Introduction

I have known Loet for over ten years. I had just completed my PhD and was looking for an area for further research. What caught my attention was the Triple Helix of university-industry-government (TH) relationships, developed in collaboration by Etzkowitz and Leydesdorff (2000). I wrote to Loet suggesting further development of the model in terms of mathematical operationalization, and he responded. From that moment our cooperation began. I recently looked in my mailbox and counted 2,525 letters from Loet. And I was just one of his many colleagues and co-authors. One can imagine how hard he worked! Loet was very meticulous in his research, striving for scientific rigor and reliability of the results obtained. While very knowledgeable and erudite as a scientist, he was also a very humble and approachable person. It should also be noted his scientific intuition and ability to identify research goals. I learned a lot from Loet, and he was not only my colleague and co-author, but also my teacher, and I was lucky to have such a teacher. In the following sections I will try to briefly describe the main stages of our cooperation and highlight the most significant, from my point of view, results, as well as possible prospects for the further development of the theory, to the development of which Loeth Leydesdorff made a decisive contribution.

Non-linear Dynamics of the TH Model of Innovations

Our collaboration initially focused on the TH model. While an impressive model of innovation, TH lacked rigorous mathematical operationalization and relied primarily on phenomenological case studies. Unlike the Double Helix (DH) model (for example, the model describing the relationship between industry and government), TH is an inherently nonlinear model. This nonlinearity arises from the topological structure of TH due to the so-called “triadic closure” (Bianconi et al., 2014), where every third actor can disrupt the connection between two other actors. However, there was no clear formal description of the mechanisms of TH functioning.

The TH system can be conceptualized in terms of its components (university, industry, and government), relationships, and functions – Wealth generation, Novelty production, and Normative control (Etzkowitz and Ranga 2012). Representation of the model as a vector in three-dimensional Cartesian space with axes corresponding to the three TH functions (Leydesdorff and Meyer, 2006) and taking into account the interactions of actors that lead to continuous change in the three main TH modes: TH1 (with a dominant role of the state), TH2 (with a dominant role of the market) and TH3 (with the dominant role of science and innovation) one can reflect the evolution of the system as a rotation of a vector, which represents TH system, in this space. In the same way, the DH system is represented by a vector rotating in two-dimensional space, and higher-order helices are represented by a vector rotating in multidimensional space.

This idea served as the basis for the formalization of TH dynamics. Nonlinearity means that these dynamics are described by nonlinear equations, and nonlinear equations arose from the TH topology, namely due to the fact that rotations in three-dimensional or higher-dimensional space are non-commutative whereas in two-dimensional space the order of two successive rotations can be interchanged without changing the result. The mathematical framework allows us to clarify the mechanisms of nonlinear dynamics and provides new possibilities for prediction. Using a mathematical model, one can show that the Triple Helix system contains self-interaction and therefore self-organization of innovation, while the Double Helix remains determined by its linear interactions. In this respect, TH is the simplest model, exhibiting nonlinear dynamics and differing little from higher order helices. We can expect that ensuing innovation systems will have a fractal structure: the national system, for example, contains sectoral and regional systems and is an integral part of technological and supra-national systems of innovation. This fractal structure follows from the dynamic symmetry of the TH, provided by the topology of institutional communication between the TH actors (Ivanova and Leydesdorff, 2014).

TH Synergy and Economic Complexity

The TH model emerged during the transition from industrial to post-industrial economies, when economic growth became highly dependent on the production of knowledge, new technologies and innovations. The effectiveness of an innovation system depends on the “synergy” of interaction between actors, which can be generated under specifiable conditions. By mapping TH as a Venn diagram of three overlapping arears, synergy can be conceptualized as an overlay of configurations that can be measured by mutual information in three dimensions (Ulanowicz, 1986, McGill, 1954). Mutual (or configurational) information can be used as a quantitative indicator to measure TH synergy (Leydesdorff and Meyer, 2006). With this indicator, the interaction of TH participants can be quantified in bits of information. The higher the synergy, the more innovative the economy is and the greater the variety of complex products it can produce.

