[Book review] Mathematics and Culture II

Review of Mathematics and Culture II. Visual Perfection: Mathematics and Creativity, Michele Emmer (Ed.), Springer, 2005 ISBN: 978-3-540-21368-0

The M/M/1 queue with mass exodus and mass arrivals when empty

An M/M/1 queue is subject to mass exodus at rate β and mass immigration at rate {αr; r≥ 1} when idle. A general resolvent approach is used to derive occupation probabilities and high-order moments. This powerful technique is not only considerably easier to apply than a standard direct attack on the forward p.g.f. equation, but it also implicitly yields necessary and sufficient conditions for recurrence, positive recurrence and transience.

Birth-death processes with mass annihilation and state-dependent immigration

A birth-death process is subject to mass annihilation at rate β with subsequent mass immigration occurring into state j at rateα j . This structure enables the process to jump from one sector of state space to another one (via state 0) with transition rate independent of population size. First, we highlight the difficulties encountered when using standard techniques to construct both time-dependent and equilibrium probabilities. Then we show how to overcome such analytic difficulties by means of a tool developed in Chen and Renshaw (1990, 1993b); this approach is applicable to many processes whose underlying generator on E\{0} has known probability structure. Here we demonstrate the technique through application to the linear birth-death generator on which is superimposed an annihilation/immigration process.

I wanna be a protocol: online media and electronic structures of kinship

Heidegger famously identified Modernity with a technological leveling of being to a single order of a “standing reserve.” In a radically different tone, Gilles Deleuze articulated a single “plane of immanence” within which ontological distinctions between mind and body, God and world, interiority and exteriority become indiscernible. Taking such philosophical declarations as points of departure, this panel will consider how a collapse of ontological distinction emerged as a thematic and structural trope in literary and cinematic modernisms. We hope to consider how writers and film-makers of the 20th c. utilize the resources of their media to ask “the question of being” that troubled their philosophical contemporaries and heirs. In this vein, we will examine how these modernist ontologies of immanence describe the crisis of a subject saturated and eclipsed by a world which comprises her while also remaining strange or opaque. Papers will ask what is lost with the departure of a distinctly human sense of “being” and how the historical arrival of an alternative ontological order may be evident in the lived experience of modernity. In this sense, the relationship to departures and arrivals becomes the modern subject’s suspicion that he is unable to do either vis á vis the world.