[Paleopsych] SW: Language and the Origin of Numerical Concepts

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Cognition: Language and the Origin of Numerical Concepts

    The following points are made by R. Gelman and C.R. Gallistel (Science
    2004 306:441):
    1) Intuitively, our thoughts are inseparable from the words in which
    we express them. This intuition underlies the strong form of the
    Whorfian hypothesis (after Benjamin Whorf (1897-1941), namely, that
    language determines thought (aka "linguistic determinism"). Many
    cognitive scientists find the strong hypothesis unintelligible and/or
    indefensible (1), but weaker versions of it, in which language
    influences how we think, have many contemporary proponents (2,3).
    2) The strong version rules out the possibility of thought in animals
    and humans who lack language, although there is an abundant
    experimental literature demonstrating quantitative inference about
    space, time, and number in preverbal humans (4), in individuals with
    language impairments (5), and in rats, pigeons, and insects. Another
    problem is the lack of specific suggestions as to how exposure to
    language could generate the necessary representational apparatus. It
    would be wonderful if computers could be made to understand the world
    the way we do just by talking to them, but no one has been able to
    program them to do this. This failure highlights what is missing from
    the strong form of the hypothesis, namely, suggestions as to how words
    could make concepts take form out of nothing.
    3) The antithesis of the strong Whorfian hypothesis is that thought is
    mediated by language-independent symbolic systems, often called the
    language(s) of thought. Under this account, when humans learn a
    language, they learn to express in it concepts already present in
    their prelinguistic system(s). Their prelinguistic systems for
    representing the world are language-like only in that they are
    compositional: Larger, more complex meanings (concepts) are built up
    by the combination of elementary meanings.
    4) Recently reported experimental studies with innumerate Piraha and
    Munduruku Indian subjects from the Brazilian Amazonia give evidence
    regarding the role of language in the development of numerical
    reasoning. Either the subjects in these reports have no true number
    words or they have consistent unambiguous words for one and two and
    more loosely used words for three and four. Moreover, they do not
    overtly count, either with number words or by means of tallies. Yet,
    when tested on a variety of numerical tasks -- naming the number of
    items in a stimulus set, constructing sets of equivalent number,
    judging which of two sets is more numerous, and mental addition and
    subtraction -- these subjects gave results indicative of an imprecise
    nonverbal representation of number, with a constant level of
    imprecision, measured by the Weber fraction. The Weber fraction for
    these subjects is roughly comparable to that of numerate subjects when
    they do not rely on verbal counting. In one of the reports, the
    stimulus sets had as many as 80 items, so the approximate
    representation of number in these subjects extends to large numbers.
    5) Among the most important results in these reports are those showing
    simple arithmetic reasoning -- mental addition, subtraction, and
    ordering. These findings strengthen the evidence that humans share
    with nonverbal animals a language-independent representation of
    number, with limited, scale-invariant precision, which supports simple
    arithmetic computation and which plays an important role in elementary
    human numerical reasoning, whether verbalized or not (5). The results
    do not support the strong Whorfian view that a concept of number is
    dependent on natural language for its development. Indeed, they are
    evidence against it. The results are, however, consistent with the
    hypothesis that learning to represent numbers by some communicable
    notation (number words, tally marks, numerals) might facilitate the
    routine recognition of exact numerical equality.
    References (abridged):
    1. L. Gleitman, A. Papafragou, in Handbook of Thinking and Reasoning,
    K. J. Holyoak, R. Morrison, Eds. (Cambridge Univ. Press, New York, in
    2. D. Gentner, S. Golden-Meadow, Eds., Language and Mind: Advances in
    the Study of Language and Thought (MIT Press, Cambridge, MA, 2003)
    3. S. C. Levinson, in Language and Space, P. Bloom, M. Peterson, L.
    Nadel, M. Garrett, Eds. (MIT Press, Cambridge, MA, 1996), Chap. 4
    4. R. Gelman, S. A. Cordes, in Language, Brain, and Cognitive
    Development: Essays in Honor of Jacques Mehler, E. Dupoux, Ed. (MIT
    Press, Cambridge, MA, 2001), pp. 279-301
    5. B. Butterworth, The Mathematical Brain (McMillan, London, 1999)
    Science http://www.sciencemag.org
    Related Material:
    Notes by ScienceWeek:
    In this context, let us define "animals" as all living multi-cellular
    creatures other than humans that are not plants. In recent decades it
    has become apparent that the cognitive skills of many animals,
    especially non-human primates, are greater than previously suspected.
    Part of the problem in research on cognition in animals has been the
    intrinsic difficulty in communicating with or testing animals, a
    difficulty that makes the outcome of a cognitive experiment heavily
    dependent on the ingenuity of the experimental approach.
    Another problem is that when investigating the non-human primates, the
    animals whose cognitive skills are closest to that of humans, one
    cannot do experiments on large populations because such populations
    either do not exist or are prohibitively expensive to maintain. The
    result is that in the area of primate cognitive research reported
