mirrored file at http://SaturnianCosmology.Org/ For complete access to all the files of this collection see http://SaturnianCosmology.org/search.php ========================================================== *ScienceWeek* * 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 press) 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: COGNITIVE SCIENCE: NUMBERS AND COUNTING IN A CHIMPANZEE 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: COGNITIVE SCIENCE: ON THE MENTAL REPRESENTATION OF NUMBER 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, 1-42 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, 40-57 Current Biology http://www.current-biology.com ScienceWeek http://scienceweek.com * Copyright © 2004 ScienceWeek All Rights Reserved US Library of Congress ISSN 1529-1472