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Issue No.03 - July-September (2005 vol.27)
pp: 4-22
Mark Glusker , Nektar Therapeutics
David M. Hogan , North Devon College
ABSTRACT
In 1840, Thomas Fowler, a self-taught English mathematician and inventor, created a unique ternary calculating machine. Until recently, all detail of this machine was lost. A research project begun in 1997 uncovered sufficient information to enable the recreation of a physical concept model of Fowler's machine. The next step is to create a historically accurate replica.
INDEX TERMS
Thomas Fowler, Augustus De Morgan, base-3, ternary, balanced ternary, signed ternary, calculating machine, 19th century, historical reconstruction
CITATION
Mark Glusker, David M. Hogan, Pamela Vass, "The Ternary Calculating Machine of Thomas Fowler", IEEE Annals of the History of Computing, vol.27, no. 3, pp. 4-22, July-September 2005, doi:10.1109/MAHC.2005.49
REFERENCES
1. Fowler to Airy, 8 May 1841, RGO 6/427, folio 54, Royal Greenwich Observatory Archives, George Biddell Airy Papers, Dept. of Manuscripts and Univ. Archives, Cambridge Univ. Library.
2. H. Fowler, "Biographical Notice of the late Mr Thomas Fowler of Torrington with some account of his inventions," Report in the Trans. Devon Assoc. Advancement of Science, vol. 7, 1875, pp. 171-178.
3. T. Fowler, A Description of the Patent Thermosiphon with Some Modes of Applying it to Horticultural and Other Useful and Important Purposes, Longman, Rees, Orme, Brown & Green, London, 1829.
4. Fowler to Baily, 19 Oct. 1841, RGO 60, folder 4, Royal Greenwich Observatory Archives, Francis Baily Papers, Misc. Correspondence 1828–1843, Dept. of Manuscripts and Univ. Archives, Cambridge Univ. Library.
5. Fowler to Brougham, 22 Jan. 1834, Brougham mss., document no. 46,624, Univ. College London Library.
6. T. Fowler, Apparatus for Raising and Circulating Hot Water Etc., UK patent 5711, 1828, British Museum, London.
7. T. Fowler, Tables for Facilitating Arithmetical Calculations Intended for Calculating the Proportionate Charges on the Parishes in Poor Law Unions and Which Are Useful for Various Other Purposes, Longmans, London, England, 1838. (Referred to subsequently as Thomas Fowler, Tables.)
8. J. Bharati, Vedic Mathematics, Motilal Banarsidass, Delhi, 1965.
9. L.E. Sigler, Fibonacci's Liber Abaci: A Translation into Modern English of Leonardo Pisano's Book of Calculation, Springer, 2002.
10. C.G. Bachet Problem 5, Appendix in Problèmes plaisants et délectables [Interesting and Satisfying Problems], 2nd ed., Albert Blanchard, 1993 (in French).
11. B. Hayes, "Third Base," Am. Scientist, vol. 89, no. 6, 2001, p. 490.
12. D.E. Knuth, The Art of Computer Programming— Semi-Numerical Algorithms, vol. 2, Harlow Addison-Wesley, 1997, p. 192.
13. T. Fowler, Tables, Introduction, p. iii-iv.
14. T. Fowler, Tables, Description and Use of the Binary and Ternary Tables, p. xxiv.
15. A. Stakhov, "Brousentsov's Ternary Principle, Bergman's Number System and Ternary Mirror-symmetrical Arithmetic," The Computer J., vol. 45, no. 2, 2002, pp. 221-235.
16. A. De Morgan, "Description of a calculating machine, invented by Mr Thomas Fowler of Torrington in Devonshire," Archive Papers vol. 23, no. 24, The Royal Society, London, June 1840. Text of this document is reproduced in its entirety at http://www.zib.de/zusehttp://www.mortati.com/ glusker/fowlerdemorgan.htm.
17. "Notice of Mr Fowler's new Calculating Machine, Communicated by Professor Airy," Transactions of Sections, vol. 10, British Assoc. for the Advancement of Science, Sept. 1840, p. 55.
18. "On a New Calculating Machine by Mr. Fowler," Transactions of Sections, vol. 11, British Assoc. for the Advancement of Science, Sept. 1841, pp. 39-40.
19. Buckland to Airy, 20 May 1840, RGO 6/427, folio 48, Royal Greenwich Observatory Archives, George Biddell Airy Papers, Dept. of Manuscripts and Univ. Archives, Cambridge Univ. Library.
20. Fowler to Baily, 19 Oct. 1841, RGO 60/4, misc. correspondence 1828–1843, Royal Greenwich Observatory Archives, Francis Baily Papers, Dept. of Manuscripts and University Archives, Cambridge Univ. Library.
21. T. Fowler, Description of the table part of the New Calculating Machine invented by Thomas Fowler of Great Torrington, Devon in 1842, pamphlet, printed by M. Fowler, Great Torrington, Devon, England, 1844, and compiled in Mathematical Tracts 1848, A. De Morgan, ed., Ref. L (bound pamphlet 39) item 26, Senate House, Univ. of London Library.
22. S. Johnston, "Making the Arithmometer Count," Bull. Scientific Instrument Soc. no. 52, 1997, pp. 12-21. An excellent account of the evolution of the arithmometer, also available online at http://www.mhs.ox.ac.uk/staff/saj/textsarithmometer.pdf .
23. E.M. Horsburgh ed. Handbook of the Napier Tercentenary Celebration, or Modern Instruments and Methods of Calculation, Tomash Publishers, 1982. (Vol. 3 in the Charles Babbage Inst. Reprint Series for the History of Computing, reprint of original work from 1914.) A detailed description of the Millionaire calculator is on pp. 117-122.
24. M.R. Williams, A History of Computing Technology, Prentice Hall, 1985. Chapter 3 ("Mechanical Calculating Machines") explains the importance of a reliable carry mechanism in the development of the first calculating machines.
25. N.P. Brousentsov et al., "Development of Ternary Computers at Moscow State Univ."; http://www.computer-museum.ru/englishsetun.htm .
26. Quotation derived from A. Stakhov, "Brousentsov's Ternary Principle, Bergman's Number System and Ternary Mirror-symmetrical Arithmetic," The Computer J., vol. 45, no. 2, 2002, p. 222.
27. S.V. Klimenko, "Computer Science in Russia: A Personal View," IEEE Annals of the History of Computing, vol. 21, no. 3, 1999, pp. 16-30.
28. D. Swade, The Difference Engine: Charles Babbage and the Quest to Build the First Computer, Viking, 2001, pp. 310-312.
29. Merkle to Hogan, personal correspondence, 4 Mar. 2002.
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