# Internal order and areal patterns in South Asian numerals

Mamta Kumari, Ezequiel Koile, Marc Allassonnière-Tang

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## To cite this version:

Mamta Kumari, Ezequiel Koile, Marc Allassonnière-Tang. Internal order and areal patterns in South Asian numerals. STUF, 2026, 78 (4), pp.699-724. 10.1515/stuf-2025-2021. hal-05464367

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Mamta Kumari*, Ezequiel Koile and Marc Allassonnière-Tang

**Internal order and areal patterns in South
Asian numerals**

https://doi.org/10.1515/stuf-2025-2021

**Abstract:** The linguistic diversity present in South Asia stems from its historical mix of cultures, as well as its heterogeneous topography. This diversity can be observed in numeral systems, which play an important role in cognitive and cultural history. We provide the first typological overview of numeral systems in South Asia, presenting a database of 122 languages – mostly Austroasiatic, Dravidian, Indo-Aryan, and Tibeto-Burman, with a majority of data from original fieldwork. We also provide a framework for analyzing numeral systems based on the internal ordering of their complex numerals (teens, crowns, running numbers, hundreds, and thousands). Quantitative analyses based on decision trees and phylogenetic regressions suggest that internal ordering of complex numerals are generally stable in each language family along history, although horizontal transmission due to historical contact phenomena are observed as well. Our study also has a societal impact: the diversity of numeral systems featured here is quickly disappearing, and we claim that it is of the utmost importance to document and preserve it.

**Keywords:** numeral systems; linguistic typology; internal order; language contact; complex numerals

# 1 Introduction

Numeral systems have become a nearly universal feature of human societies in the present, and have played an important role in our cognitive and cultural history (Bender and Beller 2011, 2012). They allow us counting, calculating, record keeping, communicating quantities in a standardized way, as well as keeping a cultural heritage. Nevertheless, numeral systems are not strictly necessary: some cultures have developed sophisticated artifacts for counting and record keeping without using a formal numeral system. Examples of this are quipus, tally sticks, abaci, and knots on a string (Bender and Beller 2012; Epps et al. 2012).

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<footnote>*Corresponding author: Mamta Kumari, Max Planck Institute for Evolutionary Anthropology, Leipzig, Germany, E-mail: kumari_mamta@eva.mpg.de</footnote>

<footnote>Ezequiel Koile, Pontificia Universidad Católica del Perú, San Miguel, Peru, E-mail: ekoile@pucp.edu.pe</footnote>

<footnote>Marc Allassonnière-Tang, CNRS/MNHN/University Paris City, Paris, France, E-mail: marc.allassonniere-tang@mnhn.fr</footnote>
Numeral systems have been analyzed from various disciplines, including an-
thropology, linguistics, history, and mathematics (Comrie 2022; Hurford 1987; Xu
et al. 2020). In particular, they have received extensive linguistic study from the
cognitive and typological approaches. Linguists and cognitive scientists are inter-
ested in cross-linguistic properties of numeral and counting systems as they suggest
this is a species-specific cognitive property. The origin of a conventional counting
sequence has been proposed to lie in the transition from counting by gestures to
counting by words (O'Shaughnessy et al. 2022; Wiese 2007). Languages vary in the
span of their numeral systems (Comrie 2021; Greenberg 1978), from restricted ranges
of very few numerals (Donohue 2008; Hammarström 2010) or approximate numer-
osity (Xu et al. 2020) to productive numeral systems. For example, Mundurukú
(Tupian) has an approximate numeral system with terms for “one”, “two”, “few”, and
“many”. Several languages have restricted exact numeral systems that can only
express numerals up to a certain value, such as terms for 1–3 and ‘many’ for example
in Araona, Achagua, Baré, and Hixkaryana (Xu et al. 2020). Chomsky (1997) suggests
that the number faculty developed as a byproduct of the language faculty, preserving
discrete infinity mechanisms and eliminating other special features of language. On
the other hand, Bloom (1994) and Hurford (1987) argue that the number faculty is
dependent on semantic interpretations of the language faculty, with the grammar of
the counting routine providing its discrete infinity property. Children learn the
linguistic counting routine before understanding numerical representations,
allowing them to “bootstrap” a generative understanding of number out of the
productive syntactic and morphological structures available in the numeral system.

Numeral systems also offer important grounds for both synchronic and
diachronic linguistic analyses. In many cases, their forms are known over time, for
which their study can provide insight into the development of a language, the im-
pacts of diverse cultures, and inter-community contacts (Barlow 2023; Bowern and
Zentz 2012; Calude and Verkerk 2016; Matisoff 1995). Studying numeral systems can
assist scholars in understanding the historical evolution of languages. For instance,
the older traditional numeral system of Brahui (Dravidian) was vigesimal (base 20),
whereas they currently use the borrowed decimal (base 10) Iranian numerals (Chan
et al. 2019). Brahui is not the only language moving toward decimality; numerous
languages throughout the world are expected to no longer use their traditional
numeral system in the following generation. Bowern and Zentz (2012) explore the
variation in restricted numeral systems of Australian languages, revealing extensive
diversity in them, contrary to previous assumptions. Their study clearly shows how
diverse the numeral system could be shedding light on the complexity and variation
across different languages. Similar to this, Epps et al. (2012) explore the variation in
numeral systems, particularly focusing on restricted numeral systems associated
with hunter-gatherer groups. The study reveals that while correlations with
subsistence patterns are relatively weak, numeral trends show clear areal patterns. Mazaudon's (2009) study on the Tibeto-Burman numeral systems also sheds light on the diversity, and different strategies of forming numerals. It also highlights the use of overcounting with and without fractions as cognitive approaches to expressing quantities.

Other peculiarities of numeral systems found in the languages of the world include systems based in body parts and mixed base systems (Comrie 2005; Donohue 2008; Evans 2011; Laycock 1975; Lean 1991; Schapper and Klamer 2014). Examples of body-based systems include Hixkaryana, with a system ranging up to 10, based on body parts. On the other hand, Sandawa and Ilongot feature mixed quinary-decimal systems (bases 5 and 10) (Comrie 2005). Rapid globalization is causing the loss of traditional numeral systems, especially those belonging to small groups or societies, and their replacement by those of neighboring dominant languages. Comrie (2005) states that numeral systems are even more endangered than the languages themselves to which they belong. Numeral systems are also endangered in widely spoken languages, for example, Japanese and Thai numerals have been largely replaced by Chinese numerals (Comrie 2005).

