Research ReportSerial and syntactic processing in the visual analysis of multi-digit numbers
Introduction
The human ability to combine visually presented letters and digits into words and numbers, to understand them, and to say them aloud is anything but trivial. Most adult readers are able to convert letter strings and digit strings into words and numbers while applying complex conversion rules, and they do so quickly, effortlessly, and with only a few mistakes. Although letters and digits have similar visual characteristics, the visual analysis of letter strings and digit strings is performed by two separate cognitive systems, located in separate brain regions (Abboud et al., 2015; Crutch & Warrington, 2007; Déjerine, 1892; Priftis et al., 2013; see review in Dotan & Friedmann, 2019). Here we examine the visual analysis of digit strings in detail and ask why it is separate from the that of letter strings.
Dotan and Friedmann (2018) recently proposed a detailed cognitive model for reading aloud digit strings as numbers. In accordance with previous studies (e.g., Benson & Denckla, 1969; Dehaene, 1992; McCloskey, 1992), this model postulates separate processes for the visual analysis of the digit string and the verbal production of the corresponding number words. The model further proposes that visual analysis consists of 5 sub-processes: encoding the digit identities; encoding their relative order; detecting how many digits the number has; encoding the positions of 0; and grouping the digits into triplets. The first two processes provide the sequence of digits in the number. The latter 3 processes encode the syntactic structure of the digit string (hereafter “decimal structure”). The decimal structure (number length, 0 positions, grouping into triplets) and the ordered digit identities are redundant pieces of information, however, there may be good reasons for the visual analyzer to put extra effort into extracting the decimal-structure information from the digit string via dedicated processes: this information is especially important for the subsequent processing stages (Cohen & Dehaene, 1991; Dotan & Friedmann, 2018). In particular, if the task at hand requires converting the number to its verbal representation (e.g., when reading aloud), the digit string's decimal structure is important because it determines the syntactic structure of the number's verbal representation – the number of words to be produced and their lexical classes (ones, tens, etc.; Cohen & Dehaene, 1991; McCloskey et al., 1986). Thus, reliable encoding of the decimal structure may help create the verbal representation more quickly and with fewer errors. The decimal structure is also important if the task requires converting the number to the quantity it represents – e.g., when deciding whether a number is smaller or larger than another number. In this case, the number length may be required to initialize the digits-to-quantity conversion mechanism (Dotan & Dehaene, 2020b), and 0 seems to be processed in the quantity system in a different way than other digits (Pinhas & Tzelgov, 2012).
These particular properties of numbers provide a principled reason for the existence of the 3 syntactic processes within the digit visual analyzer. Importantly, they also provide a possible reason for the cognitive separation of the visual analyzers of digit and letter strings: even if letters and digits are visually similar, the syntactic structures of letter strings and digit strings are quite different. The structure of a digit string is described above; letter strings have structure as well, e.g., the word's morphological structure, the distinction between consonants and vowels, etc. Thus, understanding how the numeric visual analyzer handles the number syntax may shed light not only on the number reading mechanisms, but also on the reasons for the distinction between word-parsing and number-parsing processes. The present study focuses on two specific aspects of the visual analysis of numbers: the order of processing the digits and the putative dedicated process that encodes the position of 0.
Only a few studies have examined the order of processing the digits in a digit string. Most of these have aimed to arbitrate between two models – either processing the digits in parallel or processing them serially from left to right – and used a number-comparison paradigm. In this paradigm, participants see two multi-digit numbers and are asked to judge which is larger, or, alternatively, they see a single number and are asked to compare it to a fixed reference number. These studies have concluded that the digits of 2- and 3-digit numbers are processed in parallel, but in longer numbers, they are processed serially (Bahnmueller et al., 2016; Dotan & Dehaene, 2020b; Meyerhoff et al., 2012).
