MetcalfesLaw

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The value of a network is proportional to the square of the number of people using it. The idea is that each person acts a valuable resource to all the other people, so each person sees value N, and there are N people.

Sometimes called the law of the telecosm, as opposed to the law of the microcosm (which says that smaller ICs are also quicker). Coined by BobMetcalfe?, the inventor of Ethernet. See http://www.digitalcentury.com/encyclo/update/metcalfe.html for a bio.

See:

http://www.gildertech.com/public/telecosm_series/metcalf.html for GeorgeGilder's essay on the law.
ReedsLaw, an "extension" of Metcalfe's Law.
TheTippingPoint, a book.
[A refutation of Metcalfe's Law and a better estimate for the value of networks and network interconnections], which argues that value grows as n log n.

MetcalfesLaw has an effect on the WikiLifeCycle -- at some point explosive growth occurs as the value of the network exceeds the cost of participating.

But the cost of participating can vary. If the cost raises because of Wiki:WikiSuccessCanInhibitNewWriters, the network can diminish thus stopping the explosive growth and putting the WikiLifeCycle into stability, preventing the wiki from the final stages of "fall and decay" (or GatedCommunity) and WikiShutDown. That could explain the stall which major WikiPedias are experiencing since 2007-2008, with frozen number of [active] and [very active wikipedians], [edits], [new articles]: the encyclopedia and its individual articles are more complete, hence more difficult to expand and correct for the average user of the site. But if we improve the usability of the wiki, maybe we can attract new users who were not able to edit due to technical issues, not for lack of knowledge, thus lowering the cost of partecipating and start again with an explosive growth, i.e. bringing again the WikiLifeCycle to the "MetcalfesLaw kicks in" stage. A sort of less frightening WikiPhoenix? restart. The Wiki maybe will reach a new stability, or start again improving its efficiency.

The ConnectedGraphSquaringProblem is a converse observation that explains the diminishing value as the network grows larger and larger. This is possibly predicated on the limited or finite capacity of one individual for tracking relationships, and thus as the number of possible connections grows the links grow weaker, thus diminishing the value of the network. This is also discussed on the page for TheTippingPoint.

limited or finite capacity of an individual for tracking relationships -- this is an assumption on my part. Evidence for/against welcome. -- EricScheid

Perhaps MetcalfesLaw really is a solution to the ConnectedGraphSquaringProblem and an answer to CommunityMayNotScale. The nice thing about community growth is that the power of the graph grows at O(N**2) (or even O(2**N) by ReedsLaw) while the number of people only grow at O(N). This means that more people can solve the problem.

True, the overhead costs of maintaining the graph cause TheTippingPoint, but maybe that doesn't matter. All you need is the potential to exercise those connections. This is what ReedsLaw is all about.

Either law you choose, the point is that community growth managed well has a strong potential to not implode but become self reinforcing, as links between agents reinforce the structure of that society. The more those connections can be made, the larger the society can grow. -- SunirShah

It has occured to me that perhaps MetcalfesLaw and the ConnectedGraphSquaringProblem are actually talking about two completely different things, and don't conflict at all. MetcalfesLaw seems to state that at some point, the benefits of participation outweigh the costs, so lots more people will participate. At no point does it claim what level of participation is required to reap the benefits - even the most minimal participation may do it. The ConnectedGraphSquaringProblem notes that at a given point, everyone interacting with everyone else becomes too costly to maintain. Bringing the two together would seem to indicate that at some point, a community is going to reach a population explosion, and when that happens, fairly soon people aren't going to be able to connect with everyone in the community. So, you'll have a bunch of people who are probably engaging at the same level as before, but not with everyone in the community. -- LeeDavisThalbourne

Compare http://en.wikipedia.org/wiki/Dunbar%27s_number

MetcalfesLaw

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