalization/simplification to both prove your point and as a point of criticism of your opponent.
We need to leave enough room for the apology/press conference/hand job where we announce a new partnership to launch a restaurant/film project.
Now this whole process is mildly entertaining when it involves young attractive celebrities, but relocate the set to a Grizzlebees sharing a bloomin onion (keep um coming) with the assistant editor of cnet and the idea of a catfight is going to make me hurl.
*Disagreement with Sean Penn will get you both.
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!!!!!
n(n-1)/2 = n^2 ????
Ehhh, doubtful....
I've been saying the same thing for years.
It's a square of the useful contributions (signal to noise ratio, where 0.8 or 80 percent useful posts to noise posts or transmissions is baseline = 1, by the delta of the change above the baseline (subtract the square of the delta of the change below the baseline).
In other words, if you get too much spam or "oops, hit the reply to all posts" or endless Re:Re:Re:Re:Re:Re:Item Of Interest replies that quote all the prior posters, it severely impacts the networks effectiveness.
Kind of like meetings, really.
-- Tigger warning: This post may contain tiggers! --
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.
I would actually argue that the value of any network more closely follows Ahmdal's Law, in that the rate of improvement will gradually slip and eventually become negative, whether you are talking about a human network or a computer network. As you increase the numbers, you increase the overheads and therefore decrease the amount of time you can spend on productive communication and actual work.
A good example would be peer-to-peer networks. Those networks that are relatively simply organized and have small numbers of interconnects scale much better than those that follow a Penrose network design.
This is not to say Penrose networks are bad. They are very, very powerful, because they give you maximal fault tolerence and minimal latency. In cases where you've lots of nodes computing largely independently but absolutely HAVE to talk to each other rapidly and reliably, there is no better design. There are such problems.
99% of what 99% of users will be doing will NOT fall into this category. Unless you're a pilot and are using the aircraft's computers to boost your SETI@Home scores.
For most situations, you do NOT want a Penrose design. The most common social and technological network design is heirarchical, though simple grids are also popular. They're simple, fast, efficient and offer a good trade-off between the different aspects of networking.
To put it bluntly, Metcalfe is an idiot.
It's a small world and it smells funny; I'd buy another if it wasn't for the money; Take back what I paid (SoM)
There are diminishing marginal returns for new nodes on the Internet. For example, when you read a NY Times article decrying a white power dating service that was created, do you think: Wooh! Hoo! Girls gone tatoo! I've got to go visit that site! Nope. Me neither. How about when the Kinshasa tourism board sets up "Visit Beautiful Kinshasa"? No way I'm going there. No value to me (except as a joke). Most of us don't give a crap about 90% of the stuff out there. It wasn't that way 10 years ago, when the web was new. Each new site was an adventure. Thus, we have diminishing marginal returns. Easy way to measure. Give "free" internet to volunteers for 1 month. Now, 1/2 of them are only going to get 50% of the internet (determined by sites selected by domains at random). How much will the other 1/2 pay to get it back? Bid it out to them. (You must have an effective monopoly on coverage for this to work). Again, do the same, but block only 40%. Then 30% then 20% then 10%. What does your graph look like? This will tell you the marginal value of random nodes.
A *law* and *rule of thumbs* are totally different. Mixing them is like saying that Newton's laws are just guidlines that nature is nice to obey.
I can't belive nobody thought of this.
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?
Don't care = n^2
or
Don't care = nlog(n)
Hmm... Anyone, anyone?
Doesn't it really depend on the use of the netowrk ? I can argue that the value is proportional to N, N^2, 2^N.
I can't belive nobody thought of this.
Ah! You have at last solved for me one of the great mysteries of life - why the universe has not yet been destroyed by abuttered-cat generator failure.
You see, the hypothesized use of a buttered cat as a source of energy could in fact by exploited if only some means of levitation were introduced - no matter the means nor the amount of energy required. If you drop your buttered cat, affixed to a variable-height rod which runs into an electric generator, above a levitation device powered by the output from the generator, the buttered cat's spin as it descends will inevitable produce enough energy for the levitation device to cause the cat to slow in its descent, hovering at level and producing an indefinite power flow to the generator.
If power is siphoned off the generator to some other use, the levitation device will weaken and the cat will fall some, spinning faster and generating more power, enough to stall its descent again. As such, the more power drawn from this Buttered-Cat Generator, the greater its power output.
