Weaving Algebraic Patterns

Abstract

The Analytical Engine has a startling place in the history of computing. To the best of our knowledge, no machine had ever before been conceived along its lines. More remarkably, some of its key principles of design would actually be reinvented a century later by people who were, apparently, ignorant of it. If imitation is the sincerest form of flattery, then so is re invention or re discovery, at least when born from ignorance. It tells us much about how ahead of one’s time the original creator was. This reinvention of Babbage’s idea was particularly poignant because it would become the fount of fruitful and rich phylogenetic pathways in the later evolution of the digital computer and the emergence of computer science. Dissatisfaction is a prime generator of the creative urge, dissatisfaction with the status quo and the desire to change it to something better. Charles Babbage was unhappy with the waste of human mental labor in computing mathematical tables, which led to his desire to free human beings from this tedium—hence, the Difference Engine. However, the Difference Engine produced its own discontent. As Luigi Frederico Menabrea (1809–1896), an Italian military mathematician (and, later, prime minister of Italy) would explain apropos the Difference Engine, its use was limited to one particular kind of computation. It could not be applied to the solution of “an infinity of other questions” of interest to mathematicians. It was this limitation and the attendant discontent that led Babbage to conceive the machine he called the Analytical Engine, the operation of which he believed would encompass the full range of algebraic problems. The Difference Engine was not general enough. Babbage desired a computing engine that could range over the whole of “mathematical analysis.” As he explained in a letter to the Earl of Rosse, then president of the Royal Society, his Analytical Engine would have the power to perform the “most analytical complicated operations.” Here, then, is Babbage’s promise: a mathematical machine with “nearly unlimited” powers. Babbage’s name for his new machine is significant.