{'fraction_non_alphanumeric': 0.05126877265665458, 'fraction_numerical': 0.038839979285344384, 'mean_word_length': 4.7844311377245505, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
Computational Geology 10 – The Algebra of Deduction

Introduction In "The Algebra of Unit Conversions" (Computational Geology 7, Sept., 1999), I called attention to one of the giant steps in the development of mathematics: the replacement of numbers by symbols such as x, y, and z. This invention of symbolic algebra by Frangois Viete (1540-1603) was one of the great intellectual breakthroughs of the Renaissance. With symbolic algebra, equations could be manipulated to solve problems. It was no longer necessary to use the ancient, ad hoc algorithms of the Islamic scholars. In this column, I will describe another enormous step in the history of algebra. In this algebra, symbols do not represent quantities but rather words or sentences. Expressions containing these symbols can be manipulated to deduce the consequences of prior expressions or to evaluate the validity of arguments. This algebra is taught in freshman courses on logic and critical thinking. It informs the -logy of geology, biology, and other sciences. The story of symbolic logic begins with Gottfried Wilhelm Leibniz (1646-1716), a universal genius and co-inventor of the infinitesimal calculus (see CG-5 "If Geology then Calculus," March, 1999). A diplomat and political advisor by profession, Leibniz was, according to Solomon and Higgins (1996, p. 190), "what we would call in this day and age a jet-setter." In his spare time, he was a well known philosopher (Russell, 1937; Durant and Durant, 1963, Chapter 23) and mathematician (Hofman, 1974; Bell, 1937, Chapter 7; Hollingdale, 1991, Chapter 11). "He thought incessantly. His unresting curiosity was attracted to everything..." (Bell, 1945, p. 149). According to the Encyclopedia Britannica Online, he was one of the creators of geology (see Box 1). According to Edwards (1979, p. 231), "the breadth of his fundamental contributions... is probably not matched by the work of any subsequent scholar."