**By Loet Leydesdorff**

What is the difference between “interdisciplinarity” and “synergy?” Why does it matter? How can indicators of interdisciplinarity and synergy be conceptualized and defined mathematically? Can one measure interdisciplinarity and synergy?

Problem-solving often requires crossing boundaries, such as those between disciplines. However, interdisciplinarity is not an objective in itself, but a means for creating synergy. When policy-makers call for interdisciplinarity, they may mean synergy. Synergy means that the whole offers more possibilities than the sum of its parts. The measurement of synergy, however, requires a methodology very different from interdisciplinarity. In this blog post, I consider each of these measures in turn, the logic underpinning each of them, and I specify the definitions in mathematical terms.

*Interdisciplinarity*

Discussions about interdisciplinarity can be confusing, because the concept itself is composite. However, interdisciplinarity has recently been operationalized in bibliometrics in ways that are amenable to measurement.

Stirling (2007) distinguished between (*i*) variety, (*ii*) balance, and (*iii*) disparity as three aspects of interdisciplinarity. Rafols and Meyer (2010, p. 266) provided the figure below, which has become iconographic for visualizing the distinctions among the three components of interdisciplinarity in a collaboration. It shows:

- Variety as the number of disciplines in the collaboration;
- Balance as evenness of distribution,
*ie*., the relative strength of each discipline in the collaboration; - Disparity or similarity as the degree of difference among the disciplines involved in the collaboration. For example, a biochemist and a sociologist are more distanced in terms of their disciplines than a biochemist and a physicist.

With colleagues (Leydesdorff *et al*., 2019), I have proposed *DIV* as a diversity indicator combining the three components [each shown in brackets] as follows:

*DIV* is based on multiplication of:

- Variety defined as (
*n*), with_{c}/N*N*being the total number of classes available and*n*the number of classes with values larger than zero;_{c} - The Gini Index used as a measure of balance;
- Disparity based on the disparity measure in Rao-Stirling diversity (Δ = ∑
_{i},_{j}p_{i}p_{j}d_{ij}), albeit normalized differently (*cf*. Rousseau 2019).

*Synergy*

The term *synergy* originates from the Greek word συνεργία which means “working together.” In general, synergy is the creation of a whole that is greater than the sum of its parts: additional options that become available because of a collaboration across disciplines can be measured.

If we consider a configuration of collaborating disciplines, the total number of possible configurations in this situation is (by definition) equal to the sum of the realized options and the not-yet-realized but possible ones. Shannon (1948) defined the proportion of non-realized but possible options [(*H*max* – Hobs*) / *H*max] as redundancy (*R*) and the proportion of realized options as relative uncertainty. If redundancy increases, the *relative* uncertainty decreases.

Whenever information is *appreciated*, a meaning is generated. The same information can be appreciated differently by different disciplines. Whereas information can be communicated, meanings can be shared. Sharing can generate an *intersubjective* layer with a dynamic different from information processing. The redundancy in the loops and overlaps can be measured in *negative* bits of information—as feedbacks which reduce uncertainty. Meanings refer intersubjectively to “horizons of meaning” that are instantiated in events. Whereas the events are historical, appreciations are analytical. Knowledge-based distinctions add to the redundancy by specifying empty boxes. A calculus of redundancy which remains consistent with Shannon’s information theory can be envisaged; this is described in more detail in Leydesdorff, *et al*. (2018).

*Discussion*

I have argued that “interdisciplinarity” is a dimension very different from “synergy.” Policy-makers often call for interdisciplinarity when surplus is expected from collaborations across boundaries. However, this surplus can be considered as the result of synergy. The measurement of synergy requires a methodology different from the measurement of interdisciplinarity. The measurement of interdisciplinarity using diversity indicators is described above.

The generation of redundancy is based on mutual information. By appreciating the overlaps as redundant, however, another calculus can be formulated. The focus shifts from “past performance” to the cases that have not yet happened; that is, the zeros. The envisaged calculus remains connected to and is consistent with Shannon’s information theory, but can be used to study the domain of meanings and intentionality as relevant for generating surplus in scientific and extra-scientific collaborations.

The distinction between interdisciplinarity and synergy is essentially between process and outcomes and being able to measure each of these separately. The operationalizations and bibliometric measures help us to refine our ability to evaluate the extent and value of interdisciplinary research. For example, in bio-medical “translation research” (from bench to bedside) or university-industry-government relations, synergy is often more important than interdisciplinarity. The external stakeholders structure the configuration; this structuring can be appreciated in the case of synergy.

Like other performance indicators, the measurement of interdisciplinarity is used to evaluate *past* performance. However, systems may run out of options. Synergy measures options that have not-yet occurred and thus shifts the orientation from the past to the future. The generation of synergy, however, may be counter-intuitive in terms of action because the interacting dynamics lead overall to a dynamics which is complex and non-linear (*cf*. Schumpeter’s (1939) “creative destruction”). The assessment of options informs policy-making differently from the sum of the perspectives of different disciplines.

Software for measuring the various indicators of “interdisciplinarity” and “synergy” in a data matrix is available from http://www.leydesdorff.net/software/interdisc.2020 and http://www.leydesdorff.net/software/synergy.triads, respectively.

**To find out more**:

Leydesdorff, L. and Ivanova, I. A. (2020). The Measurement of ‘Interdisciplinarity’ and ‘Synergy’ in Scientific and Extra-Scientific Collaborations. *Journal of the Association for Information Science and Technology.* (Online open access): https://doi.org/10.1002/asi.24416. This also provides full references.

