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“Everything wants to be connected“, is the famous ‘Renan Law’ of my friend and colleague Sheldon Renan. But, why does everything in the universe want that? What is this self-interest or incentive to connect? And what does one do after the technical connection? On how many levels and how strongly must we connect to achieve meaningful cooperation? And, what is even more difficult, to achieve cooperation between people with very different backgrounds?
There is a lot we can say about those questions, but let me first introduce some often-mentioned concepts or Networking Laws and see how they differ, so they are put in context and in perspective. I will avoid much of the mathematical symbols here, or put them double between brackets, since I know formulas can incite panic attacks in, for instance, sociologists and many other non-scientifically minded people.
First of all ‘Network Effects’ can be formally defined as: “How much does the Value change, proportional with the Number of people that participate in a network of connections/ relations”.
((The Value is noted ‘V’, and the number of reached people in the network is noted ‘N’)).
These effects are the engines for New Power (connected demand side, see ) and they make networks grow and interconnect. Growth of Value can trigger growth in wealth, job creation and prosperity so it is worthwhile to study and implement them.
1. Sarnoff’s Law for broadcasting networks, radio, TV and media publication & distribution.
The first networking effect is Sarnoff’s Law, that states that the value of an one-to-many information distribution network (SA: uitzaai) grows proportionally with the number of readers (books, newspapers)/ listeners (radio) / viewers (TV, movies). Or in other words: number of eyeballs of consumers. Such networks simply count viewers or views, without any regard for differences between or expectations of the users.
David Sarnoff has been able to convince with this ‘law’ the many local broadcasting stations in the US to interconnect and broadcast one or more nation-wide TV channels like ABC and NBC. More eyeballs, bigger audiences for the politicians and more value for the advertisers ! This network effect – more is better – is still the driving force behind ‘publicity’ and PR and is now in the process of being transposed on to online media on the Internet, where the media advertise themselves, insisting that us looking at their broadcasts is THE way of using the Internet.
Figure: NL adds market. Forecast online 2015: 1.5 billion euro’s, double digit growth
I strongly disagree with this notion that spreading commercial content is the purpose of Internet, getting more irritated every day by the bombardment of propaganda and commercials and their influence on the actual content of the Internet, swamping everything with sex-and-violence memes, which tend to drag it down to the lowest common denominator level, like water. In contrast with what Internet did allowed its users, to find themselves the the highest levels of their interests. Sarnoff’s Law applies to one-direction messages with identical content, from a central source to as many passive, tranquilized ‘information consumers’ as possible – who, by the way, pay for the adds through taxes or the price of the products or services they are encouraged to buy and consume.
And ‘value’ in this context means value for the broadcaster and commercial or public service advertisers. Politicians and business persons are very fond of this form of network use to promote themselves or their products. They want to be in the centre of the public attention golden triangle of “screen, beer and bites” in which we live. And it is unfortunately also at the core of the business models of Google Search and Facebook etc. But as I’ve written above, users start to get annoyed by commercial breaks about things the do not want to buy, or lots of loud little, attention-grabbing and inescapable tiny films, monopolizing more and more space on our computer screens and phones, and for which we pay in subtle, indirect ways. This IMHO is not a wrong intention of the advertisers, as long as their stuff is not forced unavoidably upon us, made obligatory so other choices are excluded. Business commercials and state propaganda have this same tendency to dominate.
((Sarnoff: Value ~ N viewers = 1+1+1+ …+1; N times)). ((one -to -many, or 1:N ))
Media Value adds up, which means the value counts up, is cumulative (NL: additief), irrespective of the diversity in demand or interests of the viewers. Of course, in some types of one-to-many publication, the number sold of a book or numbers of ‘views’ of a blog or ‘likes’ of a picture is a positive measure of income, popularity and/or appreciation, and can be used for ranking and attracting more viewers/readers. So Sarnoff’s Law is a driver for growth of the World Wide Web too. Documents etc. are put online on the WWW to get more eyeballs on the page and reach and communicate with possibly interested people, who can still choose themselves.
