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Cognitive Neuropsychology, 2014 http://dx.doi.org/10.1080/02643294.2013.869202 Shared versus separate processes for letter and digit identification Michael McCloskey and Teresa Schubert Department of Cognitive Science, Johns Hopkins University, Baltimore, MD, USA Letters and digits, although similar in many respects, also differ in potentially significant ways. Most importantly, letters are elements of an alphabetic writing system, whereas digits are logographs. In this article, we explore whether letters and digits are identified by a single character identification process that makes no fundamental distinction between the two types of characters, or whether instead letter and digit identification processes diverge at least in some respects. We present evidence from an acquired dyslexic patient, L.H.D., who is impaired in both letter and digit identification. Working within a theoretical framework specifying the levels of representation implicated in letter identification, we systematically compare L.H.D. s letter and digit processing. The results provide evidence that letter and digit identification implicate the same levels of representation, and further that L.H.D. s identification errors for both letters and digits arise at the same point in processing. On the basis of these results, we argue for a shared process that mediates identification of both letters and digits. Finally, we discuss relevant previous results in light of this conclusion. Keywords: Reading; Letters; Digits; Pure alexia; Acquired dyslexia; Numerical. Just as the ability to identify letters is critical for reading, the ability to identify digits is crucial for the use of Arabic numerals. In some respects letters and digits are very similar: Both are relatively simple two-dimensional visual shapes that function as symbols in writing systems. In other respects, however, letters and digits are significantly different. Most notably, letters are elements of an alphabetic writing system, whereas digits are logographs (e.g., Besner & Coltheart, 1979; Cipolotti, 1995; Dalmás & Dansilio, 2000; Holender & Peereman, 1987). Individual letters (e.g., C) do not correspond to words or concepts, but (at least roughly speaking) to phonemes. Written forms that bear meaning are produced by combining letters into words (e.g., CAT). In contrast, individual digits (e.g., 8) represent entire words and concepts and are not visual symbols for phonemes. A second potential difference between letters and digits concerns allographic variation. Letters have the property that very different visual shapes Correspondence should be addressed to Michael McCloskey, Department of Cognitive Science, Johns Hopkins University, Baltimore, MD 21218, USA (E-mail: michael.mccloskey@jhu.edu). The second author was supported by an National Science Foundation (NSF) Integrative Graduate Education and Research Traineeship (IGERT) grant to the Johns Hopkins Department of Cognitive Science. We are grateful to L.H.D. for her cooperation and patience over many sessions of testing, and we thank Jeremy Purcell for creating the figure of L.H.D. s lesion. In addition the pure alexia database compiled by Amalie Hjorth Ditlevsen was invaluable as a source of pure alexia articles. # 2014 Taylor & Francis 1

McCLOSKEY AND SCHUBERT (e.g., G, g) may correspond to the same letter identity. That is, the alternative forms of a letter may include not only variants of the same basic shape (e.g., G and G), but entirely distinct shapes (e.g., G and g). The distinct visual forms of a letter are referred to as allographs for example, G and g are allographs of the letter G. Within-letter allographic variation is so extensive that two allographs of the same letter (e.g., G and g) may be less similar visually than two shapes that map onto different letter identities (e.g., G and C). In contrast, digits vary less in their visual forms. Digits lack separate upper- and lower-case shapes; nor do print and script versions of a digit typically vary widely. Although several digits have alternative forms (e.g., 4 and 4), these could perhaps be described as variants of a shared basic shape, as opposed to clearly distinct shapes. The similarities and differences between letters and digits raise questions about the cognitive mechanisms that underlie letter and digit identification: Are letters and digits identified by a single character identification process that makes no fundamental distinction between the two types of characters, or might the processes for letter and digit identification diverge at some point, reflecting the differences between the letter and digit categories? The available data do not provide a straightforward answer. A substantial body of results indicates that processing of Arabic numerals (e.g., 4872) is dissociable at some levels from processing of words, including number words (e.g., Dehaene & Cohen, 1996; McCloskey, Caramazza, & Basili, 1985). However, few of these results speak specifically to processes for identifying letters and digits. Some findings from research on acquired reading disorders appear consistent with a shared identification process for letters and digits (e.g., Katz & Sevush, 1989; Patterson & Wilson, 1990; Starrfelt & Behrmann, 2011). For example, Starrfelt and Behrmann s (2011) careful review of number-reading results from studies of pure alexia suggests that patients showing impaired letter identification almost always are also impaired (albeit often less severely) in digit identification. Other results, however, suggest significant processing differences between letters and digits (e.g., Anderson, Anderson, & Damasio, 1990; Starrfelt, 2007). In this article, we present evidence from an acquired dyslexic patient, L.H.D., who is impaired in letter identification. On the basis of results from our prior study of L.H.D. s reading, we first present a detailed characterization of the cognitive mechanisms that mediate letter identification and localize L.H.D. s impairment to a particular point in this cognitive architecture. Building upon this foundation, we then present results comparing L.H.D. s processing of letters and digits and argue that the results suggest a shared process for letter and digit identification. Finally, we examine results from prior studies in light of our results and conclusions. CASE HISTORY L.H.D. is a right-handed woman who was 69 years old when testing began in 2010. She holds an MBA, and worked as an executive in the banking industry prior to her retirement. 