Abstract
Even the brief analysis of the history of the invention of mechanical computing devices from the 17th to early 20th centuries that we provide in this chapter demonstrates the rich potential available to mathematics educators today. The first devices designed by Schickard and Pascal showed a technological complexity when dealing with the issue of representing even simple arithmetic operations, such as addition, by means of gears and wheels. The knowledge they developed, along with the ideas they did not succeed to put in practice, inspired further generations of inventors who not only pursued the search for better aids for calculation practices but also envisioned novel mathematical structures allowing for a more universal approach to computing which, along with technological know-how, eventually led to the modern era of electronic computers, the Internet, and other digital tools and technology-rich environments. At the end of the chapter, we explore the educational potential of this historical development.
On a toujours cherché les moyens de diminuer la fatigue d’esprit et d’abréger le temps qu’entrainent les opérations arithmétiques (People always looked for ways to make the spirit less tired and to reduce the time taken by arithmetic operations).
Louis Thomas (Chevalier de Colmar) 1852
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
For more details about the complex history of this invention, see, for example, Cajory (1909).
- 2.
Notice necessary to those who will have the curiosity to see the arithmetical machine and to use it.
- 3.
Sir Bulstrode Whitelocke (1605–1675) was Head of the English diplomatic mission in Sweden in 1653; Morland took part in that mission.
- 4.
- 5.
Durand-Richard (2010, p. 293).
- 6.
“M. de Prony s’était engagé avec les comités de gouvernement, à composer pour la division centésimale du cercle, des tables logarithmiques et trigonométriques, qui, non-seulement ne laissassent rien à désirer quant à l’exactitude, mais qui formassent le monument de calcul le plus vaste et le plus imposant qui eût jamais été exécuté, ou même conçu” (Anon. 1820, p. 7, cited by Babbage 1832, p. 155; Babbage 1961, p. 316).
- 7.
Reuleaux, Franz (1829–1905).
- 8.
A calculating machine built based on Odhner’s principles by Grimme, Natalis & Co (founded in 1871) in Germany (Braunschweig). The manufacture was led by Franz Trinks (1852–1931) who was also inventor of the Trinks-Arithmotyp, a key-driven mechanical calculator (Lenz 1924, p. 76).
- 9.
Another name used for a bead abacus.
- 10.
For more on modern development, see Martinovich’s chapter in this book.
References
Ageron, P. 2016. L’arithmomètre de Thomas: sa réception dans les pays méditerranéens (1850–1915), son intérêt dans nos salles de classe. In Proceedings of the 2016 ICME Satellite Meeting of the International Study Group on the Relations Between the History and Pedagogy of Mathematics, ed. L. Radford, F. Furinghetti, and T. Hausberger, 655–670. Montpellier, France: IREM de Montpellier.
Anon. 1820. Note sur la publication proposée par le gouvernement anglais des grandes tables logarithmiques et trigonométriques de M. de Prony. Paris: Didot.
Babbage, C. 1832. On the economy of machinery and manufactures. London: Knight.
Babbage, C. 1961. On the division of mental labour. In On the principles of and development of calculator, ed. P. Morison and E. Morrison, 315–321. New York: Dover Publications Inc.
Bacon, F. 1623. De dignitate & augmentis scientiarum. London: J. Haviland.
Bacon, F. 1640. Of the advancement and proficience of learning. Oxford: L. Lichfield. [The first English translation of Bacon 1623.].
Baker, C. 1839. Infant schools. In Central society of education, vol. 3, 1–48. London: Taylor and Walton.
Beeson, M. J. 2004. The mechanization of mathematics. In Alan Turing: Life and legacy of a great thinker, ed. C. Teuscher, 77–134. Berlin-Heidelberg-New York: Springer.
Belanger, J., and D. Stein. 2005. Shadowy vision: Spanners in the mechanization of mathematics. Historia Mathematica 32 (1): 76–93.
Bloch, L. 2016. Informatics in the light of some Leibniz’s works. Paper presented at XB2 Xenobiology Conference, Berlin.
Blikstein, P. 2013. Digital fabrication and “making” in education: The democratization of invention. In FabLabs: Of machines, makers and inventors, ed. J. Walter-Herrmann and C. Buching, 1–21. Bielefeld: Transcript Publishers.
Bradis, V.M. [Бpaдиc B. M.]. 1929. Пpиближeнныe вычиcлeния [Priblizhennye vychisleniya] (Approximative calculations). In Ha пyтяx к пeдaгoгичecкoмy caмooбpaзoвaнию: Ha пyтяx мaтeмaтики [Na putyakh k pedagogicheskomu samoobrazovaniyu: Na putyakh matematiki] (Various approaches to the self-directed pedagogical studies: Ways to mathematics), ed. M.M. Rubinschtein [M.M. Pyбинштeйн], 87–116. Moscow: Mir.
Cajory, F. 1909. A history of the logarithmic slide rule and allied instruments. New York: The Engineering News Publishing Company & London: Archibald Constable & Co.
Campbell-Kelly, M., W. Aspray, N.L. Ensmenger, and J.R. Yost. 2013. Computer: A history of the information machine. Boulder: Westview Press.
