Four Models For Networks

JF Koh, June 1997


This paper deals with four possible models that might be applied to the development of the global computer network known as the Internet. The purpose of this paper is to hazard an exploration of these theories per se. In the column on the right, their application is made by a mapping of theory to practice using hyperlinks to a separate document charting the developments of the Internet — this will be the Internet Time-line Project.

The initial conceptual approach immediately suggests the problems of isolating the theories in abstract form, unable to validate themselves on the concrete grounding of the everyday. As such, in the left column I will seek to illustrate with examples without, as far as possible, borrowing historically from the Internet.

The models dealt with here will include:

  • Deleuze and Guattari's rhizome
  • Rothschild's bionomics
  • Chaos theory
  • Malpas and Wickham's governance and failure

Deleuze and Guattari's rhizome

The rhizome erupted as a reaction of what Deleuze calls "the outside" to the stagnant traditions of the French institution of philosophy:

Closed upon itself, and holding the lid down on its own discipline, philosophy has often mistaken vacuity and ineptness for wisdom and rigor and the foul odors of inbreeding for signs of intellectual and moral integrity. To open the lid, so that a gust of fresh air may come in from the outside, is not to waste time deciphering the signs of an upcoming end of philosophy.

(Boundas, 1993: 1)

Rather, the rhizome seeks to transform the landscape of philosophy instead of replacing it, to rupture the landscape of inbred arborescence so used to itself. What Deleuze meant by "the outside" is a meta-dimension through which lines can bridge various territories without homogenizing them1.

An example of "styles or modes of expression" (Goodchild, 1996: 85), or of writing and reading, Deleuze and Guattari's rhizome is named by analogy after the laterally proliferating plant as opposed to vertically expanding trees, the methodological difference being between multiplicity and laterality in the former, and dichotomy and bifurcation in the latter. Perhaps the connector "as opposed to" ought to be re-worded: in rhizomatic thinking, rhizomatic thinking should not be thought of as being dichotomously opposed to tree logic, for that is a mode of conception typical of tree logic; rather, it is an offshoot2, an escape via a "line of flight" (Deleuze and Guattari, 1993: 32) facilitated by processes of deterritorialization and reterritorialization — strategic operations of "asignifying rupture" (ibid.) in space which Deleuze and Guattari explain by means of the example of the wasp pollinating the orchid.

If deterritorialization ruptures the line that delimits the conceptual or physical space of the subject, then reterritorialization redraws that line, although not necessarily restoring it. Indeed, more often than not the subjective space is redefined. Deleuze and Guattarri's dynamic rhizome assures us that the previous demarcation was merely a transcient state, a lamp post passing by in the scenery.

1 This column on the right represents such an "outside" hypertextual dimension. It links the column on left (or to be technically precise, this document as a whole) with other documents, all located on the 'flat' dimension (see below) of the Web. The links are the lines located in the meta-dimension, and they do not homogenize the territories — that is, the Web documents all stay different even after they have been linked.

2 In Adrian Miles' rhizome-inspired Hyperweb, "a web is a colony of tubers".

The very analogy by means of which Deleuze and Guattari name their concept can be used to illustrate the processes of deterritorialization and reterritorialization3, by a line of reasoning substituting rhizome-the-concept and rhizome-the-plant respectively for the orchid and the wasp. Rhizome-the-concept, an "aparallel evolution" (ibid.: 33, in the words of Remy Chauvin) on a plane of existence entirely removed from the physical realm of rhizome-the-plant, deterritorializes by breaking out of its conceptual dimensions to form a methodological image of rhizome-the-plant. Rhizome-the-plant then reterritorializes on rhizome-the-concept by lending its methodology and acting as a signifying carrier of rhizome-the-concept (in a sense, rhizome-the-plant offers its name along with all the connotative baggage, thereby making rhizome-the-concept its client). Yet rhizome-the-concept has deterritorialized rhizome-the-plant by making it serve the concept's signifying mechanism. The link is formed at only a stratum in each of the two — the concept remains the concept and the plant remains the plant, but each has produced a "surplus value of code" for the other to capture, and each has operated a "becoming" of the other (ibid.).

