Calculation


Calculation forms a critical part of our ability to discern phenomena at scales other than our biologically-enabled scales of receptivity. As such it forms an important concept in the study of scale.

Calculation And Computation

The physical embodiment of complex numerical relationships through interconnected mechanical parts that concealed by a case, hence masking the motion of the gears, displayed only the input and output numbers.

Calculating Machines


From "Calculation and Computation," encyc. History of Ideas, p.421:

Some celebrated early modern examples were Blaise Pascal’s (1623–1662) adding machine (1642) and Leibniz’s adding and multiplication machine (1685). Earlier in the same century (1623), the German mathematician and linguist Wilhelm Schickard (1592– 1635) had mechanized the set of numbered sliding rods that John Napier (1550–1617) had devised in 1617 to simplify astronomical calculations. Both Pascal and Leibniz sought to profit selling their machines to merchants and natural philosophers. Galileo Galilei (1564–1642) tried the same with his improved computing dividers.
Many of the early modern natural philosophers were heavily involved in calculating innovations. Additional contributions include “calculation by analysis” to the coordinates of René Descartes (1596–1650), by differentiation and integration in the calculus tradition that prefigures in Simon Stevin (1548–1620) and materializes in Newton and Leibniz, and by the analysis of multiplication and division into addition and subtraction through the logarithms that Napier introduced in 1614.
As with the method of algorists, the speed in calculation by logarithms assumed the availability of relevant tables. The transformation of these tables into scales inscribed in, first, circles sharing a fixed center and, soon after, scales that slid beside each other while sharing a fixed framework, found its ultimate presentation in the logarithmic slide rule, configured by William Oughtred (1574–1660) as early as 1621. The interactive proliferation of both tables of logarithms and logarithmic slide rules determined the history of calculation from the early modern period until the very recent decades.
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.