However, should the levitation device ever fail, I hypothesized that the buttered cat should fall and, and the moment of impact, spin infinitely fast, so as to allow both the cats feet and the buttered side of the toast to strike the ground simultaneously. Obviously, an infinite spin would require an infinite amount of energy, which would cause the complete and total destruction of the universe as energy lost to radiation - an infinite amount thereof - spread across the universe at c.
I have long since wondered how it is that this has not yet happened. The only solutions imaginable thus far were that no civilization had yet built a buttered-cat generator, or that they had maintained it so perfectly that failure had not yet occurred, or perhaps that somewhere, one had already failed, and he wave of destruction has merely not yet reached us.
But thanks to your brilliant mastery of common sense, the solution is clear to me now: the buttered cat is not an invulnerable system, and would destroy itself well before the moment of impact. In fact it is questionable whether it could fall far enough to generate enough spin to even power the levitation device.
This does have interesting applications as a weapons technology, however; should one manage to sufficiently reinforce the buttered-cat and lob it at a target, the amount of kinetic energy in the torn-apart fragments of cat and toast could possibly rival any conventional weaponry available today, and be produced at a significantly lower cost...
-Forrest Cameranesi, Geek of all Trades
"I am Sam. Sam I am. I do not like trolls, flames, or spam."
Moore is on record as stating that it's not a law, but a metric.
Hrm, I remember his name from 5 years ago because of his infantile and inflammatory writing back then. Nice to see he won't be able to claim fame for having his own law named after him anymore. I can't find the original column anymore, but from an old Slashdot article:
"InfoWorld Pundit (and inventor of Ethernet) Bob Metcalfe just posted his 99/6/19 column entitled: 'Linux's '60s technology, open-sores ideology won't beat W2K, but what will?" in which he predicts that "Linux will fizzle against Windows" and compares the Open Source community to communism and the Back-to-the-Earth Movement.'
Might be a reasonable technician but he's a horrible analyst.
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
I think the value of this research is (worthless)*sqrt(bullshit).
the usefulness, or utility, of a network equals the square of the number of users.
Ok, so we have about 200 users; thus 200^2 = 40,000. So, the usefulness of our network is 40,000 what? Furlongs?
Ronald said nothing. He flung himself from the room, flung himself upon his horse, and rode madly off in all directions.
See Ron Burt's work...
Who defines useful. What is useful to you may be quite important to me, and vice-versa. While you might not be interested in dwarfs having sex with chickens, I might thrive on it. There are plenty of sites of questionable content, many of which have banner ads. This tells me that there is atleast some interest. Think about phones. What if cell phones couldn't call land lines, or if AT&T couldn't call Cingular or Verizon. The cellular networks would be almost useless. Even if you could get you colleagues and family on the same system, at some point, you'd find someone on an incompatible system. I think that's the point of the article. Now, whether or not you can actually place a value on this is, or come up with an actual number is another thing altogether.
The linked article refers to the actual useage we draw from a network as an example of it's value. But clearly there is far more value to be tapped. Look at Neural Nets. With only a few nodes, they can actually learn.
Consider the untapped power of the connected masses. The potential computational power of all connected home desktops in North America is far greater than the most powerful supercomputer. Even Google, which has an estimated computational capacity surpassing the most powerful supercomputer and approaching that of the human brain.
Estimates are that
the Human brain computes somewhere between 100 TERAflops and 1000 Teraflops,
and Google performs somwhere between 100 and 300 teraflops.
Thoughts on the Emergence of Computing Intelligence
Knowing the number of nodes that visit slashdot. I guess this is highly valuable? to the n^2?
Firstly, the logarithm they're talking about is base 2 (for those of you like me who didn't recognise the twentieth power of two).
My aunt dials up a few times a week to check her email and surf the website of the national broadcaster. The n^2 law assumes her connection is as useful to the interent as one of the Google servers. All power to her.
I’m old enough to remember 16K of memory being described as “whopping”
Well, I always thought the potential value of a network, all else being equal, was *directly* proportional to n^2 - n, where n is the number of nodes.
As a corollary of that, if you invent a new, screamingly fast but incompatible network medium, and get halfway through building the first network card, you have created a network of value 0.5 * -0.5, i.e. it's worse than useless.
