# Calculation and Computation

## Late Modern Period

Abacuses and artifacts from the associated tradition of counting boards with pebbles or beads share the honor of being ancestors of the digital computer along with the various mechanical and electromechanical desktop calculating machines produced from 1850 to 1950. They are joined by an ensemble of mechanical and (later) electromechanical tools and machines used for punching holes into cards, which represent computable variables, for sorting these cards according to the variable to be computed, and for tabulating and printing the results. They are best known as punched card machines, based on the part of the process that was least subjected to mechanization. Going back to the end of the nineteenth century, punched card machines were rented by companies that were ancestors to IBM (International Business Machines) to, first, the United States Census Bureau, and, subsequently, censuses for nations around the world. Calculating and punched card machines were extensively used for filing, accounting, and related activities that involved the processing of large amounts of data in larger enterprises, which have ranged from railroads to insurance companies. The U.S. Social Security Administration also used hundreds of punched card mechanisms and machines to implement a social security system that, in 1935, had to handle information about the wages paid by three million employers to their twenty-six million employees.

In addition to the slide rule, the list of what has been a posteriori placed under analog computers includes calendars, sundials, orreries, astrolabes, planetariums, material models of all kinds (including scale models), mathematical and other mental models, graphs that could be as complex as the nomograms of Maurice D' Ocagne (1862–1938) and his followers (used from the late nineteenth century until the recent decades), computing linkages, artifacts with mechanical integrators and differentiators, curve tracers and kinematic mechanisms in the tradition of planimeters and associated artifacts, harmonic analyzers and synthesizers like the one that Lord Kelvin had built as a tide predictor, mechanical, electromechanical, and electrical analyzers for general (e.g., Bush's differential analyzer) and special purposes (e.g., Bush's electric power network analyzers), electrolytic tanks, resistive papers and elastic membranes used as models, and countless mechanisms and machines produced and used in fire control (internal, external, and terminal ballistics). Case studies have retrieved the histories of many other cases of unique tools and machines, including those used for crucial tidal calculations in the Netherlands.

Changes in calculating machinery were coupled with changes to make the calculus correspondingly operational. Remembered more as the author of the state-of-the-art calculating machines during the interwar period, Bush was also the author of influential writings on the "operational calculus," which capitalized on a tradition of modifications of the calculus that adjusted it to the ever-changing needs of engineers who thought of themselves as equal to any scientist. In the 1930s and in the 1940s, punched card machines were reconfigured to be useful in scientific calculations. Bush's differential and network analyzers were also used in the scientific calculations of the period immediately before and after World War II. Calculating machines were used in scientific calculations even earlier and so were slide rules.

The various branches of the state have had an organic role in fostering technological change. To the examples of the extensive use of digital punched card machinery by civilian apparatuses such as the census should be added the involvement by the military in purchasing analog fire control mechanisms and machines; of the state's exclusive involvement in cryptography-related calculation and computation even less is known, with the exception of the celebrated Colossus machine during World War II. Using the Colossus machine, a British team that included in its members the mathematician Alan Turing (1912–1954) broke the code produced by a German machine known as the Enigma. The military had actually used hundreds of punched card machines in World War I for materiel inventory and for medical record keeping. Interwar support for military needs changed so remarkably that the computing bombsight and the anti-aircraft director were by World War II extremely complex artifacts with thousands of mechanical, electrical, and electronic parts. The competing development of the computing bombsight, which increased the target reach for a bomber, and the anti-aircraft director, which increased the reach of ground-based fire targeting the bomber itself, has formed a vicious circle that exemplifies the contradiction of modern technology. In the United States, the development of accurate bombsights during World War II was a secret second only to the construction of the atomic bomb. The extreme technological contradiction to date may have been that the most accurate computing bombsight was used to drop the first atomic bomb, a lethal weapon like none before it, the efficient release of which required the least accuracy.