Saturday, October 27, 2012

Mathematics for Sustainability 3

The second of my four themes for the planned "Mathematics and Sustainability" course is "Changing".  I think of this as the core section.  I would like my students to develop some intuitions about stocks and flows, rates of change, and dynamical systems.

In putting this material front and center I am recapitulating an experience which was important for me both as a mathematician and as someone concerned about environmental sustainability: I mean reading, in about 1975, the famous book The Limits to Growth, which had appeared a few years before. The "System Dynamics" models in Limits (basically graphical representations of differential-difference equations) fascinated me.  I built models of my own of similar kinds, and explored them numerically with a hand calculator and (when that failed) through a dial-up link to a minicomputer, a Modular One located at the University of Warwick.  I don't think it is fanciful to see my research interest in "large scale" and "long time" properties as linked to these early numerical experiments.  More relevant to an undergraduate course, though, is the appreciation that this "playing" gave me for the robustness of qualitative descriptions like feedback, overshoot, collapse, oscillation, exponential and resource-constrained growth.  Despite its quantitative focus - inevitably controversial - the basic focus of Limits was, it seems to me, this qualitative one.

In order to help students share this kind of experience I would like to give them the opportunity to build models using a variation of the System Dynamics approach.  Nowadays there are several software packages available that build models directly from the kinds of diagrams that are used to represent system dynamics models.  I am looking at using Insight Maker for the course, because it is free and runs in a web browser.  I hope to have the students develop their own models using Insight Maker and share and comment on each others' models via the course blog.  At the same time I plan to use Insight Maker in class to explain some basic ideas like stocks and flows, exponential and logistic growth; and perhaps we'll construct some models (like an aggregated climate model) using Insight Maker just to show what can be done.

Evaluating student software projects is fraught with pitfalls (at least,so it seems to me) - I think that seeing how the students explain to each other via the blog what it is their models actually accomplish will provide important information about how good a level of understanding they have attained.

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