Can Interdisciplinarity be quantified?

Dr Ebrahim Patel

The faculty of LIS have built up their expertise in some of the UK’s best universities. With their well-established silos and ways of working, it should be no surprise that the dictionaries of Oxford and Cambridge – the grandest of these institutions – provide a firm and quite straightforward definition of ‘interdisciplinarity.’ Oxford says that interdisciplinarity is “the quality or fact of involving or drawing on two or more branches of knowledge,” and Cambridge agrees, defining it as, “the fact of involving two or more different subjects of areas of knowledge.”

In actuality, the experience of interdisciplinarity is anything but straightforward. How ‘different’ should these subjects (or disciplines) be? Is the involvement of such a minimal number (two) of subjects sufficient?  What weighting should be attached to each subject? Importantly for us, coming from such traditionally disparate backgrounds as art and mathematics, how do we even begin to look for the interdisciplinarity therein?  Inherent in all this is the idea of connections between disciplines, so a natural starting point to answer these questions quantitatively is by using a network science approach.  

‘Discipline’ through community  

Firstly, what is a discipline?  A popular way to define it is by looking at a larger, underlying, network of academic papers. This ‘raw’ network depicts each paper as a node and connects a paper to another paper if one cites the other; such a method of using citations is also referred to as bibliometrics. Taking this network as a whole, disciplines can then be identified as groups of such papers. But this leads us to another question: how to define these ‘groups’? The more technical term is ‘communities,’ and community detection is itself a fertile research area. Generally speaking, a community in such a network is a group of nodes that are ‘as close as possible to each other’ and simultaneously as far apart as possible to other groups. At an extremely simplified level, similarity between two papers A and B could be the number of citations it takes to go from A to B; that is, if A cites B then they have similarity 1, and if B subsequently cites C, then A and C have similarity 2 (see Fig. 1).  

Fig. 1: Papers and their citations, coloured to indicate communities (left), and the three corresponding subjects and their connections, where a thicker line indicates a stronger connection (right).

If you consider the exponentially growing number of papers that are published, community detection is an extremely hard task (so hard that it forms part of a famous set of undecided problems that even the best computers can’t get a handle on). And so, using some simplification schemes – such as data cleaning, focusing on specialist subjects (such as journals instead of papers), and accepting solutions that are ‘good enough’ – this grouping has been achieved by repositories such as the Web of Science (WoS).  For example, whenever a paper is published in the International Journal of Hygiene and Environmental Health, it will be assigned the subject classification of Infectious Diseases. And we can infer the likelihood of citing or being cited by other papers from this network of WoS subjects. This means we can now work with this coarse-grained subject network provided by WoS instead of the finer network of papers.  

“Consensus map of disciplines”

A more intuitive name for such a network might be a “subject/discipline map,” since it acts as a navigation tool for visualising the distance (similarity) and paths between subjects. Of course, this is not the only such map because different databases inevitably produce different maps. Thus, by comparing 20 of these different subject maps, Kevin Boyack and Richard Klavans – two pioneers in the field of bibliometrics and mapping the disciplines – recently produced a “consensus map of disciplines” (see Fig. 2). Strikingly, this map is circular, i.e., it is neither hierarchical (like a family tree) nor star-shaped (like a bicycle wheel). Reassuringly for LIS, this effectively means that no discipline is favoured over another. Furthermore, it is easy to make new discoveries here; they could instantly be identified on the circumference of the circle (between connected disciplines such as H = humanities and SS = social science) or, more adventurously, they could lie in the empty centre, where any subject could potentially collaborate with any other. This map, therefore, provides some measure of interdisciplinarity – the more central you are, the more interdisciplinary your work will be. Overall, Klavans and Boyack advocate for this non-centric map of the disciplines because it conveys the following important message to students: new discoveries can arise from many directions and interdisciplinary research takes high value.

Fig. 2: The map of disciplines (Klavans & Boyack, 2009).  Each discipline is abbreviated, e.g., M = mathematics and CS = computer science.  Line thickness indicates strength of connection between disciplines.

A recipe for exploration  

We’ve highlighted how network science can help map the disciplines, quantify interdisciplinarity and potentially enable the identification of areas ripe for an interdisciplinary exploration. The analogy of a baking a cake provides a final conundrum, which can’t be addressed by the above approach. As someone with a sweet tooth, it gives me no pleasure to say that, given that flour, eggs, sugar, and butter are the main ingredients, we can still bake a cake with little (or even no) sugar. That is, the Oxford and Cambridge processes of ‘drawing on’ and ‘involving’ is actually insufficient in producing the desired outcome. In other words, interdisciplinarity can’t just be about what goes in, but equally about what comes out. Thus, as the LIS website states, “interdisciplinarians join forces to achieve more together than disconnected minds can do on their own.” But how we measure this is a challenge because it suggests that ‘true’ interdisciplinarity must be ‘emergent,’ which by its very nature, can’t be quantified. Perhaps then we should be content with exploring but never quite pinning down the definition, trusting that the thrill of the risk of combining various disciplines pays off in providing solutions that would never have been found in any other way.

2009. Klavans& K. Boyack, 2009.  “Towards a Consensus Map of Science,” Journal of the American Society for Information Science and Technology, 60(3):455-476.

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