The linguistic diversity of South Asia, especially India, stems from its historical mix of cultures, faiths, and empires, as well as its heterogeneous topography. This rich linguistic tapestry is the result of the natural evolution of each language, as well as the contacts between many communities. India is one of the world's most linguistically diverse countries, and this diversity can be observed in their numeral systems. However, while the numeral systems in South Asia are relatively diverse (Mamta 2024), few researchers have analyzed them systematically from either a qualitative or a quantitative perspective, due to the lack of available data. We fill this gap by examining the subtleties of South Asian languages' cardinal numeral systems and using them to typologize the language families of this region.

In the following sections, we first aim to display the various patterns of numeral systems in terms of internal ordering of their constituents and numeral base in South Asian languages. Then, we expect to show that within language families, internal ordering of numerals is generally stable, reflecting vertical transmission through linguistic inheritance. Furthermore, we also expect to demonstrate that, due to historical contact between the linguistic communities in the region, some numeral features are transmitted horizontally.

In Section 2, we describe the diversity of language families and their numeral systems in the region on the basis of broadly two features: base and internal order. In Section 3, we focus on the four main language families in the region: Austroasiatic, Dravidian, Indo-Aryan, and Tibeto-Burman. We run quantitative analyses to investigate the influence of vertical and horizontal transmission in the development of numeral systems. We show our conclusions in Section 4.
## 2 Numeral systems in South Asia

We chose two parameters for studying the typology of numeral systems in South Asia: numeral base and internal order of complex numerals. A total of 122 languages have been included, from primary and secondary sources. For 63 languages, primary data were collected from fieldwork by the first author, using questionnaire and interview methods, composing the *South Asian Numerals Database* SAND (Mamta 2023). The data were transcribed in IPA after being recorded with a Zoom H1 Recorder. For the remaining 59 languages, Chan's numeral database has been used. While there are many more Dravidian, Indo-Aryan, Tibeto-Burman and Austroasiatic languages listed in Glottolog, materials were not available for them, therefore, an effort has been made to cover as many languages as possible (with reliable data) in the four major language families of the region. The data were then coded based on the applicable parameters (see the full data in the Supplementary Material <fnref n="1" />). In the following, we start by setting some definitions, and continue with the characterization of numeral systems.

### 2.1 Preliminary definitions

In this subsection, we provide a brief overview of the terminology used along this article. We first define an *atom* as any numeral that cannot be split into constituent parts, such as English *'two' (2)*. A *base* is an atom that is combined systematically with lower numerals to yield *complex numerals*. Examples of a base include *'ten' (10)* in English, which can take the allomorphic forms *-teen* and *-ty*, e.g. in *fif-teen* (*5 + 10*) and in *twen-ty five* (*2·10 + 5*), respectively (see next subsection). Every numeral which is not an atom or a base, is considered a *complex numeral* and by definition it is formed by at least one atom and one base, either using the full lexical forms of them or by a morphological derivation. In the examples above for English, *ten*, *-teen* or *-ty* (*10*) is the base, and atoms *five* (*5*) and *two* (*2*) are attached to them through different mathematical operations.

We will use the term *internal order*<fnref n="2" /> of numerals to refer to the order in which the constituents of a complex numeral are placed. We define internal orders for five types of complex numerals in each system, namely: internal orders for *crowns*,

<footnote n="1">1 The Supplementary Material is available at (https://doi.org/10.1515/stuf-2025-2021), the OSF repository can be accessed here: https://osf.io/7x8b2.</footnote>

<footnote n="2">2 In this study in Section 2.3, when we are talking about internal orders (base-initial and base-final), we are treating ‘teens’ and ‘running numbers’ as an additive base, and ‘crowns’, ‘hundreds’ and ‘thousands’ as a multiplicative base. For example, if 42 is (4·10) + 2 or (10·4) + 2, they both will be treated as 40 + 2 (additive base), where 2 is addend and 40 is augend, and the order is base-initial. Similarly, if 42 is 2 + (4·10) or 2 + (10·4), they will be treated as 2 + 40 and the order is base-final. If 40 is</footnote>
*hundreds*, *thousands*, *teens*, and *running numbers*. The first three are mostly formed by multiplication: *Crowns* are typically formed by the multiplication of an atom and a base (in the case of South Asian languages, 10 or 20 depending on the language), for example 4-10 in 'forty'. However, higher numerals can also be represented by a completely new atomic form, bearing no connections to either atom or base (Calude and Verkerk 2016), for example *kuri* (20) in Bengali. In a decimal system, the numerals representing 10, 20, ..., 80, 90 are crowns. With the same logic as for crowns, integer multiples of 100 and 1,000 are being referred to as *hundreds* and *thousands* respectively. Hundreds are numerals representing 100, 200, ..., 800, 900, while those representing 1,000, 2,000, ..., 8,000, 9,000 are thousands. The last two categories of complex numerals are mostly additive in nature. *Teens* are the numbers 11 to 19. All numerals excluding atoms, bases, teens, crowns, hundreds, and thousands are called *running numbers*. In this study, we refer to them as those between consecutive crowns, i.e. 21–29, 31–39, ..., 81–89, 91–99.

## 2.2 Numeral base

To comprehend how a numeral system builds its expressions, we must first define the concept of a base, which is crucial to the formation of complex numerals. A number *n* is referred to as a *base* in a numeral system if it is used frequently in numeral expressions such as:

$$ (1) \quad N = x \cdot n \pm y $$

which means that the number *x* is multiplied by the base *n*, and then the number *y* is added or subtracted, in order to generate the number *N* (Hammarström 2010). Languages have a variety of numeral bases, including quinary (base 5), octal (base 8), decimal (base 10), vigesimal (base 20), duodecimal (base 12), sexagesimal (base 60), and octagesimal (base 80), among others (Comrie 2021). The numeral systems described above are *productive*, and we call numbers with $x \neq 0$ in (1) *complex numerals* (e.g. English *thirty four* where $x = 3$ and $y = 4$), while those with $x = 0$ are *atomic numerals* (e.g. English *two*, where $x = 0$ and $y = 2$), which are not derived from other numerals. On the other hand, some languages only use a limited set of atomic numerals, not presenting the structure in (1). Such systems are being referred to as 'restricted'. They do not require a base; instead, they span a limited range of numbers, such as up to 2, 3, 5, or 10, without any systematicity. The

<footnote>atomic in a particular language, then numeral 42 in the same language could be 40 + 2 or 2 + 40, which is base-initial and base-final respectively.</footnote>
diversity of bases found in the numeral systems of South Asian languages is shown in Figure 1.

