Editing Octal (section)

===By Europeans===
* It has been suggested that the reconstructed [[Proto-Indo-European|Proto-Indo-European (PIE)]] word for "nine" might be related to the PIE word for "new".  Based on this, some have speculated that proto-Indo-Europeans used an octal number system, though the evidence supporting this is slim.<ref>{{cite book
 |last=Winter
 |first=Werner
 |chapter=Some thoughts about Indo-European numerals
 |title=Indo-European numerals
 |series=Trends in Linguistics
 |volume=57
 |editor1-last=Gvozdanović
 |editor1-first=Jadranka
 |date=1991
 |publisher=Mouton de Gruyter
 |location=Berlin
 |isbn=3-11-011322-8
 |pages=13–14
 |chapter-url=https://books.google.com/books?id=S-hmNOLuDGsC&pg=PA13
 |access-date=2013-06-09
 |archive-date=2023-04-01 
 |archive-url=https://web.archive.org/web/20230401131711/https://books.google.com/books?id=S-hmNOLuDGsC&pg=PA13
 |url-status=live
 }}</ref>
* In 1668, [[John Wilkins]] in ''[[An Essay towards a Real Character, and a Philosophical Language]]'' proposed use of base 8 instead of 10 "because the way of Dichotomy or Bipartition being the most natural and easie kind of Division, that Number is capable of this down to an Unite".<ref>{{cite book
 |last=Wilkins
 |first=John
 |title=An Essay Towards a Real Character and a Philosophical Language
 |date=1668
 |location=London
 |pages=190
 |url=https://books.google.com/books?id=BCCtZjBtiEYC&pg=PA190
 |access-date=2015-02-08
 |archive-date=2023-04-01 
 |archive-url=https://web.archive.org/web/20230401131651/https://books.google.com/books?id=BCCtZjBtiEYC&pg=PA190
 |url-status=live
 }}</ref>
* In 1716, King [[Charles XII of Sweden]] asked [[Emanuel Swedenborg]] to elaborate a number system based on 64 instead of 10. Swedenborg argued, however, that for people with less intelligence than the king such a big base would be too difficult and instead proposed 8 as the base. In 1718 Swedenborg wrote (but did not publish) a manuscript: "''En ny rekenkonst som om vexlas wid Thalet 8 i stelle then wanliga wid Thalet 10''" ("A new arithmetic (or art of counting) which changes at the Number 8 instead of the usual at the Number 10"). The numbers 1–7 are there denoted by the consonants l, s, n, m, t, f, u (v) and zero by the vowel o. Thus 8 = "lo", 16 = "so", 24 = "no", 64 = "loo", 512 = "looo" etc. Numbers with consecutive consonants are pronounced with vowel sounds between in accordance with a special rule.<ref>[[Donald Knuth]], ''[[The Art of Computer Programming]]''</ref>
*Writing under the pseudonym "Hirossa Ap-Iccim" in ''[[The Gentleman's Magazine]]'', (London) July 1745, [[Hugh Jones (reverend)|Hugh Jones]] proposed an octal system for British coins, weights and measures. "Whereas reason and convenience indicate to us an uniform standard for all quantities; which I shall call the ''Georgian standard''; and that is only to divide every integer in each ''species'' into eight equal parts, and every part again into 8 real or imaginary particles, as far as is necessary. For tho' all nations count universally by ''tens'' (originally occasioned by the number of digits on both hands) yet 8 is a far more complete and commodious number; since it is divisible into halves, quarters, and half quarters (or units) without a fraction, of which subdivision ''ten'' is uncapable...." In a later treatise on [[Hugh Jones (reverend)#Publications|Octave computation]] (1753) Jones concluded: "Arithmetic by ''Octaves'' seems most agreeable to the Nature of Things, and therefore may be called Natural Arithmetic in Opposition to that now in Use, by Decades; which may be esteemed Artificial Arithmetic."<ref>See H. R. Phalen, "Hugh Jones and Octave Computation," ''The American Mathematical Monthly'' 56 (August–September 1949): 461-465.</ref> 
* In 1801, [[James Anderson of Hermiston|James Anderson]] criticized the French for basing the [[metric system]] on decimal arithmetic.  He suggested base 8, for which he coined the term ''octal''. His work was intended as recreational mathematics, but he suggested a purely octal system of weights and measures and observed that the existing system of [[English units]] was already, to a remarkable extent, an octal system.<ref>James Anderson, On Octal Arithmetic [title appears only in page headers], [https://books.google.com/books?id=olhHAAAAYAAJ&pg=PA437 Recreations in Agriculture, Natural-History, Arts, and Miscellaneous Literature] {{Webarchive|url=https://web.archive.org/web/20230401131644/https://books.google.com/books?id=olhHAAAAYAAJ&pg=PA437 |date=2023-04-01  }}, Vol. IV, No. 6 (February 1801), T. Bensley, London; pages 437-448.</ref>
* In the mid-19th century, Alfred B. Taylor concluded that "Our octonary [base 8] [[radix]] is, therefore, beyond all comparison the "''best possible one''" for an arithmetical system." The proposal included a graphical notation for the digits and new names for the numbers, suggesting that we should count "''un'', ''du'', ''the'', ''fo'', ''pa'', ''se'', ''ki'', ''unty'', ''unty-un'', ''unty-du''" and so on, with successive multiples of eight named "''unty'', ''duty'', ''thety'', ''foty'', ''paty'', ''sety'', ''kity'' and ''under''." So, for example, the number 65 (101 in octal) would be spoken in octonary as ''under-un''.<ref>Alfred B. Taylor, [https://archive.org/details/reportonweights00taylgoog Report on Weights and Measures], Pharmaceutical Association, 8th Annual Session, Boston, 1859-09-15. See pages 48 and 53.</ref><ref>Alfred B. Taylor, Octonary numeration and its application to a system of weights and measures, [https://books.google.com/books?id=KsAUAAAAYAAJ&pg=PA296 Proc. Amer. Phil. Soc. Vol XXIV] {{Webarchive|url=https://web.archive.org/web/20230401131638/https://books.google.com/books?id=KsAUAAAAYAAJ&pg=PA296 |date=2023-04-01  }}, Philadelphia, 1887; pages 296-366. See pages 327 and 330.</ref> Taylor also republished some of Swedenborg's work on octal as an appendix to the above-cited publications.