Knowledge-generating efficiency in innovation systems: The acceleration of technological paradigm changes with increasing complexity

• Knowledge-generating cycles in US patents partially coincide with long (Kondratieff) waves.
• The relative efficiency of successive knowledge-generating cycles increases.
• The interaction among dimensions sets limits to the maximal efficiency of innovation systems.
• Time spans of knowledge-generating cycles can be analyzed in terms of Fibonacci numbers.

Time series of US patents per million inhabitants show cyclic structures which can be attributed to the different knowledge-generating paradigms that drive innovation systems. The changes in the slopes between the waves can be used to indicate efficiencies in the generation of knowledge. When knowledge-generating systems are associated with idem innovation systems, the efficiency of the latter can be modeled in terms of interactions among dimensions (for example, in terms of university–industry–government relations). The resulting model predicts an increase in efficiency with an increasing number of dimensions due to the effects of self-organization among them. The dynamics of the knowledge-generating cycles can be analyzed in terms of Fibonacci numbers; successive cycles are expected to exhibit shorter life cycles than previous ones. This perspective enables us to forecast the expected dates of future paradigm changes.