The Tribology of the Helixes: Relations between Triple, Quadruple and Quin tuple Helix Models

This special issue attempts to advance the state-of-the-art in research on relations between Triple, Quadruple and Quintuple Helix models with the publication of Leydesdorff and Lawton Smith’s (2022) paper Triple, Quadruple, and Higher-Order Helices: Historical Phenomena and (Neo-)Evolutionary Models as well as five invited contributions that intend to respond to the arguments expressed in their paper. Leydesdorff and Lawton Smith argue that the dynamics of innovation mainly derive from the Triple Helix (e.g. universityindustry-government interactions), and Quadruple, Quintuple, and N-tuple helices can be decomposed into different combinations of interacting triple helices. They also justify their arguments from a theoretical and methodological perspective. When initially presented at the 2021 Triple Helix Conference as a keynote speech, Leydesdorff and Lawton Smith’s paper provoked active discussions. In order to continue scholarly exchanges on the topic, the editors invited international scholars, whose research interests lie on the border with helical approaches to innovation, to respond to Leydesdorff and Lawton Smith (2022) and join the discussions on relations between the different Helix models from various perspectives. By fostering discussions among leading scholars on the relations between the different Helix models, we hope readers will get to better know each of the models and thus optimise their strategies when applying them to empirical investigations and policy analyses. The papers collected in this special issue also infer a need to re-think Triple, Quadruple and Quintuple Helix models, which is also reflected in the Helix Models’ originators’ more recent (co-authored) works (Cai & Etzkowitz, 2020; Carayannis, Campbell, & Grigoroudis, 2021; Leydesdorff, 2021). Indeed, rapid changes occurred in our societies, triggered by technical advancements and

social crises. Thus the Helix models, as theoretical tools trying to capture the mechanisms of innovation processes in society, also need to be re-examined and further developed.
In order to collate this special issue, the editors first established a list of experts in the field as potential contributors. Then, they selected invited contributors who could broadly represent different disciplinary and geographical perspectives. However, some of our invited authors could not make it due to their busy schedules. Nevertheless, the discussions on helical approaches to innovation will, by no means, stop here. We welcome both established and early-career researchers to submit papers to our journal to continue the discussions.
Among the five invited contributions, four are response papers (Carayannis & Campbell, 2022;Deakin, 2022;Park & Stek, 2022;Xue & Gao, 2022), and one is a full research paper (Cai, 2022). Elias Carayannis and David Campbell gave birth to Quadruple and Quintuple Helix models. Mark Deakin and Han Woo Park have both been engaged in Triple Helix studies for a long time, and each of them has co-authored publications with Loet Leydesdorff (e.g. Leydesdorff & Deakin, 2011;Leydesdorff & Park, 2014). In this special issue, Park invited Pieter Stek, a growing scholar in scientometrics as co-author. Lan Xue is a leading scholar in science, technology and innovation policy in China and is internationally well-known in the field. In his contribution to the special issue, he invited Yuchen Gao -a well-published young scholar in innovation studies -as a co-author. Yuzhuo Cai is co-Editor-in-Chief of the Triple Helix journal. He has recently published a high-impact article on Theorising the Triple Helix model, co-authored with Henry Etzkowitz (Cai & Etzkowitz, 2020).
Deakin's (2022) paper has been positioned as the first response paper since it re-interprets (somehow clarifies) the propositions and arguments of Leydesdorff and Lawton Smith (2022). Moreover, he also relates the theoretical discussions on Triple Helix and Quadruple Helix to the EU's policy practices, particularly the Research and Innovation Strategies related to Smart Specialisation (RIS3) and the Entrepreneurial Discovery Process (EDP). His analysis reveals both the theoretical power of the Triple Helix model and its useful policy implications. He argues that the Triple Helix serves to overcome the limitations of the Quadruple Helix by relaying where the novelty production, wealth generation and normative control lying between them rest in relation to the N-Tuple helices of that higher-order policy model which they claim to know about.
In the second paper, Park & Stek (2022) ask: Is it necessary to develop a new unit of analysis in place of Leydesdorff and Smith's (2022) suggestion of triad relationships? To Park and Stek, it is hard to simply say yes or no. On the one hand, sticking to simple Helix models helps make the analysis and measurement more precise and practical at the operational level. On the other hand, when reducing complex systems to a collection of triple helices one takes the risk of overlooking particular overarching dynamics that the literature on sociotechnical transitions and higher-order helices aims to capture. Park and Stek's position is that measurements of three helices and four helices are both possible and significant, and the two measures can enhance each other. Xue and Gao (2022) appreciate Leydesdorff and Lawton Smith's (2022) suggestion on decomposing higher-order helices into multiple interrelated triple helices since such an approach helps open the black-box of higher-order helices. At the same time, they propose the concept of agile governance, which refers to a set of actions or methods that are flexible, agile, and adaptive, based on an inclusive and sustainable decision-making process. They argue that an array of flexible and adaptive actions or methods are necessary to make the governance on the higher-order helices model more agile to keep pace with the rapid changes of society.
As a response to Leydesdorff and Lawton Smith (2022), Carayannis and Campbell (2022) re-affirm their propositions on Quadruple and Quintuple Helix models, highlighting that knowledge democracy enables innovation and the environmental challenges drive for sustainable knowledge production and innovation. At the same time, Carayannis and Campbell also call for scholars of different Helix models to jointly develop an emerging unified theory of helical architectures (EUTOHA), especially given the current situation in Europe with conflicts and struggles between democracies and autocracies. They imply that both the Triple Helix model and Quadruple/Quintuple Helix models could be supplementary since the former explains the dynamics of knowledge production and innovation and the latter conceptualise innovation ecosystems, both essential in research and policy analysis.
Finally, Cai (2022) responds to Leydesdorff and Lawton Smith's (2022) and others' (Cai & Lattu, 2021;Carayannis et al., 2021;Zhou & Etzkowitz, 2021) call for synergy building between Triple, Quadruple and Quintuple Helix models, and proposes a neo-Triple Helix model of innovation ecosystems. This model distinguishes two sets of triads or triple helices: 1) the university-industrygovernment triple helix interactions, regarded as innovation dynamics or genes, and 2) the interactions of innovation genes, social structures and the natural environment. The neo-Triple Helix model can be simply described as triads within triads in terms of spatial relations or two-layer triple helices in terms of the dialectical relationship of cause-and-effect. Such a perspective helps clarify debates on different Helix innovation models and advance helical approaches through synergy building.
We are pleased and honoured to have been able to create this special issue which provides us with a unique opportunity to engage with leading scholars in the field and to discover emerging trends in helical approaches to innovation. Although the papers in the special issue present novel and diverse perspectives for enhancing theoretical grounds and practical applications of helical approaches, many of their arguments are still in the process of developing. The discussions in this special issue clearly show that Triple Helix research, along with studies on other Helix models, is alive and thriving. As Cai cites Lundvall's words in the closing paper of this issue, 'What qualifies as a good theory of innovation is not carved in stone but has to evolve as a result of changes in society and our attempts to understand these challenges' (Fagerberg, Martin, & Andersen, 2013: 7). The Triple Helix journal aims to collect high-quality scholarly work on helical approaches to innovation, presenting state-of-the-art research to our readers. While we are committed to strengthening the research agenda of Triple Helix (Cai & Amaral, 2021), we also welcome contributions connecting the Triple Helix model with other approaches in innovation studies.

Marcelo Amaral
Fluminense Federal University, Co-Editor-in-Chief of Triple Helix mgamaral@gmail.com