MATH ESSAY WRITING_14 PAGES

Mathematics, Sustainability, and a Bridge to Decision Support Author(s): Mary Lou Zeeman Source: The College Mathematics Journal, Vol. 44, No. 5 (November 2013), pp. 346-349 Published by: Mathematical Association of America Stable URL: http://www.jstor.org/stable/10.4169/college.math.j.44.5.346 Accessed: 18-02-2017 18:37 UTC

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GUEST EDITORIAL

Mathematics, Sustainability, and a Bridge to Decision Support Mary Lou Zeeman

Mary Lou Zeeman ([email protected]) is the Wells Johnson Professor of Mathematics at Bowdoin College. She received her Ph.D. at Berkeley, worked at U. T. San Antonio for 15 years, and has held postdocs at the IMA and MIT, as well as visiting positions at Michigan and Cornell. Her research interests include dynamical systems, population dynamics and fisheries, neuroscience, endocrinology, and climate science. Zeeman is also involved in several interdisciplinary initiatives focused on the health of the planet. She co-directs the Mathematics and Climate Research Network, which links researchers across the U.S. and beyond to develop the mathematics needed to better understand the earth’s climate (http://www.mathclimate.org). She helped found the Institute for Computational Sustainability based at Cornell University, and she is on the organizational team of the Mathematics of Planet Earth 2013 initiative.

The Mathematics of Planet Earth. Scientific societies, universities, and organi- zations around the world have come together this year to focus attention on the Math- ematics of Planet Earth (MPE 2013). The MPE web portal [6] lists research programs, curriculum materials, public events, hosts a daily blog, and more. The initiative con- tinues beyond 2013, so please keep sending events and ideas to the portal. This issue of The College Mathematics Journal, part of the MPE initiative, has articles that il- lustrate all four MPE themes: a planet to discover; a planet supporting life; a planet organized by humans; and a planet at risk. All four are essential for understanding our changing climate and addressing our pressing sustainability challenges. We are used to the idea that mathematically-rich subjects such as statistics, economics, engineering, and climate science have a role to play in supporting decision-making at the front lines of sustainability challenges. What about those of us in mathematics departments? We, too, have a lot to contribute.

What is decision support? The core idea, according to the National Research Council [7], is “making scientific knowledge useful for practical decision making.” What might that entail for mathematicians? We could, for example, help translate sci- entific results into non-technical language—especially when uncertainty is involved. Or we could provide data, analysis tools, and software. I’ve deliberately phrased these suggestions to emphasize a professional service component of decision support. Ser- vice, of course, can be rewarding in its own right, but the reader of this JOURNAL may wonder how decision support is tied to mathematics research or the mathematics

http://dx.doi.org/10.4169/college.math.j.44.5.346

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curriculum. Let’s explore this by analogy with the application of mathematics to other disciplines. Mathematical biology is my example; you may substitute your favorite application.

Analogy with mathematical biology. There is a well-established bridge between the mathematics and biology communities. As interdisciplinary researchers, we can position ourselves wherever we feel most comfortable on the bridge. Some of us like to work at the biology end of the bridge, immersing ourselves in lab experiences and collaborating directly with experimentalists to understand what can be measured, what can be controlled, and what are sources of uncertainty. From there, we collabora- tively develop models and design experiments to test hypotheses, tease apart systems, and unravel biological mysteries. Others prefer to work in the middle of the bridge, abstracting the ideas and analyzing the structures that recur in the models. For ex- ample, there are thriving mathematical biology communities that study coupled oscil- lators, excitability, and bifurcation, generalizing those ideas to networks, and explor- ing the delicate balance nature walks between stability and adaptability in a stochastic world. Finally, others prefer to work at the mathematical end of the bridge, proving theorems that unify the consequences of these structures, and developing methods for their analysis. Over a career, some enjoy moving back and forth across the bridge. An essential feature of the bridge is the two-way nature of the interactions. Both disciplines are enriched with new insights, new questions, and new ways of looking at old questions.