1 According to both L.H.D. and her husband, her premorbid reading, spelling, and numerical skills were excellent. In February 2007, L.H.D. suffered a ruptured left posterior cerebral artery aneurysm. The haemorrhage and ensuing surgery left her with a large left ventral lesion. The lesion has its posterior extent at the occipital pole, follows the medial portion of the occipital lobe into the temporal lobe, and ends at the temporal pole (Figure 1). Affected regions include striate and ventral extrastriate cortex, with involvement of the hippocampal region, parahippocampal gyrus, lingual gyrus, and fusiform gyrus. 1 Although L.H.D. worked in the banking industry, her responsibilities focused on strategic planning and did not involve unusual amounts of exposure to digits (as, for example, might have been the case for a bank teller or accountant). Rather, her premorbid experience with digits and letters appears to have been typical for an educated professional. 2 Cognitive Neuropsychology, 2014

LETTER AND DIGIT IDENTIFICATION Figure 1. Magnetic resonance imaging (MRI) displaying L.H.D. s lesion. Horizontal images are parallel to the anterior commissure (AC) posterior commissure (PC) line. Left side of images corresponds to the right hemisphere. Ophthalmological exam revealed a right homonymous hemianopia without macular sparing. Detailed case history and neuropsychological assessment results are presented in Schubert and McCloskey (in press). Here we summarize findings with potential relevance for the present study. No signs of neglect were evident in L.H.D. s picture copying, line bisection, line cancellation or drawing from memory, and her direct copy of the Rey Osterrieth complex figure was in the normal range (Fastenau, Denburg, & Hufford, 1999). She displayed moderately severe anomia in confrontation naming and spontaneous speech. For example, on the Boston Naming Test (Kaplan, Goodglass, & Weintraub, 1983) she correctly named only 8 of 24 items before the test was discontinued. Spelling assessment revealed mild impairment: L.H.D. was 88% correct in both written and oral spelling for a set of words that normal control participants spell with a mean accuracy of 98% (range 93 100%). Almost all of her errors were phonologically plausible misspellings, suggesting an impairment in retrieving lexical orthographic representations for spelling. L.H.D. S SINGLE-WORD READING L.H.D. s performance in single-word reading tasks was slow and inaccurate. Over a period of nearly two years she read aloud more than 6000 words and pronounceable nonwords with an accuracy of 62% for the words and 44% for the nonwords. Virtually all of her errors took the form of letter substitutions (e.g., CARPET CARPEF, PERSON PERCOB). On approximately one fourth of the trials, L.H.D. named some or all of the letters (not always correctly) before producing a whole-word response; on the remaining trials, she responded to the word as a whole without overt letter naming. Across two administrations of a 70-word list that varied word length (from 4 8 letters) while controlling word frequency, L.H.D. s reading accuracy did not vary as a function of word length, x 2 (4, N ¼ 140) ¼ 0.46; p..9. However, for latency measured to the onset of correct responses, L.H.D. showed a length effect on response time, F(2.4, 38.5) ¼ 3.12, p,.05, Greenhouse Geisser corrected, with a slope of approximately 500 ms/letter. Cognitive Neuropsychology, 2014 3

McCLOSKEY AND SCHUBERT COGNITIVE READING MECHANISMS Schubert and McCloskey (in press) probed the nature and implications of L.H.D. s reading impairment within the theoretical framework illustrated in Figure 2. This framework focuses on the peripheral reading processes that mediate letter identification. The letter identification processes provide input to central reading processes that activate semantic and phonological representations of words. The framework s assumptions about the peripheral letter identification processes are derived from Caramazza and Hillis (1990a, 1990b; see also Rapp & Caramazza, 1991), who proposed that letter identification involves a progression through three levels of representation. When a word is presented, early visual processes generate from the retinal image a feature map that represents low-level visual features (e.g., oriented edges). Next, processing of the feature map gives rise to a second level of representation at which the stimulus is segmented into separate characters, and the shape of each character is represented. At this level, each character is represented as a configuration of activated visual features (Caramazza & Hillis, 1990b), although the features are presumably different from those in the earlier visual feature map. For example, the shape of each letter in the word CAT is represented as a distinct configuration of activated features, as illustrated in Figure 2. Caramazza and Hillis (1990b) refer to this level as the letter shape level. However, we use the term character shape level instead, to emphasize that the level represents shapes prior to, and for purposes of, subsequent identification. At this level, no determination has been made that a shape corresponds to a particular letter, or even that it is a familiar form. For example, at the character shape level, actual letters are not distinguished in any way from pseudoletters (letterlike shapes that are not real letters). Letter identification occurs in the mapping from the character shape level to the third level, that of abstract letter identities. In the case of CAT, the character shape representation for the leftmost character Figure 2. Schematic of the three hypothesized levels of representation in letter identification (based on Caramazza & Hillis, 1990a, 1990b). would activate the abstract letter identity for the letter C, thereby accomplishing identification of the first letter in the word. FUNCTIONAL LOCUS OF L.H.D. S READING DEFICIT On the basis of results from a broad range of tasks, Schubert and McCloskey (in press) concluded that L.H.D. s central reading processes were intact, and that her reading errors stemmed from a deficit in letter identification. More specifically, they argued that L.H.D. was impaired in mapping from character shape representations to abstract letter identities. In the following sections, we summarize the results giving rise to this conclusion. Intact character shape perception Several results indicated that L.H.D. s visual processing of letters was intact through the stage of constructing character shape representations. For example, L.H.D. was 100% correct in copying pseudoletters, indicating that she was intact in constructing shape representations for these characters and hence presumably for actual letters as well. Figure 3(A) illustrates one of the stimuli and L.H.D. s copying response. 4 Cognitive Neuropsychology, 2014