The diversity of production and the rareness of the products produced can provide the basis for constructing measures of economic complexity, such as e.g. the Economic Complexity Index (ECI) of Hidalgo and Hausman (2009), which can be used to rank countries in terms of economic competitiveness and predict future growth. Chinese case study revealed a correlation between synergy and ECI (Ivanova, 2022). Thus, abstract pieces of information can be associated with economic variables such as growth. Also, Triple Helix synergy can be associated with turnover (Ivanova, Strand, and Leydesdorff, 2019).

The TH metaphor can also be applied to construct complexity measures. Similar to the ECI, a patent complexity index (PatCI) can be constructed based on a matrix of countries and patent classes. The three dimensions – countries, product groups, and patent classes – can be then combined into a Triple Helix complexity index that explicitly captures manufacturing, knowledge, and geographic dimensions that capture trilateral interactions between knowledge production, wealth generation, and normative control (Ivanova, Strand, Kushnir and Leydesdorff, 2017).

Synergy vs. Interdisciplinarity

The notion of “synergy” in the context of the TH model should not be confused with the notion of “interdisciplinarity”. Interdisciplinarity involves crossing boundaries between disciplines. Because crossing boundaries can help solve interdisciplinary problems, policymakers may refer to interdisciplinarity as synergy, which means that the interaction of agents produces a net effect greater than the sum of their individual effects.

The operationalization and measurement of interdisciplinarity is different from TH synergy. Interdisciplinarity can be measured using different versions of diversity indicators developed in ecology and economics, and TH synergy is calculated on the base of information theory. TH synergy is measured as redundancy, which indicates an increase in the number of options not yet implemented. Unlike most performance indicators, which focus on measuring historically realized options, TH synergy shifts the focus to options that are possible but not yet realized.

The number of available options is crucial for innovation system evolution. A system which is out of options is deadlocked. The operationalization of “interdisciplinarity” and “synergy” – as different and partially overlapping indicators – makes it possible to distinguish between past- and future-oriented indicators (Leidesdorff and Ivanova, 2021).

Redundancy and Meaning

What seems most interesting in this line of Loet’s research originated from the study of the synergy indicator. The problem with the TH indicator was that configurational information in more than two dimensions is no longer Shannon-type information since it can be negative, moreover, it is a signed information measure which possibly changes sign when adding additional dimensions. Technically, the problem of sign reversal can be solved by introducing “positive overlap” into the Venn diagram (i.e., where overlaps are not subtracted but added to the overall uncertainty), so that negative values of configuration information can be considered as redundancy. But this operation lacked sufficient conceptualization.

Drawing on Luhmann’s theory of social systems and/or Giddens’ structuration theory, Loet has shown that this may indicate an excess of meanings attached to information in reflexive communications. In a system of three or more groups of agents with different meaning-processing structures (“communication codes”), each agent encodes and decodes information using different algorithms. Codes structure communications as selection mechanisms with respect to “horizon of expectations”. The same information is processed differently by each group and is supplied with different meanings. This mechanism provides a source of additional options that affect the dynamics of the system. Additional options are added to the redundancy (Leidesdorff and Ivanova, 2014).

Interacting selection mechanisms can drive the development of redundancy; that is, options that are available, but have not yet been used. An increasing number of options is crucial for the viability of innovation systems more than is past performance. A calculus of redundancy different from and complementary to information calculus is envisaged. (Leydesdorff, 2021 at p.1)

Modeling and measuring of meaning processing in terms of redundancy generation provides extensions to the Shannon’s mathematical theory of communication (Leidesdorff, Ivanova, & Johnson, 2014).

