CS378W, History of Computing
Week 3, Weekly Report
Due 2004 Sep 9
Computing between 1500 and 1800: The Pascal Adding Machine (CBC p. 39-42)
Bryant Tang
2004 Sep 9
Blaise Pascal was born in 1623 (3). As a child, he watched his father - a tax receiver - use the abax (a form of the abacus) to perform addition and subtraction (3). However, he felt that the method was boring and set out to create a machine that would be able to do those mathematical operations in a quicker fashion (3). He drew up the design for what would become known as the Pascaline, but the local workmen were unaccustomed to working on delicate instruments, leading Pascal to learn the basics of mechanics in order to build the machine on his own (4, p. 40). It is also known as the Pascale, Pascalene and Pascal's Adder (1).
In 1642, he constructed the first example of the Pascaline, which had the main advantage of being able to deal with carries during addition (2). It was made from metal and was about the size of a shoebox, with eight windows and a row of toothed wheels built into the top of the device (1). Within each window is a drum on which was displayed the various result digits, with two rows of numbers on each drum; the red row was used for subtraction while the black row was used for addition (1). In order to use the machine, one had to "insert a stylus into the toothed wheel at the [desired position] and rotate the wheel clockwise until the stylus encountered the fixed stop" (4, p. 40) and the results were displayed in the windows. The toothed wheels were designed such that the rightmost wheel had twelve spokes, the one next to it had twenty spokes and each of the remaining wheels had ten spokes, the reasoning behind such a design was that the first two wheels were specifically designed to work with the French currency, while the rest were for use with numbers other than the national currency of France (1).
The internal mechanism is an interesting system of gears and weights. Such a machine could have been designed such that the carries were implemented by using a long tooth to rotate the next gear as an individual gear went from 9 to 0. However, if multiple gears were lined up in the 9 position, a great amount of force would have been required to move all the gears (2). Instead, Pascal used a weighted ratchet between the main gears, so that when a main gear went from 9 to 0, "pins slip out of the weight allowing it to fall and, in the process, the little spring-loaded foot . . . will kick at the pins sticking out of [the neighboring wheel], driving it around one place" (4, p. 42). This system caused the Pascaline to produce "clunk" noises with each successive carry (4, p. 42). It also restricted the movement of the gears, as they could only be turned in a single direction, making the users perform subtraction by the nines complements method (1). This involved finding the nines complement of the number to be subtracted (9 minus the number) and then adding it to the number from which it was to be subtracted and then performing the end-around carry by mentally adding the first digit ignored during the carry to the displayed result (1).
Despite its revolutionary design, the Pascaline never made it into full production. The sensitive inner workings were prone to producing incorrect results if the Pascaline was bumped, shaken or otherwise physically moved (4, p. 42). The weighted ratchets were also liable to jam and the method for subtracting numbers was inelegant and impractical (1). Lastly, the machine was expensive relative to the cost of manual labor and white collar workers pressured employers not to adopt the machine in a move that would have cost them their jobs (3). Thus, the Pascaline never made it into widespread acceptance as a computational device. Despite all that, Pascal ultimately produced around fifty different machines (4, p. 40), some of which are displayed in museums today (3).
Notes
1. Greg Michaelson, "About Pascaline," http://www.macs.hw.ac.uk/~greg/calculators/pascal/About_Pascaline.htm (Heriot-Watt University, accessed 2004 Sep 8).
2. Jonathan Phillips, "Pascal and Leibniz's Adding Machine," http://agentsheets.com/Applets/pascals-adding-machine/readme.html (Center for Lifelong Learning and Design, accessed 2004 Sep 8).
3. "Pascaline," http://www.thocp.net/hardware/pascaline.htm (The History of Computing Project, accessed 2004 Sep 8).
4. William Aspray, ed., Computing Before Computers (Ames, IA: Iowa State University Press, 1990 ). Also available online at http://www.computerhistory.org/collections/DocumentArchive/Documents/Books/Computing Before Computers/CBC.html (Computer History Museum, accessed 2004 Sep 8).