An occurrence is explained by being related to prior events through known laws. Other intellectual activities may also constitute explanation - but this much certainly does. Ideally, an explained occurrence (0) could have been predicted in a connected way - by extrapolation from prior events (e) via the same laws (L). Schematically, 1 Explanation: 0 -Lt, 2, 3-(e e e )'-AI t 2 3 01 Prediction: (e e e )I-L , 2, 3_ +.11 t 2 3 t Thus Mars' backward loop in late summer, 1956, is explained by showing how this follows from (e ) its mean distance from sun and earth, (e ) its t 2 mean period of revolution, (e ) its past positions relative to earth, etc. 3 - by way of the laws of Celestial Mechanics (including (Lt) Kepler's Laws and Galileo's, (L2) Newton's, and (L3) those of Laplace and Lagrange. Moreover, this loop (0) could have been predicted from such events (e -e ) via the laws of Celestial Mechanics. t 3 This is an ideal situation. It crystallized late in the history of planetary theory. The Greeks found explanations for heavenly motions: the back ward loops were explained to their satisfaction. But they could not predict these motions, not in terms of Attic explanatory cosmologies.

The recovery of Dante's metaphysics-which are very different from our own-is essential, argues Christian Moevs, if we are to resolve what has been called 'the central problem in the interpretation of the Comedy.' That problem is what to make of the Comedy's claim to the status of revelation, vision, or experiential record - as something more than imaginative literature. In this book Moevs offers the first sustained treatment of the metaphysical picture that grounds and motivates the Comedy, and the relation between those metaphysics and Dante's poetics. Moevs arrives at the radical conclusion that Dante believed that all of what we perceive as reality, the spatio-temporal world, is in fact a creation or projection of conscious being. Armed with this new understanding, Moevs is able to shed light on a series of perennial issues in the interpretation of the Comedy.

This book constitutes the refereed proceedings of the 19th International Symposium on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes, AAECC-13, held in Honolulu, Hawaii, USA in November 1999. The 42 revised full papers presented together with six invited survey papers were carefully reviewed and selected from a total of 86 submissions. The papers are organized in sections on codes and iterative decoding, arithmetic, graphs and matrices, block codes, rings and fields, decoding methods, code construction, algebraic curves, cryptography, codes and decoding, convolutional codes, designs, decoding of block codes, modulation and codes, Gröbner bases and AG codes, and polynomials.