As far as we know, only one study has examined the order of processing the digits in a reading aloud task (Friedmann et al., 2010). This study described two adults with a reading disorder that selectively impaired their encoding of the relative order of digits in a digit string. These two individuals made many digit transposition errors when reading numbers. Crucially, they made more errors for digits farther to the right, with the maximal number of transpositions being between the decade and the unit digits. One explanation of this finding is that the digits were processed serially, from left to right. Several specific architectures can explain why such serial processing could result in the error rate increasing for digits farther to the right; for example, the cognitive load may increase with additional digits, or later digits may receive less attentional resources. Note, however, that serial processing is not the only interpretation of a left-to-right increasing error gradient; an alternative interpretation could be an attentional bias to the left. We return to this point in the Discussion.
Friedmann et al. (2010) clearly showed the error rate was higher for digits farther to the right. However, the two participants in their study had a digit-order encoding deficit, which may have affected the order of processing the digits, so it is hard to generalize any conclusion to the general population. In our study, to assess serial versus parallel processing in number reading, we examined the error-by-position pattern for participants without cognitive disorders. As we shall see, we observed a similar serial-like pattern here too.
In readers without disorders, another effect is sometimes observed: fewer errors in the leftmost and rightmost digits than in the inner digits (Chanceaux & Grainger, 2012). This outer-character advantage is a common finding in tasks using letter strings (Estes et al., 1976; Gomez et al., 2008; Hammond & Green, 1982; Townsend et al., 1971; Tydgat & Grainger, 2009; Wolford, 1975). One explanation of this effect is crowding. More specifically, the two outer characters have fewer neighboring characters than inner characters, so they are less susceptible to visual interference. Note that the outer-digit advantage is not mutually exclusive to serial or parallel processing – it may exist in both.
Experiments showing an outer-digit advantage have typically used a character-detection task, arguably evoking a visual analysis process that differs somewhat from the process involved in reading words and numbers. Still, as we go on to explain, here we observed a similar outer-digit advantage with a number-reading task. In the Discussion, we return to possible interpretations of the outer-digit advantage.
Dotan and Friedmann (2018) proposed that 3 visual analysis processes encode the digit string's decimal structure: encoding the number length, grouping the digit string into triplets, and encoding the positions of 0. Of these three processes, for the former two, Dotan and Friedmann showed clear neuropsychological dissociations: they found at least one individual for whom each of the two processes was selectively impaired (participants MA, ED, NL). In contrast, for the “zero detector”, they only found a subtle dissociation: participant EY, who had a selective deficit in digit position encoding, made digit position errors in the digits 2–9 but not in 0. Another relevant study was by Cohen and Dehaene (1991). Their patient YM made digit substitution errors in the digits 2–9 but not in 0 and 1. The effect was clear, but YM showed the superiority of 0 and 1 only in some tasks, so this effect could not be unambiguously attributed to the visual analyzer. Thus, although both studies showed 0 is different from the other digits, additional evidence may be useful to unequivocally support the notion of a dedicated zero-detection process within the visual analyzer. In the present study we provide such evidence, and we also examine in more detail how 0 and 1 are processed.
Another issue is the role of the digit 1. The principled reason for a zero-detection process is presumably the special role of 0 in the number system. In the verbal system, 0 is never pronounced when it appears in a multi-digit string. In the quantity system (Approximate Number System, ANS; Dehaene, 1997), zero – “nothing” – is perceived as qualitatively different from the “something” quantities (Pinhas & Tzelgov, 2012). The role of 1 does not seem to be as special in either system. In the verbal system, the digit 1 creates a verbal irregularity only in the case of teen words (in English as well as in Hebrew, in which the present study was conducted). In the ANS, 1 may be processed like any other quantity. This raises the possibility that the visual analyzer does not treat 1 in a special manner as it treats 0, or at least not to the same extent. Indeed, Dotan and Friedmann (2018) hypothesized that the special treatment of 1 is not a default behavior of the visual analyzer, but occurs only in the context of a reading aloud task. In their study, participants showed superior processing of both 0 and 1, and the task was reading numbers aloud. In the present study too, our findings suggested that at least when the task is reading numbers aloud, 1 is treated in a special manner.