LETTER AND DIGIT IDENTIFICATION Figure 3. (A) Sample trial from the pseudoletter direct copy task, illustrating L.H.D. s intact performance. (B) Two sample trials from the direct copy transcoding task, illustrating L.H.D. s errors. (C) Two sample stimuli from the letter decision task. Additional evidence of intact character shape perception came from a within-case letter same different judgement task. Pairs of upper-case (e.g., ENJ ENJ) or lower-case (e.g., mrq mrq) letter strings were presented. In each pair, the strings were either identical (e.g., FRG FRG) or differed at a single position (e.g., QRF QJF). L.H.D. s same different judgements were 100% correct, indicating that she was intact in perceiving the shapes of the letters. Impaired visual letter identification In contrast to her intact performance on tasks probing letter shape perception, L.H.D. was impaired on tasks requiring letter identification (i.e., mapping character shape representations to abstract letter identities). First, her naming of the letters in random letter strings was impaired (e.g., XWKSY XMKSV). The letter-naming errors could not be attributed to a deficit in retrieving or producing letter names, because L.H.D. s performance in oral spelling tasks demonstrated intact letter name retrieval and production. Rather, the errors implied a deficit in letter identification. Second, whereas L.H.D. was intact on within-case letter same different judgements (e.g., gbm ghm), she was impaired in a crosscase same different task. In this task, two strings differing in case were presented (e.g., DFA dfa), and L.H.D. was asked to judge whether the letter identities were the same or different. The within-case same different task can be performed on the basis of character shape representations, but the cross-case task requires letter identification (i.e., activation of abstract letter identities). In contrast to her perfect performance on withincase same different judgements, L.H.D. was only 84% correct on cross-case judgements, a highly significant difference. Finally, L.H.D. was impaired in a direct copy transcoding task in which she copied letter strings (e.g., FHO), changing from upper to lower case or vice versa. Figure 3(B) presents two examples of her errors. Because of the requirement to change case, this task requires letter identification. L.H.D. s impaired performance could not be attributed to a deficit in producing the written response; her written spelling performance indicated that she was intact in written letter production. Accordingly, her transcoding errors provide further evidence of a deficit in visual letter identification. L.H.D. s pattern of performance across the various letter tasks points clearly to a deficit in visual letter identification. More specifically, L.H.D. is intact in constructing character shape representations, but impaired in mapping these representations onto abstract letter identities, such that she occasionally activates an erroneous letter identity. LETTER DECISION AND ALLOGRAPH REPRESENTATIONS Results from a letter decision task led to a more precise functional localization of L.H.D. s deficit, as well as suggesting an additional level of representation within the letter identification system. Four-character strings were presented, and L.H.D. was asked to indicate for each character whether or not it was a real letter. Half of the characters were real letters, and half were pseudoletters. Figure 3(C) presents two examples of the stimuli. L.H.D. was virtually perfect, correctly classifying 415 of 416 characters (99.8%). Cognitive Neuropsychology, 2014 5

McCLOSKEY AND SCHUBERT identification) can be interpreted by assuming that letter identification processes are intact through the activation of allograph representations, with the impairment affecting the mapping from allographs to abstract letter identities. Figure 4. Letter identification processes with allograph representations. L.H.D. s deficit is localized to the mapping between allograph and abstract letter identity levels. Allographs corresponding to the same letter are shown together for display purposes only; the allograph level does not represent information about which allographs correspond to the same letter identity. The dissociation between impaired letter identification and intact letter decision has also been observed in other patients (e.g., Brunsdon, Coltheart, & Nickels, 2006; Caplan & Hedley- Whyte, 1974; Chanoine, Teixeira Ferreira, Demonet, Nespoulous, & Poncet, 1998; Dalmás & Dansilio, 2000; Miozzo & Caramazza, 1998; Volpato, Bencini, Meneghello, Piron, & Semenza, 2012) and has been taken as evidence for a level of stored allograph representations prior to the level of abstract letter identities. As illustrated in Figure 4, Schubert and McCloskey (in press) proposed in particular that allograph representations intervene between the character shape and abstract letter identity levels, such that character shape representations first activate allograph representations, which in turn activate abstract letter identities. Within this modified theoretical framework, L.H.D. s performance (and that of other patients showing a dissociation between intact letter decision and impaired letter DIGIT IDENTIFICATION PROCESSES The detailed characterization of letter identification processes emerging from the study of