Still, even though the common rhizome formed by rhizome-the-concept and rhizome-the-plant is one of signification, according to the principle of asignifying rupture the continuous deterritorialization and reterritorialization not only results in the effacement of each of the two signifying identities, but also in a floating unity beyond signifying possibility.

Each of these becomings brings about the deterritorialization of one term and the reterritorialization of the other; the two becomings interlink and form relays in a circulation of intensities pushing the deterritorialization ever further. There is neither imitation nor resemblance, only an exploding of two heterogeneous series on the line of flight composed of a common rhizome that can no longer be attributed to or subjugated by anything signifying.


Deleuze and Guattari have named five other principles of the rhizome. They are:
  • Connection and heterogeneity

3 Internet technology is a result of deterritorialization and reterritorialization between various technologies, most notably:
Unlike in a tree structure, each heterogeneous point in a rhizomatic system can and must have connections to all others, unconstrained by any bifurcating order. There is no underlying principle, no point of deterministic origin4, no tyranny of centrality, although stabilizing points may dominate constellations of other points. The principle of dichotomy has to be abandoned, for it is too self-contained and does not open itself to connections with other domains — for example in the case of linguistics, these other domains would be "collective assemblages of enunciation" (ibid.: 30).

The rhizome instead focuses on extending links to "modes of coding [from diverse spheres5] (biological, political, economical, etc.) that bring into play not only different regimes of signs but also states of things of differing status" (ibid.: 29). The rhizome is thus more reflective of, for one, actual social spheres in which there is no one universal language, no homogeny, but a complex interaction between all the articulatory modes ("linguistic, ... perceptive, mimetic, gestural, and cognitive") of the "throng of dialects, patois, slangs, and specialized languages" (ibid.: 30).

The rhizomatic method of study differs from the method of the tree in that it does not attempt to break the whole into structural elements, nor seek a return to roots, but instead forms an analysis by opening it to "other dimensions and other registers" (ibid.).

  • Multiplicity

    Goodchild puts it this way:

    [C]oncepts are considered as neither one nor multiple in meaning, but have a multiplicity of meanings which change in nature with each new connection made — a multiplicity having neither points nor terms, but only lines of variation.

    (1996: 85)

4 Even if it were possible to find the points of origin of the Internet (see ARPA, TCP/IP), they determine no tyranny over the structure or organization of its continued development.

5 Internet technology arose from connnections between technology and various other realms, including cybernetics, politics and military defence.
But first, a little about multiplicities6: it is a characteristic of the rhizome which differentiates it from the tree. The essence of the multiplicity lies in the linking between points (starting with the line of flight or deterritorialization), not in the structural positioning of points so cherished in the tree7. A multiplicity is complete in itself, in that it has not the pivotal point so essential in trees. Its operations go beyond the politics of subject and object positions; instead, the rhizome has "determinations, magnitudes, and dimensions that cannot increase in number without the multiplicity changing in nature" (Deleuze and Guattari, 1993: 30). In other words, the effect of the multiplicity extending links to other dimensions is that it transforms itself, changes its nature, becomes no longer the same8.

While the tree imagines a "supplementary dimension" governing or "overcoding" (ibid.: 31) its structure, the multiplicity is constituted only by the exact number of realms or dimensions in which it resides and fills, and in that sense, the multiplicity is 'flat'9. The "line of flight or deterritorialization according to which [multiplicities] change in nature and connect with other multiplicities" is articulated on a "plane of consistency" (ibid.: 31), a dimension-between-dimensions outside of the multiplicities, a grid that maps the links10.