2. Metcalfe’s Law for telecommunication networks with CONVERSATIONS and interconnection of networks.
The second network effect is Metcalfe’s Law that states that the Value of a communication network growth is proportional with square of the number of participants connected to it. Take for instance, a (mobile) telephone conversation or an exchange of email messages. The reason is that each of the N people connected can talk to N (minus one, yourself) other people or computers.
((Value ~ N^2 = N+N+N+ …. +N; for N people/computers who can communicate with each other)).
Robert M. Metcalfe who defined this law, is also the inventor of the hugely successful (and disruptive) Ethernet Protocol. Developed to let computers share local area network resources, this is now also applied to sharing, using long-distance fiber optical cables. The value of such N:N telecommunication and computer-computer networks thus grows faster with N than 1:N media networks. It is also the reason why all fixed telephone and mobile telephone networks in the world are interconnected so that everybody can reach each other. It is also the driver for interconnection between datacom networks: the INTERnet and its attached services, which is, of course, a network of interconnected networks. It facilitates the SHARING of network infrastructure for digital transport. And it drives peering and transit connections between ISP’s and Carriers: a non-zero-sum game (win/win situation); a strong incentive to build and interconnect FTTX networks, so they can scale up and be hugely successful.
Because of this Law the present total value of the telecommunication industry is multiple times that of the media industries combined in the world, contrary to what the media themselves would have us believe, including film and television celebs advertising themselves. To say it more compactly: “Content is not king – communication is “ (quote of Odlyzko).
That people consider the possibility of connecting to billions of others as valuable can be concluded from the fact that they are willing to pay for calls and internet access. That growth of network Value is however, in practice, tempered by the fact that this law does not take into account the different strenghts of the links/relations between people. Or to put it more bluntly:”maybe I can talk to anybody in Brazil, but maybe I have nothing to discuss, not even to chat, except about the weather and to exchange some cat photos”. The lower than square value growth has been derived in  as the Odlyzko-Tilly Law which may be more realistic than Metcalfe’s Law and Reed’s Law but still way bigger than Sarnoff’s Law of media broadcasting. (( V ~ N * Log N))
3. Reed’s Law of GROUP MEMBERSHIP –Value of Social ( tribe internal) network
The third network effect is in fact based on the “social networking behaviour” of people, as opposed to infrastructure investments and was formulated in 1999  by prof. David P. Reed van MIT . Reed’s Law states that the value for users of big networks, and more specific: social networks, grow in proportion exponentially with the number of participants (members of tribes).
You can either be or not be a member of a closed (user) group/ sharesome  or tribe. So if there are N of those groups/clubs this gives 2 to the power N possibilities for memberships, growing exponentially when more groups are added.
Just try it yourself make a matrix of vertical N groups and make horizontal rows of persons who are (1) or are not (0) member of those groups. This chats (charts?) the total number of possibilities and defines the total value of social networks that support tribes.
(( Reed’s Law: Value ~ 2^N = 2 * 2* 2* ……*2. N times))
Why is being a member so valuable to people? It is the strong urge to belong, to be appreciated and be protected by fellow tribe members. That is, among other reasons, the drive to text/ sms/ Whatsapp/ tweet all day and night with your friends: you confirm and are confirmed, socially, with group knowledge, you are member of the tribe, wherever you are at a given moment. It is very important for young people and they are willing to pay for it.
Reed’s Law of Possibilities may have limitations, since not everybody can become a member of every club, because one’s language, clothing and conduct must be acceptable to the other members of the clan. In addition, the fear of being refused or expelled can be significant. That is why members constantly confirm their mutual bonds. One does not need to be an anthropologist to see this. (Sometimes the recently initiated members even have to show themselves to be worthy of being a member by having to behave in a nasty way to non-members outside the tribe.) These social urges make the value growth of Reed’s Law of group membership grow exponentially: faster and larger than either Sarnoff’s or Metcalfe/Odlyzko-Tilly’s.
