Neural correlates of merging number words

Origins of numbers: a shared language-of-thought for arithmetic and geometry?

Concepts of exact number are often thought to originate from counting and the successor function, or from a refinement of the approximate number system (ANS). We argue here for a third origin: a shared language-of-thought (LoT) for geometry and arithmetic that involves primitives of repetition, concatenation, and recursive embedding. Applied to sets, those primitives engender concepts of exact integers through recursive applications of additions and multiplications. Links between geometry and arithmetic also explain the emergence of higher-level notions (squares, primes, etc.). Under our hypothesis, understanding a number means having one or several mental expressions for it, and their minimal description length (MDL) determines how easily they can be mentally manipulated. Several historical, developmental, linguistic, and brain imaging phenomena provide preliminary support for our proposal.

Syntactic theory of mathematical expressions

Mathematical expressions consist of recursive combinations of numbers, variables, and operators. According to theoretical linguists, the syntactic mechanisms of natural language also provide a basis for mathematics. To date, however, no theoretically rigorous investigation has been conducted to support such arguments. Therefore, this study uses a methodology based on theoretical linguistics to analyze the syntactic properties of mathematical expressions. Through a review of recent behavioral and neuroimaging studies on mathematical syntax, we report several inconsistencies with theoretical linguistics, such as the use of ternary structures. To address these, we propose that a syntactic category called Applicative plays a central role in analyzing mathematical expressions with seemingly ternary structures by combining binary structures. Besides basic arithmetic expressions, we also examine algebraic equations and complex expressions such as integral and differential calculi. This study is the first attempt at building a comprehensive framework for analyzing the syntactic structures of mathematical expressions.

Top-Down Number Reading: Language Affects the Visual Identification of Digit Strings

Reading numbers aloud involves visual processes that analyze the digit string and verbal processes that produce the number words. Cognitive models of number reading assume that information flows from the visual input to the verbal production processes-a feed-forward processing mode in which the verbal production depends on the visual input but not vice versa. Here, I show that information flows also in the opposite direction, from verbal production to the visual input processes. Participants read aloud briefly presented multi-digit strings in Hebrew, in which the order of words is congruent with the order of digits (21 = twenty-and-one), and in Arabic, in which the ones word precedes the tens word (one-and-twenty). The error-by-digit-position curve was affected by language: relative to Hebrew, in Arabic the error rate was slightly lower for the unit digit and slightly higher for the decade digit, indicating that in Arabic the unit digit was processed earlier and the decade digit later, in accord with the Arabic word order. This language-dependent processing order originated in the visual level and was not a verbal confound, because it persisted even when I controlled for the serial position of the decade/unit word in the verbal number by using numbers with 0 (two hundred three/two hundred thirty). I conclude that the visual analyzer's digit scanning order, decade-first or unit-first, is not fixed but affected by the language in which the number is produced-a top-down, verbal-to-visual information flow.

Syntactic chunking reveals a core syntactic representation of multi-digit numbers, which is generative and automatic

Representing the base-10 structure of numbers is a challenging cognitive ability, unique to humans, but it is yet unknown how precisely this is done. Here, we examined whether and how literate adults represent a number’s full syntactic structure. In 5 experiments, participants repeated number-word sequences and we systematically varied the order of words within each sequence. Repetition on grammatical sequences (e.g., two hundred ninety-seven) was better than on non-grammatical ones (hundred seven two ninety). We conclude that the participants represented the number’s full syntactic structure and used it to merge number words into chunks in short-term memory. Accuracy monotonously improved for sequences with increasingly longer grammatical segments, up to a limit of ~ 4 words per segment, irrespectively of the number of digits, and worsened thereafter. Namely, short chunks improved memorization, whereas oversized chunks disrupted memorization. This chunk size limit suggests that the chunks are not based on predefined structures, whose size limit is not expected to be so low, but are created ad hoc by a generative process, such as the hierarchical syntactic representation hypothesized in Michael McCloskey’s number-processing model. Chunking occurred even when it disrupted performance, as in the oversized chunks, and even when external cues for chunking were controlled for or were removed. We conclude that the above generative process operates automatically rather than voluntarily. To date, this is the most detailed account of the core representation of the syntactic structure of numbers—a critical aspect of numerical literacy and of the ability to read and write numbers.

