A lot of research into linguistic relativism revolves around questions which were once summarised in the Sapir-Whorf Hypothesis. This post consists of an essay I wrote a few years back when I was at university. It is a summary of the history of linguistic relativism, which outlines its main fields of research and their results. It is written in a rather boring, dense style, and I promised myself that I will soon reformulate it, so that people who are not used to reading this kind of essay can also learn something about linguistic relativism and how thought, language and culture might be interrelated. But for the time being, I only have this one. So, here goes:
The Sapir-Whorf Hypothesis
This essay traces the history of the Sapir-Whorf Hypothesis (SWH)  and explores current developments in linguistic relativity research. It also highlights an area for further research into the relationship between Language, Thought and Reality .
The SWH states that the structure and lexicon of a language influence how its speakers perceive the world (2,3). It is named after anthropologist and linguist Edward Sapir (1884-1939) and his student Benjamin Lee Whorf (1897-1941). Linguistic relativism, however, had been around long before: in ancient Greece, Aristotle engaged with the idea that the structure of language reflects the structure of thought (4), and in 18th and 19th century Germany, linguistic relativity became the subject of philosophical enquiry amongst philosophers like Herder and von Humboldt, the latter considering thought and language inseparable and the diversity of languages reflecting a diversity of worldviews (3,5).
Through studying the Inuit and in opposition to the ethnocentric evolutionism in American anthropology with its disdain for speakers of unwritten languages, anthropologist Franz Boas (1858-1942) suggested that unwritten languages are as complex as written ones and that languages do not prevent speakers from acquiring concepts for which they lack words, because culture can shape language so that new thoughts can be expressed in it (7).
Boas’ student Sapir believed that people’s worldviews are influenced by the tools their languages provide to interpret the world, stating:
“No two languages are ever sufficiently similar to be considered as representing the same social reality. The worlds in which different societies live are distinct worlds, not merely the same worlds with different labels attached.”(8)
Whorf, who studied the lost writing systems of the Mayas and the languages of the Aztec and Hopi, was fascinated by the different concepts he believed speakers of different languages gain, claiming: “We dissect nature along lines laid down by our native languages” (9,10,1).
Neither Sapir nor Whorf suggested that a culture’s worldview is determined only by its language. Linguistic relativism as promoted by Boas, Sapir and Whorf emphasises that language, thought and culture are inextricably linked, each language containing its own worldview and the semantics of different languages being incommensurable (10,11).
Whorf received much posthumous criticism. One of his critics, Lenneberg claimed that the mere presence of linguistic differences between cultures is no evidence for the presence of psychological differences  and that many of the conceptual differences Whorf found between Indian languages and English are due to awkward translations, with Whorf, for example, translating all different meanings of prefixes attached to Apache verbs and comparing such meaning sequences to the overall meaning of English sentences. According to Lenneberg, Whorf’s translations also distort the fact that language contains metaphors whose literal meanings speakers are unaware of (12). However, rendering the literal meanings of metaphors to show conceptual differences can be justified: while speakers may not be aware of a metaphor’s literal meaning, it can still shape their worldview.
Pullum criticised Whorf for referring to Eskimo as having seven distinct words for snow  and for thereby misrepresenting Boas’ statement that Eskimo has distinct roots to form words related to snow just as English has morphologically distinct words for things related to water (14). Moreover, stating that – contrary to Whorf’s claim – Hopi uses spatial imagery to express temporal concepts, mainly through postpositions and adverbs, Malotki criticised Whorf for representing Hopi language as timeless and its speakers as having no concept of time (9,13).
Neither Sapir nor Whorf stated a hypothesis. Against the background of Einstein’s relativity theory, Whorf wrote of a “linguistic relativity principle”, implying that thought and cognition, like space, time and mass, are relative – to the structures of the language with which they have evolved (1,9).
What is referred to as the SWH goes back to Lenneberg and Brown, who reformulated Whorf’s “linguistic relativity principle” as a hypothesis:
1. Structural differences between language systems will, in general, be paralleled by non-linguistic cognitive differences, of an unspecified sort, in the native speakers of the two languages.
2. The structure of anyone’s native language strongly influences or fully determines the worldview he will acquire as he learns the language. (6)
The SWH can be a weak claim stating that language facilitates or influences thought (linguistic relativism) or a strong claim stating that thought is entirely dependent upon language (linguistic determinism) (2,9).
