*Enhancing the Effectiveness of Team Science*define interdisciplinarity as follows:

“Interdisciplinary research integrates the data, tools, perspectives, and theories of two or more disciplines to advance understanding or solve problems. Transdisciplinary research aims to deeply integrate and also transcend disciplinary approaches to generate fundamentally new conceptual frameworks, theories, models, and applications.”

In an ideal universe, we'd have highly trained experts who are able to closely examine the papers written by the person or group under consideration, interview the people involved, and even ethnographically follow their work. Let's say that there were really fast, and could do this at a rate of one hour per person (absurdly quick, if you know anything about qualitative social science). My little sample of 40 people would take all week to analyze.

Let's use a data science approach. In particular, pay attention to the ideas of

*integration*and

*diversity*. From reading Latour's

*Science in Action*, we see that scientific claims are constructed and made firm by tying a new claim to an existing web of established facts, which are recorded in the peer-reviewed scientific literature. Or in plain language, scientific papers have citations, and it's reasonable to expect that an interdisciplinary paper has a different pattern of citations than a monodisciplinary paper.

Over the past decade, this idea has been transformed into metric via the Rao-Stirling diversity index, or SDI, which varies between 0 for monodisciplinary and 1 for maximally interdisciplinary. The form is similar to the Gini index. In a 2007 paper, "A general framework for analyzing diversity in science, technology and society", Andy Stirling translated ideas from ecology to note that mathematically, diversity is how a set of objects is apportioned over a set of categories. In particular, diversity is represented by the sum of proportions between all categories

*i*and

*j*multiplied by the distance between

*i*and

*j.*

For scientific papers, we can use citations as our objects, and library categories as our categories. We then need to figure out the distance measure. Rafols, Porter, and Leydesdorff in 2010 ("Science Overlay Maps: A New Tool for Research Policy and Library Management") looked at the patterns of citations across every paper indexed in Web of Science in 2007 to see how often papers in Web of Science subject category

*A*cited papers in Web of Science subject category

*B*, and normalized that matrix to find the cosine similarity between all pairs of categories. 1 - the cosine similarity gives us a distance. Rafols et al point out that the large scale epistemic structure of science is fairly stable, so this matrix should still give us a good idea of the diversity of categories.

It gets a little more complicated, because while the Rao-Stirling diversity index makes sense for a single object in one category that cites many things in many categories, we're dealing with corpi of all the papers written by a scientist. Imagine that we have a person who's written an interdisciplinary paper mostly in chemistry (SDI=0.5). If they write another paper that with the same pattern of citations, their Rao-Stirling score shouldn't change. Yet if we have a physicist who written a monodisciplinary paper in biology (SDI=0.1) and she suddenly writes a paper that cites a bunch of physics paper (SDI = 0.1), her Rao-Stirling score should increase. If we simply average out the SDIs, that isn't the case.

Cassi, Mescheba, and Turckheim point out in 2014's "How to evaluate the degree of interdisciplinarity of an institution" that Rao-Stirling diversity is mathematically isomorphic to the equations used to calculate the rotational moment of inertia of a cluster of points. If we're calculating the Rao-Stirling diversity index for many objects, we can find the moment of intertia around the common "center of gravity" for all the citations. Cassi and Turckheim expanded their work in 2017 "Analysing Institutions Interdisciplinarity by Extensive Use of Rao-Stirling Diversity Index", and have some R code available.

My github has a notebook, 2-Measuring Interdisciplinarity with Rao-Stirling Diversity Indexes, which has the code that demonstrates how this all works. Meanwhile one outcome is this visualization of 2018 Nobel Laureate Kip Thorne's SDI's per year,