Number - Linguistic Determinism (Exact Numeration) Flashcards
Dehaene (1997)
Argued for an innate “number sense”, where humans innately attuned and skilled in numerical representation
Dehaene et al (1999) - exact and approximate representation; behavioural evidence
Trained Russian-English bilinguals either exact or approximate addition in one of their two languages > (1) performance in both tasks improved post-training, regardless of language of training; (2) when tested on trained exact, subjects performed faster in training versus non-training language; (3) when tested on approximate, performance equivalent in two languages > arithmetic knowledge acquired during training with exact stored in language-specific format, and showed language-switching cost due to required internal translation of arithmetic problem
Similar findings when training on more complex arithmetic tasks, including different bases of number system, cube roots, and logarithms
Compared trained vs novel exact and approximate problems involving similar magnitudes > (1) for exact, performance better on trained, suggesting each new fact stored independently of neighbouring magnitudes, perhaps as sequence of words; (2) for approximate, no cost of generalising to novel problems in same range of magnitudes
Dehaene et al (1999) imaging evidence
fMRI experiments under same task showed (1) for approximation calculations, activity in areas for visuo-spatial processing and analogical mental transformations, suggesting approximate calculation involves representation of numeration on a spatial number line; (2) for exact, large and left-lateralised activation in left interior frontal lobe, implicated in verbal association tasks
fMRI low temporal resolution, but higher temporal resolution ERPs showed its topography compatible with fMRI activation, with negative measures for exact, not approximate, over left interior frontal electrodes at 216ms, a timing consistent with previous studies implicating ERP during verb generation tasks
Preverbal infants and non-human primates
Behavioural and neurophysiological experiments revealed preverbal infants (Wynn, 1998) and nonhuman primates (Dehaene et al., 1998) only able to represent first three numbers exactly, with increasingly inaccurate approximation for larger numbers > language causally related to exact representation of number concepts beyond three
Gordon (2004) - Pirahã
Hunter-gatherers in Brazil with population <200
Field observations by missionaries revealed a lack of exact number words (Everett, 2005), whereas many languages contain recursive counting system, facilitating theoretically infinite arithmetic
One-two-many counting system, but inconsistencies as Hói, instead of meaning one, refers to roughly one, and can be used as spatial descriptor (small)
Increasingly cognitively demanding non-linguistic numerical tasks, such as reproducing number of culturally familiar objects in varying spatial arrays, showing no evidence of exact number concepts above three
Performance indicated use of visuo-spatial approximation strategies, such as those implicated in preverbal infants and nonhuman primates (Dehaene et al., 1998; Wynn, 1998)
Accounted for cultural familiarity as well as varying cognitive demands to ensure no possible influence of cognitive load instead of language being responsible
Frank et al (2008)
Need to tease apart culture and language (Majid, 2018)
Series of memory experiments similar to Gordon (2004) on Pirahã, showing impaired performance
Claimed not a case of absent language preventing exact numerical representation beyond three per se, but a lack of learning culturally learned tool of counting
Other Amazonian groups with limited number vocab shown similar performance for sets larger than three/four, and use similar approximation strategies (Pica et al., 2004)
Pirahã no currency, don’t measure distance > largely innumerate culture where approximation may suffice
Ideal Testing Population
One in fully numerate culture, but lacking number words (Majid, 2018)
Spaepen et al (2011)
Compared 4 Nicaraguan home-signers (communicate approximate numeration) to controls fluent in ASL in reporting number of items shown on presented card (task similar to Gordon, 2004) > 100% accuracy up to three, with much variation beyond this, with error rate and distance from correct answer increasing with pressure demands (time-constraints), suggesting insufficient time to utilise approximation strategy
Like Gordon (2004), also ran non-linguistic match-tp-sample experiment, including cross-modal tasks (visual presentation, tactile response; removing visuo-spatial strategies), with home-signers accurate up to three, but low accuracy beyond this, but ASL near-ceiling throughout
Spaepen et al (2011) Criticisms
Only 4 home-signers tested > difficult to get more, but statistical power
Home-signers may have required varying levels of numerical representation for communication with family
Senghas et al (2004)
Development of community sign language in Nicaragua, whereby sudden increase in deaf children in 1960s resulted in educational institutions that facilitated emergence of sign language > generationally, signer grew in number, with intergenerational linguistic input increasing
Variation of number signs in 1970s > conventionalised set in 1990, usually iconic with one-to-one mapping between number of fingers extended and value > early 1990s rapid standardisation and one-handed
Flaherty and Senghas (2011)
Similar tasks to Gordon (2004) and Spaepen et al (2011), seeing generational difference in performance on non-linguistic numeration cognition task, particularly seen in reproduction/memory of concepts larger than 3, except for one-to-one matching tasks > ephemeral tasks required a “count list” (recursive counting system)
Rudimentary exact numeration abilities in older non-counters e.g., could successfully give a number of coins corresponding to monetary notes > developed strategies in response to demands of numerate culture, but not exact representation as not recursive, just learning of an equivalency
Wynn (1990) - count list
Proposed learned early, before using it to access cardinal value of a set, and is only after children map quantities 1, 2, and 3, to number words, have an insight that links short sequence, one-to-one, to beginning of longer count list
Adult non-counters never experienced initial one-to-one mapping, so no previously memorised count list
Frank et al (2011)
Verbal interference in English speakers disrupts encoding of exact number, showing it to be case, suggesting it may be language per se that is necessary for exact numerical representation
Criticisms of Linguistic Determinism of Number
In rare cases, language dysfunction doesn’t abolish exact arithmetic, suggesting a partially non-linguistic source of exact numerical representation (Butterworth, 1999) > however, analogous to preverbal infants vs nonhuman primates, dysfunction implies a previous use, which may establish long-lasting arithmetic abilities or memorisation of count list (Wynn, 1990)
Wolff and Holmes (2010) argue number to be a case of language as an augmenter, such that linguistic representations (counting system) combine with non-linguistic representations (approximation) to perform tasks that could not be completed with either type alone > however, experiments do not strictly suggest that non-linguistics involved in exact numeration, as no non-counters excel, but linguistic representation necessary, therefore linguistic determinism > however, Frank et al (2011) verbal interference suggests language used on-line, so not deterministic, but cross-cultural evidence needed