There is something that has crept in almost surreptitiously onto the Internet, and which is implied by Reed’s Law, is that every human now can be member of more than one tribe/ sharesome at the same time : “Multi Tribe Membership” (MTM). Before the Internet that was well-nigh impossible. Not so long ago if you were born in a village somewhere, in a certain family at a certain social level, or certain neighborhood, the rest of your life could practically be charted until you died, no matter how hard you tried to raise your social status, for instance through education. Your own family members would frown if you started relations outside your social level, religion or tribe. And everywhere people would tag/ judge you by your accent, dress or skill as “somebody from lower middle class in X”.
You could go to the best schools, be a member of an elite sports club, listen to classical music and frequent the opera and ballet; people would still remind you of your class / family/ regional origins. The only escape was to move to the city or to another country, or join a different culture.
Now thanks to the Internet and other social media you can escape, be a banker in the morning, ride your Harley with your club in the afternoon and dance the tango’s at a samba school in another city. So you can be a member of multi tribes.
It is the exclusivity of these closed ‘tribes’ that attracts people. You join the group to be with people like yourself, with the same prejudices, dresses, who you can trust and feel safe with. The same cultural backgrounds and codes in Tweets, and by demonising outsiders. You can like this or not but he urge to be part of a group and be appreciated as a valuable member in that community is very strong, rational or not. And the urge not to be expelled is strong. In some parts of the world to be expelled from a village or clan can mean that you will not survive because access to water, food and shelter is taken from you. So Reed’s Law of the value of memberships is strong, and may indeed be more valuable for society than the value of its communication networks.
4. Van Till’s Law for the value of COOPERATION & COLLABORATION
The fourth network effect, even more strong and powerful than the first three as an engine for the Collaboration and Sharing Economy we now live in is Van Till’s Law that states that the shared value for the Peer-to-Peer commons in which participants cooperate and collaborate in a network (which is more than just be a member) grows proportionally with N Factorial, [4,5,6].
((Van Till’s Law of Shared Value V ~ N! = N * N-1* N-2 * ……*2 *1)).
This grows even faster than exponentially (viral) because this concerns the maximal (upper limit) number of combinations you can make by networked cooperation between N unique diverse and non-interchangeable) individuals, each contributing his/her first-class skills. and crafts.
Example: with a deck of playing cards, each card unique, you can lay 52 ! different rows (combinations/ sequences) of cards on the table: 52 ! = 52 * 51 * 50 * etc . With each card you choose from the deck that you lay down you have one less you can choose from. The 52 factorial combinations are are huge number 3.1456688 E+69 , which is bigger than the number of atoms estimated to be in our solar system. So this upper limit is impractical to estimate the value of cooperation. But it makes sense to show the richness of constructive possibilities when we connect & combine skilled people beyond the boundaries of their many closed tribes. The number of possible combinations of unique idea’s is limitless, only constrained by lack of imagination and cultural and conservative prejudices and silo’s with vested interests. These are the boundaries we have to cross if we want to create value and give our children a future.
Crucial to Van Till’s Law is not the upper bound of its Value, but that cooperation and co-creation by participants, with the best  contributions and their first-class skills, whatever their background, online and off-line, works in a multiplicative way to create value, as opposed to adding up, as with broadcasting.
This supports the popular slogan of the P2P Open Share Economy: “To share in as mart way is to multiply value for all contributors” (in the Dutch language: “Delen is vermenigvuldigen” (cc). This is a pun in Dutch, based on the double-meaning of ‘delen’,as both ‘sharing’ and ‘division’, the latter being the opposite of ‘multiplication’; it seems to say ‘division is multiplication’, which is a nice paradox). If a valuable person joins your team, who can really DO something extremely well and contribute it as promised, it can multiply the value of the whole team. Besides, the group can act as a magnet to others, thus speeding up and progressively enhancing the learning process.
P2P ‘Sharing’ implies in this context not only physical resources and tools but also of practical knowledge and information about solving problems. Knowledge and information does not diminish if you share it and therefore is abundant, non-scarce and thus inexhaustible.
