| Description: |
Morphospaces, Adaptive and Epigenetic Landscapes, Phylogenetic Networks, and n-Dimensional Niches are imaginary worlds constructed upon the basis of theoretical models or the mathematical analysis of multivariate data. Their power often lies not only in aesthetics and the improvement of our conceptual understanding, but also in the planning of experiments, the decisions of what field data to collect, or the re-interpretation of already collected data. How do we help biologists interpret and appreciate the mathematical models and analyses that underlie these imaginary worlds? I will illustrate four models that instantiate the paleontologist Dolph Seilacher's dictum: "I wouldn't have seen it, if I hadn't believed it." Analyses of multivariate, multi-scale nonlinear phenomena require new tools and conceptual approaches. Four of the biological software applications that we have developed are based upon computational geometry, spatial statistics, graph theory, cellular automata, and fractals. Some of the questions that will be addressed are: How do designs emerge without designers? How can complex patterns be generated by simple rules? When do slogans like “survival of the fittest” break down? How do we test trees as hypotheses or ask how tree-like is a network? In this context, mathematics is a lens that helps us see from a perspective. In particular, I believe that if the mathematics is easily accessible to biologists, then they are not only apt to use mathematics, but also they are more likely to understand how mathematics helps them with their work. Furthermore, this approach helps biologists better appreciate Richard Hamming’s dictum that: “The purpose of computing is "insight", not numbers. |