This paper applies I.M. Gelfand's distinction between adequate andView original: http://arxiv.org/abs/1202.5115
non-adequate use of mathematical language in different contexts to the newly
opened window of model-based measurements of intracellular dynamics. The
specifics of geometry and dynamics on the mesoscale of cell physiology are
elaborated - in contrast to the familiar Newtonian mechanics and the more
recent, but by now also rather well established quantum field theories.
Examples are given originating from the systems biology of insulin secreting
pancreatic beta-cells and the mathematical challenges of an envisioned
non-invasive control of magnetic nanoparticles.