If such skilled persons and constructive teams are woven together, brought together by Networkers and Btwieners  and a flock or maze builds up, it suddenly is possible to have 50,000 people on a Hong Kong square, or Paris demonstration, behave and act together like one non-violent coordinated stable unit.
It turns out that Btwieners, with the help of smartphone networks, can bring stability by binding people from multiple closed groups together across boundaries, instead dividing them by hate and conflicts erupting from multi-ethnic tribes clashing with each other.
The value and wealth generated by the interconnection between real top craftsmen and -women is too powerful to resist. This is also my recipe for smart cities and chains of cities beyond that:
Interconnect across boundaries the members of selfish and proud sects and tribes together into a Network, by way of problem solving, by which you need each others specialists, and by constructive shared goals that are impressive. Cathedrals where built that way, by craftsmen who respected each others work. We can do that in the P2P Commons of the Collaborative Networked Economy too. Interconnect across boundaries members of selfish and proud sects and tribes into a problem solving Network, requiring the skills of all available specialists, to achieve goals of excellence. Cathedrals were built that way, by craftsmen who respected each other’s work, whatever their background. We can do that again in the P2P Commons of the Collaborative Networked Economy too, but we first must learn to form well working Weavelets, constructive groups with “collective intelligence”.
I sincerely hope that the Fourth Network Effect of collaboration will get us out of the 2008 recession at last
May the 4th law Force be with you !!
Jaap van Till, TheConnectivist
PS.1 The business community is noticing the same four network effects as phases in Social Media binding of clients. For instance Gaurav Mishra of 20:20WebTech identified four “phases” in connecting with clients and groups of clients: 1. Content 2.Collaboration 3. Community 4. Collective Intelligence. With each step the effort becomes more invisible, but also more difficult. And yes: curators, conversations, co-creation and recommendation/reputation/ trust play critical roles.
 Blog about New Power https://theconnectivist.wordpress.com/2014/12/20/new-power-on-the-rise-user-side-synthecracy/
 Andrew M. Odlyzko and Benjamin Tilly http://www.dtc.umn.edu/~odlyzko/doc/metcalfe.pdf
 D.P. Reed, “Weapon of math destruction: A simple formula explains why the Internet is wreaking havoc on business models,” Context Magazine, Spring 1999. http://web.archive.org/web/20080526050751/http://www.contextmag.com/setFrameRedirect.asp?src=/archives/199903/digitalstrategy.asp
 J.W.J. van Till, 2004 “The Fourth Internetworking Law” http://tnc2004.terena.org/core_getfileeee3.pdf?file_id=389
 Jaap van Till, in the Dutch language: chapter in SURF WTR book 2008 http://www.scienceguide.nl/pdf/VanTill200804.pdf
 “De Verbonden Stad” – Essays over de stedelijke omgeving in de context van Diversiteit en Mobiliteit – Luud Schimmelpennink, Jaap van Till, Kyra Kuitert, Lucia Lindler, Luc Sala ; April 2015; http://www.boekcoop.nl
 Jaap van Till Definition of a Sharesome https://theconnectivist.wordpress.com/2014/12/28/definition-of-a-sharesome-nl-een-deelzaam/
 Jaap van Till Definition and importance of Btwieners https://theconnectivist.wordpress.com/2014/11/08/slides-of-my-social-networking-masterclass-workshop-at-osdc2014/
 Jaap van Till Van Till’s Principle (VTP) of well connectedness https://theconnectivist.wordpress.com/2014/07/14/van-tills-principle-of-maximum-well-connectedness/
 Het Kantelings Alfabet – Verandering begint met Delen – ; Een co-creatie van een divers gezelschap van kantelaars, dwarsdenkers, verbinders, friskijkers en verkenners ; april 2015; E: firstname.lastname@example.org
( Version April 7, updated for better readability by the “trau-maths-ised”, with thanks to @trutherbot and @digitalErmit on Twitter
( Version April 11, book  was published,  added )
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License. 2015, Jaap van Till, vantill (at) gmail (dt) com