Calculating without reading? Comments on Cohen and Dehaene (2000)

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  • This article was downloaded by: [Monash University Library]On: 07 October 2014, At: 17:16Publisher: RoutledgeInforma Ltd Registered in England and Wales Registered Number: 1072954 Registeredoffice: Mortimer House, 37-41 Mortimer Street, London W1T 3JH, UK

    Cognitive NeuropsychologyPublication details, including instructions for authors andsubscription information:http://www.tandfonline.com/loi/pcgn20

    Calculating without reading?Comments on Cohen and Dehaene(2000)Agnesa Pillon a & Mauro Pesenti aa Universit catholique de Louvain, BelgiumPublished online: 10 Sep 2010.

    To cite this article: Agnesa Pillon & Mauro Pesenti (2001) Calculating without reading?Comments on Cohen and Dehaene (2000), Cognitive Neuropsychology, 18:3, 275-284, DOI:10.1080/02643290042000143

    To link to this article: http://dx.doi.org/10.1080/02643290042000143

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  • CALCULATING WITHOUT READING? COMMENTSON COHEN AND DEHAENE (2000)

    Agnesa Pillon and Mauro PesentiUniversit catholique de Louvain, Belgium

    Cohen and Dehaene (Cognitive Neuropsychology, 2000, Vol. 17, pp. 563583) reported the case of a purealexic patient who preserved some calculation abilities despite severely impaired Arabic numeral read-ing. They argued that these residual abilities and the general pattern of performance of the patient canbe fully explained within their anatomo-functional triple-code model. Here, we show how the lack ofspecification of the assumed architecture, the failure to provide sufficiently detailed data, and theabsence of adequate refutation of alternative accounts make this study unsuitable for constrainingtheories of numerical cognition.

    INTRODUCTION

    In Calculating without reading, Cohen andDehaene (2000; hereafter, C&D) report the case ofa pure alexic patient (VOL) whose performancepattern suggests complex relations between therepresentations and processes involved in mappingArabic onto verbal numerals and those involved inretrieving various aspects of numerical knowledgefrom Arabic numerals. The case is used to addressspecific aspects of numerical knowledge involved invarious tasks, and how they are related within a gen-eral architecture of number processing andcalculation.

    In this comment we argue that although C&Doffer plausible theoretical propositions related tothis issue, their study does not meet two basicrequirements for a single-case study to constraintheories of normal cognition. The first unfulfilledrequirement is that it must be possible to derive a

    patients pattern of performance from thecharacteristics of the assumed architecture (i.e., thefunctional components and their relations) and thenature of representations and computational prin-ciples of its components, especially those assumedto be impaired (Caramazza, 1986, 1992). We thinkthat, in C&Ds study, the nature of representationsand computations in the hypothetical numericalarchitecture is not sufficiently detailed to allowVOLs pattern of performance to be interpretedreliably. The second unfulfilled requirement bearsupon a more general principle of scientific argu-mentation. Data support a theory not only if they fitthis theory, but if they compel us to prefer it to otherplausible ones. In a single-case study, this entailsnot only accounting for a patients performancewithin ones own set of assumptions, but also reject-ing, with adequate evidence, accounts based onother plausible postulates. C&D never consideralternative accounts for their data and, accordingly,

    COGNITIVE NEUROPSY CHOLOGY, 2001, 18 (3), 275284

    2001 Psychology Press Ltdhttp://www.tandf.co.uk/journals/pp/02643294.html DOI:10.1080/02643290042000143

    275

    Requests for reprints should be addressed to Agnesa Pillon or Mauro Pesenti, Unit de Neuropsychologie cognitive, Facult dePsychologie, Universit catholique de Louvain, place Cardinal Mercier 10, B-1348 Louvain-la-Neuve, Belgium (Email:pillon@neco.ucl.ac.be; pesenti@neco.ucl.ac.be).

    AP and MP are Research Associates of the National Fund for Scientific Research (Belgium). We wish to thank Xavier Seron,Dana Samson, and an anonymous reviewer for helpful comments on an earlier draft of this article, and the PAI/IUAP Program fromthe Belgian Government for financial support.

