Computers and Change-Ringing

Concept Images , Computers , and Curriculum Change

It seems self-evident that the way to teach mathematics is to start from simple concepts familiar to the learner and to build more complex ideas through a sequence of activities growing steadily in sophistication. It is a salutary experience to learn that a curriculum carefully built in this way can cause serious difficulties in learning. The problem arises because the human mind does not opera...

Ringing the changes

Ringing Js refinements

Both the four-point and the uniform cubic B-spline refinement (i.e. subdivision) schemes double the number of vertices of a closed-loop polygonal curve P and respectively produce sequences of vertices fk and bk. The Js refinement proposed here produces vertices vk=(1–s)fk+sbk. Iterative applications of Js yield a family of curves parameterized by s. It includes the four-point curve (J0), the un...

Quantum oscillations and black hole ringing

We show that strongly coupled field theories with holographic gravity duals at finite charge density and low temperatures can undergo de Haas van Alphen quantum oscillations as a function of an external magnetic field. Exhibiting this effect requires computation of the one loop contribution of charged bulk fermions to the free energy. The one loop calculation is performed using a formula expres...

Listening for Ringing Black Holes

The gravitational radiation produced by binary black holes during their inspiral, merger, and ringdown phases is a promising candidate for detection by the first or second generation of kilometer-scale interferometric gravitational wave antennas. Waveforms for the last phase, the quasinormal ringing, are well understood. I discuss the feasibility of detection of the quasinormal ringing of a bla...