Chazal, G. 2002. Les réseaux du sens: De l’informatique aux neurosciences. Revue Philosophique de Louvain 100 (1): 321–324.
Cole, J.R. 1995. Pascal: The man and his two loves. New York: New York University Press.
Cortada, J.W. 1993. Before the computer: IBM, NCR, Burroughs, and Remington Rand and the industry they created, 1865–1956. Princeton, NJ: Princeton University Press.
Cragon, H.G. 2000. Computer architecture and implementation. Cambridge: Cambridge University Press.
Davis, M. 2000. Engines of logic: Mathematicians and the origin of the Computer. New York: W. W. Norton & Company.
Diderot, D., and J.-B. le Rond d’Alembert (Eds.). 1751[-1772]. Encyclopédie, ou dictionnaire raisonné des sciences, des arts et des métiers. Paris: Briasson et al.
Durand-Richard, M.-J. 2010. Le regard français de Charles Babbage (1791–1871) sur le “déclin de la science en Angleterre.” Documents pour l’histoire des techniques 19 (2): 287–304.
Freeth, T. 2002. The Antikythera Mechanism: 2. Is it Posidonius’ Orrery? Mediterranean Archaeology and Archaeometry 2 (2): 45–58.
Freeth, T. 2014. Eclipse prediction on the ancient Greek astronomical calculating machine known as the Antikythera mechanism. PLoS ONE 9 (7): e103275.
Freeth, T., A. Jones, J.M. Steele, and Y. Bitsakis. 2008. Calendars with Olympiad display and eclipse prediction on the Antikythera mechanism. Nature 454 (7204): 614–617.
Glaser, A. 1981. History of binary and other nondecimal numeration. Los Angeles: Tomash Publishers.
Graf, K.-D. 1995. Promoting interdisciplinary and intercultural intentions through the history of informatics. In Integrating information technology into education, ed. D. Watson and D. Tinsley, 139–150. Dordrecht: Springer Science + Business Media. https://doi.org/10.1007/978-0-387-34842-1.
Green, C.D. 2005. Was Babbage’s analytical engine intended to be a mechanical model of the mind? History of Psychology 8 (1): 35–45.
Halliwell, J.O. 1838. A brief account of the life, writings, and inventions of Sir Samuel Morland, Master of Mechanics to Charles The Second. Cambridge: Metcalfe & Palmer.
Horsburgh, E.M. 1914. Modern instruments and methods of calculation: A handbook of the Napier tercentenary exhibition. London: G. Bell & Sons.
Jackson, L.L. 1906. The educational significance of sixteenth century arithmetic from the point of view of the present time. New York: Teachers College, Columbia University.
Johnston, S. 1996. The identity of the mathematical practitioner in 16th-century England. In Der ‘mathematicus’: Zur Entwicklung und Bedeutung einer neuen Berufsgruppe in der Zeit Gerhard Mercators (Duisburger Mercator-Studien), ed. I. Hantsche, 93–120. Bochum: Brockmeyer.
Johnston-Wilder, S., and D. Pimm. 2004. Teaching secondary mathematics with ICT. Maidenhead: Open University Press.
Jones, M. 2016. Reckoning with matter: Calculating machines, innovation and thinking about thinking from Pascal to Babbage. Chicago: Chicago University Press.
Kidwell, P.A., A. Ackerberg-Hastings, and D.L. Roberts. 2008. Tools of American Mathematics Teaching, 1800–2000. Baltimore: Johns Hopkins University Press.
Lardner, D. 1834. Babbage’s calculating engine. Edinburgh Review 59: 264–327.
Leibniz, G.W. 1685/1929. Leibniz on his calculating machine (Translated from Latin by Mark Kormes). In A Source Book in Mathematics, ed. D.E. Smith, 173–181. New York: McGraw-Hill.
Leibniz [= Leibniz, G.W.] 1703 [1720]. Explication de l’arithmétique binaire qui se sert des seuls caractères 0 & 1; avec des remarques sur son utilité, & sur ce qu’elle donne le sens des anciennes figures Chinoises de Fohy. Histoire de l'Académie royale, des sciences, avec les mémoires de mathématique & de physique, [section “Mémoires”,] 85–89.
Lenz, K. 1924. Die Rechenmaschinen und das Maschinenrechnen. Wiesbaden: Springer.
Lions, J.-L. 1991. De la machine à calculer de Pascal aux ordinateurs. La Vie des sciences 3: 221–240.
Lister, M., J. Dovey, S. Giddings, I. Grant, and K. Kelly. 2009. New media: A critical introduction. London and New York: Routledge.
Marguin, J. 1997. L’arithmomètre de Thomas n° 1398. Bulletin de la Sabix 18: 31–42.
Markushevich, A.I., A.Y. Hinchin, and P.S. Alexandrov [Mapкyшeвич, A. И., A. Я. Xинчин, П. C. Aлeкcaндpoв]. 1951. Энциклoпeдия элeмeнтapнoй мaтeмaтики [Entsiklopediya elementarnoĭ matematiki] (Encyclopedia of elementary mathematics). Moscow & Leningrad: GTTL.
