The earliest known mechanical (analog) calculator was the antikythera mechanism, apparently a highly complex gear driven orrery made of bronze, was discovered in pieces in a ship believed to have been wrecked in 67 BC off the island of Antikythera, between Greece and Crete (Rice 1995; Bako 2001). Several attempts have been made to reconstruct its functions (e.g., Price 1959), which appear to have been related to calendar or astrological predictions. The most recent study, by Freeth (2002, 2002a) suggests that it may have been made by Posidonius on the island of Rhodes from formulas developed by Archimedes, described by Cicero as "showing the motions of the sun, the moon, and the five planets". Freeth's computer model of a possible reconstruction based on the extant fragments of the mechanism has 41 gears to display the positions of the Sun, Moon, Mercury, Venus, Mars, Jupiter and Saturn in the zodiac based on Babylonian and Archimedian tables.
Figure 5. A full scale commercially available reconstruction of the Antikythera mechanism by John Gleave, Orrery Maker, based on the Price (1959) reconstruction. Height 12.25 inches. Left: The front dial - showing the annual progress of the sun & moon through the zodiac, against the Egyptian calendar, rendered in Greek on the outer annulus. Right: The back dials. The upper back dial displays a four year period and has five concentric inscribed rings, most probably each with 47 divisions giving the Metonic Cycle of 235 synodic months, which equals 19 solar years. The lower back dial gives the cycle of a single synodic month, and the subsidiary dial the Lunar year of 12 synodic months. (Pictures and text from Gleave ????)
Hand operated gear driven numeric calculators were first invented in the 17th Century with Blaise Pascal's Pascaline (THOCP 2002) in the 1640's being the best known. The by the last quarter of the 19th century pinwheel calculators were being produced commercially (Tafoya 2002), with the most successful Odhner design (Figure 6) being in commercial production for nearly 100 years, from 1874 through the 1970's (Tout 2000; Odhner ????).
Figure 6. Odhner calculators. Middle row from Tout (2000), Top and bottom from Odhner (????). Top shows the original machine built in 1874. The middle row are machines of 1935-45 vintage. The left picture, with the covers removed, shows the mechanism. The right hand picture shows the cog-wheel set for the number (reading from top to bottom) 0087654321. The bottom picture is a 1970's vintage machine.
Cogwheel mechanical calculators, developed later than the pinwheel versions above, as represented by Monroe, were also brought to a high peak of perfection in the middle of the 20th century for performing numerical calculations in engineering and science72. As a science student, I never had an opportunity to use the punch card data processing technology, but I did occasionally gain access to some of the marvelous mechanical calculators for carrying out the arithmetical calculations required for physics or biology experiments.
Figure 7. Monroe electromechanical calculator technology was based on cog wheels and levers. Photographs from Museum of HP Calculators: Early Calculators. The machine on the left was electrically driven. The one on the right was cranked by hand. I used both types - http://www.hpmuseum.org/prehp.htm
Digital computing began in the 1890's with punch card and tabulating technology, where the presence of presence of a hole closed a switch (i.e., "on" and the absence left it open "off"). Tabulating machines used combinations of holes to represent decimal digits. Until the invention of practical electronic computers in the 1950's, punch card tabulating technology (or the related paper tape technology73) provided the only way to automate record processing, and the automation was limited to comparatively simple counting and accounting activities74. Counting, sorting and other processing tasks were achieved mechanically - doing arithmetic using gears, cogs and spring-loaded pins. From 1928, standard punch cards were divided into 80 columns, where the pattern of holes punched in each column encoded a number or alphabetic character75. The 80 alphanumeric character contents of each card could be read or processed, and printed out as lines on a report for human consumption. When tabulating machines incorporated electric relays, they could be manually "programmed" using plug boards - where jumper wires connected circuits for various calculating and processing functions. The latest tabulating machines produced used a punch card wrapped around a drum to specify how each column of punches on a data card should be processed. Processed outputs could be stored for further processing as punched cards or delivered to users as printouts. In the 1960's and '70's, even though punch cards were no longer used for processing, they continued to provide a data capture interface with the increasingly powerful digital computers, with the cards forming processable transaction and accounting records76. The peak consumption of punch cards was in 1967, when the US consumed approximately 200 billion cards - or about 1,000 cards for every living person in the US at that time. Some organizations still use punch cards today for ancient "legacy" systems Dyson (1999).