Meaning generation is defined as the positional counterpart of relational communication of information. The model distinguishes between communication relationships and correlations between relationship patterns. The information exchanged between actors is provided with (different) meanings that are generated from the perspective of hindsight, that is, against the arrow of time (cf. Rosen, 1985; Dubois, 1998). Meanings can be shared, and sharing generates redundancy. Increasing redundancy provides new options and reduces uncertainty. The generation of options may be more important than historical implementations. A system without sufficient options can be locked-in. Redundancy can be used as a measure of unrealized options and enables us to quantify the creation of new options. Increased redundancy not only stimulates innovation in the ecosystem by reducing prevailing uncertainty; it also enhances the synergy of interaction between participants in the innovation system. Calculating redundancy allows us to quantify the creation of new options as mutual redundancy. The dynamics of information, meaning and knowledge can be assessed empirically using the sign of mutual information as an indicator. The TH synergy indicator was used to analyze regions and sectors where uncertainty was significantly reduced. (Leydesdorff and Ivanova, 2016; Leydesdorff, Petersen, and Ivanova, 2017; Leydesdorff, Johnson, and Ivanova, 2018; Leydesdorff, Ivanova, and Meyer, 2019).

Further Perspectives

The main result of Loet’s conceptual breakthrough is that it shifts the focus from “innovation” (which has a relatively narrow scope) to “information”, which is a much more comprehensive concept. In a broad sense, the theory of meaning contributes to second-order cybernetics, where, unlike engineering cybernetics, the observer is a participant in the observed system. Second-order cybernetics also refers to the study of complex meaning-processing systems, such as social systems, in which reflexivity, self-reference, and self-organization play a major role. The building blocks of these systems are not only groups of agents, but also communications between these groups. Communications create new communications in accordance with the selection environments and control the evolution of systems.

Areas of applicability of second-order cybernetics include, but are not limited to, cognitive science, political science, living systems, sustainable development, management and organization theory, etc. Leydesdorff’s extension of Shannon’s communication engineering theory to the reflexive transmission of information allows for the addition of a numerical dimension to second-order cybernetics. Different kinds of data can be measured and compared, allowing the TH metaphor to be applied to topologically similar systems composed of heterogeneous agents. The evolutionary dynamics of a system are controlled by information processing within the system.

What really matters is not the information itself, but the interpretation of what it means for the system with respect to possible future system’s states, that is, the meaning given to that information. The dynamic interactions between more than two agents generate recognizable patterns which can be modelled and measured with help of non-linear evolutionary equation.

The theory of meaning may provide a uniform way to analyze systems of different origins. Recent applications of this theory include the description of financial market assets’ price movement, the spread of Covid-19 infectious disease, and rumors propagation (Ivanova, 2022a and b, 2023). The results show that the model’s predictions are consistent with empirical data in systems of different origins.

Conclusion

Loet had diverse scientific research interests. But it seems to me that his most important contribution is summarized in Loet’s latest book: “The Evolutionary Dynamics of Discursive Knowledge: Communication Theoretical Perspectives from Empirical Philosophy of Science” which builds a bridge from knowledge-based innovation to the broader realm of inter – social communications and a theory of knowledge.

Building on a sociological perspective which includes Parson’s social systems theory, Simon’s theory of complex systems, Giddens’ “structuration theory,” Luhmann’s sociological theory about meaning-processing in communications and Shannon’s mathematical theory of communications as applied to information-theoretical operationalization of the possible synergies in Triple-Helix relations he articulated core ideas and introduced new conceptual tools for understanding, analyzing, and measuring inter-societal communications. The scientific significance of this line of research is that it takes the first step from a quantitative theory of communication to a quantitative theory of meaning and reflexive communication of information.

Loet laid the theoretical and methodological foundations which can serve as the base for further development of the quantitative theory of meaning in inter-social communications in complex systems. On the practical side, this theory has the potential to have many applications across a wide variety of areas of social activity. The importance of reflective communication research and Loet’s contributions to this field still remains to be fully appreciated.