Demise and Revival
Much criticism against the SWH came from cognitive psychology, which at the time held that concepts come first, with language only naming them, and from universal grammar, claiming that syntax is an innate human mechanism underlying all language. Their arguments – people’s difficulty to put thoughts into words, the fact that linguistic phenomena such as ambiguity, deixis and co-reference require extra-linguistic resources or that people can mentally rotate objects by using imagistic representations – concerned linguistic determinism, which was also disproved by the discovery of universal tendencies in colour categorisation, ethnobotanical nomenclature and kinship terms, suggesting that thought and perception cannot entirely depend on language (3,13,11). But evidence against linguistic determinism often served as an argument against all forms of the SWH, and when it was shown that a previous claim supporting it – that speakers of Chinese, which does not clearly mark counterfactuals, cannot recognise counterfactual arguments – was based on mistranslations, the SWH was completely discredited (13,15).
Its revival began in the 1970s, when researchers began to examine how language relates to non-linguistic phenomena like cognition, finding evidence for weaker forms of the SWH (16,3). In the 1990s, linguistic relativity research was inspired by Slobin’s “thinking for speaking” hypothesis, which holds that language influences thought whenever people think with the intention to speak, selecting aspects of their mental representations which are relevant for their specific language (3,17).
With growing evidence that human minds are modular and deal with various domain-specific tasks, the idea that specific aspects of language influence specific aspects of cognition gained ground (2). It was suggested that cognition is organised on three levels, the lowest involving physiological mechanisms, the highest being concerned with meaning, and thought processes in between relying significantly on language, translating visual or auditory input into symbolic meaning and instilling cognitive habits (18,15,3).
On the following pages, three areas of linguistic relativity research will be discussed: colour perception, spatial metaphors for time and numerical cognition.
The question whether or not colour terms influence people’s perception and whether colour categories are determined arbitrarily or not has been the subject of much debate. Since we know today that many aspects of colour perception are influenced by neurophysiological factors, the area is not ideal for linguistic relativity research. Nevertheless, it has remained a major field and continues to yield interesting results (2,19).
In 1953, Lenneberg and Roberts found that speakers of Zuni, a language with only one word for yellow and orange, have more difficulty recalling these colours than English speakers, presumably because they lack terms for them (20). This was considered evidence for linguistic relativity. However, in 1969, Berlin and Kay, who studied colour perception in speakers of 20 different languages, discovered universal patterns, claiming that colour terms in all languages emerged from 11 focal colours, which evolved in a five-stage process, with black and white appearing first, red second, yellow, green and blue third, brown fourth, and purple, pink, orange and grey fifth, so that languages with only two colour terms always have words for black and white and languages with three colour terms words for black, white and red (19,21). This view became predominant despite the fact that its empirical basis was rather questionable: the set of participants often contained only one bilingual person per language and the 11 colour terms miraculously corresponded to the most frequent American-English terms in Thorndike’s “Teacher’s Handbook”  (15).
In 1972, Heider confirmed the universalist account in a study of Dani, a New Guinea language with only 2 colour terms – light and dark: Dani speakers memorised focal colours better than non-focal ones despite lacking terms for them and behaved in cognitive tasks as if they had the English system. Heider claimed that colour memory was influenced not by language but by perceptual salience. Heider’s material was later found to be biased, with focal colours being more saturated than non-focal ones. Using a new test array, Lucy and Shweder, in 1979, proved Heider wrong and claimed that colour recognition was based not on focality but on the availability of colour terms (15,3).
Moreover, in 1999, Davidoff et al. (22), who studied Berinmo, a Papua New Guinea language, found categorical colour perception at language-defined boundaries and concluded that there are no universal foci. They claimed that different category boundaries in Berinmo and English correlate with and possibly cause differences in colour memory, learning and discrimination (22,19).
The debate about universal tendencies versus relativity in colour naming has not been resolved yet. It is likely that universal forces determine colour naming and that the spectrum is not segmented arbitrarily, but that naming differences – where they exist – correlate with differences in colour memory, learning and discrimination (19).