6 The World Wide Web can be considered a multiplicity.

7 A Web site can be linked to any other site without regard to any structural or hierarchical position — all sites find themselves at the same level as soon as they are on the Web.

8 The usefulness or 'intelligence' of the Web is directly proportional to its links, quantitatively and qualitatively. Whenever a new link is added, it changes the Web as a whole.

9 As mentioned in Sidenote 7, there is no hierarchy on the Web. All sites compete on an equal basis — there is no privileged position to begin with.

10 See Sidenote 1.

  • Cartography and decalcomania

    The links through which concepts map onto one another are active constructions based on flexible and functional experimentation11, not "infinitely reproducible principles of tracing" (ibid.: 35). Such models of successive tracing includes structural and generative ones which give rise to inbreeding along a "genetic axis" (ibid.: 34) or fundamental blueprint. The tree method capitalizes on and takes for granted such intrinsic tracings to find the way either up or down the structure. Rhizomatic links, on the other hand, requires, adapts to and capitalizes on feedback12 in their formation. Most importantly, the rhizome has "multiple entryways"13, whereas the tree only has the singular blueprint (ibid.: 35).

Of historical significance is the purpose of the rhizome introducing a "gust of fresh air" from the outside. In France where philosophy is instituted as part of public culture, and where tree logic is the fundamental champion of state philosophy, the rhizome pit the "war machine-book against the State apparatus-book" (ibid.: 32). The very process of the rhizome has built within it the subversion of the state-tree.

Rothschild's bionomics

11 The carrier of the Internet, TCP/IP, was developed on the basis of such flexible and functional experimentation.

12 The adoption of standards and protocols on the Net relies on feedback in the form of RFCs (Requests For Comment).

13 The architectural design of the Net is deliberately open to allow for various forms of technologies to connect to it, whether they be different types of computers, media (audio and visual), or activity (education, research, commerce, etc.)

In 1990, Michael Rothschild's book, Bionomics: Economy as Ecosystem, offered a biological perspective on economics. Rothschild called for an end to the Newtonian assumption of static technological conditions which has underpinned the theories of classical economics since the industrial revolution — assumptions which have put classical models out of touch with reality. He instead proposed a "parallel relationship between an ecosystem based on genetic information and an economy derived from technical information" (Rothschild, 1990: Postscript). Both ecosystem and economy are dynamic and constantly evolve based on their respective type of informational sequencing14.

Rothschild likens capitalist economies to ecosystems, where such phenomena as "competition, specialization, cooperation, exploitation, learning" (ibid.: Preface) are common to both. Organic and economic evolution are thus respectively understood in terms of genetic and technological currency. According to Rothschild, the only difference is one of speed, in the order of a million times. He argues that technological change takes place so fast that we have been unable to recognize biological evolution as its close cousin. He notes other similarities along organizational and operational lines, namely complex hierarchies and relationships of interdependence.

14 It is not difficult to imagine how this could be applied to the Internet.

Furthermore, a shared self-regulating, self-organizing, "delicate, yet robust balance" can be observed, based on "intricately linked feedback loops"15 (ibid.). Rothschild claims that while DNA is the only substance on earth that can replicate itself, information also ensures its own survival through replication (ibid.: Introduction). He is not the first to make such a claim: the evolutionary biologist Richard Dawkins made essentially the same claim in 1976, referring to the replication of ideas which he called "memes" (Mangan & Wallace, 1996: 232). Rothschild provides other evidence to support his proposed parallel between biological evolution and economies.

Essentially, bionomics encourages an understanding of "economic systems as developmental organisms whose life processes needed to be reinterpreted" (Rothstein, 1996). As such, Rothschild advocates leaving economies to the "naturally occurring" processes of market forces (1990: Preface), rather than interfering with the complex economic ecosystem which can result in unpredictable problems.

15 The adoption of technology and standards on the Net has not been based on any external regulating or organizing agency, but on feedback (see Sidenote 11) and public testing — see for example the popular adoption of the early e-mail programme MSG.

