Networks, power-laws and mycorrhizae

A recurring theme in H800 is the way our thinking about new technologies is both enabled and constrained by the language we use to talk about them. However precise and scientific we try to be, we always end up speaking and therefore thinking metaphorically, because we must press old words into service, imaginatively bending them into shape to express new things in different contexts.

Take the term network. It’s a metaphor which helps us to imagine light-speed electronic packet-switch connections between computers in terms of the knotted mesh of criss-cross woven fibres which people have been using to catch their supper these last 100,000 years or so. But it turns out networks are not just a beautiful technology metaphor. They’re also a branch of mathematics, one which can help us both to imagine computer networks, and to reach a much deeper understanding of their structure, meaning and growth.

Network theory studies the distribution of nodes and links in many different kinds of network. 20th century network theory predicted that nodes and links should be distributed more or less randomly, resulting in a Gaussian distribution or even spread over time across the network. But contemporary network theory, which is dominated by the Romanian physicist Albert-Laszlo Barabasi, challenges the idea that complex networks behave like this. Barabasi discovered that complex networks are what he calls “scale-free”, because there is no typical number of links per node, and so no simple scaling. Chris Jones, of Lancaster University’s Centre for Studies in Advanced Learning Technologies (CSALT), puts it like this:

These networks differ from random networks in which nodes are connected without any organising principle. Scale-free networks show a degree of organisation; in particular they display a power-law distribution. Those nodes with only a few links are numerous, but a few nodes have a very large number of links.. The rationale behind this kind of distribution rests on some simple propositions. Firstly networks grow through the addition of new nodes and these new nodes link to pre-existing nodes. Secondly there are preferential attachments within the network such that the probability of linking to a pre-existing node is higher if that node already has a large number of attachments. (Jones 2004, p83)

One result of this type of distribution is a high degree of clustering, with a small number of mega-hubs dominating a landscape of thinly-connected nodes. Another is the paradoxically important role played by weak or bridging links – those relatively distant and occasional ties between clusters which were first noticed by Everett Rogers and which serve to tie the whole network together. As Jones comments, “these links are central to the dissemination and propagation of ideas and are of particular interest in education.” (Jones, 2004, p84)

Barabasi crunched the numbers on many kinds of complex network – transistor connections in computer chips, actors cited in the IMDB, the connections between proteins in cellular metabolism, the structure of the internet itself – and found they all showed the same power-law distribution. Far from being random, complex networks actually “evolve, following robust self-organising principles and evolutionary laws that cross discipline boundaries.” (Barabasi, 2002)

These discoveries have implications for how we think about technology-enhanced learning, prompting us to switch focus away from the technology and onto the networks we construct to support learners. As Chris Jones suggests, “the move from interaction with computers to interaction through computers has now moved on to interaction in relation to computer networks.” (Jones, 2004, p89)

The CSALT group offer the following definition of this networked learning:

Networked learning is learning in which ICT is used to promote connections between one learner and other learners, between learners and tutors, and between a learning community and its learning resources. (Jones, 2004 p89)

Jones suggests that learners themselves constitute nodes in the network, along with educators, groups, web objects and destinations – while others argue that learners should be seen not as nodes but as link-makers in the network, actors who instantiate the network by linking between its nodes (eg Ingraham, 2004). Either way, networked learning is seen as a self-conscious process in which the network environment is manifest to the learners, who are thus enabled to focus on the organisational dynamics of the network itself.

These dynamics in turn shape the behaviour of online communities, whether they are peer2peer sharing networks, activism networks, flashmobs, or communities of learners. And according to Finnish activity system theorist Yrjo Engestrom the relationship between the network infrastructure and the collaborative communities that arise from it is analogous to the symbiosis between plant root systems and underground fungal filaments known as mycorrhizae.

Like power-law networks, mycorrhizae exhibit very rapid and massive growth, like online social networks they exhibit intertwining mutualism, and like other complex networks they exhibit a kind of clustering – when a filament encounters a food source the whole fungal colony mobilises itself to concentrate resources on exploiting the source. I really love this metaphor, which like all good rhetorical figures is intriguing and beautiful as well as extremely functional. Thinking about these giant underground fungal organisms is a powerful aid to understanding the structuration of online networks:

Mycorrhizae are difficult if not impossible to bound and close, yet not indefinite or elusive.. They are made up of heterogeneous participants working symbiotically, thriving on mutually beneficial .. partnerships.. A mychorrhizal formation is simultaneously a living, expanding process (or bundle of developing connections) and a relatively durable, stabilized structure; both a mental landscape and a material infrastructure. (Engestrom, 2007, p48)

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Jones C, 2004. Networks and learning: communities, practices and the metaphor of networks. ALT-J Research in Learning Technology, Vol 12 No 1

Barabasi A-L, 2002. Linked: the New Science of Networks. Perseus Publishing

Ingraham B, 2004. Networks and learning: communities, practices and the metaphor of networks – a response. ALT-J Research in Learning Technology. Vol 12 No 2

Engestrom Y, 2007. From communities of practice to mycorrhizae. In Hughes, J., Jewson, N. and Unwin, L. (eds) Communities of Practice: Critical Perspectives, London, Routledge.