A: London, England, United Kingdom

# Babbage Describes the Logic and Operation of Machinery by Means of Notation

1826

In 1826 mathematician and engineer Charles Babbage published "On a Method of Expressing by Signs the Action of Machinery," Philosophical Transactions 111 (1826) 250-65, 4 plates. This was the first publication of Babbage's exposition of his system of mechanical notation that enabled him to describe the logic and operation of his machines on paper as they would be fabricated in metal. Babbage later stated that "Without the aid of this language I could not have invented the Analytical Engine; nor do I believe that any machinery of equal complexity can ever be contrived without the assistance of that or of some other equivalent language. The Difference Engine No. 2 . . . is entirely described by its aid" (Babbage, Passages from the Life of a Philosopher [1864], 104).

Babbage considered his mechanical notation system to be one of his finest inventions, and thought it should be widely implemented. It was a source of frustration to him that no other machine designer adopted it (probably because no other engineer during Babbage's time attempted to build machines as logically and mechanically complex as Babbage's). More than one hundred years later, in the 1930s, when developments in logic were applied to switching systems in the earliest efforts to develop electromechanical calculators, Claude Shannon demonstrated that Boolean algebra could be applied to the same types of problems for which Babbage had designed his mechanical notation system.

"While making designs for the Difference Engine, Babbage found great difficulty in ascertaining from ordinary drawings-plans and elevations-the state of rest or motion of individual parts as computation proceeded: that is to say in following in detail succeeding stages of a machine's action. This led him to develop a mechanical notation which provided a systematic method for labeling parts of a machine, classifying each part as fixed or moveable; a formal method for indicating the relative motions of the several parts which was easy to follow; and means for relating notations and drawings so that they might illustrate and explain each other. As the calculating engines developed the notation became a powerful but complex formal tool. Although its scope was much wider than logical systems, the mechanical notation was the most powerful formal method for describing switching systems until Boolean algebra was applied to the problem in the middle of the twentieth century. In its mature form the mechanical notation was to comprise three main components: a systematic method for preparing and labeling complex mechanical drawings; timing diagrams; and logic diagrams, which show the general flow of control" (Hyman, Charles Babbage [1982], 58).

Hook & Norman, Origins of Cyberspace (2001) no. 37.