D: The Infinite Square Roots of -1
p. 229-235
Abstract
We present D, a synbol that can be used in the universal alphabet that provides a computational path to the nilpotent Dirac equation (Diaz & Rowlands, 2004) and which results in a tractable computer representation of the infinite square roots of -1. We outline how the representation is derived, the properties of the representation, and how the form can be used. Think of D as an infinite table of 1's in any representation e.g. binary or hexadecimal. Any specified column Di of the table has the property that when multiplied with a row Di, the result is a representation of -1. Di multiplied with Dj anticommutes as - (Dj*Di) and produces Dk in a way identical to Hamilton's quaternion i, j, and k. With an infinite and uniquely identifiable set of such triad forms D can be considered both a symbol and because of this behaviour, an alphabet.
Text
References
Bibliographical reference
Bernard M. Diaz and Peter Rowlands, « D: The Infinite Square Roots of -1 », CASYS, 19 | 2006, 229-235.
Electronic reference
Bernard M. Diaz and Peter Rowlands, « D: The Infinite Square Roots of -1 », CASYS [Online], 19 | 2006, Online since 29 August 2024, connection on 10 January 2025. URL : http://popups.lib.uliege.be/1373-5411/index.php?id=2586
Authors
Bernard M. Diaz
Department of Computer Science
The University of Liverpool
Peach Street, Liverpool, UK, L69 7ZF
Peter Rowlands
Science Communication Unit, Department of Physics
The University of Liverpool
Peach Street, Liverpool, UK, L69 7ZF