Towards a conceptual model of randomness

In deterministic modelling, processes are identified and understood in terms of basic mathematical and physical laws and axioms. In stochastic modelling, a random element is permitted and modelling is frequently undertaken using empirical probability distributions. These two modelling approaches are perhaps best exemplified in biology and ecology where measurements of natural processes have an apparent randomness and, at the same time, deterministic differential equations attempt to bridge the gap between the biology and the underlying physics. Using the intermediary of the theory and application of mathematical chaos, it is suggested that these two mathematical ‘world views’ may be able to be reconciled. It is suggested that a new and relevant view may be of stochasticism as being a manifestation of a strange attractor arising from a set of non-linear differential deterministic equations.