Oceanian counting algorithms (original) (raw)
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The Original Counting Systems of Papua and New Guinea
The Arithmetic Teacher
Different groups of Papuans and New Guineans have used a wide variety of devices and techniques, as well as systems of numeration, to tally and, less frequently, to record quantities of goods and multiples of people, shells, days (until a meeting or ceremony), and animals. It is as yet impossible to provide a comprehensive guide to the counting systems of Papua and New Guinea or to provide a key to their geographic distribution as K. W. Galis has done for West Irian. Readers who wish to enquire into the systems employed by specific groups of people or into the distribution of a particular method or device should consult the bibliography that follows. This article is confined to a survey of the kinds of tallying, recording, and counting systems used, with examples only of each major type provided.
Analytical data for EU project 785793
The bibliography lists the resources used to characterize counting practices in Polynesia and map their geographic distribution. The data were analyzed in: Overmann, Karenleigh A. (2020). The curious idea that Māori once counted by elevens, and the insights it still holds for cross-cultural numerical research, Journal of the Polynesian Society. Overmann, Karenleigh A. (2020). Counting by “elevens” and why nine and two make twenty: The material roots of Polynesian numbers. Journal of Mathematics and Culture. Forthcoming. This project has received funding from the European Union’s Horizon 2020 research and innovation program under grant agreement No. 785793.
Journal of the Nigerian Languages Project, Volume 3, 2021
Indigenous counting systems and numbering have unique attributes that are linked to the cultures of their speech communities. Indigenous people have used various methods of counting and numbering things based on the meaning they intend to communicate, in terms of their value and significance. A counting system starts from small simple singleword numbers and grows to large complex numbers that may be descriptive in nature. As the numbers increase, they become more difficult to count, requiring the use of certain key numerals as pivots to produce their multiples in a cyclical pattern. However, these pivotal numerals upon which a particular counting system is based vary from one tradition to another. The introduction of base-10, the concept of 'zero' as a number, and the use of binary logic in digital technology have become universal standard methods of addressing such ethno-cultural variations. They are significant in the discourse of language and globalization, especially in the computation and business environment of today. This paper seeks to contribute to the discussion on the need to model the features of indigenous counting systems such that they benefit from the inherent gains of base-10 and related applications of the modern day. It adopts a semantic-pragmatic approach to describe and analyse indigenous numbering patterns against those of base-10, using the Abureni numerals as the data for the study. The objective is to show the points of synergy that the numerals could be modeled for base-10 applications in a manner that they sound natural in the indigenous language, in terms of context and meaning. The paper concludes that the features of an indigenous counting system can be patterned to produce a base-10 model of it, without disrupting the traditional numbering pattern of the target language.
Revising the history of number: how Ethnomathematics transforms perspectives on indigenous cultures
Revemop, 2020
Many accounts of the history of number rely on written evidence such as clay, stone, and wood engravings or paintings. However, some of the oldest cultural groups (between 5 000 and 30 000 years old) have had only recent contact with the rest of the world, namely between 80 and 140 years ago but these were oral cultures without written records. Finding out about their understanding of number has involved analysis of the types of counting but also how counting related to the rest of their cultural relationships. There is some surprising evidence of diversity of number systems, longevity of the systems, and the interplay with cultural practices that begs respect for Indigenous cultures. Brief summaries of this history of number in Papua New Guinea and Oceania and the diversity of systems is followed by how this new knowledge can inform school mathematics learning in any part of the world.Keywords: History of number. Indigenous mathematics. Papua New Guinea. Melanesia. Pacific. Longevi...
Innovative Numerals in Malayo-Polynesian Languages outside of Oceania
In this paper, we seek to draw attention to Malayo-Polynesian languages outside of the Oceanic subgroup with innovative bases and complex numerals involving various additive, subtractive, and multiplicative procedures. We highlight the fact that the number of languages showing such innovations is more than previously recognized in the literature. Finally, we observe that the concentration of complex numeral innovations in the region of eastern Indonesia suggests Papuan influence, either through contact or substrate. However, we also note that sociocultural factors, in the form of numeral taboos and conventionalized counting practices, may have played a role in driving innovations in numerals.
