Nonlinear Biology

Abstract

In the previous chapter we looked at examples of nonlinear dynamics in the physical sciences, where Albert Einstein was surprised that such phenomena can be understood. Here we consider some nonlinear formulations of Life’s dynamics, beginning again with the small (biochemistry) and working through the growth of form and population dynamics to several aspects of neuroscience. Along the way we will notice a distinctive feature of biological sciences — the number of possible entities in any species (proteins, DNA molecules, organs, neural structures, and brains, and so on) is very large. Indeed, this number is often immense in the sense defined by physicist Walter Elsasser,¹ meaning that available possibilities, although finite in number, cannot be physically realized; thus the sets of items being studied in the life sciences are heterogeneous, rather than homogeneous as in the physical sciences. To keep account of these many possibilities, living systems are conveniently organized into hierarchical levels, interacting nonlinearly among themselves like those of Horace Lamb’s hydrodynamic turbulence (see Sect. 6.8.7).

In this chapter, the professions of scientists will be noted as they are introduced, because this information is relevant to understanding the role that physical science has played in the formulation of mathematical biology.