L.H.D. s reading provides a foundation for developing hypotheses about digit identification. The early levels of the letter identification process generation of a visual feature map and construction of character shape representations are almost certainly shared with digits. These levels of representation do not even distinguish familiar and unfamiliar shapes (e.g., real letters vs. pseudoletters) and presumably have no basis for distinguishing letters from digits. Beyond the character shape level, however, digit and letter identification might diverge, reflecting the differences between letters and digits. For example, because digits arguably lack true allographic variation, digit identification might be accomplished by a process that does not include an allograph level of representation. Rather, character shape representations may directly activate abstract digit identity representations. Another possibility, suggested by Miozzo and Caramazza (1998), is that digits have allograph but not abstract identity representations, such that number-semantic representations are activated directly from digit allographs. One might even consider the possibility that given their status as logographs, digits require neither allograph nor abstract identity levels; rather, semantic representations could be activated directly by the character shape representations for digits. In contrast to these separate-process hypotheses, a shared-process account assumes that despite the potentially significant differences between letters and digits, a single character identification process mediates identification of both character types. According to this view, letters and digits share not only the feature map 6 Cognitive Neuropsychology, 2014

LETTER AND DIGIT IDENTIFICATION Figure 5. Schematic depiction of a shared character identification process for letters and digits. and character shape levels of representation, but also the allograph and abstract identity levels, as illustrated in Figure 5. On the strongest form of shared-process hypothesis, the categorical distinction between letters and digits is completely irrelevant to the character identification process. We argue that L.H.D. s performance conforms closely to that expected on this strong sharedprocess account. L.H.D. S DIGIT PROCESSING Impaired digit naming Across multiple testing sessions, 1033 strings of 4 to 8 digits were presented with unlimited exposure time. L.H.D. s task was to name the individual digits in sequence (e.g., stimulus 9452, correct response nine four five two ). Although L.H.D. s responses were spoken digit names, we henceforth present examples with the response transcribed into digit form (e.g., 9452 rather than nine four five two ). L.H.D. s naming response was correct for only 813 of the 1033 strings (78%). Her error rate was lower for 4-digit strings (12%) than for 5- to 8-digit strings (23%), x 2 (1, N ¼ 1033) ¼ 9.18, p,.01. Error rate within the 5- to 8-digit range was essentially constant (e.g., 22% for both 5- and 8-digit strings). At the individual digit level, L.H.D. erred in naming 269 of the 6716 total digits (4.0%). Virtually all of her errors (266/269) were digit substitutions (e.g., 3197 3127). The remaining 3 errors were omissions in which L.H.D. was unable to name the digit. Comparison of digit and letter naming Comparison of L.H.D. s digit and letter naming revealed strikingly similar patterns of performance. In three testing sessions, both random 6-digit strings and random 6-letter strings were presented (in separate blocks) for naming. Digit strings (e.g., 957271) were generated from the digits 1 9, and letter strings (e.g., FNKXNS) were generated from the 21 upper-case consonants. Across testing sessions, L.H.D. named the characters in 274 digit strings and 274 letter strings. L.H.D. s accuracy was higher for digit strings than for letter strings: She was correct for 77% of the digit strings (210/274) and 53% of the letter strings (144/274), x 2 (1, N ¼ 548) ¼ 34.76, p,.001. At the individual character level, L.H.D. erred on 4.9% of the digits (81/1644) and 11.1% of the letters (183/1644), x 2 (1, N ¼ 3288) ¼ 42.85, p,.001. Despite the overall digit letter difference, examination of error rates for individual characters did not reveal a strict categorical division between digits and letters. Rather, digit and letter error rates overlapped considerably. For example, the 4.0% error rate for the letter G was lower than the error rate for 7 of the 9 digits; and the 10.6% error rate for the digit 8 was higher than that for 12 of the 21 letters. Except for the overall accuracy difference, L.H.D. s naming performance was extremely similar for digit and letter strings. First, for both Cognitive Neuropsychology, 2014 7

McCLOSKEY AND SCHUBERT letters and digits, virtually all of the errors were substitutions (e.g., 148479 158479, FVMXGY FDMXGY). Second, systematic character perseveration errors were apparent in the substitution errors for both letter and digit strings. Using methods described in detail in McCloskey, Macaruso, and Rapp (2006), Fischer-Baum, McCloskey, and Rapp (2010), and McCloskey, Fischer-Baum, and Schubert (in press), we conducted perseveration analyses separately for digit and letter strings. The analyses revealed that far more often than expected by chance (p,.0001 for both letter and digit analyses), erroneous digits and letters (e.g., the 5 in the 148479 158479 error, and the D in the FVMXGY FDMXGY error) were present in one or both of the two immediately preceding responses. (For example, the FVMXGY FDMXGY error immediately followed the response FBRXTD, which contains a D.) These results demonstrate that some of the substitution errors for both letter and digit strings were perseverations from prior responses. This similarity between letters and digits is especially noteworthy in light of the fact that perseverations are not a pervasive feature of L.H.D. s performance. For example, although her spelling is impaired, L.H.D. does not show perseverations in oral or written spelling. Finally, the serial position functions were extremely similar for letter and digit strings. Figure 6(A) plots the error rate for letters and digits as a function of position within the string. For both