Academic journal article Mathematics and Computer Education

Infinity: New Research Frontiers

Academic journal article Mathematics and Computer Education

Infinity: New Research Frontiers

Article excerpt

INFINITY: NEW RESEARCH FRONTIERS Edited by Michael Heller and W. Hugh Woodin Cambridge University Press, 2011, 311 pp. ISBN: 978-1-107-00387-3

In 2006, an invitation-only international conference was held in San Marino on the concept and meaning of infinity in the contexts of mathematics, physics, cosmology, philosophy, and theology. One of the results of that conference was the book Infinity: New Research Frontiers, consisting of fourteen chapters, each examining the infinite from one or more perspectives. The contributors are a veritable Who's Who on the study of the infinite from the view of mathematics (W. Hugh Woodin, UCBerkeley), theology (Michael Heller, Copernicus Center for Interdisciplinary Studies), philosophy (Graham Oppy, Monash University), and physics (Anthony Aguirre, UC-Santa Cruz). The book is introduced by set theory popularizer and science-fiction writer Rudy Rucker (San Jose State University).

The first chapter, by the theologian Wolgang Achtner (Liebig University), sets the stage by looking at how the concept of infinity transformed science and theology. The next five chapters examine infinity from a mathematical perspective. Several of the readings in this passage are challenging as the authors assume a solid knowledge of set theory. Hugh Woodin' s discussion of the large cardinal axioms in set theory and of Ologic are particularly engrossing. Also of note is Harvey Friedman's (Ohio State) chapter on concept calculus, a formal method for connecting ordinary commonsense reasoning to rigorous mathematical thinking.

The next four chapters look at the question of infinity in physics and cosmology. In these chapters, the reader is treated to current scientific thinking about the indivisibility of space, the infinite extension of space, the geometry of space, inflationary cosmology, and the multiverse. …

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