Integral Biomathics reloaded: 2015

Abstract

Recap and antrorseMany biological phenomena do not have adequate mathematical representations. This is because living systems use structures that are not yet grasped by our present conceptions of mathematics and computation. In particular they are circularly organized and they use recursions. Mathematics and computation at the present time deal only superficially with circular organization or the consequences of recursion. We just have not yet found a way to adequately deal with such matters 1 ! Current approaches to complex problems rely on modelling, but one aspect of the problem is that they rely on a single form of mathematics, switching from it to another to address the next aspect, and so on. All this switching is an indication of how inadequate our mathematical tools are to date (ODE/PDE systems, stochastic models, discrete state-transition systems, topological algebra, etc.). Biological systems function at all these levels simultaneously. Yet, the real problem is that even the simplest recursions are beyond our capacity to analyse at the present time. It is not biology that is too messy to be modelled; it is our use of current mathematical paradigms that are not able to adequately address these biological problems (Root-Bernstein, R. S., 2012). These paradigms are keeping biology within the fixed boundaries of physics, the domain of nonliving matter. Despite being the most advanced mathematics-based natural sciences discipline, physics is currently experiencing its own crisis when trying to overcome the dichotomy between its major theories (Smolin, 2006) and remains not sufficiently developed to explain living systems. Is this a chance in disguise?We believe that further advances in the sciences -physical, biological, social -require new levels of integration across the domains. It is a commonplace to seek a "paradigm shift" (Kuhn, 1962) to advance the frontiers of a scientific domain. Such shift can also uplift the network of interdisciplinary connections among existing research areas. However, we are seeking more than a shift that advances the network of the complex dynamical system of knowledge. We seek to advance the nature of the links of this network by encouraging the development of mathematical and computational methods that will at once change the shapes of the nodes and the links, thus performing a simultaneous "quantum jump" in multiple disciplines, to enable a new integration and rationalization of knowledge: Integral Biomathics. The major implications of this new paradigm for reinventing and re-engineering mathematics and computation address the life sciences and medicine. They encompass meanwhile also the foundations of creativity and cognitive processes in the sciences and the arts, as well as the phenomenology of consciousness in general.