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  • neither seek nor report evidence to evaluate otherpossible accounts. We will show how the failure tomeet these two basic requirements makes C&Dsstudy unable to constrain models of numerical cog-nition. We first summarise C&Ds observationsand the derived theoretical claims. Then we exam-ine each of these claims and ask whether they arecommensurate to the level of detail of the theoreti-cal framework and to the amount and nature of evi-dence provided.

    C&DS ACCOUNT OF VOLSPATTERN OF PERFORMANCE

    Although her comprehension of Arabic numeralsand her production of verbal numerals were correctper se, VOL was impaired at reading aloud single-digit Arabic numerals. When solving arithmeticalproblems, she correctly read aloud the operands inabout 20% of the cases. Yet, she gave the result ofthe target problem with a relatively good level ofaccuracy in subtraction, addition, and division(72%, 61%, and 66% correct, respectively), but notin multiplication (only 13% correct). Interestingly,she gave the correct result for the problem errone-ously read in 77% of the cases (e.g., 59 was read asfour times six and answered twenty-four). This con-trast between impaired naming and multiplicationand relatively spared comparison and other arith-metic operations led C&D (2000, p. 580) to pro-pose two distinct routes for Arabic numeralprocessing, one that is the mandatory input path-way to naming and multiplication processes, andthe other that is able to supply comparison, addi-tion, subtraction, and simple division routines. Inpatient VOL, only the direct Arabic-to-verbalmapping route would be impaired, whereas theindirect semantic route (i.e., through access to andmanipulation of the quantities represented bynumerals) would be spared. Multiplication prob-lems could only be solved by retrieval of the corre-sponding facts stored as verbally coded associationslinking operands and products. Arabic-to-verbalmapping would thus be the prerequisite for multipli-cations, which explains answers stemming fromerroneous reading of operands through this route.

    C&D also tentatively link these functional pro-posals with an anatomical organisation of their tri-ple-code model (Dehaene & Cohen, 1995),according to which, digit structural representationand quantity information are processed by bothhemispheres, whereas only the left hemisphere pro-cesses verbal numerals. VOLs lesion damaged theleft-hemispheric digit recognition processes, pre-cluding the transcoding of Arabic numerals intowords (hence, the retrieval of stored multiplicationfacts) and the access to the left-hemispheric quan-tity representation. Her residual numerical abilitieswould reflect intact right-hemispheric processes.

    C&DS THEORETICAL CLAIMS ANDTHE SIGNIFICANCE OF THE DATA

    Do Arabic numeral reading errors reflectfunctional Arabic-to-verbal mappingimpairments?

    C&D hypothesise that VOLs naming difficultiesarise from the verbal system being deprived of itsnormal input, but without specifying whether thedamage was to the Arabic recognition system or tothe Arabic-to-verbal mapping system. Here, wefocus on the functional aspects of this claim, anddiscuss its anatomo-functional aspects in the lastpart of this section.

    At a functional level, structural processing ofdigits seemed relatively spared. VOL could dis-criminate digits from letters, and her errors did notreflect visual confusions. Therefore, the deficitcausing VOLs naming difficulties would lie in theasemantic Arabic-to-verbal mapping system.However, this conclusion stems from C&Ds priorassumption that Arabic numerals are named with-out semantic access, which is quite controversial(for a discussion, see McCloskey, 1992; Seron &Nol, 1995). It might turn out to be right but, to bestated as a motivated account of VOLs naming dif-ficulties, alternative assumptions must be empiri-cally ruled out, the more straightforward beingreading digits through semantic access. Then,VOLs naming errors would stem from an inabilityto access semantics from the structural representa-tion of Arabic digits. Unfortunately, C&D do not

