Much Heaviness

Seeing Heaviness

Participants watched a recording of the motions produced when another person wielded a pendulum. The participants’ task was to judge the heaviness of the pendulum. We found that participants were similarly adept at judging the pendulum’s heaviness as when participants wield the pendulum themselves and perceive heaviness haptically. It is hypothesized that people are able to make these visual he...

Lightness, Heaviness and Gravity

Lightness, heaviness and gravity

Heaviness in Circle Rotations

We are concerned with describing the structure of the set of points in the unit interval which, when subjected to rotation by irrational α modulo one, for all finite portions of the orbit contain at least as many points in the bottom half of the interval as in the top half. Specifically, an inductive procedure for describing the set based on the continued fraction expansion of α is developed, l...

Heaviness in Toral Rotations

Abstract. We investigate the dimension of the set of points in the d-torus which have the property that their orbit under rotation by some α hits a fixed closed target A more often than expected for all finite initial portions. An upper bound for the lower Minkowski dimension of this strictly heavy set H(A,α) is found in terms of the upper Minkowski dimension of ∂A, as well as k, the Diophantin...