Syntactic priming reveals an explicit syntactic representation of multi-digit verbal numbers

When we say or understand verbal numbers, a major challenge to the cognitive system is the need to process the number's syntactic structure. Several studies showed that number syntax is handled by dedicated processes, however, it is still unclear how precisely these processes operate, whether the number's syntactic structure is represented explicitly, and if it is - what this representation looks like. Here, we used a novel experimental paradigm, syntactic priming of numbers, which can examine in detail the syntactic representation of multi-digit verbal numbers. In each trial, the participants - Arabic-Hebrew bilinguals and Hebrew monolinguals - heard a multi-digit number and responded orally with a random number. The syntactic structure of their responses was similar to that of the targets, showing that they represented the verbal number's syntax. This priming effect was genuinely syntactic, and could not be explained as lexical - repeating words from the target; as phonological - responding with words phonologically-similar to the target; or as a numerical distance effect - producing responses numerically close to the target. The syntactic priming effect was stronger for earlier words in the verbal number and weaker for later words, suggesting that the syntactic representation is capped by working-memory limits. We propose that syntactic priming could become a useful method to examine various aspects of the syntactic representation of numbers.

Children's neural activity during number line estimations assessed by functional near-infrared spectroscopy (fNIRS)

Number line estimation (NLE) is an educational task in which children estimate the location of a value (e.g., 25) on a blank line that represents a numerical range (e.g., 0-100). NLE performance is a strong predictor of success in mathematics, and error patterns on this task help provide a glimpse into how children may represent number internally. However, a missing and fundamental element of this puzzle is the identification of neural correlates of NLE in children. That is, understanding possible neural signatures related to NLE performance will provide valuable insight into the cognitive processes that underlie children's development of NLE ability. Using functional near-infrared spectroscopy (fNIRS), we provide the first investigation of concurrent behavioral and cortical signatures of NLE performance in children. Specifically, our results highlight significant fronto-parietal changes in cortical activation in response to increases in NLE scale (e.g., 0-100 vs. 0-100,000). Furthermore, our results demonstrate that NLE performance feedback (auditory, visual, or audiovisual), as well as children's grade (2nd vs. 3rd) influence cortical responding during an NLE task.

Cortical collateralization induced by language and arithmetic in non-right-handers

The functional overlap of language and arithmetic is debatable. Although some studies have reported independent representations of arithmetic and language in the brain, other studies have reported shared activity of the two cognitive domains in the inferior frontal gyrus. Although most previous studies have evaluated right-handed individuals, variability of hemispheric dominance in non-right-handed individuals should provide important information on the functional collateralization of these two cognitive domains. The present study evaluated the cortical lateralization patterns of the two cognitive domains using functional magnetic resonance imaging in 30 non-right-handed participants who performed language and arithmetic tasks. We found that language and arithmetic tasks demonstrated shared activity in the bilateral inferior frontal gyrus (IFG). Furthermore, the lateralization patterns of language and arithmetic tasks were correlated with each other. Most participants with language dominance in the left hemisphere also exhibited dominance of arithmetic tasks in the left hemisphere; similarly, most participants with language dominance in the right hemisphere exhibited dominance of arithmetic tasks in the right hemisphere. Among all the brain regions, the precentral gyrus, which is located slightly posterior to the IFG, exhibited the highest correlation coefficient between laterality indices of language and arithmetic tasks. These results suggest a shared functional property between language and arithmetic in the brain.

Shared neural resources of rhythm and syntax: An ALE meta-analysis

A growing body of evidence has highlighted behavioral connections between musical rhythm and linguistic syntax, suggesting that these abilities may be mediated by common neural resources. Here, we performed a quantitative meta-analysis of neuroimaging studies using activation likelihood estimate (ALE) to localize the shared neural structures engaged in a representative set of musical rhythm (rhythm, beat, and meter) and linguistic syntax (merge movement, and reanalysis) operations. Rhythm engaged a bilateral sensorimotor network throughout the brain consisting of the inferior frontal gyri, supplementary motor area, superior temporal gyri/temporoparietal junction, insula, intraparietal lobule, and putamen. By contrast, syntax mostly recruited the left sensorimotor network including the inferior frontal gyrus, posterior superior temporal gyrus, premotor cortex, and supplementary motor area. Intersections between rhythm and syntax maps yielded overlapping regions in the left inferior frontal gyrus, left supplementary motor area, and bilateral insula-neural substrates involved in temporal hierarchy processing and predictive coding. Together, this is the first neuroimaging meta-analysis providing detailed anatomical overlap of sensorimotor regions recruited for musical rhythm and linguistic syntax.

Cortical circuits for mathematical knowledge: evidence for a major subdivision within the brain's semantic networks

Is mathematical language similar to natural language? Are language areas used by mathematicians when they do mathematics? And does the brain comprise a generic semantic system that stores mathematical knowledge alongside knowledge of history, geography or famous people? Here, we refute those views by reviewing three functional MRI studies of the representation and manipulation of high-level mathematical knowledge in professional mathematicians. The results reveal that brain activity during professional mathematical reflection spares perisylvian language-related brain regions as well as temporal lobe areas classically involved in general semantic knowledge. Instead, mathematical reflection recycles bilateral intraparietal and ventral temporal regions involved in elementary number sense. Even simple fact retrieval, such as remembering that 'the sine function is periodical' or that 'London buses are red', activates dissociated areas for math versus non-math knowledge. Together with other fMRI and recent intracranial studies, our results indicated a major separation between two brain networks for mathematical and non-mathematical semantics, which goes a long way to explain a variety of facts in neuroimaging, neuropsychology and developmental disorders.This article is part of a discussion meeting issue 'The origins of numerical abilities'.