Moreover, recent findings suggest that brain organisation may be relevant for linguistic relativity research, with colour names influencing colour perception mainly in the left hemisphere (19): in a recent study, Gilbert et al. (24) presented participants with coloured squares, one of which, the target, had a different colour than the rest. They found that participants identified targets faster across lexical categories than within them (e.g. a blue amongst greens versus a green amongst greens of a different hue). But this effect only occurred when stimuli were presented to the right visual field (RVF), with visual fields projecting contra-laterally to the cerebral hemispheres and the LH – in right-handed individuals – being specialised for language. The effect disappeared with verbal interference tasks – remembering eight-digit numbers – but not with spatial ones. Gilbert et al. concluded that language influences colour discrimination in the RVF but not in the LVF and that this lateralisation has a verbal basis, with language activating lexical codes online (24).
Drivonikou et al. (25) examined the boundaries between blue and green, blue and purple as well as blue and pink and found that colour discrimination across lexical categories was faster than within categories and that this effect was stronger for stimuli displayed in the RVF, but – unlike Gilbert et al. – they also found a significant, albeit weaker, category effect in the LVF. This LVF/RH effect could be language-based like the RVF/LH effect, but would have to cross the corpus callosum to reach the RH, which would explain why it is weaker. This explanation is supported by the longer response times in Drivonikou et al.’s study and by another study on a Korean colour boundary, in which fast participants showed category effects only in the RVF/LH, whereas slow participants showed them in both visual fields (26).
Another explanation is that category effects in the LVF/RH may reflect universal categorical colour discrimination, which may also be present in infants (25). Although the existence of pre-linguistic categorical colour perception is controversial, some researchers speculate that, if it exists, pre-linguistic categories could be a starting point for the elaboration of linguistic categories. Toddlers appear to have categorical perception for stimuli displayed in the LVF instead of the RVF, and the shift from the LVF to the RVF could be caused by the acquisition of colour terms (19). Franklin et al. (27) studied two groups of children – learners, who had not yet learned colour terms, and namers, who already knew these terms – and found that learners showed categorical perception in the LVF but not in the RVF, whereas namers showed categorical perception in the RVF but not in the LVF, suggesting that it is the acquisition of colour terms that causes the shift. The fact that split-brain patients show no trace of categorical perception in the LVF/RH suggests that pre-linguistic categories would be completely erased after such a shift (27,19).
Lateralised language-dependent perception may not be limited to colours: Gilbert et al. (28) also found a RVF/LH versus LVF/RH asymmetry when using animal silhouettes as stimuli: when stimuli were presented in the RVF, participants were faster at identifying targets across lexical categories and slower at identifying targets within categories (e.g. a cat amongst dogs versus a cat amongst other cats). Again, the effect decreased with verbal interference tasks but not with spatial ones. On a perceptual account, it is possible that the visual input activates a lexical representation, which, through feedback mechanisms, changes the perception of the input, so that the activation of “dog” makes the stimulus look more like a prototypical dog. Within the same lexical category, target identification becomes difficult, because stimuli that look like a prototype are similar to each other, but between categories, identification is easier, because cats and dogs have different prototypes. It is also possible that, on a post-perceptual account, a lexical difference complements a perceptual difference and thus accelerates target identification between categories, whereas the same name for targets and distractors competes with perceptual differences, slowing identification down (28). Further research shall reveal which linguistic effects found in colour perception generalise to other aspects of cognition and which ones are unique to colours (19).
Spatial Metaphors for Time
With increasing evidence that some aspects of colour perception are influenced by neurophysiological constraints, linguistic relativity researchers began to ask whether the influence of language on thought may be greater for abstract concepts like time. They began to study how speakers of different languages perceive and metaphorically conceptualise time. In language, time is often represented in spatial metaphors, but it is not entirely clear whether people only use them when speaking about time or whether they also mentally represent time in spatial terms (29,30).
Casasanto & Boroditsky (29) carried out a series of non-linguistic experiments and found an asymmetrical relationship between space and time, with temporal language depending much more on spatial metaphors than spatial language depends on temporal representations: people are perfectly able to ignore temporal information when gauging distances but cannot ignore spatial information when gauging duration.
While spatiotemporal metaphors may be universal, the specific space/time mappings vary across languages: English speakers, for example, linguistically represent the future as lying in front of themselves and Mandarin speakers as lying below themselves (13). The Aymara of South America, together with speakers of Quechua, metaphorise the future as lying behind and the past as lying in front of themselves. “Qhipa uru”means “back days” and describes the days to come based on the idea that one can see the past but not the future, the word “nayra” for “front” also meaning “eye”/“sight”. Aymara speakers also use gestures to behind themselves when speaking about the future, suggesting that this is not a mere linguistic metaphor but a cognitive reality for them (31,32).
