[3] Today, undecimal numerals have applications in computer science,[4] technology,[5] and the International Standard Book Number system.
[9] For about a century, the idea that Māori counted by elevens was best known from its mention in the writing of the American mathematician Levi Leonard Conant.
xv In 2020, an earlier, Continental origin of the idea the Māori counted by elevens was traced to the published writings of two 19th-century scientific explorers, René Primevère Lesson and Jules de Blosseville.
[1] They had visited New Zealand in 1824 as part of the 1822–1825 circumnavigational voyage of the Coquille,[12] a French corvette commanded by Louis Isidore Duperrey and seconded by Jules Dumont d'Urville.
On his return to France in 1825, Lesson published his French translation of an article written by the German botanist Adelbert von Chamisso.
de la mer du Sud ... c'est là qu'on trouve premierement le système arithmétique fondé sur un échelle de vingt, comme dans la Nouvelle-Zélande (2)..."[13]: p. 27 [...east of the South Sea ... is where we first find the arithmetic system based on a scale of twenty, as in New Zealand (2)...]Lesson's footnote on von Chamisso's text: "(2) Erreur.
[14][15] In the same 1821 publication, von Chamisso also identified the Māori number system as decimal, noting the source of the confusion was the Polynesian practice of counting things by pairs, where each pair was counted as a single unit, so that ten units were numerically equivalent to twenty:[14][15] "We have before us a Grammar and Vocabulary of the Language of New Zealand, published by the Church Missionary Society.
The natives of Tonga count the bananas and fish likewise by pairs and by twenties (Tecow, English score)."[14]: pp.
441–442 Lesson's use of the term "undécimal" in 1825 was possibly a printer's error that conjoined the intended phrase "un décimal," which would have correctly identified New Zealand numeration as decimal.
[19] De Blosseville also mentioned it to the Scottish author George Lillie Craik, who reported this letter in his 1830 book The New Zealanders.
[20] Lesson was also likely the author of an undated essay, written by a Frenchman but otherwise anonymous, found among and published with the papers of the Prussian linguist Wilhelm von Humboldt in 1839.
It was mentioned in 1920 by the British anthropologist Northcote W. Thomas: "Another abnormal numeral system is that of the Pangwa, north-east of Lake Nyassa, who use a base of eleven."[26]: p.
[31] However, they ultimately rejected the initiative, deciding a common scale based on spoken numbers would simplify calculations and conversions and make the new system easier to implement.
[3] The debate over which one to use seems to have been lively, if not contentious, as at one point, Lagrange suggested adopting 11 as the base number, on the grounds indivisibility was actually advantageous; because 11 was a prime number, no fraction with it as its denominator would be reducible:[3][32] Delambre wrote: "Il était peu frappé de l'objection que l'on tirait contre ce système du petit nombre des diviseurs de sa base.
Il regrettait presque qu'elle ne fut pas un nombre premier, tel que 11, qui nécessairement eût donné un même dénominateur à toutes les fractions.
He noted the difficulty was resolved if all the fractions had the same denominator: Lagrange wrote: "On voit aussi par-là, qu'il est indifférent que le nombre qui suit la base du système, comme le nombre 10 dans notre système décimal, ait des diviseurs ou non; peut-être même y aurait-il, à quelques égards, de l'avantage à ce que ce nombre n'eût point de diviseurs, comme le nombre 11, ce qui aurait lieu dans le système undécimal, parce qu'on en serait moins porté à employer les fractions 1⁄2, 1⁄3, etc."[33]: p.
9 Undecimal (often referred to as unodecimal in this context) is useful in computer science and technology for understanding complement (subtracting by negative addition)[4] and performing digit checks on a decimal channel.
[37] In the novel Contact by Carl Sagan, a message left by an unknown advanced intelligence lies hidden inside the number pi.