letters and digits, the error rate is low in the first position, increases sharply at the second position, is intermediate at positions 3 5, and rises again at position 6. These serial position functions for letter and digit strings differ from those we obtained in studying L.H.D. s reading of words. In singleword reading tasks, L.H.D. showed high letter identification accuracy at the early positions in a word, with steadily increasing error rates at progressively later positions (Schubert & McCloskey, in press). We speculated that the saw-toothed functions for letter and digit strings might reflect a strategy of processing the strings Figure 6. (A) Serial position functions for naming 6-character letter and digit strings. (B) Serial position functions for delayed naming of 4-character letter and digit strings. in chunks, rather than as wholes. For example, if L.H.D. processed digit strings (e.g., 578435) in two-digit chunks (57 84 35), the expected result would be a saw-toothed serial position function very similar to the observed function, assuming lower accuracy for the later (second) than for the earlier (first) position in each chunk. The departures from a perfectly regular saw-tooth pattern may reflect (in addition to simple noise in the data) some variation over trials in chunking of strings (e.g., occasional chunkings such as 57 8 4 35). In an effort to encourage L.H.D. to process letter and digit strings as wholes, we tested her in a delayed naming task with letter and digit strings. On each trial, a string was presented for 2000 ms, and L.H.D. was required to wait until stimulus offset before naming the characters. Strings were limited to four characters (e.g., GLJM, 8476) to minimize memory demands. (Results from a control task with dictated strings indicated that L.H.D. had no difficulty retaining 8 Cognitive Neuropsychology, 2014

LETTER AND DIGIT IDENTIFICATION four-character strings for subsequent report.) Twelve blocks (six letter blocks and six digit blocks) were presented in counterbalanced order, with 25 trials per block. The resulting serial position functions, presented in Figure 6(B), suggest that the task was at least moderately successful in inducing L.H.D. to process the strings as wholes. For both letter and digit strings, the serial position functions now more closely resemble those observed for L.H.D. s singleword reading. Error rate was lowest at the initial position and highest at the final position. However, both functions nevertheless show something of a saw-tooth pattern, suggesting that L.H.D. may at least occasionally have been identifying the characters in two-character chunks despite having to produce her overt responses only after stimulus offset. These results support the interpretation that the serial position functions from the initial letter- and digit-string tasks differed from the functions observed for singleword reading primarily because L.H.D. processed the strings, but not the words, in small chunks. More important for present purposes, though, is that just as in the initial string-naming task, the shape of the serial position function in the delayed naming task was extremely similar for letters and digits. To summarize, comparison of L.H.D. s digitand letter-string naming showed very similar patterns for letters and digits: Errors for both letters and digits were almost exclusively substitutions; perseverations were evident in both letter and digit naming; and the serial position functions were extremely similar for letters and digits in two different tasks. These results are consistent with a deficit affecting a single character identification process that is shared between letters and digits. The only result that might suggest a distinction between letter and digit identification processes is L.H.D. s higher accuracy for digits as a set than for letters as a set. Having shown that L.H.D. s letter- and digitnaming impairments appear similar at an empirical level, we proceed to a more theoretically grounded investigation of the underlying mechanisms. We first report results demonstrating that L.H.D. s digit-naming errors stem from a deficit in visual digit identification. Then, in accord with the shared-process hypothesis, we present evidence that digit identification, like letter identification, implicates an allograph level of representation and that L.H.D. s impairment for digits, like her deficit for letters, arises in mapping allograph to character identity representations. Visual digit identification deficit Results from two tasks demonstrate that L.H.D. s digit-naming errors reflect a deficit in visual digit identification, and not a deficit in digit name retrieval, or some general deficit in numerical processing. Naming digits versus dot patterns Stimuli in this task were random four-number strings with individual numbers ranging from 1 to 6. The strings were presented either in digit form (e.g., 3526), or in the form of the dot patterns that appear on the facets of dice (see Figure 7 for an example). L.H.D. s task was to name the four digits or dot patterns in sequence. The same 96 strings were tested in the digits and dice conditions. Trials were blocked by condition, with eight 24- trial blocks presented in counterbalanced order. L.H.D. s accuracy was 99% (95/96) for strings in the dice condition, but only 85% (82/96) for digit strings, x 2 (1, N ¼ 192) ¼ 12.22, p,.001. Scoring of individual items within strings indicated that L.H.D. erred on 2 of the 384 individual dot patterns (0.5%), and 17 of the 384 digits (4.4%), x 2 (1, N ¼ 768) ¼ 12.14, p,.001. L.H.D. s near-perfect performance in the dice condition argues against the possibility that her errors in naming digits resulted from an impairment in digit name retrieval. Rather, the clear dissociation between the digits and dice conditions Figure 7. Sample stimulus for the dice naming task. Cognitive Neuropsychology, 2014 9