Rothschild's biological metaphor and his packaged laissez-faire approach has found "supporters at the Cato Institute, [and] also caught the attention of countercultural devotees of Internet culture who had been developing the organic metaphor in other arenas" (Rothstein, 1996). Kevin Kelly for one has taken the metaphor to the realm of technology in his book Out of Control: The New Biology of Machines, Social Systems and the Economic World. He argues that as the possibility of design in its own isolated sphere runs to the end of its course, design (techne) has begun to borrow processes from evolution (gaia), not fully understanding how these processes work but nevertheless knowing that they do, from hindsight of millions of years of evolution. For example, genetic algorithms use processes of evolutionary crossover mutations (Scanlon, 1997). While the artificial is becoming 'natural, the natural is becoming artificial through the introduction of science in emerging fields such as genetic engineering and biotechnology. Kelly envisions a future already in the making, in which the distinctions16 between "the made" and "the born" are erased:

The realm of the born — all that is nature — and the realm of the made — all that is humanly constructed — are becoming one. Machines are becoming biological and the biological is becoming engineered.

(1994: ch1-a.html)

However, The New York Times journalist Rothstein has cautioned that these visions have a generalizing tendency: "right now, anything is treated as life if it is a sufficiently complex system requiring the transfer of information" (Rothstein, 1996). Bob Metcalfe, inventor of the ethernet and one of the technological pioneers of the Internet, has made a pointed reference to Kelly's biological metaphor and discounts the laissez-faire approach:
I think what we need to do is to convince them [subscribers to the biological metaphor of the Internet] that the Internet is actually a network of computers and that it's not alive and it's best it not be anarchistic, that it needs to be better managed. That's what I meant ... I've read Kevin Kelly's book on "Out of Control" and yeah, that's exactly the mindset which I think is inappropriate for the successful management of the Internet.

(August 1996: Interview)

16 In the early 1950s, JCR Licklider, one of the founding fathers of the Internet, envisioned the future symbiosis between humans and computers, the two functioning as a single unit.
Metcalfe's approach is one of management: remedying traffic bottlenecks17, ordering anarchy and improving pricing structures.

Chaos theory

Chaos theory began emerging in the 1970s as multiple disciplines realized that complex, dynamical, nonlinear systems followed universal laws. The connection was made across such diverse fields as biology, ecology, chemistry, physics, fluid dynamics, weather studies and economics. Computing offered special techniques for the study of complexity of nonlinear motion. "To some physicists chaos is a science of process rather than state, of becoming rather than being" (Gleick, 1993: 5; emphasis added).

Like bionomics shedding the chains of Newtonian world-view, chaos theory disavowed the classical method of scientific inquiry to break the object of study down to its simplest form and to disregard experimental noise. Instead, it called for a shifting of the lens to incorporate a wider view, to look at complex systems with all their noise and interrelations, to practise holistic inclusion rather than logical isolation:

17 Click through to some early attempts at smoothing out network traffic.

[W]hile some parts of the universe may operate like machines, these are chosed systems, and closed systems, at best, form only a small part of the physical universe. Most phenomema of interst to us are, in fact, open systems, exchanging energy or matter (and, one might add, information) with their environment18. Surely biological and social systems are open, which means that the attempt to understand them in mechanistic terms is doomed to failure.

(Toffler, 1985: xv)

The similarities of chaos theory with bionomics do not end with philosophical rhetoric. Molecular biologists have discovered processes of "feedback loops19" in organic chemistry which explain the self-replication of DNA (ibid.: xvii). Feedback loops, together with other processes identified by chaos theory, compel complex, nonlinear and seemingly anarchic systems to eventually reach and maintain a state of equilibrium and order in the long run. Economics is one area in which chaos theory is applicable (Gleick, 1993: 83-86). Thus chaos theory supports the assertions of bionomics that the processes of economics resemble those of biology.