    PILLON AND PESENTI

    276 COGNITIVE NEUROPSYCHOLOGY , 2001, 18 (3)

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  • specify the characteristics of their asemantictranscoding system, and they do not derive nor testspecific predictions about the pattern of namingerrors generated when the system is not properlyaddressed. For instance, in case of damage to theasemantic route, should one expect substitutionsbetween phonologically similar verbal numerals, orbetween semantically similar (i.e., close in magni-tude) numerals as expected in case of damage to thesemantic route? In the reading tasks, VOL was pre-sented with one- to four-digit Arabic numerals,and she made almost exclusively digit substitutionerrors. If the visual representation computed on thebasis of Arabic numerals cannot properly addressthe Arabic-to-verbal mapping system, one shouldexpect VOL, besides substitutions, to make syntac-tic errors due to loss or exchange of digit positionsduring transfer. Such errors were not observed,which shows that she at least retained the ability toanalyse the positions of multi-digit numerals, tomaintain and transfer these positions to thetranscoding system, and to map them into theappropriate multi-word numeral structure. Thisseems rather inconsistent with a destruction ordeafferentation (C&D, 2000, p. 573) of theprocessing component whose output is used by theArabic-to-verbal mapping system. C&D should atleast explain why only the lexical part (identity ofthe digit) of the structural representation was notcorrectly transferred and processed, while its syn-tactic part (positional structure) was.

    Thus, the data reported do not allow the readerto decide whether Arabic naming errors stem fromimpairment to the asemantic or to the semanticroute. C&D argue that their hypothesis naturallyfollows from observations made with other tasks.Since VOL could access quantity information fromArabic numerals but could not read them aloud,then naming necessarily relies on an asemantic pro-cessing route. In the next two sections, we discussthe relevance of the evidence supporting the

    premise of this argument and explain why it isinadequate.

    Distinct processing routes for naming andcomparing Arabic numerals?

    VOL could accurately compare two Arabic numer-als though she could not read them aloud. Thiswould support the idea of two processing routes if itis shown that a single route cannot yield, whendamaged, different levels of performance reflectinginherently different levels of difficulty of the tasks.

    If naming and comparing rely on the same pro-cessing route, the structural representation ofArabic numerals would give access to their meaningand, thereafter, to the verbal numerals retrievedfrom the phonological lexicon. Assuming thatVOL can compute structural and magnitude repre-sentations, the functional damage would then belocated in the structural-to-magnitude representa-tion addressing procedures, causing weak activationof the numeral meaning, and resulting in approxi-mate/degraded quantity information. This couldnevertheless allow VOL to give accurate responsesin a magnitude comparison task since it is logicallypossible to compare numerals without accessingtheir exact magnitude (as demonstrated byDehaene & Cohen, 1991). This is especially truefor the comparison task used in C&Ds study,where the numerical distance between the numbersin the pairs ranged from 2 to 26 (mean distance:8.8). Accessing only approximate quantity infor-mation might thus suffice in most cases. Moreover,accurate responses might be given even when thequantity information accessed is totally wrong, pro-vided that the relative size of the two numbers is notreversed1. This account would not hold if it hadbeen shown that VOL could access exact quantities(e.g., verifying whether there is a correct matchbetween Arabic numerals and arrangements ofpoker chips of various numerical values, compari-

    COGNITIVE NEUROPSYCHOLOGY, 2001, 18 (3) 277

    CALCULATING WITHOUT READING?

    1 C&D rejected in advance this objection by arguing that VOL made very few reversing errors when reading aloud pairs of two-digit numerals. In our view, this only suggests that if VOL had based her responses in comparison on the quantity information sheaccessed in reading, the probability of errors in comparison would be very low. Note that data in comparison and in naming werecollected with different stimuli on different occasions. It would have been more convincing if VOL had had to read aloud andimmediately after to compare the pairs.

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  • sons with splits one or two, etc.). In this study,nothing compels us to accept that VOL showed abetter access to quantity information than could beexpected on the basis of her number reading perfor-mance (C&D, 2000, p. 567). The data are com-patible with the hypothesis of two distinctprocessing routes, but they do not need to make thishypothesis.

    We showed that, in VOLs performance, noth-ing allows one to characterise...

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