MATHEMATICAL MODELS, COMPUTER-AIDED THINKING AND THE SCIENTIFIC METHOD

Mathematical models have increased in complexity due to a phenomenal increase in computer capacity, not due to an equally phenomenal increase in our understanding. In fact, as model complexity continues to grow, we are likely approaching the barrier of “mathematical chaos” wherein model output can no longer conform to the unique reality of the natural system being simulated (classical prediction fails). Thus, the question arises, how can we use mathematical models of increasing complexity to truly increase our understanding of natural systems”? We believe that the answer involves bringing the scientific method (verification by experiment) back into the knowledge-generating process, and using the computer not for classical prediction but to extend our ability to think and hypothesize about complex natural systems (computer-aided thinking). Such an approach is illustrated by an analysis of Pu lysimeter experiments at the Savannah River Site which showed anomalous Pu distributions below the source with unexplained above source migration. The initial conceptual model of the transport process was based on steady-state and then fully transient soil water movement coupled to surface reactions between reduced and oxidized Pu species. Simulations yielded reasonable below-source distributions, but little above-source transport. The conceptual model was then modified to include Pu absorption by plant roots (there was lysimeter grass growth) and upward movement in the transpiration stream. Resulting simulations suggested such movement had to be rapid with a Pu accumulation on the soil surface due to annual dieback. Model-motivated isotope ratio analysis then verified such a residue. Thus, there was strong support for plants being an important pathway for Pu transport, but not a clear picture of the biochemistry involved. This further motivated laboratory experiments on corn that verified rapid Pu transport in the transpiration stream and probable involvement of Pu chelating agents. Data suggest that corn may co-metabolize Pu with Fe, an essential nutrient, thereby increasing greatly the mobility of complexed Pu in plant tissue. In the case of deterministic chaos, the only way forward may be model extrapolation from a data set (not prediction) followed by experimental exploration of the results.