18 The Internet, although undeniably a network of machines, cannot be studied in separation from its social, political and economic context. It might be more rewarding to consider it as an open system. Cf. Bob Metcalfe's position.

19 See Sidenote 11 for rhizomatic feedback.

Any process to which the laws of chaos theory may be applied must fulfil the minimum condition of nonlinearity. That is, its occurrence does not follow a simple straight line — if you restart the process, it does not duplicate its earlier path. Instead, it follows another one of the infinite number of possibilities. It exhibits "irreversibility" or randomness in its behaviour (Toffler, 1985: xx). It is an open system and appears to have the element of uncertainty20.

Nonlinearity means that the act of playing the game has a way of changing the rules.

(Gleick, 1993: 24)

The laws of chaos predict that in general:

  • "Simple systems give rise to complex behaviour."
  • "Complex systems give rise to simple behaviour."
  • "[T]he laws of complexity hold universal, caring not for the details of a system's constituent atoms."

    (Gleick, 1993: 304)

More specifically, they state that in nonlinear systems, processes of "self-organization" can compell order to arise spontaneously out of seemingly chaotic behaviour (Toffler, 1985: xv).

20 The Internet is an example of a nonlinear, irreversible system. It is far too complex to be duplicated and cannot be isolated from a virtually infinite number of conditions.

Malpas and Wickham's governance and failure

Jeff Malpas and Gary Wickham in their paper, "Governance and Failure: On the Limits of Sociology", attempt to address the shortcomings of sociological inquiry which has been treating success, not failure, as entirely central. Sociology and indeed everyday practices imagine the world in terms of "practices, projects and processes that operate relatively unproblematically" (1995: 38), leaving no room for any functional consideration of failure or of incompleteness as inevitable in any ongoing project. For the most part, we tend to act on the belief that:

Failure ... is an aberration, a temporary breakdown within the system; it is a tear in the social fabric, albeit a tear that, in the case of the many small failures that figure in our individual lives, may amount to little more than a pulled thread.


In the conventinally imagined landscape of machinic success, these pockets of failure are dismissed as eruptions of transcient imperfection and have thus been ignored21. They are not, to use a casual phrase, part of the plan. They do not belong. They are there only to be conquered.

In proposing an alternative, Malpas and Wickham borrow from Foucault's notion of governmentality to encourage a shift away from treating the idea of failure as a non-entity with no contributory significance towards eventual success. The proposed new approach recognizes the inevitability of incompleteness in any large, ongoing task, and presents a philosophical examination of "the connections between notions of failure and practices of control" (ibid.: 39). Whereas incompleteness in the sociological landscape of success is seen as a structural lack and as being synonymous with failure, Malpas and Wickham's notion of incompleteness is part of and nothing new to the existing terrain, and failure an inevitable feature in the long term.

The inevitability of failure of any particular governing practice is also a result of interference from other governing practices with which the original practice is inextricably interlinked. Furthermore, failure originates from within the governing practice itself, like processes of resistance in a machine. Here, such resistance plays a useful role by creating a tension with the will to success, a tension that drives the project forward. Notable examples will be the role of the devil's advocate in the Catholic church, or that of opposition parties in government.

Malpas and Wickham use the metaphor of the machine to illustrate their meaning of failure as a useful feature. Just as the parts of any machine "mutually limit and direct each other", so too failure — inevitable within the governing practice — should be seen as "serving to direct and shape the process of governance" (1995: 43).

21 The US government's threat between 1993 and 1996 to charge Phil Zimmerman with munitions export for distributing the encryption programme, PGP, is a classic case of ignoring — even denying — the inevitability of failure. The US National Security Agency imposes strict restrictions to keep the powerful encryption algorithms, which it classifies as military technology, within US borders, but these algorithms had already leaked outside the US in various forms not counted as munitions, including printing on T-shirts (Barrett, 1996: 179).


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