What does mathematics have to do with human behavior? Simply put, math can help us lead more altruistic, moral lives. In this sense, some of the ideas gleaned in moral math are concepts traditionally tended by religion.
Moral Math practitioners cull mathematics to find ideas that can benefit social behavior. Then they shape these ideas into ways that allow even non-mathematicians to grasp the overall sense, even while remaining unskilled with the mathematical details.
Sarah Voss, a Moral Math pioneer, first heard the term in private conversation with Sal Restivo, a leading contributor to the sociology of mathematical knowledge. Sarah subsequently used the term in a presentation on “‘Moral’ Math and the Golden Rule” at the 2004 joint annual meeting of the Society for the Scientific Study of Religion and the Religious Research Association.
Interest in Moral Math is growing. In 2008, for instance, the Werner Institute for Negotiation and Dispute Resolution hosted a first-of-its-kind conference which applied chaos theory, complexity and emergence to the field of conflict resolution.
NEW PROJECT: Moral Math Training Sessions
Sarah Voss is putting together a new opportunity to explore the potential of Moral Math. This latest project offers a variety of experiential exercises –all drawn from math– to academics, mediators, religious leaders, and others interested in developing fresh tools of peace or better applying old ones.
Specifically, the study researches, develops, presents, and evaluates a series of three related training sessions designed to help identify new tools for achieving consensus. These workshops differ from other attempts to find such tools in that they involve ideas mined from mathematics which are communicated via experiential exercises, then related by analogy to selected examples of social behavior.
Information gleaned from the sessions will address whether ideas mined from math can encourage positive social behaviors. Project results will also inform three of ten chapters in a book about Moral Math.
Session 1, Algorithmic Ethics, draws from non-zero-sum game theory to help people discover how math can promote new ways to consider and resolve conflicts. One example involves equitable cake division, where participants learn algorithmic methods for cutting the cake. After considering what such methods might suggest about dividing a country or gerrymandering election districts, trainees would, of course, get to eat the divided cake. Another example is the Dollar Auction, a variation of the non-zero-sum game known as the Prisoner’s Dilemma. Session surveys ascertain how well this exercise can help show the understanding needed to prevent, say, an arms race.
Session 2, Living Better on the (Chaotic) Edge, uses ideas from complexity theory to create interactive exercises that highlight self-organizing emergence. One example to be included is an exercise that involves red and green cards, a die for randomness, and a simple set of instructions about the conditions under which participants exchange a red for a green card, or vice versa. The project director developed this exercise and has used it in both religious and academic settings. Response to this experiential exercise indicates how the power of this work. For instance, during an unrelated presentation at a 2005 UNESCO conference in Seattle, two men who grew up in Austria after the Holocaust began an emotionally distancing and disturbing conversation that eventually brought all discussion in a section on Trustworthiness and Justice to an abrupt halt. Even one of the two professional facilitators of the section was near tears as she concluded that the best thing to do was to simply move forward with the agenda. The final report of the conference noted what happened next: “The whole room was experiencing the pain of humanity… then Sarah Voss’ presentation on Moral Math gracefully allowed us to ‘shift back’ and reclaim respect and dignity.” Subsequent discussion indicated that the perceived neutrality of mathematics contributed to significant healing experiences within the group. The expectation in this session is that such highly interactive exercises can assist individuals in understanding how moral character emerges.
Session 3, Cantorian Religion Can, draws on the idea, first seen in What Number Is God? (SUNY, 1995), that an eclectic, pluralistic religion is emerging – one made of the set of all religions. This religion is structurally different from others in the same sense that mathematician Georg Cantor’s “set of all sets” is structurally different from all other sets. We ask: Can a carefully developed presentation on this idea foster greater tolerance of religious diversity?
To support this work or to find out how to participate in the sessions, please contact Sarah Voss here.
For further reading
Abstract: Moral Math and the Golden Rule
RRA/SSSR presentation by Sarah Voss, University of Nebraska, Omaha, 2004
What does mathematics have to do with how well we treat each other? This paper examines ways in which contemporary scholars are applying mathematical ideas to social behavior. Of particular emphasis are ideas drawn from complexity theory, fuzzy logic, game theory, and neuroscience. Specifics include how self-organizing emergence can shed light on prejudice, expectations about cooperative behavior from the study of non-zero-sum games, the social potential of fuzzy tax forms and “provisional” ethics, the value of new brain implications for “tend and befriend” behavior. Also addressed are the strengths and limitations of such “moral” math.
Generating Trust through “Moral” Math
by Sarah Voss, in Unity and Diversity in Religion and Culture: Exploring the Psychological and Philosophical Issues Underlying Global Conflict. International Readings on Theory, History and philosophy of Culture #22, under UNESCO auspices. ed. by Lubava Moreva, St. Petersburg: Eidos, 2006.
While most of us recognize theoretical mathematics as a source for many of the gains humankind has made in science and technology, fewer of us are aware that some of these same mathematical ideas can be and are being applied to issues of social behavior. This essay explores several of the most recent of these ideas. Specifically, it examines concepts drawn not only from simple algebra, but also from the theory of complexity and its offshoots, from fuzzy logic, and from non-zero-sum game theory. An underlying assumption of this essay is that we generate trust whenever we engage in the Golden Rule. Thus, the kind of social behavior which we hope to stimulate with models drawn from mathematics is that which focuses on treating the “other” as you yourself would like to be treated.
Therefore all things whatsoever you desire that men should do to you, do you even so to them. – New Testament, Matthew 7:12, from the Christian tradition, circa 30 CE.
Many of us have seen various formulations of this Golden Rule, but here is one version, drawn from the world of mathematics, which you may not be so quick to recognize:
“The mathematical golden rule states that for any fraction, both numerator and denominator may be multiplied by the same number without changing the fraction’s value.”
For example, one half equals two fourths (1/2= 2/4), derived, of course, by doing unto the “one” (“1″) as you would do unto the other (the “2”). While it seems to take a lifetime (or more) for us to learn to practice this golden rule in our social lives, it only takes a few years of elementary school for most of us to grasp the concept through mathematics. In spite of the simplicity of this observation, only recently have social scientists begun to consider mathematics as a source for ethical guidance.
Once discovered, however, this notion – that we can make better moral decisions with the help of theoretical mathematics – seems to be spreading rapidly. Today, scholars are using a number of mathematical ideas and techniques to better understand the social behavior of cooperation, fairness, and altruism. …
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