**References**:

Leydesdorff, L., Johnson, M. and Ivanova, I. (2018). Toward a Calculus of Redundancy: Signification, Codification, and Anticipation in Cultural Evolution. *Journal of the Association for Information Science and Technology*, **69**, 10: 1181-1192. (Online) (DOI): http://doi.org/10.1002/asi.24052

Leydesdorff, L., Wagner, C. S. and Bornmann, L. (2019). Interdisciplinarity as Diversity in Citation Patterns among Journals: Rao-Stirling Diversity, Relative Variety, and the Gini coefficient. *Journal of Informetrics*, **13**, 1: 255-264.

Rafols, I. and Meyer, M. (2010). Diversity and network coherence as indicators of interdisciplinarity: Case studies in bionanoscience. *Scientometrics*, **82**, 2: 263-287.

Rousseau, R. (2019). On the Leydesdorff-Wagner-Bornmann proposal for diversity measurement. *Journal of Informetrics*, **13**, 3: 906-907.

Schumpeter, J. ([1939], 1964). *Business Cycles: A Theoretical, Historical and Statistical Analysis of Capitalist Process*. McGraw-Hill: New York, United States of America.

Shannon, C. E. (1948). A Mathematical Theory of Communication. *Bell System Technical Journal*, **27** (July and October): 379-423 and 623-656.

Stirling, A. (2007). A general framework for analysing diversity in science, technology and society. *Journal of the Royal Society Interface*, **4**, 15: 707-719.

* Biography: Loet Leydesdorff Ph.D. is Professor Emeritus at the Amsterdam School of Communications Research (ASCoR) of the University of Amsterdam in the Netherlands. He has published extensively in science and technology studies (STS), systems theory, social network analysis, scientometrics, and the sociology of innovation*.

Dear Loet, Do I understand correctly that the potential of mathematics directly depends on the iconography used to visualize a complex object, as well as on the terms that describe this iconography?

If this statement is true, then we can assume that the result of a mathematical solution to the problem of interdisciplinarity and synergy cannot be correct or incorrect. This mathematical solution always corresponds to the context of the original theoretical, iconographic, and terminological axioms. Therefore, do I understand correctly that if mathematicians use a different axiomatic context, the objective effectiveness of the mathematical description of interdisciplinarity and synergy may change?

You may be interested to know that the complexity of the concept can be reduced if the overall context of interdisciplinarity and synergy is divided into three contexts: interdisciplinarity, interdisciplinary interactions, and an interdisciplinary approach.

Interdisciplinarity is a term that refers to the possibility of expanding the horizon of scientific worldviews through the use of knowledge and cognitive tools of various scientific disciplines.

Interdisciplinary interactions are a term referring to integrating factors that contribute to the formation of logical structures of complementary scientific disciplines, which lead to the expansion of the horizon of scientific worldview and, consequently, to the solution of complex multifactorial problems of science and society.

Interdisciplinary approach is a way to expand the horizon of scientific worldview in the direction of enriching knowledge, methodology and language of one scientific discipline at the expense of knowledge, methodology and language of another scientific discipline.

In this context, interdisciplinarity is just a sign of the possibility of expanding the scientific worldview. An interdisciplinary approach is a way to expand the scientific worldview through the interaction of two complementary disciplines. Interdisciplinary interaction is a way to expand the scientific worldview with the participation of several complementary disciplines (multidisciplinary approach), as well as through the integration and generalization of complementary scientific knowledge and knowledge of the philosophy of religion and myth (systemic transdisciplinary approach).

The term “expanding the horizon of the scientific worldview” hides a new picture of the object or picture of the world. It is likely that each new horizon of the scientific worldview will require an adequate mathematical description of a new mathematical apparatus. It is even more likely that the limit level of the horizon will require a mathematical description of the isomorphism of space, time, and information of the unified world. What do you think?

I am not sure whether I completely follow you. Let me give it a try:

Q: This mathematical solution always corresponds to the context of the original theoretical, iconographic, and terminological axioms. Therefore, do I understand correctly that if mathematicians use a different axiomatic context, the objective effectiveness of the mathematical description of interdisciplinarity and synergy may change?

A: It seem to me that this is also the case for a discursive reflection. Whenever one uses “a different axiomatic context, the effectiveness of the [mcathemaltical] description of … may change.”

Q: It is even more likely that the limit level of the horizon will require a mathematical description of the isomorphism of space, time, and information of the unified world. What do you think?

A: This seems speculative to me. Personally, I don’t expect “a unified world” as a kind of limit value. But we may drift here off the subject of this blog.

Best, Loet

Dear Colleen

Thank you for reaching out across the qualitative/quantitative divide. This divide is a typical example of disparity. See also related variety:

Frenken, K., Van Oort, F., & Verburg, T. (2007). Related variety, unrelated variety and regional economic growth. Regional studies, 41(5), 685-697.

Best, Loet

Loet Leydesdorff, Thank you for this blog post. Although I am not a mathematician, nor do I profess to know much about quantum physics, as an educator, I appreciate your article that clarifies the difference between interdisciplinarity (as process) and synergy (as outcome), which is helpful to explain these constructs, which increase diversity and understanding of different ways of knowing, thinking, and practice for collective creativity, innovation, and inclusion.