The Road to Novelty III: Symmetry Bridges

Abstract

The polar information concept introduced in Part II, which consists of decision information (Bits & Bytes) and symmetry information (CoIn), will be positioned in Part III in historical-philosophical perspective against the background of the deliberations by D. Hume, I. Kant, E. Husserl, K. Popper, J. Habermas and K. Mainzer. In doing so, we assess the relevance of the concept with respect to the standpoints of these philosophers on the acquisition of knowledge (towards the New). As a first substantial result, we ascertain a convergence of approaches regarding symmetry-centred cognition (CoIn) in the historic works of Hume, Kant and Husserl. This emerging convergence was later on obstructed to lasting effect by Popper’s rejection of the ‘primacy of repetition’. As Mainzer shows, the concept of symmetry enjoys a significant renaissance in the natural sciences; however, as also evident from Mainzer’s work, its relevance for thought and understanding remains hidden from the specific perspective of these very sciences. It is only with more recent insights from cognitive science regarding categorisation, the use of metaphors, and the formation of analogies (G. Lakoff, S. Pinker, D. Hofstadter, E. Sander) that the discussion on the nature of insight is once again developing towards our extended information concept.Following the discussion of various approaches to understanding insight, some of them historic and some of them recent, a contrasting comparison of these approaches yields an insight that reaches beyond them. This insight points towards a core of essence that is common to all these approaches. The core materialises as the limit of convergence of these approaches on ever higher levels of abstraction and is provided by our information-theoretic CoIn foundation. On this ultimate level of abstraction, the double nature of the economic principle also re-emerges, which already loomed in Part II. Using these theoretical foundations, we are finally able to prove a fundamental asymmetry between the worlds of decisions and insights. This asymmetry implies that there can be no symmetry bridge between those two worlds and, because the limits to algorithmization are equivalent to the limits of the decision access, neither the decision approach nor any algorithmization can serve to access Novelty in the sense of access to cognition. We call this result the bridge theorem.