From Figure 1, we see that the most prevalent base in this region is decimal, as is the case for almost all Tibeto-Burman and Indo-Aryan languages spoken in this linguistic area. However, we do find the presence of vigesimal and mixed systems in the sample as well. Munda languages of the Austroasiatic family such as Ho, Kharia, Mundari, and Korku still exhibit a vigesimal system (Table 1). Mixed systems have multiple types of base, for example consider Sora language (duodecimal-vigesimal) below (Table 2). Here, we are not following the definition of imperfect decimal system given by Carrier (1981).

A few other languages like Onge, Jarawa, and Great Andamanese have restricted systems. These languages are not included in our analyses of base and internal order, as they have a very limited set of numerals. The other case present in the data, although quite rare, is the presence of a parallel system. As (Comrie 1999) noted with

<figure><img src="image_6.png" /><figcaption>**Figure 1:** Languages analyzed in this article. Colors represent the base of the numeral system, and shapes represent the language family.</figcaption></figure>
<table><caption>**Table 1:** Examples of decimal and vigesimal numeral systems in our database.</caption><thead><tr><th rowspan="2">Language</th><th colspan="2">Adi<br>(Tibeto-Burman)<br>Decimal</th><th colspan="2">Mundari<br>(Austroasiatic)<br>Vigesimal</th></tr><tr><th>Numeral</th><th>Gloss</th><th>Numeral</th><th>Gloss</th></tr></thead><tbody><tr><td>10</td><td>ijin</td><td>10</td><td>gel-eja</td><td>10-CL</td></tr><tr><td>20</td><td>ijin appi</td><td>10.2</td><td>hiši</td><td>20</td></tr><tr><td>30</td><td>ijin anum</td><td>10.3</td><td>mid hiši gel</td><td>1.20 + 10</td></tr><tr><td>40</td><td>ijin appi</td><td>10.4</td><td>bár hiši</td><td>2.20</td></tr><tr><td>50</td><td>ijin pilŋo</td><td>10.5</td><td>bár hiši gel</td><td>2.20 + 10</td></tr><tr><td>60</td><td>ijin akke</td><td>10.6</td><td>api hiši</td><td>3.20</td></tr><tr><td>70</td><td>ijin kinit</td><td>10.7</td><td>api hiši gel</td><td>3.20 + 10</td></tr><tr><td>80</td><td>ijin pi:ŋi</td><td>10.8</td><td>upun hiši</td><td>4.20</td></tr><tr><td>90</td><td>ijin konaŋ</td><td>10.9</td><td>upun hiši gel</td><td>4.20 + 10</td></tr><tr><td>100</td><td>liŋko</td><td>100</td><td>moče hiši</td><td>5.20</td></tr></tbody></table>

Haruai numerals, it is typical for the two (or more) numeral systems to coexist side by side at a given time. We call this case a *parallel system*. In the case of South Asian languages, the coexistence of two independent decimal and vigesimal systems in the same language generally indicates the scenario of movement from vigesimality towards decimality. This is the case of Kharia (Austroasiatic), where older generations still use the traditional vigesimal system while younger generations use the borrowed decimal system in the present day (Mamta 2024).

## 2.3 Internal order of complex numerals and higher multiplicative numerals

The second parameter we examine is the order of the constituents of complex cardinal numerals, which is known as the internal order of cardinal numerals as mentioned in the previous section. In terms of this order, a complex numeral in a system can be classified as base-initial or base-final, as introduced by Allassonnière-Tang and Her (2020). Languages that place the base after the atoms are known as base-final languages, whereas base-initial languages place the base before the atoms. Consider (2a) for Khoibu: in the numerals for 17 and 18, the base 10 precedes the atoms 7 and 8 respectively; therefore, the order of the teens (11–19) in this language is called ‘base-initial’. In contrast to that, in Car-Nicobarese, (2b), 7 and 8 precede the base 10 in 17 and 18 respectively, therefore defined as a ‘base-final’.
<table><caption>**Table 2:** Example of a mixed numeral system.</caption><thead><tr><th>Language</th><th>Sora<br>(Austroasiatic)<br>Mixed</th><th></th></tr><tr><th>Number</th><th>Numeral</th><th>Gloss</th></tr></thead><tbody><tr><td>10</td><td>gelji</td><td>10</td></tr><tr><td>11</td><td>gelmuy</td><td>11</td></tr><tr><td>12</td><td>migel</td><td>12</td></tr><tr><td>13</td><td>migel-boy</td><td>12 + 1</td></tr><tr><td>14</td><td>migel-bago</td><td>12 + 2</td></tr><tr><td>20</td><td>bokuri</td><td>20</td></tr><tr><td>30</td><td>bokuri gelji</td><td>20 + 10</td></tr><tr><td>31</td><td>bokuri gelmuy</td><td>20 + 11</td></tr><tr><td>32</td><td>bokuri migel</td><td>20 + 12</td></tr><tr><td>60</td><td>yakuri</td><td>3-20</td></tr><tr><td>90</td><td>unji-kuri-gelji</td><td>4-20 + 10</td></tr><tr><td>91</td><td>unji-kuri-gelmuy</td><td>4-20 + 11</td></tr><tr><td>100</td><td>bo sua</td><td>1-100</td></tr></tbody></table>

(2) (a) Khoibu [Tibeto-Burman] - base-initial (Mamta's fieldwork)
17 **cipləi-ini** **10+7**
18 **cipləi-təcət** **10+8**

(b) Car-Nicobarese [Austroasiatic] - base-final
(Chan et al. 2019, https://lingweb.eva.mpg.de/channumeral)
17 **sát sín** **7+10**
18 **héuhərɛ sín** **8+10**

