8. Tools to extend thinking by considering feedback loops

Preamble: This activity combines the sentiment of CE1 and CE2, namely, "changes in... technology... have changed our needs and capacities for mathematical thinking" with best practices to "help readers appreciate the idea that everyone can think mathematically." Starting in World War II, technology has incorporated feedback into systems of many interacting parts. In one sense this development goes beyond calculus, which allows the calculation of, say, the trajectories of missiles, but not the adjustment of the trajectory in response to information about whether the missile hit the moving target. In another sense, this development is simpler than calculus because it often depends on simulations that move in discrete steps, not finding exact algebraic solutions with continuous varying time or other variables. A sense of these two features can be gained using the simple tool of a spreadsheet. More complicated feedback systems can be simulated using user-friendly software, such as Stella (shown in this introductory video).

Preparation: View "Positive and Negative Feedback Loops," https://www.youtube.com/watch?v=CLv3SkF_Eag

Goals
Review basic spreadsheet commands
Understand basic ideas about feedback
Understand and apply social interpretation as a means to expose the restrictiveness that comes with using any quantitative tools

Activities
0. Review basic spreadsheet commands (if needed; look at page 6)

1. Overreacting thermostat

• Explanation of thermostat-temperature feedback, with some exercises
• Try the exercises on paper: http://www.faculty.umb.edu/peter_taylor/thermostat.docx
• Now try it on the spreadsheet: http://www.faculty.umb.edu/peter_taylor/thermostat.xlsx

2. Economic management game

• Explanation of the game
• Try a cycle of the game on paper: http://www.faculty.umb.edu/peter_taylor/longwave.docx
• Now try it on the spreadsheet: http://www.faculty.umb.edu/peter_taylor/longwave.xlsx

3. Plus-delta feedback on activity

4. Follow-up: To appreciate the restrictiveness that comes with using any quantitative tools, read pages 2-5 of preprint of Taylor, P. J. (1997). How do we know we have global environmental problems? Undifferentiated science-politics and its potential reconstruction. Changing Life: Genomes, Ecologies, Bodies, Commodities. P. J. Taylor, S. E. Halfon and P. E. Edwards. Minneapolis, University of Minnesota Press: 149-174

5. Follow-up: Review formulas in instructor's versions of the spreadsheets and play with these versions: thermostat, economic management (tba)