10 in Mangarevan
takau
10 counting units; for fish counted in pairs, this represents 20 fish.
HISTORICAL · DECIMAL WITH BINARY STEPS
Mangarevan
Spoken counting with groups of 10, 20, 40, and 80. The counting unit depends on the object.
Convert numbers- Place
- Mangareva, Gambier Islands, French Polynesia
- Period / variant
- Traditional object-specific counting, documented in the 19th–20th centuries
EXAMPLES
tataua
40 · Decimal with binary steps
40 counting units = two paua = four takau.
Worked example
Read 40 in Mangarevan
First choose the counting unit. Then read any groups of 80, 40, 20, and 10, followed by the remaining units.
- tataua
tataua names 40. Count this group once.
Check
40 = 40 counting units
Sources and notation notes
One unit can contain one turtle, two fish, four coconuts, or eight octopuses. Multiply the counting-unit total by that quantity to find the number of objects.
Bender & Beller · Mangarevan invention of binary steps for easier calculation (2013)
Number-word dictionary
Number words are the signs in this tradition. This dictionary shows the documented words and their meanings, preserving the spelling used by the sources. Some words name whole groups or connect parts of a number.
- ta’i
- 1
- rua
- 2
- toru
- 3
- ’a
- 4
- rima
- 5
- ono
- 6
- ’itu
- 7
- varu
- 8
- iva
- 9
- takau
- 10 counting units
- paua
- 20 counting units
- tataua
- 40 counting units
- varu
- 80 counting units in the grouping context
- tauga
- counting unit; its object quantity depends on the goods
How the words fit together
Express the count as multiples of 80, followed by at most one 40, one 20, one 10, and the remaining ones. The input counts tauga; choose how many objects each tauga contains before converting it to objects.
- Choose the counting unit: a turtle, a pair of fish, four coconuts, or eight octopuses.
- Read the largest part first: a number before varu multiplies 80. A single varu names 80.
- Then add any tataua (40), paua (20), and takau (10), each used once at most. Finish with the remaining 1–9 units.
- For example, toru varu paua takau toru is 3 × 80 + 20 + 10 + 3 = 273 counting units.
20 in Mangarevan
paua
20 counting units = two takau. The basic unit still depends on the object.
40 in Mangarevan
tataua
40 counting units = two paua = four takau.
80 in Mangarevan
varu
80 counting units = two tataua. In the unit range, varu also means eight; context distinguishes the meanings.
273 in Mangarevan
toru varu paua takau toru
3 × 80 + 20 + 10 + 3 = 273 counting units; an example given in the research paper.
Supports 1–799 counting units using Bender and Beller’s documented construction. These spoken forms do not automatically count individual objects. The language also has an ordinary decimal system; historical accounts of specialized counting vary.
History
Bender and Beller’s 2013 analysis draws especially on Te Rangi Hiroa’s ethnography. The specialized system counted valued goods alongside an ordinary decimal system; it was not a universal replacement for decimal counting.
How to read it
Express the count as multiples of 80, followed by at most one 40, one 20, one 10, and the remaining ones. The input counts tauga; choose how many objects each tauga contains before converting it to objects.
- Choose the counting unit: a turtle, a pair of fish, four coconuts, or eight octopuses.
- Read the largest part first: a number before varu multiplies 80. A single varu names 80.
- Then add any tataua (40), paua (20), and takau (10), each used once at most. Finish with the remaining 1–9 units.
- For example, toru varu paua takau toru is 3 × 80 + 20 + 10 + 3 = 273 counting units.
Limits
Supports 1–799 counting units using Bender and Beller’s documented construction. These spoken forms do not automatically count individual objects. The language also has an ordinary decimal system; historical accounts of specialized counting vary.
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