A mathematics-decision support bridge. We are beginning to build a similar bridge between mathematics and decision stakeholder communities. The term ‘stake- holder’ includes all who care about a decision, particularly those who make it and those impacted by it. For example, regarding a decision of where to build a wind farm and what kind of turbines to use, stakeholders include private investors, the energy com- pany, local residents, town councils, land trusts, field naturalists, and others. Those of us who enjoy working at the stakeholder end of the bridge immerse ourselves in the decision question, collaborating directly with stakeholders to understand the dif- ferent components of the system, what can be measured, what can be controlled, what creates uncertainty, what is valued, and what are the associated costs, economic and otherwise. (See [12] for a description of how to bring stakeholder communities to- gether to describe a complex system). From there, we collaboratively develop models, design computer experiments to test scenarios, tease apart systems, and identify new decision options. In the early stages of bridge building, it may feel like isolated deci- sions are separated by their specific details. But, just as in mathematical biology, from multiple case studies common structures emerge, generating abstractions to explore at the middle of the bridge and stimulating new mathematics all along the bridge. One of my favorite emerging structures is that of resilience. Systems with inherent positive feedback often exhibit multiple stable states. For example, rangelands can be grassy or become wooded or desertified, depending on patterns of grazing, fires, and precip- itation [12]. The resilience of a state measures how much perturbation a system can withstand without transitioning to a qualitatively different state. Estimating resilience, therefore, involves understanding the interplay between between deterministic basins of attraction and the stochastic characteristics of noise and disruptive events in a grad- ually changing environment [10, 11, 12]. More examples of mathematical structures common to decision questions are showcased in the MPE daily blog, and education and workshop pages [6].

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Strengthening the bridge. Enrichment for the communities at both ends of the mathematics-biology bridge derives from healthy overlap between individuals along the bridge. To increase this overlap, we have a range of opportunities for individuals at all levels to broaden their reach along the bridge. In mathematical biology, we have curricula for undergraduate and graduate students, funding agencies that spon- sor immersion experience programs for researchers, and interdisciplinary societies, conferences, and institutes. Let’s do the same thing for the mathematics-decision support bridge. Let’s apply our collective, intelligent minds to create opportunities for individuals to broaden their reach. In the language of the National Research Council, let’s figure out how the mathematics community can help “create the condi- tions for the production of decision-relevant information and for its appropriate use” [7, p. 34].

Getting involved. We all have something to contribute to this effort, if we choose. We may step onto the bridge ourselves, or we may empower others to do so. One way to step onto the bridge is to seek out a sustainability organization and learn what questions it grapples with. At the local level, for example, this could involve joining a sustainability solutions seminar series. To connect with decision makers at the state or federal level, Angus King, a former Governor of Maine and current U.S. Senator, rec- ommends talking to to a “staff member for energy and the environment”. King points out, “Decision-makers are often in search of compelling data as a basis for public pol- icy and effectively presented mathematical data can have a significant influence on policy outcomes.” (Personal communication, 2013).

How do we empower others? Straightforward mechanisms include supporting in- terdisciplinary seminars, guest speakers, cross-disciplinary conference travel, and so on. Those of us who are senior are in a position to facilitate discussions about how to evaluate and reward colleagues for deeply intellectual decision-support work, whose tangible products are not research publications. This is especially important for tenure decisions. At Bowdoin, the scholarship criterion for tenure candidates is “professional distinction recognized by members of their guild outside the College,” [1], a criterion that can certainly encompass the production of decision-relevant information and its appropriate communication.

In the classroom. We must also create opportunities for our students to increase their reach along the math-decision support bridge. Sustainability questions are highly multidisciplinary, blending mathematics with science, social science, and economics. None of us can be expert in all these disciplines, so it takes cross-disciplinary team- work and courage to attack the questions. There are many ways to broaden the cur- riculum to help students develop those skills. In doing so, we also broaden the appeal of mathematics to students. There are excellent examples in the articles in this issue, and more examples on the MPE education and curriculum materials pages [6]. They range from one-day modules for core math classes [2] to annotated reading lists by climate experts around which to design seminar courses [5]. The Multidisiplinary Sus- tainability Education project at Ithaca College is a model for enriching mathematics and science education by using sustainability questions as an organizing principle for linking existing courses from several departments [4, 8]. I experienced a quantum leap in my own appreciation for cross-disciplinary teams when I helped develop and run Cornell’s State of the Planet course, which had the theme: Whatever your talent, what- ever your passion, you can use them to help the planet [3, 9].

