Rotational Symmetry and the Transformation of Innovation Systems in a Triple Helix of University-Industry-Government Relations

Using a mathematical model, we show that a Triple Helix (TH) system contains self-interaction, and therefore self-organization of innovations can be expected in waves, whereas a Double Helix (DH) remains determined by its linear constituents. (The mathematical model is fully elaborated in the Appendices.) The ensuing innovation systems can be expected to have a fractal structure: innovation systems at different scales can be considered as spanned in a Cartesian space with the dimensions of (S)cience, (B)usiness, and (G)overnment. A national system, for example, contains sectorial and regional systems, and is a constituent part in technological and supra-national systems of innovation. The mathematical modeling enables us to clarify the mechanisms, and provides new possibilities for the prediction. Emerging technologies can be expected to be more diversified and their life cycles will become shorter than before. In terms of policy implications, the model suggests a shift from the production of material objects to the production of innovative technologies.