At which point your investors run away in droves and the half a card is all you have left. Badum.
shouldn't that be that the spam goes up exponentially? if it was the usefullness, then society would work hard to break down barries of access, instead of putting up so many barriers. for example, when was the last time president bush returned your email?
The explosion in value in those cases is actually a result of Reed's Law, which states that the connectivity value of Group Forming Networks (GFNs) grows at 2^n
See Reed's Locus, "That Sneaky Exponential",
http://www.reed.com/Papers/GFN/reedslaw.html
Flout 'em and scout 'em,
and scout 'em and flout 'em;
Thought is free. - Shakespeare [The Tempest]
So how much more useful it is depends on the person.
For some the potential of being able to spam 2 x more people might even be worth more than 2 x - because it'll cost more to set up separate spamming systems to spam two unconnected networks.
To the marketing people if 1.1 x or 2 x puts you at No. 1 position, it's worth 10x more than No. 2 position.
To someone who only uses it to communicate with a _single_ loved one, it's not worth much more.
So saying that someone could calculate just by pure math alone the value of a network is naive.
A decently thought out survey of a random 1000 people would even be better.
Also: using "AT&T vs the rivals" as an example doesn't work, because AT&T is connected to the rivals - their users can still contact each other.
So there would only be a smaller increase in value (to the users) by merging the networks, compared to if the two networks were not even connected at all.
If the the various networks were not connected at all, connecting them could actually decrease the value of largest network significantly in the eyes of the owners - they are no longer the number 1, and worse - it will become harder for them to become a monopoly - whereas previously more and more people may want to switch to their network because it is the largest - more of their friends are likely to be on that network and the networks are not interoperable.
Right. So when is Wikipedia going to buy the universe with some of that value they're sucking up? I stand by my claim.
"Anything that can be refuted... will."
S1: "This statement can be refuted".
If S1 is refuted, then it is true, and therefore not refutable, and so false.
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It has been shown that Murphy's Law, despite its name, is actually just a rule of thumb.
I wonder why market forces are discussed in the paper. From my understanding the "Laws" of computer science operate in a vacumn of other information. I think this paper is allowing in information that discracts a reader from the actual math behind the law. Sure adding market forces and bussiness information may make a point about growth and need of high bandwith pipes. The question was changed to make his statement correct. If the original question was adressed, I doubt the paper would have merit.
Well, if you multiply the number of users by itself, you obviously get a lot of square users as the final value of a big network.
This seems to match what I see on the net. You get groups of people tied together by their blogs, mailing lists, &c (even sites like this!), but without too much strong interaction otherwise.
I can't be bothered to analyse it formally, but I suspect that n.log(n) might be a natural value for such a network-of-networks.
Ceterum censeo subscriptionem esse delendam.
You confuse "value" with $$, padewan. Only on the Dark Side are they one and the same.
Flout 'em and scout 'em,
and scout 'em and flout 'em;
Thought is free. - Shakespeare [The Tempest]
Maybe I sniffed a little too much snark when I was writing that last post, but my point remains the same. If there's "value", then someone saved some "$$". There's no confusion here and you shouldn't belive that silly Lucas propaganda. To talk of value that people won't strive for or benefit from is nonsense. If it has value, then people will pay or do the equivalent in work to get.
Let's say that Wikipedia doubles in value with every million users after the first, and that at first it's worth me putting one minute of my time in to improve. After eleven million users, it becomes worth 2^10~1000 minutes of my time. After 201 million users, it would be worth 2^200~10^20 minutes of my time. Collectively, because of the tremendous value that Wikipedia generates from even adding a few users, the entire human race should gear itself to producing more Wikipedia users either through birth, AI, or space exploration. Rivals must be absorbed or aborted because even if they lure a few users, they'll take huge amounts of value away from Wikipedia.
If this sounds ludicrous, it's because it is. There's no network with exponentially increasing value. Don't bother continuing with the Jedi talk, there's no such network. If you continue with your question, first find a network whose value increases exponentially with each additional user.
Just as well that Metcalfe has been discredited, because he is an open-source-hating nitwit. IIRC this was revealed when he was interviewed here on Slashdot a couple of years ago. Somebody correct me if I'm wrong.