What Concept of Logic and Information for Nanobiosystems?

Prospects for bioinspired automata and nanobiological modelling

Salvatore Santoli

INT - International Nanobiological Testbed Ltd. (London)

via A.Zotti 86, I-00121 Rome, Italy

 

It is argued that the moving from the nonequilibrium, classical and/or quantum microscopic dynamics underlying the macroscopic behaviour of living matter, up to kinetic and thermodynamic level descriptions of its structure-function solidary unity, implies the setting forth of a novel conceptual framework, involving both a novel system of formal logic, dubbed here kinetic logic, and an energy-free non-commutative geometric approach to the holistic, information-driven hierarchical self-organizing and cognitive dynamics of living systems. This paper was inspired by a passage in John von Neumann's Collected Works where, in a discussion about some problems in connection with the logical organization of a numerous set of complex organs in automata, possibly biomimetic or even biological, he advocated the advent of "a new system of formal logic" moving "closer to another discipline which has been little linked in the past with logic. This is thermody-namics, primarily in the form it was received by Boltzmann". Now, the Boltzmannian approach to thermodynamics is actually of kinetic, i.e. nonequilibrium, character. Accordingly, an attempt is made here to try and find a set of isomorphisms between operations in the logical space and the corresponding kinetic flows in the phase space. Moreover, it will be shown how self-referential paradoxes of evolutionary behaviour in standard atemporal logic give way to non-paradoxical dynamic flows in the physical phase space in such system of kinetic logic. It will be shown that a new concept of information can arise from a new system of formal logic; indeed, logic and information share a physical basis. A deepening of this connection and the possible outcomes will be discussed in a further section. While a kinetic formal logic would allow the overcoming of problems stemming from logical paradoxes and semantic aspects ofљ biological information processes in bioinspired technologies involving biomimicry of the organization ofљ complex sets of nanoscale members, e.g. intracellular and neural nets, or models of biological organs, an approach based on the Heisenberg quantum/classical noncommutative group of symmetries leads to novel envisageable technologies for Nanobiology, mainly consisting of nanoscale tomographies described by the informational properties of the group. This approach would be fit e.g. for studies in the biology of flight or swimming, both at very low and high Reynolds numbers, as movements consisting of resonant coupling or coherence of environmental force fields with the inside dynamic ongoings of the living organism through their neural images. This geometric, non-dynamical or energy-free approach would remove the possibility of inter-level semantic dyscrasias insurmountable by the dynamic (i.e. energy-based) approach, and would also substantiate the possibility of a concept of information for nanobiosystems which is based on a quantifiable quality in phase space, so replacing Shannon's abstract notion as inadequate to describe far-from-equilibrium, highly dissipative and evolutionary nonlinear processes and incapable to overcome the puzzle of biosystems as being exclusively classical.

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