Interval Computations on the Spreadsheet

This paper reviews work on using interval arithmetic as the basis for next generation spreadsheet programs capable of dealing with rounding errors, imprecise data, and numerical constraints. A series of ever more versatile computational models for spreadsheets are presented beginning from classical interval arithmetic and ending up with interval constraint satisfaction. In order to demonstrate the ideas, an actual implementation of each model as a class library is presented and its integration with a commercial spreadsheet program is explained. 1 LIMITATIONS OF SPREADSHEET COMPUTING Spreadsheet programs, such as MS Excel, Quattro Pro, Lotus 1--2--3, etc., are among the most widely used applications of computer science. Since the pioneering days of VisiCalc and others, spreadsheet programs have been enhanced immensely with new features. However, the underlying computational paradigm of evaluating arithmetical functions by using ordinary machine arithmetic has remained the same. The wor..

Analogue Gravity

Analogue models of (and for) gravity have a long and distinguished history dating back to the earliest years of general relativity. In this review article we will discuss the history, aims, results, and future prospects for the various analogue models. We start the discussion by presenting a particularly simple example of an analogue model, before exploring the rich history and complex tapestry of models discussed in the literature. The last decade in particular has seen a remarkable and sustained development of analogue gravity ideas, leading to some hundreds of published articles, a workshop, two books, and this review article. Future prospects for the analogue gravity programme also look promising, both on the experimental front (where technology is rapidly advancing) and on the theoretical front (where variants of analogue models can be used as a springboard for radical attacks on the problem of quantum gravity)