Number systems

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This is a list of number systems used in or proposed for Toki Pona. In large part because the main number systems are intentionally limited, constructing alternative systems is a common project for tinkerers with the language.

Additive number systems[edit | edit source]

Additive number systems or sign-value notation represents numbers using a sequence of numerals which each represent a distinct, usually smaller, quantity. For example, the numeral "10" may be said as "five five". Examples in natural languages include the Roman and Egyptian numerals.

Pre-pu number systems[edit | edit source]

A system created before the publication consists only of the words wan ("one") and tu ("two"). Larger numbers consist of adding these two numbers. This is similar to counting in Gumulgal, an Australian Aboriginal language.[1]

tu tu tu wan

tu tu tu wan

seven (2 + 2 + 2 + 1)

pu number systems[edit | edit source]

There are two standard number systems shown in the book Toki Pona: The Language of Good, both of which are additive.[2] jan Sonja provides the words ala (zero), wan (one), tu (two), mute (three or more, "many"), and ale (infinity, "countless").

Another system provided by jan Sonja, used for complex and precise counting, consists of the words wan (1), tu (2), luka (5), mute (20), and ale (100). As stated by her, this system was influenced by the Canadian dollar banknotes (the $50 note having no equivalent due to its relative rarity).[3]

luka tu

luka tu

seven (5 + 2)

mute mute mute luka luka luka tu wan

mute mute mute luka luka luka tu wan

78 (20 + 20 + 20 + 20 + 5 + 5 + 5 + 2 + 1)

This system can be sometimes ambiguous, for example, the phrase len luka tu may mean "seven pieces of clothing" or "two gloves [clothing for the hands]". It was proposed for ali, a variant of ale, to chiefly stand for the number 100.[citation needed]

Positional number systems[edit | edit source]

Seximal[edit | edit source]

A seximal (base 6) positional system uses these digit words. The words for 3 and 4 are generally considered nonstandard; this system is a notable place where they may occur.

Digit Word
0 ala
1 wan
2 tu
3 tuli or san
4 po or neja
5 luka

The word kulupu or a dedicated shortening, kulu, is used for six, which is not a digit as it takes the role of 106 by definition.

nasin nanpa kijetesantakalu[edit | edit source]

nasin nanpa kijetesantakalu is a joke seximal number system created by soweli nata in 2020, where each digit is kijetesantakalu with a different stressed syllable.

Hybrid number systems[edit | edit source]

Hybrid systems are a combination of addive and positional systems.

nasin nanpa pona[edit | edit source]

nasin nanpa pona is a hybrid number system and an extension to the advanced pu system, created by jan Kapilu and jan Tepo in 2021. Numbers up to a hundred at the same as pu, however, if numbers smaller than 100 precede ale, then ale gets multiplied by this number. Conventionally, the word wan precedes ale for "100" to avoid confusion with the pu system.[4]

This system may be classified as a centisimal (base 100), as hundred is the base of all larger numbers.

tu ale

tu ale

200 (2 × 100)

wan ale ale

wan ale ale

10 000 (100 × 100)

It allows for larger numbers to be expressed compactly.

mute mute mute luka luka tu ale luka tu ale mute

mute mute mute luka luka tu ale luka tu ale mute

720 720 ([([72 × 100] + 7) × 100] + 20)

In the book The Wonderful Wizard of Oz (Toki Pona edition), jan Sonja used this system for the date format on the title page.[5]

tenpo sike nanpa mute2 ale mute2 tu tu

tenpo sike nanpa mute ale mute tu tu

Year 2024 ([20 × 100] + 20 + 2 + 2)

References[edit | edit source]

  1. Harris, John (1987). Australian Aboriginal and Islander mathematics (PDF). Australian Aboriginal Studies.
  2. Lang, Sonja. (25 May 2014). Toki Pona: The Language of Good. Tawhid. ISBN 978-0978292300. OCLC 921253340.
  3. ma pona pi toki pona. (19 August 2023). "suno pi toki pona | toki pona day 2023 #3". ma pona pi toki pona [@maponapitokipona]. YouTube. "[...] [The number system] was influenced by the commonly found banknotes demominations in Canada".
  4. jan Kapilu, jan Tepo. "nasin nanpa pona" (in Toki Pona). Wyubsite. Archived from the original on 3 February 2022. Retrieved 5 February 2024.
  5. Baum, L. Frank. (3 February 2024). The Wonderful Wizard of Oz (Toki Pona edition). Translated by Sonja Lang. Illustrated by Evan Dahm. Tawhid Press. ISBN 978-0978292379. (Original work 1900.) p. 2.