Engaging the Human Motor System in Exploring and Understanding Dynamical Systems

Understanding nonlinear dynamical systems can be difficult, yet humans have
an innate capacity for understanding and controlling difficult dynamical systems
in the context of physical movement. The central question explored in
this thesis is whether human motor learning and control capabilities can be
used as a means of studying dynamical systems in general. For example, is
it possible to explore the behaviour of an economy, a population threatened
with extinction, or even the climate using the same mechanisms that allow
us to explore and master the dynamics of activities such as walking, juggling,
skating, cycling, and driving?

A technique referred to as Continuous Interactive Simulation is proposed
that builds on existing techniques for interactive visualisation and computational
steering of dynamical systems. Continuous Interactive Simulation differs
from these approaches in both the nature and degree of interaction with a sys-tem. The emphasis is on active physical participation in the dynamics of a
system rather than passive observation.

This technique was applied to a series of case studies that required subjects
with no technical knowledge in mathematics or the analysis of dynamical systems to attempt to solve problems concerning the properties and behaviour of nonlinear dynamical systems. These case studies focused on the discovery and refinement of dynamic behaviours and control strategies. The systems came
from a range of domains and included a Lotka-Volterra predator prey system,
an inverted pendulum, a dynamic IS-LM model from economics, and the Wonderland model of environmentally sustainable economic growth. These systems included continuous time, continuous time with delayed variables, and discrete time dynamical systems. Each case study included a mapping of a problem to a “movement-based interface” with an appropriate implementation and subsequent usability study. The results of these studies were used to identify key issues in the development of a general purpose framework for Continuous Interactive Simulation and to guide the development of preliminary guidelines for its general application.

The overall results of this research demonstrate that human motor learning
and control capabilities can indeed be used to help explore and understand
the behaviour of dynamical systems in general. Through a process of physical
interaction and skill development subjects were able to discover a repertoire of
dynamic behaviours for the example systems. In the process they discovered
features of the systems including various forms of equilibria and cycles as well
as how to steer the system between those features. Subjects were also able to
refine particular strategies for controlling the systems with respect to specified
performance criteria.

The approach that has emerged from this work provides a relatively assumption
free way of exploring the behaviour of a wide variety of dynamical
systems through physical interaction and skill development. The primary
achievement of this research is to demonstrate the basic feasibility of this novel
approach and its application to a variety of dynamical systems. Areas in which
additional work is required to further the development and application of the
approach are also identified.