The physical network (which we will later call a W1 network) can not escape the effects of diminshing returns, nor for that matter can the virtual (which we will come to call a W3 network). But the evolution of digital technology radically favors the latter over the former. The advances made in hardware developement, production and implementation, dramatic as they may be, are trivial in comparison with the advances made in explotating the data that resides upon them.
As I point out further on, these two networks are not only interdependet upon each other - they are in competition. But, for the sake of describing a particular sort of completness - the virtual, I will assume the pre-existence of a hardware network, albeit a definitely incomplete one. I am not discounting the importance of discussing hardware network completeness, there are all sorts of social, political, economic issues of rank to be hashed out - just not here.
When speaking of virtual networks residing upon pre-existent hardward networks. Here is my complement law to Metcalfe's:
The cost of a virtual network does not increase in proportion to the square of its nodes.
If both Metcalfe?s and my laws are correct, virtual networks would seem capable of reversing the law of diminishing returns, and ?the more ? the merrier? axiom bounded by no practical limits, should rule the day. At some point in maximizing a network's value, as the cost curve for increased membership consistently moves in the opposite (downward) direction to the upwards pointing value curve, the inclusion of each new node will be determined soley on the relevance of its potential contribution to other nodes.
The posibility of near-zero transaction cost environments gives rise to theories of completeness, where "all the bits that fit" are included in a virtual network, increasing the population until every member, and every bit of data, of even the slightest significance are admited to the fold.
The net gain of our actions is the benefit derived minus the costs incurred. It is rational to assume that costs increase with effort, time and distance - the further one must walk to fill a bucket of water, the more energy expended, and and the less time available to do something else. In an physical network, each connected node represents a cost, be it for cables, hardware, resource time, or electrical power. If a new node is added - the network designers must consider the extra costs occurred in relation to the benefits gained.
If we take telephone networks as an example, the infrastructure costs of adding lines and nodes is not uniform ? land line installations in geographically remote areas will obviously be disproportionately costly compared to city installations, and many societies provide subsidies or demand bulk service commitments from their telcos to adjust for this. Yet taken as a whole, the costs in infrastructure and power consumption for the world's telephone network are easily offset by gains in utility. Though some infrastructural nodes are ?cheap? to include and others ?expensive?, in sum, benefits outweigh costs.
Now if we look past issues of infrastructure (hardware and lines) to matters of address-structure we will uncover a fascinating phenomenon. The ubiquity of telephones (in the developed world at least) is so commonplace and humdrum that we forget the startling fact that we have created a network that is immune to overcrowding. Our telephone system is essentially global and homogeneous ? using globally accepted standards, and no matter how many new nodes are connected, the benefits of expanding membership outweigh the costs. There is no economic rationale for creating two or more non-connecting telephone networks, no matter how many new telephones, telephone companies, and telephone lines are added to the one that already exists.2
Our global postal network does the same trick - through the technology of distribution we extend past the limitations of time and space. Imagine the following ridiculous conversation.
- Call Fiona and tell her we have approved the plan.
- I can't call her ? she is on GEC and we are on DBB
- You mean the two systems can't connect? How stupid. Well then write her a letter!
- I can't write her. She is FedEx and we are BRM . I can't email her either. She's on AOL and we are on Gmail.
- Why isn't she on Gmail too?
- Gmail is full - overcrowded. They have no more room for new subscribers.
For all I know Gmail, Hotmail, Yahoomail etc. might one day refuse new members on grounds of overcrowding, but the prospect seems exceedingly unlikely since the hardware resources per subscriber are, if not trivial, easily absorbed in the greater (profit) scheme of things.
Actually it is the complexity of addressing and connecting nodes that puts the heaviest burdens on digital networks and once (and if) those problems are solved, the complexity of addressing and accessing specific content on or across nodes. Completeness is desirable if it adds to efficiency of access ? if not, then the division of networks and the compartmentalisation of resources are preferable alternatives.
The complaint, so often heard in the early stages of Internet development ? ?too much information?, gradually looses its rationale, as each additional node (or web site) contributes to the description of the entire Internet corpus, making the discovery of appropriate resources easier ? not more difficult.
From a state of completeness ? we design tools of selectivity. Google ? the catalogue of all the web pages, Amazon ? the catalogue all the books and eBay ? the catalogue of all the PEZ-dispensers, are parade examples of the advantages of cleverly filtered completeness, but above all it is the Internet itself, the medium of Google, Amazon and eBay, that proves the robustness and scalability of completeness in digital networks.
According to the reigning theory of communication which we will deal more with further on, efficiency in transmitting information is increased by pre-existent knowledge ? the more someone knows the less you have to tell them, and of course inversely, the more you know the less you have to ask. By removing, once necessary, but now artificial, barriers between data stores in our networks we are increasing efficiency ? not reducing it. More costs less. As Bakos and Brynjolfsson have written:
[...] the near-zero marginal costs of reproduction for digital goods make many types of aggregation more attractive. While it is uneconomical to provide goods to users who value them at less that the marginal cost of production, when the marginal cost is zero and users can freely dispose of good they do not like, then no users will value the goods at less than their marginal cost. As a result economic effiency and, often, profitability are maximized by providing the maximum number of such goods to the maximum number of people for the maximum amount of time.3
1 For example, if you have four nodes, or computers, on a network, say, an office intranet, its "value" would be four squared (4^2), or 16. If you added on addition node, or PC, then the value would increase to 25 (5^2). See http://www.mgt.smsu.edu/mgt487/mgtissue/newstrat/metcalfe.htm
2 Of course one might do so for reasons of secrecy.
3 Bakos and Brynjolfsson Aggregation and Disaggregation of Information Goods Internet Publishing and beyond MIT Press, Cambridge 2000