Calculating Machines and numerical tables – a reciprocal history

The aim of this chapter is to study the history of the design and use of calculating machines to produce anduse numerical tables, from the time of Babbage’s plans for difference and analytical engines to the modern digitalcomputer, including in this analysis the role played by analog machines between the two. We will examine howthe place and role of numerical tables changed throughout the different stages of this mechanization. It is ourhypothesis that these processes of mechanization and, ultimately, automisation and digitalization, result in theprogressive internalization of aspects of the dynamical relation between humans and tables into the machine.This chapter considers several major stages in the devising of machines for the making and use of tables, fromdifference engines to computers. Following these stages, we investigate how increasing demands for calculatingpower go hand in hand with advances in the new technological possibilities offered by machines. The way by which machines were introduced and accepted for mathematical computations will also be examined. Eventhough this chapter is thus structured according to the changes in the machines, the focus will be on how thesechanges have affected numerical tables. By doing so, it will become clear how it is not only the machine whichshapes the history of the numerical table, but, also how the numerical table has impacted on the design anduse of calculating machinery. In fact, as we will argue, the history of calculating machinery is reciprocal to thehistory of the numerical table. With the development of modern computers, in which data and programs can bemanipulated in the same way, this reciprocity is expressed by an increasing interchangeability between tablesand algorithms