Numeral systems have been investigated in the literature, mostly from a typological perspective, to describe and explain their cross-linguistic convergence and divergence (Comrie 1997; Greenberg 1978; Hammarström 2010). For instance, the distribution of numeral bases in languages worldwide is the main subject of a WALS chapter (Comrie 2013). However, most of the existing research considers numeral systems as homogeneous entities: for example, studies on base/atom order mostly consider that the order is rather synchronized cross-linguistically with only few exceptions. As an example, Allassonnière-Tang and Her (2020) considered a database of 400 languages, annotated as either base-initial or base-final. We argue that such a categorical approach is understandable as a starting point. However, the analysis should go much deeper to reflect the real diversity of numeral systems. For example, a language could have base-final hundreds and base-initial thousands. Calude and Verkerk (2016) also claimed that this issue of order in numeral components has
received little attention. They show that, in Indo-European languages, larger numerals display greater consistency in their constituent parts and ordering, but smaller numbers (11–19) show significant cross-linguistic heterogeneity. We further fill this gap of gradience in numeral studies by providing data and analyses from languages of South Asia, which are highly diverse in terms of numeral systems (Her et al. 2019; Mamta 2024).

An overview of our data shows that the internal order of teens and running numbers exhibit more variation than the internal orders of crowns, hundreds, and thousands (see Figure 2). Analyzing the borrowing scenario in the numeral systems, which will be briefly discussed in the next section, can provide an explanation for this variation.

The first panel of Figure 2 shows the ordering of running numbers, and the second one shows the order of teens (see (2) above). With a few exceptions, every language uses the same method for forming its running numbers: base-final or base-initial. Example (3a) for the running numbers demonstrates that they are ordered as

<figure><img src="image_7.png" /><figcaption>**Figure 2:** Internal order of the constituents in the formation of complex numerals in languages of South Asia. Shapes indicate language families, and colors indicate the constituent order.</figcaption></figure>
base-initial in Lotha. Example (3b) shows the reverse order that is base-final for Sanskrit.<fnref n="3" />

(3) (a) Lotha [Tibeto-Burman] - base-initial (Mamta's fieldwork)
35 **tʰum-rɔ** moŋo (3.10)+5

(b) Sanskrit [Indo-Aryan] - base-final (Mamta's fieldwork)
35 pənc-*trīn-*ʃət 5+(3.10)

The third, fourth, and fifth panels in Figure 2 show the internal order of thousands, hundreds, and crowns, respectively. Cross-linguistically, the predominant order is base-final for these three levels of numerals. Some exceptions are found only in the Tibeto-Burman language family, where the order for all three parameters is base-initial.

Consider the examples (4a–c):

(4) Internal order of (a) crowns, (b) hundreds, and (c) thousands (Mamta's fieldwork)

(a) i. Adi [Tibeto-Burman] - base-initial
50 **ijin** pilŋo 10.5

ii. Toda [Dravidian] - base-final
50 ebb-əd 5.10

(b) i. Thadou [Tibeto-Burman] - base-initial
200 **zə**-ni 100.2

ii. Bhoti [Tibeto-Burman] - base-final
200 **jib-gjə** 2.100

(c) i. Khoibu [Tibeto-Burman] - base-initial
4000 **lisin** pʰəli 1000.4

ii. Kota [Tibeto-Burman] - base-final
4000 nan *sauərmɛ* 4.1000

When comparing all the components (Figure 3), we observe that nearly all Tibeto-Burman languages generally have a base-initial order for complex numerals, and also for higher multiplicative numerals. By contrast, with a few exceptions, Indo-Aryan languages display base-final orders. The few exceptions in these two language families occur presumably as a result of language contact and language shift.

Like Indo-European languages (Calude and Verkerk 2016), the language families studied here (including Indo-Aryan, which is a part of Indo-European) also exhibit all three possible orders: (1) fully base-initial, (2) fully base-final, and (3) a combination of both orders at various points along the number line. Figure 3 clearly shows that the

<footnote n="3">³ In this study, in order to define the ordering of the complex numerals, we have taken 30 as a whole instead of 3.10.</footnote>
<figure><img src="image_8.png" /><figcaption>**Figure 3:** Internal order for running numbers, teens, thousands, hundreds, and crowns for the main families in the full dataset (Austroasiatic, Dravidian, Indo-Aryan, and Tibeto-Burman). The tree topology corresponds to the phylogeny inside each family, and supra-family relationships are linked following the global tree introduced in (Bouckaert et al. 2022). Observe that the ordering of teens and running numbers in Dravidian and Austroasiatic languages are mixed, but the crowns, hundreds, and thousands always remain base-final. This mixture might be the outcome of a contact scenario.</figcaption></figure>
base-final order of the Indo-Aryan lower numerals is an exception to this region, which is overwhelmingly base-final. Halbi and Hajong are exceptions to this. Halbi is predominantly spoken in the state of Chhattisgarh, India, and exhibits a close linguistic relationship with Gondi, a Dravidian language spoken in the southern regions of the country. Therefore, it might be due to this contact that Halbi has a vigesimal system and also that the order of the lower numerals is different from the rest of the IA languages (see Section 3.2). Hajong has a Tibeto-Burman sub-stratum (Phillips 2010), therefore at the lexical level, they exhibit some similarities with Tibeto-Burman languages. Dravidian, Austroasiatic, and Tibeto-Burman exhibit more or less base-initial order for lower numerals and base-final for higher. Tibeto-Burman is highly mixed. A very interesting fact is the change in the order of higher multiplicative numerals. For example, Spiti and Jad have base-final order for hundreds and base-initial for thousands, as shown in (5a, b) and (5c, d), respectively.

