Teens and Twenties

[Richard Parker]

In a previous message, I wrote:
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  The 'digital - quintal - decimal - vigesimal' progression in 
  numbering systems referred to by many linguists doesn't 
  actually apply to what seems to have evolved in the real 
  world. 
   
  So we might as well dump those terms
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  That was a bit abrupt, and undiplomatic (sorry, late in the evening) 
  perhaps implying that I thought all linguists were innumerate, which I don't.
   
  Glen Lean is the only person I know who has published a large-scale study
  of Austronesian and 'Papuan' numbers, and his explanation is a lot better:
   
  "In some of the older linguistic literature concerned with the description of natural language numeral systems, it was common to use the descriptive term "base" when discussing the cyclic nature of the system.  Thus we find counting systems variously termed "binary" (base 2), "ternary" (base 3), "quinary" (base 5), "decimal" (base 10), and "vigesimal" (base 20).  Using a single number to characterise a counting system is reasonably adequate when we are dealing with, say, the English counting system which, with some irregularities, is essentially a base 10 one.  The cyclic structure of many of the counting systems found in Melanesia is often more complex than the English system, in that a single system may have elements of base 2, base 5, and base 20; others have a structure in which we can discern elements of base 5, base 10, and base 20.  This was recognized in the older literature in which we find reference to "mixed base" systems and such terms as "incomplete decimal"
 systems (that is, one which had elements of both base 5 and base 10). "
   
  He then goes on to describe Salzmann's numeral analysis system, which, basically boils 
  down to noting the number of individual morphemes in a number system.
   
  "To take an example, let us suppose that we have analyzed a sequence of numerals to have the form:   1, 2, 3, 4, 4+1, 4+2, 4+3, 2x4, (2x4)+1, (2x4)+2, (2x4)+3, 3x4, ..., (4x4)+3, 20, 20+1, 20+2, 20+3, 20+4, (20+4)+1, (20+4)+2, ..., 2x20, (2x20)+1, (2x20)+2, ...
  i.e there are distinct number morphs for 1 to 4, and 20, and all other members of the sequence are composed of these."
   
  So, where this may have been called 'vigesimal' in older literature, it actually has an underlying more complex structure, easily expressed as (1-4, 20).
   
  Many of the 'Melanesian' languages of New Guinea, Vanuatu, New Caledonia, etc, have a structure that goes (1-5, 10, 20....). As do some of the 'archaic' forms in Polynesian.
   
  Some New Guinea number systems don't go as far as that.
  Sissano (discussed previously in An-Lang) has only: (1-2, with 5 doubtful)
  Ali (nearby) has: (1-5, and perhaps 10 'wo-lim')
  Bam, Biem (a bit further east) has (1-4)
  Manam (further still) has (1-5, 10....)
   
  Others, further west, are more complicated:
  Macassarese has (1-7, 9, 10....)  (The .... means I have no data on numbers after 10)
  So, Macassarese is unlike:
  Buginese  (1-7, 10, 100, 1000) 
  or 
  Tolaki (1-10, ....) 
  or *PAn (1-10, 100, 1000) although all four are 'decimal' systems.
   
  This quick coding sorts out the sheep from the goats, and prompts a detailed look back at, say, Macassarese and Buginese, to see how and why they differ in detail from nearby Tolaki.
   
  That leads to sets of number systems that are mappable, and directly comparable with the linguistic family groupings, and the possible question - if they don't match, why? 
   
  regards
   
  Richard
   
   
   

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