A rare representation of time is that of the Pormpuraawans, an Australian aboriginal community, who represent time according to cardinal directions, moving from east to west like the sun. When asked by Boroditsky and Gaby (33)to arrange pictures showing progression (e.g. a man at different ages) in the correct temporal order, Pormpuraawans did not arrange them in relation to themselves but with earlier stages in the east and later ones in the west. Gestures to the east accompanying their talk about past events indicate that they also mentally represent time this way. As shown in previous studies with speakers of languages with absolute terms for directions, Pormpuraawans are extremely good at staying oriented: all Pormpuraawans studied were able to point north, south, east or west correctly within a 20° range, whereas only 36 % of Americans pointed correctly within a 60° range, the rest being either 45-90° off compass or completely unable to indicate any direction at all.
Instead of relying on gestures showing that people mentally represent time in the spatial metaphors of their native languages, Casasanto (13) carried out psychophysical experiments comparing time perception in English speakers, who frequently represent time as a distance (“a long time”) and only rarely as a volume (“saving time in a bottle”), and in Greek speakers, who often speak about time in terms of volumes, using the words “megalos” (large, big) or “poli” (much). English and Greek speakers had to estimate the duration of brief events, which were presented along with distracting information – a container gradually filling up or a line growing across a screen. Distracted by interfering distance information, English speakers judged events involving long lines to last longer than events of the same duration involving short lines, whereas Greek speakers, distracted by the container filling, judged events involving full containers to last longer than events of the same duration involving less full containers.
The ability to estimate brief durations, given that pre-linguistic infants and animals also have it, cannot evolve through the use of temporal metaphors in language alone, as some relativists suggest. While some representations must exist pre-linguistically in both dimensions, pre-linguistic temporal representations may not be good enough for thinking about time the way adult humans do. The laws of physics being the same everywhere in the world, Casasanto suggests that pre-linguistic concepts of time as a distance and of time as a volume may exist in all infants and that language-specific mappings become reinforced and predominant as we speak (13). As far as space is concerned, McDonough et al. (34) found that English and Korean babies aged 9 months can make spatial distinctions for both English and Korean, whereas babies aged 18 months have lost this ability. Further research shall reveal if a similar pattern also exists for time.
When it comes to linguistic influences on numerical cognition, researchers have pointed out that there is an important difference between linguistic influences on processes in which language serves as input/output material and influences on processes that are overlearned (e.g. simple mathematical operations), the latter persisting even when no language is involved. The finding, for example, that the digit memory span of Welsh speakers is shorter than that of English speakers is not considered strong evidence for the SWH, because the memory span depends on the length of stimuli, and Welsh digit names are longer than English ones (15).
However, some studies found language-specific differences in number processing which could not entirely be explained by mere production problems: children speaking Belgian-French, for example, which has a simpler number system than Standard French, make fewer mistakes in number production than same-aged French children: saying “sixty-ten” (soixante-dix) for 70, “four-twenty” (quatre-vingt) for 80 and “four-twenty-ten” (quatre-vingt-dix) for 90, as Standard-French speakers do, does impede children’s performance in number processing (35,15).
Another example for linguistic relativity in numerical cognition is related to the simple number systems of Asian languages: while Western languages have irregular names for teens and decades, many Asian languages have a regular base-10 system with teens described as two-digit numbers (ten one, ten two) and decades as numbers with the ten’s names multiplied (two ten, three ten). While “13” means thirteen individual items for English speakers, it means a 10 + 3 items for Asians, which helps Asian children understand numbers faster: when they have to represent tens and units with blocks, they use two different types of blocks for tens and units, whereas same-aged Western children represent them with an equivalent amount of unit blocks (15,36).
Another study into linguistic influences on numerical cognition was carried out by Brysbaert et al. (15), who tested French and Dutch speakers who had to add two-digit and one-digit operands (e.g. 24+1) presented either verbally or in Arabic numbers. In French, the word order for two-digit numbers corresponds to the way in which the number is written (24 = vingt-quatre, twenty-four), whereas in Dutch, the word order between the unit and the ten is reversed (24 = vierentwintig, four-and-twenty). While Brysbaert et al. did find language differences, these differences disappeared when participants typed their answers instead of uttering them, suggesting that the differences were due to the fact that language was used as input/output material and that mathematical operations as such are not based on verbal processes.