(5) Internal order of higher multiplicative numerals of Jad [Tibeto-Burman]
(Mamta's fieldwork)

(a) 200 - ni-gjə 2.100 (base-final)

(b) 300 - sum-gjə 3.100 (base-final)

(c) 2000 - toŋ-ni 1000.2 (base-initial)

(d) 3000 - toŋ-sum 1000.3 (base-initial)

Further, Dravidian languages such as Eastern Muria and Far Western Muria exhibit base-final order at lower levels. This also might be a case of contact as Chan et al. (2019) explain for the borrowing of Hindi numerals in Muria. Emeneau (1957) also documents the significant impact of Indo-Aryan languages on the Dravidian numerals. Many more examples have been presented by Blažek (2009) on the borrowing of numerals in Dravidian. The same situation has been found in Austroasiatic, for example, Birhor and Asuri are spoken in regions where Indo-Aryan languages are predominantly spoken. Asuri has many loanwords from Kurukh (Dravidian) (Chan et al. 2019), as Kurukh has also been spoken in the same region. According to Sidwell (1999), the Munda languages spoken in India have been greatly impacted by the nearby Indo-Aryan languages. Therefore, all these inter and intra family differences in ordering could be explained by language contact, language shift and adoption/adaptation from the dominant language of the particular region or linguistic area.

## 3 Quantitative analyses

In this section, we quantitatively analyze the data on cardinal numerals in South Asian languages. Languages from Austroasiatic, Dravidian, Indo-Aryan, and Tibeto-
Burman are included, since we have a sufficient number of data points for each of these language families. The goal in this section is to understand which variables are more informative of the structure of numeral systems and what their relative contributions are. We carried out two analyses: Firstly, we disentangle what variables are more informative for predicting the language families and the structure of the numeral system of a language via decision trees. This tells us how much the internal order of numerals depends on phylogenetic descent. It also tells us the interactive hierarchy between the variables. Secondly, we study the tradeoff between phylogenetic and geographical signals in the structure of the numeral systems cross-linguistically. This second part gives us an idea of how much this trait is influenced by language contact.

## 3.1 Vertical descent: decision trees

Decision trees are conditional inference trees based on Monte Carlo simulations (Breiman et al. 1984; Hothorn et al. 2006), that are used to extract the interaction between various variables included in a dataset. In this section, we use decision trees to make two predictions. First, we ask the model to predict the language family of a language using the following information of their numeral system: order of teens, order of running numbers, order of crowns, order of hundreds, and order of thousands. Second, we ask the decision tree to predict the order of running numbers using the following information: language family, order of teens, order of crowns, order of hundreds, order of thousands. The decision tree is expected to show which combinations of variables are statistically significant for predicting the outputs (language family and order of running numbers). It also shows the hierarchical importance of the variables that have a statistically significant effect.

Figure 4 shows the decision tree obtained when predicting the language family from the internal order of the complex numeral using the package ggparty (Borkovec and Madin 2025) in R (R Core Team 2025). Only the variables that have a statistically significant effect are displayed in the tree. The tree can be read as follows: If the order of thousands is base-initial, it is likely to be Tibeto-Burman (purple). If the order of thousands is base-final, we then look at the order of running numbers. If the order of running numbers is base-final, it is more likely to be Indo-Aryan (orange), while if it is base-initial, it is then more likely to be Dravidian (blue). Austroasiatic languages (red) are not correctly identified, as they are either classified as Indo-Aryan (Node 3) or Dravidian (Node 4).

The quality of the decision tree is assessed by three measures: accuracy, precision, and recall. First, the accuracy indicates how good the decision tree is at making predictions in general. It is the ratio of all the correctly predicted tokens within the
entire data set. As an example, if 60 out of 100 languages have their family predicted correctly, the accuracy is equal to 60/100 = 60 %. The accuracy should be higher than what the model would get by chance, which is represented by the majority baseline, i.e., what the model would get by affiliating all tokens to the category with the most tokens in the data set. For example, if within a data set of 100 languages, the largest language family has 40 languages, the majority baseline is 40/100 = 40 %. In our data, the largest family is Dravidian, with 49 languages. The majority baseline is thus 46/111 = 44 %. Therefore, the accuracy of the decision tree should at least exceed 0.44 to be considered better than chance. Then, to further evaluate how the decision tree performs on each language family, we consider precision and recall (Ting 2010). Precision evaluates how many tokens predicted as belonging to a category are actually from that category. For example, if the decision tree predicts that 16 languages are Tibeto-Burman and within those 16 languages, all of them are indeed Tibeto-Burman, the precision for the Tibeto-Burman family is 16/16 = 100 % (regardless of how many Tibeto-Burman languages are not identified). Recall quantifies how many tokens from a category are correctly predicted. As an example, if 20 Dravidian languages are found in the data set and 10 of these languages are correctly predicted as being Dravidian, the recall for the Dravidian language family is equal to 10/20 = 50 % (regardless of how many non-Dravidian languages are wrongly classified as Dravidian). To calculate the accuracy, the precision, and the recall, we first extract a confusion matrix (Table 3) to compare the predictions of the

<figure><img src="image_9.png" /><figcaption>**Figure 4:** Conditional inference tree for predicting language family. The information fed to the decision tree is the following: order of teens, order of running numbers, order of crowns, order of hundreds, and order of thousands. Only variables having a significant predictive effect are shown in the tree.</figcaption></figure>
decision tree with the actual language family of the languages in the data. The accuracy of the model is (0 + 44+27 + 14)/11 = 0.77, which exceeds by far the majority rule baseline of 0.44. The overall performance of the classifier is thus considered as good. The detailed numbers reflect that the decision tree is good at distinguishing Tibeto-Burman (Precision = 1, Recall = 0.88) and Indo-Aryan languages (Precision = 0.73, Recall = 0.93) languages. However, it is having difficulties identifying Austroasiatic languages, as they are labeled as Indo-Aryan or Dravidian by the decision tree. Some Dravidian languages are also incorrectly labeled as Indo-Aryan.

