Mathematical and computational models can be used to develop data to help us understand the complex systems around us. The development of those data can be done analytically, statistically or by means of simulations over time. For example, notable recent progress in biosciences is the completion of the Human Genome Project, which is the first step toward a molecular genetic understanding of the human organism. To synthesize the massive sets of loosely structured data generated and to draw knowledge from them, scientists have relied heavily on mathematical and statistical models. Another example of the ubiquitous impact of modeling and simulations is numerical weather prediction, which uses mathematical models of the atmosphere and oceans to predict the weather based on current weather conditions.

Applications of modeling and simulation techniques are by no means limited to natural sciences and engineering. A well-known example of philosophical interest is the cellular automa rule set known as “Conway’s Game of Life” (or simply “Life”), which was created by British mathematician John Conway in 1970. “Life” is a fascinating cellular automaton, in which the evolution of “cells,” laid out in a virtual world in the form of a two-dimensional checkerboard, is determined by their initial states and a few simple rules that govern the interactions among cells. Amazingly rich and interesting emergent patterns can arise from different initial configurations, and those patterns can be interpreted as the origin of emergent objects in nature.

In the social sciences, simple simulations are used to implement Thomas Schelling’s models of segregation, as models of assimilation and diffusion of cultural traits. More complex models test theories of economics by creating a population of agents exchanging commodities at prices they determine from local information. Still more complex simulations determine the outcome of social policies under different conditions. These are used in domestic, international and military operations to discover the envelope of possibilities resulting from being different “what if” scenarios.

Students in this Focus cluster learned how to formulate mathematical models that can be used to answer scientific questions. They also learned a variety of techniques for studying the models, including mathematical analysis, computations and simulations.

Timing

2014-2015

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Modeling and Simulation to Answer Scientific and Social Questions