Brysbaert et al.’s findings do not invalidate relativist claims that language can facilitate or impede access to numerical concepts. The above mentioned examples come from fully literate and numerate societies. However, simple mathematical concepts might not be grasped by speakers of Oksapmin of Papua New Guinea, for example, whose counting system has no base structure, relies on body part analogies and only goes up to 27 , or by the Pirahã,an Amazonian hunter-gatherer tribe, who only distinguish between one, two and many, and even for these concepts only use comparative or relative expressions, “hói” meaning ”small size”, “hoí” meaning “somewhat larger size” and ”baagiso” meaning “many” (38,39,40,41).
Pirahã speakers probably pose the greatest challenge to linguistic universalism. Their language lacking words for exact numbers, Pirahã cannot perform simple numerical tasks (38,39). In an experiment involving everyday objects such as batteries, Gordon (38) had Pirahã carry out various numerical tasks such as looking at an array of batteries and recreating the same array or drawing a line for each battery displayed, which was a difficult task for them, because they do not write or draw. Participants’ numerical cognition turned out to be strongly influenced by their lack of numerical language: while they performed accurately in tasks involving 2 or 3 items, their performance deteriorated in tasks involving 4-10 items. However, their answers increased with increasing set sizes, suggesting that they used the analog magnitude system, one of the two signatures humans and some animals have to estimate quantities without counting, the other being the parallel-individuation system. Used for large approximate quantities, the analog system enables estimations and shows a constant coefficient of variation, with errors relative to the set size, whereas the parallel-individuation system for small numbers is precise and quick but only enables identification of up to three items (38,39).
In a similar experiment, American English speakers were tested alongside Pirahã, while a verbal interference task was imposed to prevent number rehearsal, Frank et al. (40) demonstrated that when their verbal resources are occupied, English speakers show similar results in matching tasks as Pirahã. They had Pirahã and English speakers carry out a one-to-one matching task (participants saw a certain number of spools of thread placed evenly spaced in a line and had to lay out the same line using the same quantity of un-inflated balloons), an uneven matching task (the spools were grouped into irregular sets), an orthogonal matching task (the line of spools stretched away from participants), a hidden matching task (participants had to replicate the line of spools after the experimenter had concealed it) and a nuts-in-a-can task (participants watched the experimenter put a certain number of spools into an opaque container before they had to do the same) (40,41). For simple one-to-one and uneven matching tasks – even with more than 3 items – Frank et al. did not replicate Gordon’s findings: they were easy for both English and Pirahã speakers, suggesting that one-to-one matching, which only requires the understanding that one item more or less makes a difference to the quantity of a set, is possible without numerical language. However, Frank et al. did find that Pirahã have difficulty with tasks requiring memory for exact quantities: in orthogonal and hidden matching tasks, information has to be transferred across time and space, and although these tasks were more difficult for both Pirahã and English speakers, Pirahã speakers performed worse, presumably because English speakers used various strategies to mitigate their difficulty. Without number language, the nuts-in-a-can task was extremely difficult for both Pirahã and English speakers and a statistical evaluation of their results suggests that both used the analog magnitude system (40).
Frank et al. suggest that number words serve as tools to store information through abstraction: language may not alter numerical representations but it can help speakers carry out cognitive tasks by facilitating information storage and processing. Having a concept of exact quantities does not depend on language but having a memory for such quantities does (41).
According to Everett (42), the cause of the Pirahã’s inability to perform numerical tasks is not their language per se but their culture, which influences and restricts language and possibly cognition. Everett claims that one strong value of Pirahã culture, a restriction of communication to speakers’ immediate experience, affects every aspect of Pirahã life and is the reason why they have not developed creation myths, have no collective memory of more than two generations past and do not draw or write. If Everett is to be believed, this immediacy constraint also affects Pirahã language, which is the only language in the world without colour terms, has the simplest pronoun and kinship systems and, most interestingly, has no recursion. A language that lacks recursion poses a serious challenge to universalism: Chomsky and colleagues present recursion as the defining property of the “human language faculty”, as its only element unique to language, unique to humans and universally present in all human language (44).