McCLOSKEY AND SCHUBERT suggests that the digit-naming errors reflect a deficit in visual digit identification. Identification of digits versus dictated number words Stimuli in this task were random three-number strings with individual numbers ranging from 1 to 6. In the visual digits condition, the strings were presented in digit form (e.g., 236) for 3000 ms, whereas in the auditory words condition, the strings were dictated sequences of number words (e.g., two three six ). After stimulus presentation was completed, L.H.D. responded by pointing to dice patterns on the response sheet in Figure 8. For example, given the stimulus 236, the correct response consisted of pointing to Figure 8. Dice response sheet for dictated and visual digit identification tasks. the 2-dot pattern in the first column of the response sheet, the 3-dot pattern in the second column, and the 6-dot pattern in the third column. In the auditory words condition, L.H.D. s performance was perfect: 84/84 strings and 252/252 individual numbers correct. However, in the visual digits condition, L.H.D. responded correctly to only 73 of the 84 strings (87%), x 2 (1, N ¼ 168) ¼ 11.78, p,.001, for the difference between visual and auditory conditions. At the level of individual digits, she erred in pointing to the dot pattern for 11 of the 252 digits (4.4%), x 2 (1, N ¼ 512) ¼ 11.25, p,.001, for the visual auditory difference. The dissociation between the visual and auditory conditions points clearly to a deficit in processing of the visual digit stimuli and argues against a more general deficit in numerical processing. Digit decision and digit allographs Schubert and McCloskey (in press) found that L.H.D. was intact in a letter decision task requiring her to discriminate actual letters from pseudoletters. This result provided evidence for a level of letter allograph representations, as well as indicating that L.H.D. was intact in mapping character shapes to allographs. The shared-process hypothesis predicts that we should observe the same pattern with digits. According to this hypothesis, digits as well as letters have stored allograph representations. Furthermore, given the assumption that character identification processes are the same for letters and digits, L.H.D. s intact character-shape-to-allograph mapping for letters implies that the mapping should also be intact for digits. To test this prediction, we presented L.H.D. with a digit decision task requiring her to discriminate between digits and pseudodigits. Stimulus characters were the digits 0 9 and 10 pseudodigits constructed from parts of actual digits. Sixty 6- character strings were generated randomly from the 20 characters, with the constraint that across the 60 strings each character occurred equally often in each serial position. Figure 9 presents two examples of the stimulus strings. The 60 strings were presented individually with unlimited 10 Cognitive Neuropsychology, 2014

LETTER AND DIGIT IDENTIFICATION Figure 9. Two examples of trials from the digit decision task. exposure time, and L.H.D. indicated for each character in the string whether or not the character was a real digit. The results were unequivocal: L.H.D. performed perfectly, classifying all 360 characters correctly as digits or pseudodigits. This result bolsters the conclusion that L.H.D. is intact in character shape perception. More importantly, the striking dissociation between L.H.D. s impaired digit identification and her completely intact digit pseudodigit discrimination implies that digits, like letters, activate stored allograph representations, as shown in Figure 5 (see also Miozzo & Caramazza, 1998, for additional evidence for digit allograph representations). L.H.D. s perfect performance in digit decision indicates that she is intact for digits, as for letters, in mapping from character shape to allograph representations. As in the case of letters, her impairment in digit identification lies beyond the allograph level. These results conform entirely to the predictions of the shared-process hypothesis. The following experiment offers further support for the shared-process hypothesis, providing evidence that L.H.D. s identification errors for letters and digits arise at a shared level of representation. Naming pure letter, pure digit, and mixedcategory strings In this experiment, L.H.D. named the characters in 6-character strings. In the pure letter condition, the strings were composed of upper-case consonants. In the pure digit condition, the strings were made up of digits in the 1 9 range. Finally, in the mixed-category condition, digits and letters were mixed within strings (e.g., PR4Q6N). Across the mixed-category trials, letters and digits were equally frequent. The three conditions were administered in 25-trial blocks presented in counterbalanced order. Across two testing sessions, 500 strings were presented: 150 in the pure letter condition, 150 in the pure digit condition, and 200 in the mixedcategory condition. Whole-string naming accuracy was 73% for pure digit strings (109/150), 50% for pure letter strings (75/150), and 52% for mixed-category strings (104/200). Scoring individual characters within strings, L.H.D. s error rate was 10.7% for letters in pure letter strings, 5.8% for digits in pure digit strings, 14.7% for letters in mixedcategory strings, and 7.6% for digits in mixedcategory strings. In the pure letter and pure digit conditions, all of L.H.D. s substitution errors were within-category: She made 94 letter-for-letter substitutions in the pure letter condition, and 52 digit-fordigit substitutions in the pure digit condition. In the mixed-category condition, however, L.H.D. s naming errors frequently crossed the letter digit boundary: In 54 of her 134 substitution errors, she substituted a digit for a letter (as in 6STVBW 65TBGW) or vice versa (as in BB6VK1 BBGVK1). In fact L.H.D. s errors in the mixed-category condition showed no tendency to preserve the category of the target character (see Table 1). Whether the target character was a letter or a digit, L.H.D. s erroneous responses were more often letters than digits: When the target was a letter, she made 66 letter substitutions and 22 digit substitutions, and when the target was a digit, she made 32 letter substitutions and 14 digit substitutions. The distribution of errors across letter and digit categories did not differ for letter and digit targets, x 2, 1. The failure of L.H.D. s errors to preserve the target character s digit/letter category strongly Cognitive Neuropsychology, 2014 11

