We discuss Boltzmann's explanation of the irreversible thermodynamic evolution of macroscopic systems on the basis of time-symmetric microscopic laws, providing a comprehensive presentation of what we call the typicality account. We then discuss the connection between this general scheme and the H-theorem, demonstrating the conceptual continuity between them. In our analysis, a special focus lies on the crucial role of typicality. Putting things in wider perspective, we go on to analyze the philosophical dimensions of this concept, explaining the connection between typicality and probability, and demonstrate its relevance for scientific reasoning, in particular for understanding the supervenience of macroscopic laws on microscopic laws. The second part of the paper responds to recent objections against the typicality account that have been raised in the philosophical literature. In particular, the concept of ergodicity, or a variant thereof, named "epsilon-ergodicity", which has been promoted by some authors as a crucial additional assumption on the dynamics, is shown to be of no use for its intended purpose. *

A slide show with audio taped narration of two case stories involving eating disorders was presented to 4th-, 5th- and 6th-grade school children. Students completed a series of questions about their eating behaviors and compared their eating to that of the case subjects, who served as frames of reference for such constructs as "binging. " Between 3% and 4% of girls reported self-induced vomiting and/or secretly throwing away food to avoid gaining weight. The case story method seems to provide a means for students to qualitatively assess their eating behavior relative to an external frame of reference. Teachers and other professionals working with early adolescents should be aware that dieting behaviors are clearly emerging in elementary school. The methodology used in the present study has utility not only for screening persons who may be at risk for eating disorders, but also for psycho educational programs in health and nutrition.

We discuss the total collision singularities of the gravitational N-body problem on shape space. Shape space is the relational configuration space of the system obtained by quotienting ordinary configuration space with respect to the similarity group of total translations, rotations, and scalings. For the zero-energy gravitating N-body system, the dynamics on shape space can be constructed explicitly and the points of total collision, which are the points of central configuration and zero shape momenta, can be analyzed in detail. It turns out that, even on shape space where scale is not part of the description, the equations of motion diverge at (and only at) the points of total collision. We construct and study the stratified total-collision manifold and show that, at the points of total collision on shape space, the singularity is essential. There is, thus, no way to evolve solutions through these points. This mirrors closely the big bang singularity of general relativity, where the homogeneous-but-not-isotropic cosmological model of Bianchi IX shows an essential singularity at the big bang. A simple modification of the general-relativistic model (the addition of a stiff matter field) changes the system into one whose shape-dynamical description allows for a deterministic evolution through the singularity. We suspect that, similarly, some modification of the dynamics would be required in order to regularize the total collision singularity of the N-body model.

We analyze the points of total collision of the Newtonian gravitational system on shape space (the relational configuration space of the system). While the Newtonian equations of motion, formulated with respect to absolute space and time, are singular at the point of total collision due to the singularity of the Newton potential at that point, this need not be the case on shape space where absolute scale doesn’t exist. We investigate whether, adopting a relational description of the system, the shape degrees of freedom, which are merely angles and their conjugate momenta, can be evolved through the points of total collision. Unfortunately, this is not the case. Even without scale, the equations of motion are singular at the points of total collision (and only there). This follows from the special behavior of the shape momenta. While this behavior induces the singularity, it at the same time provides a purely shape-dynamical description of total collisions. By help of this, we are able to discern total-collision solutions from non-collision solutions on shape space, that is, without reference to (external) scale. We can further use the shape-dynamical description to show that total-collision solutions form a set of measure zero among all solutions.

Flight Control, containing anthraquinone, was field tested during 1997 in Colorado as a repellent to keep Canada geese (Branta canadensis) off turf. The product was sprayed at a rate of 1. 9 kg per ha, using a boom sprayer towed by a golf cart. The reduction in goose numbers on the treatment plot was 95.1 % ten days after application. A decline of 64. 7 % in the number of goose droppings on the area was recorded.