This grant provides funding for research on the complexity of the design process. Data are obtained as discrete sequences of instructions; they form `curves` in a multi-dimensional design space, approximating an underlying design `surface`. Thus, given two points on such a surface (an initial design and a final design), there exists a geodesic (or shortest path) in theory. Yet, practical design sequences are rarely optimal in the sense of being the shortest. There are personal preferences and there are group practices which cause a design to deviate from the ideal, shortest path. Such a phenomenon is studied by analogy to a Lagrangian; the optimization of a path as the maintenance of the excess of the kinetic energy (from an individual, manifested as `creativity` or `preference`) over the potential energy (from the environment, as `outside influence` or `group practice`). If successful, this research will lead to the understanding of the `mechanics` of creation, as constrained by the environment in which the designer is in. It permits explicit experimentation with `what-if` scenarios such as: what happens when `peer pressure` exceeds a certain critical point; what if `peer pressure` is replaced by `self-drive`? The work is expected to be useful in explaining the emergence of patterns or structures exhibited in socio-economics, biological systems, and non-equilibrium chemo-dynamics.