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Into the future. I hope that some of these suggestions resonate with you, and that you will share your own examples and suggestions through the MPE blog, curriculum pages, articles in this JOURNAL, and elsewhere.

Our students are young. They are inheriting the planet as it is. Their enthusiasm for finding solutions to sustainability challenges is palpable, bringing new energy and creativity into the mathematics classroom. Harness this energy and empower them. Be honest about the state of the planet, but don’t get trapped in gloom and doom. Teach material that is about solutions more than it is about problems.

Acknowledgment. I am grateful to Marty Anderies, Steve Cantrell, Chris Cosner, Michael Henle, David McCobb, Elan Shapiro, and members of the Mathematics and Climate Research Network for helpful conversations, and to Bowdoin College and NSF for their support (DMS- 0940243 and CCF-0832788).

References

1. Bowdoin College, Faculty handbook (2012); available at http://www.bowdoin.edu/ academic-affairs/forms-policies/policies/pdf/12-13FacultyHandbook.pdf.

2. Center for Discrete Mathematics and Theoretical Computer Science, DIMACS sustainability modules for undergraduate mathematics classes (2013); available at http://dimacs.rutgers.edu/MPE.

3. T. Eisner, L. E. Fletcher, J. G. Hamilton, D. P. McCobb, and M. L. Zeeman, Empower your students: Bring a State of the Planet course to your school, Mathematics Awareness Month theme essay (2009 and 2013); available at http://www.mathaware.org/mam/2013/essays.

4. J. Hamilton, M. Rogers, T. Pfaff, and A. Erkan, Multidisciplinary collaborations in the traditional classroom: Wrestling with global climate change to improve science education, Transformations: The Journal of Inclu- sive Scholarship and Pedagogy 21 (2010) 89–98.

5. Mathematics and Climate Research Network, MCRN annotated reading lists (2013); available at http: //www.mathclimate.org/education/annotated-reading-lists.

6. Mathematics of Planet Earth, MPE 2013 web portal; available at http://mpe2013.org. 7. Panel on Strategies and Methods for Climate-Related Decision Support; National Research Council, Inform-

ing Decisions in a Changing Climate, The National Academies Press, Washington DC, 2009; available at http://www.nap.edu/catalog.php?record_id=12626.

8. T. Pfaff, A. Erkan, J. Hamilton, and M. Rogers, Ithaca College multidisciplinary sustainability education project, (2010); available at http://www.ithaca.edu/mse.

9. K. L. Rypien, J. Anderson, J. Andras, R. W. Clark, G. A. Gerrish, J. T. Mandel, M. L. Nydam, and D. K. Riskin, Students unite to create State of the Planet course, Nature 44 (2007) 775.

10. M. Scheffer, Critical Transitions in Nature and Society, Princeton University Press, Princeton NJ, 2009. 11. B. Walker and D. Salt, Resilience Thinking: Sustaining Ecosystems and People in a Changing World, Island

Press, Washington DC, 2006. 12. , Resilience Practice: Building Capacity to Absorb Disturbance and Maintain Function, Island Press,

Washington DC, 2012.

Joseph Fourier on Global Temperature

In his “Mémoire sure les températures du globe terreste et des espace planétaires” (see also p. 363), Fourier advances a principle that might be considered the theme of this issue,

In the present writing I have set myself another goal, that of calling atten- tion to one of the greatest objects of Natural Philosophy, and to set forth an overview of the general conclusions. I have hoped that the geometers will not see these researches only as a question of calculation, but that they will also consider the importance of the subject.

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