In a second analysis, we use the same method of a conditional inference tree to predict the order of running numbers using the information of language family, order of teens, order of crowns, order of hundreds, and order of thousands. The decision tree is shown in Figure 5. We see that the information on the language

<table><caption>**Table 3:** The confusion matrix of the conditional inference tree when predicting language families. The rows are the predictions of the decision tree and the columns indicate the actual values. Bold values indicate correct predictions.</caption><thead><tr><th>Prediction/Actual</th><th>Austroasiatic</th><th>Dravidian</th><th>Indo-Aryan</th><th>Tibeto-Burman</th></tr></thead><tbody><tr><td>Austroasiatic</td><td>0</td><td>0</td><td>0</td><td>0</td></tr><tr><td>Dravidian</td><td>12</td><td>44</td><td>2</td><td>2</td></tr><tr><td>Indo-Aryan</td><td>6</td><td>4</td><td>27</td><td>0</td></tr><tr><td>Tibeto-Burman</td><td>0</td><td>0</td><td>0</td><td>14</td></tr></tbody></table>

<figure><img src="image_10.png" /><figcaption>**Figure 5:** Conditional inference tree for predicting order of running numbers. The information fed to the decision tree is the following: language family, order of teens, order of crowns, order of hundreds, and order of thousands. Only variables having a significant predictive effect are shown in the tree.</figcaption></figure>
family and order of teens is the most relevant to predict the order of running numbers. If a language is Indo-Aryan, it is more likely to have a base-final order for running numbers. In other language families, a base-initial order of teens will give place to a base-initial order of running numbers, but a base-final order for teens will be indecisive for classifying the order of running numbers.

The accuracy of the model is 0.89, which is also much higher than the majority baseline of 0.67 (since most languages in the data are base-final, the majority baseline is equal to 74/111 = 67 %). The confusion matrix in Table 4 shows that most languages with base-initial running numbers are predicted correctly (Precision = 0.88, Recall = 0.97). The decision tree has more difficulties predicting languages with base-final running numbers (Precision = 0.93, Recall = 0.73) as around a third of them are predicted as being base-initial.

To summarize, the analysis by decision trees indicates that language families and the order of running numbers are highly correlated. Language families can be predicted better than chance by considering order of running numbers, while order of running numbers can also be predicted better than chance by considering language families along with other variables. Nevertheless, the analysis of decision trees does not consider spatial and phylogenetic autocorrelation simultaneously. The following section uses other quantitative methods to account for those limitations.

## 3.2 Horizontal descent: phylogenetic versus areal signal of borrowing

It is often the case that typological patterns are observed in a geographic area. Since genetically related languages tend to cluster geographically to some extent, the question often arises: Are these patterns due to shared ancestry (vertical transmission) or to language contact (horizontal transmission). In the current case-study, we have four main language families coexisting in the same area, together with a few smaller families and isolates (Figure 1). The variables of interest are the internal orders of the different constituents of complex numerals: teens, running numbers,

<table><caption>**Table 4:** The confusion matrix of the conditional inference tree when predicting the order of running numbers. The rows are the predictions of the decision tree and the columns indicate the actual values. Bold values indicate correct predictions.</caption><thead><tr><th>Prediction/Actual</th><th>Base-final</th><th>Base-initial</th></tr></thead><tbody><tr><td>Base-final</td><td>27</td><td>2</td></tr><tr><td>Base-initial</td><td>10</td><td>70</td></tr></tbody></table>
crowns, hundreds, and thousands. These seem to be relatively clustered by language family, although there are patterns repeating across families as well (Figures 2 and 3).

In order to disentangle these two effects, we run a BRMS regression considering the geographical and phylogenetic distance between each pair of languages as predictors (Dinnage et al. 2020). For the geographic component, we measured the geodesic distance (“as the crow flies”), while for the phylogenetic component, we used the patristic distance from the global tree introduced in (Bouckaert et al. 2022). The latter considers the internal structure for the family tree of each language family according to Glottolog (Hammarström et al. 2024), and connects the unrelated families at higher levels by geographical proximity.

We used Bayesian Regression Models Using “Stan” (BRMS) with a categorical distribution implemented in the brms (Bürkner 2017) package in R (R Core Team 2025). We ran 5 regressions for each set of numerals, where the predictors are phylogenetic and geographic distances, as random effects, while the dependent variable is the binary variable “word order” for each regression (orders of running numbers, teens, thousands, hundreds, and crowns). We then take the total variance and split it according to how much of it is explained by each of the two predictors – phylogenetic distance and geographic distance – and how much remains unexplained by the model. The contributions of these two predictors for each of the 5 regressions are shown in Figure 6. We can see that, in all cases, phylogeny accounts for the highest proportion of the total variance. However, the geographical contribution is non-negligible. For example, for the order of teens, 91 % of the variance is explained by phylogenetic distances, 5 % from geographic distances, and 4 % remains unexplained; while for running numbers these are 94 %, 2 %, and 4 % respectively.

As seen on the data distribution in Figure 3, apart from Tibeto-Burman languages, the word orders for crowns, hundreds, and thousands show no variation, being base-final in all other 3 major families. In addition, if we look at the behavior of word order for numerals inside each language family, the order of teens is the least homogeneous, as well as the one most evenly distributed (base-final 49, base-initial 62). We propose this intra-family heterogeneity in the order of teens is due to contact, as suggested by the considerably higher dependence on geographic distance in the order of teens with respect to the order of running numbers (Figure 6).

We created a BRMS classifier whose output is the probability for a language to have a certain word order for teens (Base-Initial or Base-Final) based on its position in the phylogenetic tree and the remaining data as an input (but agnostic about the specific datapoint). We then compare this expected probability with the actual value, to corroborate if both values agree. In the cases where we see a disagreement plus when we have a plausible argument for attributing it to contact, we add a dashed line and the legend says “likely influence”.
<figure><img src="image_11.png" /><figcaption>**Figure 6:** Effects of phylogeny and areality (contact) in the internal order of different complex numerals.</figcaption></figure>

Figure 7 shows the output of our classifier for the order of teens in each language, based on their position in the phylogeny and the rest of the data, as well as its comparison with the actual values for this variable (see Figures S1–S4 in the OSF repository for equivalent plots for the other word orders). The color of each dot represents the actual value for the word order of the teens: base-final is represented in blue, and base-initial in yellow. The position of each dot in the vertical axis represents the probability of the language having a base-initial word order for teens, i.e., the dots in the very top are classified as base-initial, while those on the very bottom are classified as base-final. All the languages in a given family with a unique word order are then grouped in a box plot to simplify visual inspection. We can see, firstly, that Tibeto-Burman is completely predicted as base-initial, as expected, since all data points in this family have this value. Indo-Aryan, with a great majority of base-final, has only one language with base-initial (Hajong). This is not correctly classified by the model (with probability 0.2 for base-initial).