McCLOSKEY AND SCHUBERT Table 1. L.H.D. s pattern of substitution errors for characters in mixed-category strings Target Letter Response Digit Letter 66 22 Digit 32 14 suggests that her errors arose at a level where both digits and letters are represented and where, in addition, digits are not distinguished from letters. At the level of representation giving rise to the errors, both digit and letter representations were evidently activated and available for selection, regardless of whether the target character was a letter or digit. Given the evidence that L.H.D. s letter identification errors originate in mapping from allograph to abstract letter identity representations, we can identify the shared level giving rise to both digit and letter errors as a level of abstract character identity representations. We therefore assume, in accord with the shared-process hypothesis, that digits as well as letters have abstract identity representations, and further that L.H.D. s deficit in activating abstract identity representations from allographs affects both letters and digits. We can now offer a straightforward account of L.H.D. s letter and digit identification performance in terms of a single deficit affecting a single process: When either a digit or a letter is presented, L.H.D. constructs an appropriate character shape representation and activates the correct allograph representation. However, activation of abstract character identity representations from allographs is impaired for both digits and letters, and as a result an erroneous representation may be selected at the abstract identity level. Because both letters and digits are represented at this level, a letter may be selected in place of a digit, or vice versa. In fact, because no distinction is made between letters and digits at the abstract identity level, erroneous characters show no tendency to preserve the digit/letter category of the target character. One result, however, remains to be explained: L.H.D. s errors in the pure letter and pure digit conditions were exclusively within category (i.e., letter-for-letter and digit-for-digit). If her deficit affects a level that includes both letter and digit representations, why do we not observe cross-category errors even in pure-list conditions? One possibility is that because L.H.D. knew that characters in the pure lists were all letters or all digits, she was able to suppress cross-category errors through a post-identification editing process. For example, if a character in a pure letter list were initially identified as a digit, the post-identification editor could have flagged the identification as erroneous, leading to reprocessing of the character. A more interesting possibility is that the preservation of target category for pure lists arises within the character identification process itself, even though this process does not in any way distinguish the letter and digit categories. In particular, the evidence that many of L.H.D. s letter and digit identification errors take the form of perseverations suggests the following interpretation: A character will occur as a substitution error only to the extent that it has some residual activation as a consequence of having been processed in the recent past. Consider, for example, an instance in which L.H.D. is attempting to identify an H after having successfully identified a B on the preceding trial. Due to her deficit in mapping from allographs to abstract letter identities, the H representation at the abstract identity level may receive little or no activation, and residual activation from the prior processing of a B may lead to selection of the B representation instead, yielding an H-to-B perseverative substitution error. According to this account, the characters occurring as substitution errors will come from the pool of characters with residual activation from prior processing. In pure letter lists, the only characters with residual activation will be letters, and in pure digit lists the only characters with residual activation will be digits. Consequently, substitutions will be letter-for-letter in pure letter lists, and digit-for-digit in pure digit lists. On this account, pure letter and pure digit lists show preservation of target category not because character 12 Cognitive Neuropsychology, 2014

LETTER AND DIGIT IDENTIFICATION recognition processes somehow reflect the letter/ digit categorical distinction, but simply because the use of pure lists ensures that the characters available to occur as substitution errors come from the same category as the target category. We note that, as required by this interpretation, perseverations were evident in all conditions of the present experiment: Substituted letters were present far more often than expected by chance in the two immediately preceding responses (p,.0001 for each condition). Our interpretation makes an interesting prediction: We should be able to demonstrate preservation of target category for entirely arbitrary categories of characters simply by presenting the characters in pure lists. The following experiment tested this prediction. Arbitrary consonant sets Two arbitrary subsets of consonants were constructed as follows: Using the data from all letter-naming tasks performed by L.H.D., 20 upper-case consonants were matched pairwise for naming accuracy. For example, accuracy was approximately the same for N and H, and for K and B. For each of the 10 resulting pairs, one member was randomly assigned to Set 1, and the other to Set 2 (e.g., N to Set 1 and H to Set 2). The result was two sets of 10 consonants that were approximately matched for naming accuracy, but otherwise arbitrarily composed. Set 1 consisted of C, F, K, M, N, P, S, T, V, Z, and Set 2 of B, D, G, H, J, L, Q, R, W, X. Lists of 25 random 6-letter strings were generated from the 10 Set 1 letters alone (Pure Set 1 lists), from the 10 Set 2 letters alone (Pure Set 2 lists), and from the combined pool of 20 letters (mixed-set lists). In a single testing session, two Pure Set 1, two Pure Set 2, and four mixed-set lists were presented for naming in counterbalanced order. L.H.D. was not informed about the division of consonants into subsets; nor was she told that the various lists differed from one another. Rather, the task was presented simply as a sequence of random letter lists. 