The Algebra of Grand Unified Theories

The Standard Model of particle physics may seem complicated and arbitrary, but it has hidden patterns that are revealed by the relationship between three "grand unified theories": theories that unify forces and particles by extending the Standard Model symmetry group U(1) x SU(2) x SU(3) to a larger group. These three theories are Georgi and Glashow's SU(5) theory, Georgi's theory based on the group Spin(10), and the Pati-Salam model based on the group SU(2) x SU(2) x SU(4). In this expository account for mathematicians, we explain only the portion of these theories that involves finite-dimensional group representations. This allows us to reduce the prerequisites to a bare minimum while still giving a taste of the profound puzzles that physicists are struggling to solve.Comment: 73 pages, 20 ps figure

Fat Cats and Thin Kittens: Are People Who Make Large Campaign Contributions Different?

Critics of campaign finance in the United States often direct their fire toward contributors who make large donations. Critics charge that large contributions are unfair, unrepresentative, and undemocratic. Accordingly, they push for "reforms" that would favor small contributions over large, and public money over private donations. Survey data on contributors contradict that stereotype of contributors of large amounts and their effects on American politics. Overall, "fat cats" differ less from contributors of smaller amounts than critics have alleged. The differences that do exist are mostly unsurprising and generally small in magnitude. Survey results show that both policy liberalism and Democratic partisanship are well represented among contributors of large sums.The supporters of McCain-Feingold argue that new restrictions on large contributions will profoundly alter American politics for the better. Their claims have no basis in fact. New laws aimed at restricting large donations in favor of smaller ones will have little effect on practical politics

Defining, Valuing, and Providing Ecosystem Goods and Services

Ecosystem services are the specific results of ecosystem processes that either directly sustain or enhance human life (as does natural protection from the sun's harmful ultraviolet rays) or maintain the quality of ecosystem goods (as water purification maintains the quality of streamflow). "Ecosystem service" has come to represent several related topics ranging from the measurement to the marketing of ecosystem service flows. In this article we examine several of these topics by first clarifying the meaning of "ecosystem service" and then (1) placing ecosystem goods and services within an economic framework, emphasizing the role and limitations of substitutes; (2) summarizing the methods for valuation of ecosystem goods and services; and (3) reviewing the various approaches for their provision and financing.Many ecosystem services and some ecosystem goods are received without monetary payment. The "marketing" of ecosystem goods and services is basically an effort to turn such recipients - those who benefit without ownership- into buyers, thereby providing market signals that serve to help protect valuable goods and services. We review various formal arrangements for making this happen