    experiments are often "anecdotal", i.e., experiments involving only a
    few or even a single animal subject.
    But anecdotal evidence can often be of great significance and have
    startling implications: a report, even in a single animal, of
    important abstract abilities, numeric or conceptual, is worthy of
    attention, if only because it may destroy old myths and point to new
    directions in methodology. In 1985, T. Matsuzawa reported experiments
    with a female chimpanzee that had learned to use Arabic numerals to
    represent numbers of items. This animal (which is still alive and
    whose name is "Ai") can count from 0 to 9 items, which she
    demonstrates by touching the appropriate number on a touch-sensitive
    monitor. Ai can also order the numbers from 0 to 9 in sequence.
    The following points are made by N. Kawai and T. Matsuzawa (Nature
    2000 403:39):
    1) The author report an investigation of Ai's memory span by testing
    her skill in numerical tasks. The authors point out that humans can
    easily memorize strings of codes such as phone numbers and postal
    codes if they consist of up to 7 items, but above this number of
    items, humans find memorization more difficult. This "magic number 7"
    effect, as it is known in human information processing, represents an
    apparent limit for the number of items that can be handled
    simultaneously by the human brain.
    2) The authors report that the chimpanzee Ai can remember the correct
    sequence of any 5 numbers selected from the range 0 to 9.
    3) The authors relate that in one testing session, after choosing the
    first correct number in a sequence (all other numbers still masked),
    "a fight broke out among a group of chimpanzees outside the room,
    accompanied by loud screaming. Ai abandoned her task and paid
    attention to the fight for about 20 seconds, after which she returned
    to the screen and completed the trial without error."
    4) The authors conclude: "Ai's performance shows that chimpanzees can
    remember the sequence of at least 5 numbers, the same as (or even more
    than) preschool children. Our study and others demonstrate the
    rudimentary form of numerical competence in non-human primates."
    Nature http://www.nature.com/nature
    Related Material:
    The following points are made by A. Plodowski et al (Current Biology
    2003 13:2045):
    1) How are numerical operations implemented within the human brain? It
    has been suggested that there are at least three different codes for
    representing number: a verbal code that is used to manipulate number
    words and perform mental numerical operations (e.g., multiplication);
    a visual code that is used to decode frequently used visual number
    forms (e.g., Arabic digits); and an abstract analog code that may be
    used to represent numerical quantities [1]. Furthermore, each of these
    codes is associated with a different neural substrate [1-3].
    2) Several features of numbers are of interest to cognitive
    neuroscientists. First, investigations of animals and infants indicate
    that the ability to process numerical magnitude can be independent of
    language. Second, identical numerical quantities can be represented in
    several different notations. Third, different numerical operations can
    be performed on the same operands. Dehaene [1] has proposed a triple
    code model that distinguishes between an auditory verbal code, a
    visual code for Arabic digits, and an analog magnitude code that
    represents numerical quantities as variable distributions of brain
    activation. Dehaene and colleagues [1-3] propose that there are
    specific relationships between individual numerical operations and
    different numerical codes. The analog magnitude code is used for
    magnitude comparison and approximate calculation, the visual Arabic
    number form for parity judgments and multidigit operations, and the
    auditory verbal code for arithmetical facts learned by rote (e.g.,
    addition and multiplication tables).
    3) Previous studies have used behavioral and neuroimaging techniques
    (both ERP and fMRI) to explore the effects of notation (i.e., Arabic
    versus verbal code) on magnitude estimation [2,3]. The authors extend
    these studies using dense-sensor event-related EEG recording
    techniques to investigate the temporal pattern of notation-specific
    effects observed in a parity judgement (odd versus even) task in which
    single numbers were presented in one of four different numerical
    notations. Contrasts between different notations demonstrated clear
    modulations in the visual evoked potentials (VEP) recorded. The
    authors observed increased amplitudes for the P1 and N1 components of
    the VEP that were specific to Arabic numerals and to dot
    configurations but differed for random and recognizable (die-face) dot
    configurations. The authors suggest these results demonstrate clear,
    notation-specific differences in the time course of numerical
    information processing and provide electrophysiological support for
    the triple-code model of numerical representation.[4,5]
    References (abridged):
    1. Dehaene, S. (1992). Varieties of numerical abilities. Cognition 44,
    2. Dehaene, S. (1996). J. Cogn. Neurosci. 8, 47-68
    3 Pinel, P., Dehaene, S., Riviere, D., and LeBihan, D. (2001).
    Neuroimage 14, 1013-1026
    4. Guthrie, D. and Buchwald, J.S. (1991). Significance testing of
    difference potentials. Psychophysiology 28, 240-244
    5. Nunez, P.L., Silberstein, R.B., Cadusch, P.J., Wijesinghe, R.S.,
    Westdorp, A.F., and Srinivasan, R. (1994). A theoretical and
    experimental study of high resolution EEG based on surface Laplacians
    and cortical imaging. Electroencephalogr. Clin. Neurophysiol. 90,
    Current Biology http://www.current-biology.com

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