Maschietto, M. 2013. Systems of instruments for place value and arithmetical operations: An exploratory study with the Pascaline. Education 3 (4): 221–230.
Mayo, E., and C. Mayo. 1837. Practical remarks on infant education, for the use of schools and private families. London: Seeley and Co.
Menabrea, L.F. 1842. Notions sur la machine analytique de M. Charles Babbage. Bibliothèque universelle de Genève 41: 352–376.
Morar, F.-S. 2015. Reinventing machines: The transmission history of the Leibniz calculator. British Society for the History of Science 48 (1): 123–146.
Mosconi, J. 1983. Charles Babbage: vers une théorie du calcul mécanique. Revue d’histoire des sciences 36 (1): 69–107.
Myers, G.W. 1903. The laboratory method in the secondary school. The School Review 11 (9): 727–741.
Nepero, I. (Napier, J.). 1614. Mirifici logarithmorum canonis descriptio. Edinburgum: A. Hart.
Nepero, I. (Napier, J.). 1617. Rabdologiae seu numerationis per virgulas libri duo: cum appendice de expeditissimo multiplicationis promptuario. Edinburgum: A. Hart.
Nordhaus, W.D. 2007. Two centuries of productivity growth in computing. The Journal of Economic History 67 (1): 128–159.
Pascal, B. 1645/1998. Lettre dedicatoire a Monseigneur le Chancelier sure le sujet de la Machine nouvellement inventée par le Sieur B.P. pour faire toutes sortes d’operations d’Arithmetique, par un mouvement reglé, sans plume ny jettons, avec un advis necessaire à ceux qui auront la curiosité de voir ladite Machine, et de s’en servir. [n.p.] (Reprinted in B. Pascal, Œuvres complètes. Tome 1. Paris: Édition de Michel Le Guern.).
Poisard, C. 2006. The notion of carried-number, between the history of calculating instruments and arithmetic. Proceedings of the Annual Conference of Mathematics Education Research Group of Australasia (MERGA), 2, pp. 416–423.
Project 2061. 1989. Science for all Americans: A Project 2061 report on literacy goals in science, mathematics, and technology. Washington, D.C.: American Association for the Advancement of Science.
Rabardel, P. 1995. Les hommes et les technologies, une approche cognitive des instruments contemporains. Paris: Armand Colin.
Raloff, J. 1982. On Beyond Babbage: The Rise of Automatic Digital Computers. Science News 121: 170–172.
Ratcliff, J.R. 2007. Samuel Morland and his calculating machines c.1666: The early career of a courtier–inventor in Restoration London. British Society for the History of Science 40 (2): 159–179.
Reuleaux, F. 1861. Der Constructeur: Ein Handbuch zum Gebrauch beim Maschinen-Entwerfen. Braunschweig: Friedrich Vieweg und Sohn.
Ryan, J.A. 1996. Leibniz’ binary system and Shao Yong’s “Yijing”. Philosophy East and West 46 (1): 59–90.
Sawday, J. 2007. Engines of the imagination: Renaissance culture and the rise of the machine. Abingdon: Routledge.
Schlauch, W.S. 1940. The use of calculating machines in teaching arithmetic. The Mathematics Teacher 33 (1): 35–38.
Sonnenschein, W.S. 1879. Description of Sonnenschein’s number-pictures, arithmometer and blackboard: their construction and use. London: W. Swan Sonnenschein.
Taton, R. 1963. Sur l’invention de la machine arithmétique. Revue d’histoire des sciences et de leurs applications 16 (2): 139–160.
Temam, D. 2009. La pascaline, la “machine qui relève du défaut de la mémoire.” Bibnum. Retrieved from: http://bibnum.revues.org/548.
Tent, M.B.W. 2012. Gottfried Wilhelm Leibniz: The polymath who brought us calculus. Boca Raton, FL: CRC Press.
Trouche, L. 2005. Des artefacts aux instruments, une approche pour guider et intégrer les usages des outils de calcul dans l’enseignement des mathématiques. Actes de l’université d’été de Saint-Flour, pp. 265–290.
Vygotsky, L.S. 1978. Mind in society: The development of higher psychological processes. Cambridge, MA: Harvard University Press.
Walford, C. 1871. The insurance cyclopaedia. London: Layton.
Wiener, N. 1988/1950. The human use of human beings: Cybernetics and society. New York: Da Capo Press.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2018 Springer Nature Switzerland AG
About this chapter
Cite this chapter
Freiman, V., Robichaud, X. (2018). A Short History of Computing Devices from Schickard to de Colmar: Emergence and Evolution of Ingenious Ideas and Technologies as Precursors of Modern Computer Technology. In: Volkov, A., Freiman, V. (eds) Computations and Computing Devices in Mathematics Education Before the Advent of Electronic Calculators. Mathematics Education in the Digital Era, vol 11. Springer, Cham. https://doi.org/10.1007/978-3-319-73396-8_13
Download citation
DOI: https://doi.org/10.1007/978-3-319-73396-8_13
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-73394-4
Online ISBN: 978-3-319-73396-8
eBook Packages: EducationEducation (R0)