Our participants read aloud multi-digit numbers presented as digit strings. Thus, unlike previous studies, we examined serial versus parallel processing in a natural reading context among adults without reading disorders. We examined the errors rates for each digit. Similar to Friedmann et al. (2010), we reasoned that if the digits were processed serially, the error rate should increase for digits farther to the right. This was indeed the case. Some of the numbers included 0 and 1; this allowed us to examine whether the processing of these two digits was superior to the processing of the digits 2–9. We found that it was. Our participants did not have any known cognitive disorders, so to elicit errors, we presented each number for a short duration.
Section snippets
Participants
Twenty-five adults participated in this study. The paradigm is new and we did not have a predicted effect size, so this sample size was determined (prior to data collection) to a reasonable standard. The participants were native speakers of Hebrew without known cognitive disorders and with normal or corrected-to-normal vision. All participants gave informed consent. One participant was extremely inattentive and was excluded before we started the data analysis. The remaining 24 participants were
Results
The task was clearly not easy: the average digit identification rate was 63% (SD = 13%; the per-participant average was between 36% and 87%). The identified digits were produced in the correct position in 86% of the cases on average (SD = 5%; the per-participant average was between 78% and 95%). Fig. 2 shows participants’ performance for each number length and exposure duration.
Summary of findings
This study examined in detail the processes we use to visually analyze digit strings when we read multi-digit numbers. Participants read aloud 3-, 4-, and 5-digit numbers presented in short exposure durations. The main findings were as follows.
1. Digit position affected performance. The rate of digit identification errors (failing to identify a digit) and digit position errors (saying a digit in the incorrect decimal position) was not uniform across decimal positions. It was affected by a
Credit author statement
Dror Dotan: Conceptualization, Methodology, Software, Formal Analysis, Writing - Original Draft, Writing - Review & Editing, Project administration, Supervision.
Ofir Eliahou: Conceptualization, Methodology, Investigation, Project administration.
Sharon Cohen: Conceptualization, Methodology, Investigation, Project administration.
Open practices
The study in this article earned Open Materials and Open Data badges for transparent practices. Materials and data for the study are available at https://osf.io/2adcs/.
Acknowledgements
This research was supported by a grant from the Jacobs Foundation (grant no. 2019-1320-05). We thank Maya Yachini and Naama Friedmann for their advice on the analysis and interpretation of the data, Tom Maayan for her help in the data processing, and Elizabeth Thompson for reviewing the manuscript.
References (58)
Visual interference in the parafoveal recognition of initial and final letters of words
Vision Research
(1973)- et al.
Serial position effects in the identification of letters, digits, symbols, and shapes in peripheral vision
Acta Psychologica
(2012) Varieties of numerical abilities
Cognition
(1992)- et al.
The neural code for written words: A proposal
Trends in Cognitive Sciences
(2005) - et al.
Cross-linguistic regularities in the frequency of number words
Cognition
(1992) - et al.
Parallel and serial processes in number-to-quantity conversion
Cognition
(2020) - et al.
A cognitive model for multidigit number reading: Inferences from individuals with selective impairments
Cortex; a Journal Devoted To the Study of the Nervous System and Behavior
(2018) - et al.
Separate mechanisms for number reading and word reading: Evidence from selective impairments
Cortex; a Journal Devoted To the Study of the Nervous System and Behavior
(2019) - et al.
Breaking down number syntax: Spared comprehension of multi-digit numbers in a patient with impaired digit-to-word conversion
Cortex; a Journal Devoted To the Study of the Nervous System and Behavior
(2014) - et al.
Computational precision of mental inference as critical source of human choice suboptimality
Neuron
(2016)