From a comparative-historical perspective, some linguists claim that, although Hajong is classified as an Indo-Aryan (IA) language (Eberhard et al. 2015), there may be a Sino-Tibetan (ST) substratum. In terms of ethnicity and culture, the Hajong people are more similar to the nearby Sino-Tibetan people groups, including the Koch and Garo, than they are to the Bengali population (Phillips 2010). Having a Sino-
<figure><img src="image_12.png" /><figcaption>**Figure 7:** Classification of internal order for teens in the four largest families.</figcaption></figure>

Tibetan stratum could be the reason for the base-initial order of teens. Emeneau (1956) and Masica (1971) argue that the linguistic diversity of India, encompassing numerous languages and language families, has been shaped by extensive historical interactions among their speakers. These interactions have fostered linguistic convergence and contributed to the development of India as a distinct linguistic area, and that can be seen here in the numerals as well. Emeneau (1956) also calls Northeast of India as a miniature 'linguistic area' where the two predominant language families (Tibeto-Burman and Indo-Aryan) share features due to areal proximity leading to convergence and language change. The overall structural drift is mainly towards the Indo-Aryan patterns due to the overwhelming dominance of the Indo-Aryan languages in this region. But the numerals in most of the cases stays untouched of this influence in the region, as we see at 'teen' level, TB languages retain their base-initial order.

Each dot represents one language: The x-axis stands for the language family, and is jittered to improve readability. The y-axis is the output of the classifier, i.e., the probability for the order of teens being base-initial, based on phylogenetic and areal information only. The color represents the actual value of the order of teens. The arrows show likely areal influences for explaining intra-family variation.

Finally, Austroasiatic and Dravidian tend to have base-initial teens from genetic descent. However, the great influence of Indo-Aryan makes several languages in
these families to have a base-final order. Notice that many of these base-final lan-
guages are classified with a low probability of being so (between 0.45 and 0.65 for
Austroasiatic, with a median at 0.55, and between 0.6 and 0.75 for Dravidian, with a
median at 0.7, compared with the over 0.95 median for Indo-Aryan for base-final and
over 0.95 median of base-initial for Tibeto-Burman). Here, we can see how contact
with Indo-Aryan influence shifts certain Austroasiatic and Dravidian languages from
their expected base-initial system to base-final.

Examples of this, where Dravidian and Austroasiatic languages have Base-initial teens possibly due to contact are Tamil (D), Telugu (D), Malayalam (D), Kannada (D), Ho (AA), Khasi (AA), Mundari (AA), and Santali (AA). For example, in Tamil ‘eighteen’ is /pedin-eṭṭu/ which is (10 + 8), and similarly in Ho ‘eighteen’ is /gel-irlija/ which is (10 + 8). In both cases, base 10 precedes the non-base (atom) numeral.

Peterson (2017) investigates centuries-long language contact between Indo-
Aryan and Munda languages in eastern-central India, with Jharkhand serving as the
focal region of a broader convergence zone extending into Bangladesh, Bihar, Nepal,
and Odisha. The analysis highlights bidirectional influences characterized by
extensive lexical borrowing from Indo-Aryan into Munda alongside shared mor-
phosyntactic innovations.

In Dravidian languages like Gondi, Duruwa, Brahui, Kui and many others, teens
are borrowed from Indo-Aryan. For example, in Gondi, numerals representing 1 to 6
are traditional Dravidian numerals and higher numerals are borrowed from Indo-
Aryan. But the interesting fact in our data is that those languages retained their
traditional vigesimal systems and just borrowed the lexical forms. In the Chan et al.
(2019) database, it has been seen that the Northern Gondi has a decimal system with
traditional Dravidian numerals from 1 to 7, some dialects have 9 and 10, after 6 they
borrow Marathi or Hindi numerals. Similarly, Hindi influence can be seen in Adi-
labad Gondi on numerals like 8, 9, 10, 11, and 20. The Chan et al. (2019) database also
emphasizes that Adilabad Gondi has a decimal numeral system mixed with tradi-
tional numerals with loanwords, but Adilabad Gondi retains more Dravidian nu-
merals than Northern Gondi. The traditional form for ‘eighteen’ in Gondi is
/pədɛŋmidi/, and the borrowed form is /ɑṭʰra/ which is the same as Hindi and Marathi
‘eighteen’. Therefore, it is clearly seen in this example that the traditional order of
teens of Gondi was base-initial, which shifted to base-final due to the contact with
Indo-Aryan. Similar to this, another Dravidian language Duruwa, which also uses a
traditional vigesimal system, only retains Dravidian numerals 1–5; for numbers
beyond 20, they switch to an Indo-Aryan numeral system combined with native
terms (Chan et al. 2019). Sridhar (1978) outlines the variation on the nature as well as
extent of Indo-Aryanization both within and across the Dravidian languages. Hock
(1996, 2001) also explains the convergence in the development of shared linguistic
features in this subcontinent.
Similar situations have been observed for some Austroasiatic languages like Asuri, Gadaba, Gta', and Juang. As mentioned above, Asuri has only retained the first three traditional Munda numerals, and they have taken the decimal system from the neighboring Indo-Aryan languages. Table 5 shows the Asuri (AA) and Hindi numerals for 1 to 20. The forms in bold are Asuri's traditional form for numerals 1 to 3, the other forms are borrowed. For comparison, Ho (AA) numerals are also presented in the table. In Dravidian again, Duruwa (D) retains their traditional vigesimal base system and numeral 1 to 5 (for comparison see (D) Tamil forms), and further it borrows from Indo-Aryan. Therefore, again, the order of their teens changes to base-final from base-initial here.