However, Everett claims that linguistic relativity, which he sees as inherently unidirectional, cannot account for his findings either, because it fails to recognise the important role culture plays in shaping language (42). While Everett may be right about the SWH as defined by Lenneberg and Brown, which, indeed, does not explicitly mention mutual influences of language and culture, the forefathers of linguistic relativism, in their writings, did advocate a dynamic system in which language, culture and thought influence each other mutually (45).
An Area for Further Research
Much research into linguistic relativity focuses on semantics and categorisation. This is not surprising given that the SWH experienced its demise at the hands of universal grammar, which considers syntax to be the same in all humans, and its revival thanks to cognitive linguists and psychologists who believed that language is connected to the meanings it has evolved to express (2,16). However, syntax should not be neglected by linguistic relativity research. It would, for example, be interesting to see whether highly recursive languages improve speakers’ memory or their ability to understand complex arguments and whether languages with little or no recursion such as that of the Pirahã prevent speakers from gaining such abilities.While syntax has long been looked at as an innate universal structure, it is time for research to look at the syntactic structures of individual languages and examine how they relate to the way in which people structure their thoughts.
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(37) Saxe. G.B. & Esmonde, I. (2005). Studying Cognition in Flux: A Historical Treatment of Fu in the Shifting Structure of Oksapmin Mathematics. Mind, Culture and Activity, 12(3&4),171-225 http://lmr.berkeley.edu/docs/saxe_esmonde_mca1234_2.pdf Last Access: 9/2/2011
(38) Gordon, P. (2004). Numerical Cognition Without Words: Evidence from Amazonia. Science, 306,15. Last Access: 6/2/2011
(39) Hespos, S.J. (2004). Language: Life without Numbers. Current Biology, Vol. 14, R927–R928. http://groups.psych.northwestern.edu/infantcognitionlab/dispatch.pdf Last Access:6/2/2011
(40) Frank, M.C., Fedorenko, E., Gibson, E. (2008). Language as a cognitive technology: English-speakers match like Pirahã when you don’t let them count. http://web.mit.edu/evelina9/www/Downloads/Other%20pubs/Frank,Fedorenko,Gibson%202008.pdf Last Access: 15/1/2011
(41) Frank, M.C., Everett, D.L., Fedorenko, E., Gibson, E. (2008). Number as a cognitive technology: Evidence from Pirahã language and cognition. Cognition 108, 819–824.
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(45) see for example: Boas, F. (1911) in Introduction to Handbook to American Indian Languages by Franz Boas &, Indian Linguistic Families in America North of Mexico by J.W. Powell. (1966). University of Nebraska Press, page 63.
Whorf, B.L. (1956). Language, Thought and Reality, Selected Writings of Benjamin Lee Whorf, Introduction by John B. Carroll Ed. Massachusetts Institute of Technology, page 156.
Yee, N. What Whorf Really Said. http://www.nickyee.com/ponder/whorf.html Last Access: 17/2/2011
 Today, the Sapir-Whorf Hypothesis is often – and perhaps more accurately – referred to as the “Linguistic Relativity Hypothesis” or the “Linguistic Relativity Principle”. However, for reasons of simplicity, the author of this essay will use the term “Sapir Whorf Hypothesis” or its acronym “SWH”.
 This is the title of a book containing selected writings by Benjamin Lee Whorf published by Lewis Carroll in 1956 (1).
 With this statement, Lenneberg pointed out what became a frequent problem of linguistic relativity research that fails to take extra-linguistic data into account. Relativist Casasanto put it like this: “The only evidence that people who talk differently also think differently is that they talk differently” (13).
 This claimtriggered an urban legend, with authors, over the years, inflating the number to up to 400 and even more and when disproved led to the creation of the neologism “snowclone” (14).
 Berlin and Kay claim that they never made reference to this book. While this may be true, it is not what was originally pointed out by Saunders and van Brakel in their paper “Are there non-trivial constraints on colour categorization?”. What has been said is that their focal colour terms corresponded to the most frequent colour terms in this book, which suggests that American English terms were used as a standard (see 23).
 Through contact with other language communities, many Oksapmin today use words of Tok Pisin, one of Papua New Guinea’s national languages, for numbers and currency. Moreover, Oksapmin has also evolved to allow for slightly more complex calculations (37).
 See Pullum’s comments on Language Log (43).