Humans, 2024
Wu, Shiyue, and Francesco Perono Cacciafoco. 2024. Understanding through the Numbers: Number Systems, Their Evolution, and Their Perception among Kula People from Alor Island, Southeastern Indonesia, Humans, 4, 1: 34-49. DOI: https://doi.org/10.3390/humans4010003 - This paper aims at documenting and reconstructing the linguistic processes generating and substantiating the use of number systems, numbers in general, elementary arithmetic, and the related concepts and notions among the Kula people from Alor Island, Southeastern Indonesia. The Kula is a Papuan population from the Alor–Pantar Archipelago (Timor area). The name of their language, Kula (or Kola), corresponds to the ethnonym. The language is, currently, endangered and not completely documented. At the level of linguistic features, numeral systems and the terms for numerals from Eastern Alor exhibit, to some extent, unique characteristics, if compared to other languages spoken in other sectors of the island. Therefore, the Kula numbering system is not only significant at the lexicological and lexicographic level, but also represents the essential role of cognitive strategies (e.g., the choice of the base for the numbering systems and the visual representation of counting with the aid of actual ‘objects’, like hands and fingers) in the coinage of numerical terms among the local speakers. Indeed, the development of numeral systems reflects the evolution of human language and the ability of humans to construct abstract numerical concepts. The way numerals are encoded and expressed in a language can impact the patterns according to which numerical notions are conceptualized and understood. Different numeral systems can indicate variations in cognitive processes involving notions of quantities and measurements. Therefore, the structure and characteristics of a numeral system may affect how numeral concepts are mentally represented and developed. This paper focuses on the number system of the Kula people and the lexical units used by the local speakers to indicate (and to explain) the numbers, with the related concepts, notions, and symbolism. The investigation delves into the degrees of abstraction of the Kula numeral system and tries to ascertain its origins and reconstruct it. Moreover, the article applies to the analysis a comparative approach, which takes into account several Papuan and Austronesian languages from Alor Island and Eastern Timor, with the dual aim of investigating, at a preliminary level, a possible common evolution and/or divergent naming processes in local numbering systems and their historical–linguistic and etymological origins. - Keywords: anthropological linguistics; language documentation; numbering systems; Kula language (Lantoka/Lamtoka-Tanglapui); Alor Island
Counting systems of the Strickland-Bosavi languages, Papua New Guinea
2016
Information on the counting systems of 12 East Strickland and Bosavi languages is collated. In seven cases the body‐part tally system is symmetrical, with cycle lengths varying from 27 to 35. In four cases, the tally system is asymmetrical or truncated and in one case detailed information is not available. Methods of counting beyond one cycle have been described for all but one of the Bosavi languages but not for any of the East Strickland languages. An additional 2‐cycle or 2, 5‐cycle system is indicated for several East Strickland languages but not for any Bosavi language. Comparison with the counting systems of languages beyond the Strickland‐Bosavi region – especially with Ok languages to the northwest and Huli to the northeast – suggests a process in which the terminology of body‐part tally systems is progressively disembedded from bodily commitment such that counting words assume the status of cardinal numbers and, thereby, facilitate expressions of the commensurability of dif...
Prodigious calculators and the Maya long count
2022
Numeration systems vary widely across traditional societies in the world. From reported societies in the Amazon with no numbers at all, to widespread spread numeration systems which count only to three, to the elaborate numerology of Ancient India which conceived of numbers larger than the atoms in the universe and the ‘long count’ of the Maya, systems very wildly. This paper argues that part of the answer may lie in the phenomenon of savant calculators who somehow infiltrate their private fascinations into a cultural nexus.
Papuan-Austronesian contact and the spread of numeral systems in Melanesia
Diachronica, 2023
This study analyzes the numeral systems of Austronesian and Papuan languages, investigating their areal distribution and considering their most likely ancestral states. The presence or absence of different methods of numeration has often been ascribed to contact-induced change. This can certainly be seen in scholarship pertaining to Melanesia, where Austronesian languages probably first came into contact with Papuan languages around 3,500 years ago. Indeed, since Proto-Austronesian is reconstructed as having employed a decimal (base-10) numeral system (with reflexes occurring throughout the Austronesian world), the presence of quinary (base-5) numeral systems in the Austronesian languages of Melanesia has commonly been attributed to contact with Papuan languages. Relying on a typological survey of 1,825 languages, this paper argues that highly conventionalized quinary systems were probably rare in Melanesia prior to the arrival of Austronesian languages. Rather, it was more likely that Austronesian speakers spread lexicalized quinary systems to Papuan groups, not the other way around. In making this argument, the paper stresses that, while numeration may be something that is linguistically encoded in a systematic fashion, it may also be realized as a cultural feature without strongly conventionalized lexicalized expressions.