Cross-linguistically, borrowing of numerals is rather prevalent (Matras 2007). There are several factors that can trigger numeral borrowing. According to Matras (2007), formal factors like trade, education, and institutional discourse lead to this kind of borrowing. This happens frequently because the borrowed system is more functional or highly regarded in the particular linguistic area. This can occur either

<table><caption>**Table 5:** Numerals one to twenty of Asuri and Hindi. Numerals in bold represent indigenous forms from Austroasiatic and Dravidian origin respectively, while those in italics are of Indo-Aryan origin. Bold values indicate correct predictions.</caption><thead><tr><th>Numerals</th><th>Asuri (AA)</th><th>Ho (AA)</th><th>Duruwa (D)</th><th>Tamil (D)</th><th>Hindi (IA)</th></tr></thead><tbody><tr><td>One</td><td>mijəd</td><td>mijəd</td><td>okut</td><td>ondru</td><td>ek</td></tr><tr><td>Two</td><td>bərija</td><td>bərija</td><td>irquk</td><td>irrəndu</td><td>do</td></tr><tr><td>Three</td><td>peja</td><td>əpijə</td><td>mu:nquk</td><td>mu:ndru</td><td>tin</td></tr><tr><td>Four</td><td>car</td><td>upnijə</td><td>na:luk</td><td>na:ngu</td><td>car</td></tr><tr><td>Five</td><td>pāc</td><td>moijə</td><td>ceŋquk</td><td>aindu</td><td>pāc</td></tr><tr><td>Six</td><td>c'eh</td><td>turuijə</td><td>c'eh</td><td>a:ru</td><td>c'he</td></tr><tr><td>Seven</td><td>sat</td><td>əijə</td><td>sat</td><td>elu</td><td>sat</td></tr><tr><td>Eight</td><td>aṭh</td><td>irlijə</td><td>aṭh</td><td>ettu</td><td>aṭh</td></tr><tr><td>Nine</td><td>nɔ</td><td>ərejə</td><td>nɔ</td><td>onbədu</td><td>nɔ</td></tr><tr><td>Ten</td><td>dəs</td><td>geljə</td><td>dəs</td><td>pattu</td><td>dəs</td></tr><tr><td>Eleven</td><td>gjara</td><td>gelmijəd</td><td>gjara</td><td>pationdu</td><td>gjara</td></tr><tr><td>Twelve</td><td>bara</td><td>gelbərija</td><td>bara</td><td>pannirəndu</td><td>bara</td></tr><tr><td>Thirteen</td><td>tera</td><td>geləpijə</td><td>tera</td><td>padimu:ru</td><td>tera</td></tr><tr><td>Fourteen</td><td>cəuda</td><td>gelupnijə</td><td>cəuda</td><td>padina:ngu</td><td>cəuda</td></tr><tr><td>Fifteen</td><td>pəndra</td><td>gelmoijə</td><td>pəndra</td><td>padina:indu</td><td>pəndra</td></tr><tr><td>Sixteen</td><td>sola</td><td>gelturuijə</td><td>sola</td><td>padina:ru</td><td>sola</td></tr><tr><td>Seventeen</td><td>satra</td><td>geləijə</td><td>satra</td><td>padinebu</td><td>satra</td></tr><tr><td>Eighteen</td><td>aṭhara</td><td>gelirlijə</td><td>aṭhara</td><td>padineṭtu</td><td>aṭhara</td></tr><tr><td>Nineteen</td><td>unnis</td><td>gelərejə</td><td>unnis</td><td>pattonbədu</td><td>unnis</td></tr><tr><td>Twenty</td><td>bis</td><td>hisi</td><td>koqek/bis</td><td>irubədu</td><td>bis</td></tr></tbody></table>
when a language has limited or non native terminology for specific numbers and quantities, or when the borrowed system is simpler to learn and is more in use in daily lives. For example, the Great Andamanese have nearly lost their numeral system and have adopted Hindi cardinal numerals (Chan et al. 2019).

# 4 Concluding discussion

This study shows that while orders of crowns, hundreds, and thousands are quite homogeneous across language families, the order of teens and running numbers is rather versatile. Since teens are used more frequently than higher numerals, they might be more resistant to borrowing. This effect is commonly observed cross-linguistically in domains such as verbal morphology. As an example, a similar frequency-driven phenomena can be seen in frequently used verbs that has an irregular past tense form in English (cf. go/went, eat/ate, vs. mention/mentioned, describe/described) (Viberg 2002). Analyses based on decision trees and regression models further support our qualitative analysis. On the one hand, the decision trees show that language families can be predicted by using order of thousands and order of running numbers. This suggests that while borrowing occurred at different levels in different language families, there is still a phylogenetic signal of numeral systems. Austroasiatic languages are probably in a transition state of borrowing numeral systems, which results in mixed order patterns. Using decision trees to predict the order of running numbers shows a similar pattern. Order of teens is one of the main predictors considered as significant. Language family is also a strong predictor, which is also expected since language family is correlated with order of running numbers. On the other hand, the regression analysis allows us to further quantify the weight of phylogeny and areality. The results also match with the qualitative analysis and the output from the decision trees: while there is still a phylogenetic signal, the geographic signal is not negligible, which suggests the presence of borrowing.

Summarizing, the main contributions of this paper can be listed as follows. First, we fill a gap of data on numeral systems in South Asia. We provide the first typological overview of numeral systems in the area, which can be used to infer weights and depths of language contact and borrowing between language families in the area. Second, we provide a structured framework for analyzing numeral systems in terms of pattern. Most previous studies considered the internal order of complex numerals as binary variables, with only one value per language. In our study, we go further by splitting the variable of internal order into orders of teens, crowns, running numbers, hundreds, and thousands. Differentiating between the order of crowns and running numbers is also extremely relevant to future typological studies, as we show that order of crowns is much more likely to be borrowed than order of
running numbers. Finally, our study also has a societal impact. We demonstrate that numeral systems are highly complex and diverse. However, this diversity is disappearing quickly. It is thus of the utmost importance to at least document this diversity, and, if possible, to preserve it.

## Abbreviations

AA Austroasiatic

BRMS Bayesian regression models using "Stan"

Drav., D Dravidian

IA Indo-Aryan

SA South Asia

SAND South Asian numeral database

TB Tibeto-Burman

**Acknowledgments:** We thank Martin Haspelmath for his useful feedback on an early version of this manuscript, and to Hedvig Skirgård for her comments on the code. This research was funded by the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme for the project "Evolution of Cognitive Tools for Quantification (QUANTA)" (grant agreement No. 951388).

**Data availability:** All data and code are stored in the OSF repository. https://osf.io/7x8b2/overview

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**Supplementary Material:** This article contains supplementary material (https://doi.org/10.1515/stuf-2025-2021).