What Does "Being an Expert" Mean to the Brain? Functional Specificity and Connectivity in Expertise

To what extent is varying cognitive expertise reflected in the brain's functional specificity and connectivity? We addressed this question by examining expertise in mathematics based on the fact that mathematical skills are one of the most critical cognitive abilities known to be a good predictor of academic achievement. We investigated processing of hierarchical structures, which is a fundamental process for building complex cognitive architecture. Experts and nonexperts in mathematics participated in processing hierarchical structures using algebraic expressions. Results showed that a modulating effect depending on expertise was observed specifically in nonexperts in the left inferior frontal gyrus around pars triangularis and frontal sulcus, the left intraparietal sulcus, and the right inferior parietal lobule. This expertise-dependent pattern of activation led to a crucial dissociation within the left prefrontal cortex. More interestingly, task-related functional networks were also modulated differently in the frontoparietal network for relatively good performance and in the frontostriatal network for poor performance. The present study indicates that a high level of expertise is evident in a small number of specific brain regions, whereas a low level of expertise is reflected by broadly distributed brain areas, along with divergent functional connectivity between experts and nonexperts.

Common neural basis of motor sequence learning and word recognition and its relation with individual differences in reading skill

To investigate the neural basis of a common statistical learning mechanism involved in motor sequence learning and decoding, we recorded same participants' brain activation in a serial reaction time (SRT) and word reading task using functional magnetic resonance imaging. In the SRT, a manual response was made depending on the location of a visual cue, and the order of the locations was either fixed or random. In the word reading task, visual words were passively presented. Compared to less skilled readers, more skilled readers showed greater differences in activation in the inferior frontal gyrus pars triangularis (IFGpTr) and the insula between the ordered and random condition in the SRT task and greater activation in those regions in the word reading task. It suggests that extraction of statistically predictable patterns in the IFGpTr and insula contributes to both motor sequence learning and orthographic learning, and therefore predicts individual differences in decoding skill.

Neural correlates of processing sentences and compound words in Chinese

Sentence reading involves multiple linguistic operations including processing of lexical and compositional semantics, and determining structural and grammatical relationships among words. Previous studies on Indo-European languages have associated left anterior temporal lobe (aTL) and left interior frontal gyrus (IFG) with reading sentences compared to reading unstructured word lists. To examine whether these brain regions are also involved in reading a typologically distinct language with limited morphosyntax and lack of agreement between sentential arguments, an FMRI study was conducted to compare passive reading of Chinese sentences, unstructured word lists and disconnected character lists that are created by only changing the order of an identical set of characters. Similar to previous findings from other languages, stronger activation was found in mainly left-lateralized anterior temporal regions (including aTL) for reading sentences compared to unstructured word and character lists. On the other hand, stronger activation was identified in left posterior temporal sulcus for reading unstructured words compared to unstructured characters. Furthermore, reading unstructured word lists compared to sentences evoked stronger activation in left IFG and left inferior parietal lobule. Consistent with the literature on Indo-European languages, the present results suggest that left anterior temporal regions subserve sentence-level integration, while left IFG supports restoration of sentence structure. In addition, left posterior temporal sulcus is associated with morphological compounding. Taken together, reading Chinese sentences engages a common network as reading other languages, with particular reliance on integration of semantic constituents.

Can neuroimaging help aphasia researchers? Addressing generalizability, variability, and interpretability

Neuroimaging studies of individuals with brain damage seek to link brain structure and activity to cognitive impairments, spontaneous recovery, or treatment outcomes. To date, such studies have relied on the critical assumption that a given anatomical landmark corresponds to the same functional unit(s) across individuals. However, this assumption is fallacious even across neurologically healthy individuals. Here, we discuss the severe implications of this issue, and argue for an approach that circumvents it, whereby: (i) functional brain regions are defined separately for each subject using fMRI, allowing for inter-individual variability in their precise location; (ii) the response profile of these subject-specific regions are characterized using various other tasks; and (iii) the results are averaged across individuals, guaranteeing generalizabliity. This method harnesses the complementary strengths of single-case studies and group studies, and it eliminates the need for post hoc "reverse inference" from anatomical landmarks back to cognitive operations, thus improving data interpretability.