In the original Triple Helix model (Etzkowitz and Leydesdorff 1995), the three “helices” of Universities, Industry and Government and the (3-way) interactions among and between them were proposed as a basis for looking at how entrepreneurship comes into being. Since the original article, other “helix-based” models have been proposed. Some vary the triple and others propose higher numbers of helix – with 4 and 5as the most typical extensions. In the article “Triple, Quadruple, and Higher-Order Helices: Historical phenomena and (neo-)evolutionary models,” Leydesdorff and Lawton Smith (2022) developed an Information-Theory based approach to look more formally at the need for higher-order helices.
In the case of two helices, processes of mutual shaping can generate historical trajectories that could have been otherwise: other options providing possible states, which have not yet historically been realized (Petersen et al., 2016). Adding a third helix makes a substantive change from an information point of view: a Triple Helix model is not just the sum of three sets of 2-way interactions. However, once this number has been reached further additions can be decomposed into sets of triads (Batagelj et al., 2014; Simmel, 1902). This leads to the suggestion that higher-dimensional helix structures potentially add little to discourse.
Four (sets of) authors were asked by the Editors of the Triple Helix to respond to Leydesdorff and Lawton Smith (2022). Many insightful and interesting points were raised including convenience, presentation and the need to allow a more unified theory model. These are discussed in this article’s “responses to just criticism” (Shostakovich, 1937). It continues the debate on triple and higher-order helices by summarising and responding to the points made by those commentators. What may be the status of triple and/or higher-order helices?
Carayannis and Campbell (2009; 2010) have argued for using quadruple and quintuple helices as models encompassing and generalizing triple-helix dynamics. In the meantime, quadruple and quintuple helices have been adopted by the European Committee for the Regions and the European Commission as metaphors for further strategy development such as in EU-programs in Smart Specialization, Plan S, Open Innovation 2.0, etc. Here we argue that the transition from a double helix to a triple helix can change the dynamic from a trajectory to a regime. However, next-order transitions (e.g., to quadruple, quintuple, or n-tuple helices) can be decomposed and recombined into interacting Triple Helices. For example, in the case of four helices A, B, C, and D, one can distinguish ABC, ABD, ACD, and BCD; each triplet can generate synergy. The triple-helix synergy indicator can thus be elaborated for more than three dimensions. However, whether innovation systems are national, regional, sectorial, triple-helix, quadruple-helix, etc., can inform policies with evidence if one proceeds to measurement. A variety of perspectives can be used to interpret the data. Software for testing perspectives will be introduced.