2 The results were exceptionally clear. As expected, L.H.D. s substitution errors in the mixed-set lists failed to respect the arbitrary distinction between Set 1 and Set 2. Table 2 presents results from the mixed-set condition. In this condition, the distribution of erroneous letter responses across the Set 1 and Set 2 categories did not differ for Set 1 and Set 2 targets, x 2, 1. On the contrary, for target letters from both Set 1 and Set 2, approximately two thirds of L.H.D. s substitution errors were Set 2 letters. Remarkably, however, L.H.D. s errors in the pure list conditions strongly preserved the category of the target letter (see Table 3). For Set 1 lists, she produced 15 Set 1 letters as substitution errors, but no Set 2 letters; and for Set 2 lists, her errors included 11 Set 2 letters and only 3 Set 1 letters. The difference in distribution of error responses between Set 1 and Set 2 targets was highly reliable, x 2 (1, N ¼ 29) ¼ 15.8, p,.001 (Yates continuity correction applied). A direct comparison between the mixed-set and pure set lists revealed a reliable difference in error pattern. For mixed-set lists, L.H.D. made 20 within-category and 18 cross-category errors, whereas for the pure set lists she made 26 within- and only 3 cross-category errors, x 2 (1, N ¼ 29) ¼ 10.48, p,.01. 3 These findings clearly imply that the preservation of digit and letter target categories for pure digit and pure letter lists should not be 2 L.H.D. showed no awareness of differences in composition among lists, and it is quite unlikely that she acquired explicit knowledge of the two categories. (Indeed, after constructing and administering the tasks, and scoring, analysing, and otherwise pondering the results, the two authors remain unable to sort the consonants into categories.) 3 It is worth noting that all three of the cross-category errors occurred on early trials of pure set lists, perhaps while out-of-set letters retained some residual activation from reading that occurred before presentation of the list. One of the errors (a J to V substitution) occurred on the first trial of a Pure Set 2 list, immediately following a mixed-set list in which the next-to-last trial included a V. The remaining two errors involved reading the LL in HLLRJB as KK on Trial 3 of the first list presented in the experiment. No cross-category errors occurred after Trial 3 in any of the four 25-trial pure set lists. Cognitive Neuropsychology, 2014 13

McCLOSKEY AND SCHUBERT Table 2. L.H.D. s pattern of substitution errors for characters in mixed-set consonant lists Response Table 3. L.H.D. s pattern of substitution errors for characters in Pure Set 1 and Pure Set 2 consonant lists Response Target Set 1 Set 2 Target Set 1 Set 2 Set 1 5 11 Set 2 7 15 Set 1 15 0 Set 2 3 11 taken as evidence for some fundamental distinction between digit and letter identification processes, or even as evidence that character identification mechanisms somehow represent and use the distinction between digit and letter categories in the process of identifying characters. We were able to produce a pattern of results closely mimicking those obtained for letters and digits (preservation of target category for pure but not mixed-category lists) for entirely arbitrary categories of consonants. In both cases, this pattern presumably arose because for mixed lists characters from both categories had residual activation and so were available to occur as substitution errors, whereas for pure lists the only characters with residual activation were characters from the same category as the target character. Digit-letter categorization and naming We have argued that the processing required for identifying a character takes place entirely without regard to whether the character is a letter or digit. Nevertheless, the digit/letter category of a character must obviously be determined at some point in cognitive processing. In a final experiment, we explored when in processing, and on what basis, the category determination is made. The experiment contrasted L.H.D. s ability to classify characters as letters or digits with her ability to name the characters. Stimuli were 64 strings of 6 characters (e.g., 2VG5QS) generated randomly from the digits 2 9 and the upper-case letters A Z, excluding I and O. (The characters I and 1, and O and 0, were excluded because these are confusable in mixed digit letter strings even for neurologically intact individuals.) Across the 64 strings, each of the 32 characters appeared equally often in each of the six serial positions. The 64 strings were divided randomly into two 32-string lists. In a single testing session, each list was presented both for letter digit discrimination and for naming, in an ABBA design. For both tasks, the strings were presented individually with unlimited exposure time. In the digit letter discrimination task, L.H.D. classified each character in the string as a letter or digit, whereas in the naming task she named each character. In the naming task, L.H.D. was correct for only 25 of the 64 strings (39%), and her error rate at the individual character level was 15% (57/384). As in the preceding experiment with mixed letter/digit strings, L.H.D. s naming errors frequently crossed the letter digit boundary: 17 of her 55 substitution errors were digit-to-letter or letterto-digit substitutions. In fact her substitution errors once again showed no tendency to preserve digit/letter category. Regardless of whether the target character was a letter or a digit, L.H.D. s erroneous responses were predominantly letters: When the target character was a letter, she made 37 letter substitutions and 3 digit substitutions, and when the target character was a digit, she made 14 letter substitutions and 1 digit substitution, x 2, 1. In sharp contrast to her impaired character naming performance, L.H.D. s letter digit classification was nearly perfect: At the whole-string level her letter digit classification decisions were entirely correct for 63 of the 64 strings (98%), and at the individual character level she was 99.7% correct (383/384), erring on only a single character. The differences between naming and letter digit 14 Cognitive Neuropsychology, 2014