“Over the last couple of years, Cosma Shalizi and I have been working together on various things, including, inter alia, the relationship between complex systems, democracy and the Internet. These are big unwieldy topics, and trying to think about them systematically is hard. Even so, we’ve gotten to the point where we at least feel ready to start throwing stuff at a wider audience, to get feedback on what works and what doesn’t. Here’s a paper we’re working on, which argues that we should (for some purposes at least), think of markets, hierarchy and democracy in terms of their capacity to solve complex collective problems, makes the case that democracy will on average do the job a lot better than the other two ways, and then looks at different forms of collective information processing on the Internet as experiments that democracies can learn from.”
“The authors prepared this booklet in order to make several useful topics from the theory of special functions, in particular the spherical harmonics and Legendre polynomials for any dimension, available to undergraduates studying physics or mathematics. With this audience in mind, nearly all details of the calculations and proofs are written out, and extensive background material is covered before beginning the main subject matter. The reader is assumed to have knowledge of multivariable calculus and linear algebra as well as some level of comfort with reading proofs.”
“In these three lectures we will discuss some fundamental aspects of the theory of self-adjoint extensions of the covariant Laplace-Beltrami and Dirac operators on compact Riemannian manifolds with smooth boundary emphasizing the relation with the theory of global boundary conditions.
Self-adjoint extensions of symmetric operators, specially of the Laplace-Beltrami and Dirac operators, are fundamental in Quantum Physics as they determine either the energy of quantum systems and/or their unitary evolution. The well-known von Neumann’s theory of self-adjoint extensions of symmetric operators is not always easily applicable to differential operators, while the description of extensions in terms of boundary conditions constitutes a more natural approach. Thus an effort is done in offering a description of self-adjoint extensions in terms of global boundary conditions showing how an important family of self-adjoint extensions for the Laplace-Beltrami and Dirac operators are easily describable in this way.
Moreover boundary conditions play in most cases an significant physical role and give rise to important physical phenomena like the Casimir effect. The geometrical and topological structure of the space of global boundary conditions determining regular self-adjoint extensions for these fundamental differential operators is described. It is shown that there is a natural homology class dual of the Maslov class of the space.
A new feature of the theory that is succinctly presented here is the relation between topology change on the system and the topology of the space of self-adjoint extensions of its Hamiltonian. Some examples will be commented and the one-dimensional case will be thoroughly discussed.”
“It is hard to believe that anyone would take seriously such a call to substitute political for scientific judgment if the program in question was physics, or computer science, or even economics.”
“Scholars and pundits alike argue that U.S. scientists could do more to reach out to the general public. Yet, to date, there have been few systematic studies that examine how scientists understand the barriers that impede such outreach. Through analysis of 97 semi-structured interviews with academic biologists and physicists at top research universities in the United States, we classify the type and target audiences of scientists’ outreach activities. Finally, we explore the narratives academic scientists have about outreach and its reception in the academy, in particular what they perceive as impediments to these activities. We find that scientists’ outreach activities are stratified by gender and that university and disciplinary rewards as well as scientists’ perceptions of their own skills have an impact on science outreach. Research contributions and recommendations for university policy follow.”
At their core, artists and scientists are not so different from one another. Both endeavor to solve our greatest mysteries through the power of imagination.
