Bayesian validation of grammar productions for the language of thought.

Probabilistic proposals of Language of Thoughts (LoTs) can explain learning across different domains as statistical inference over a compositionally structured hypothesis space. While frameworks may differ on how a LoT may be implemented computationally, they all share the property that they are built from a set of atomic symbols and rules by which these symbols can be combined. In this work we propose an extra validation step for the set of atomic productions defined by the experimenter. It starts by expanding the defined LoT grammar for the cognitive domain with a broader set of arbitrary productions and then uses Bayesian inference to prune the productions from the experimental data. The result allows the researcher to validate that the resulting grammar still matches the intuitive grammar chosen for the domain. We then test this method in the language of geometry, a specific LoT model for geometrical sequence learning. Finally, despite the fact of the geometrical LoT not being a universal (i.e. Turing-complete) language, we show an empirical relation between a sequence's probability and its complexity consistent with the theoretical relationship for universal languages described by Levin's Coding Theorem.

Arithmetic on Your Phone: A Large Scale Investigation of Simple Additions and Multiplications.

We present the results of a gamified mobile device arithmetic application which allowed us to collect vast amount of data in simple arithmetic operations. Our results confirm and replicate, on a large sample, six of the main principles derived in a long tradition of investigation: size effect, tie effect, size-tie interaction effect, five-effect, RTs and error rates correlation effect, and most common error effect. Our dataset allowed us to perform a robust analysis of order effects for each individual problem, for which there is controversy both in experimental findings and in the predictions of theoretical models. For addition problems, the order effect was dominated by a max-then-min structure (i.e 7+4 is easier than 4+7). This result is predicted by models in which additions are performed as a translation starting from the first addend, with a distance given by the second addend. In multiplication, we observed a dominance of two effects: (1) a max-then-min pattern that can be accounted by the fact that it is easier to perform fewer additions of the largest number (i.e. 8x3 is easier to compute as 8+8+8 than as 3+3+…+3) and (2) a phonological effect by which problems for which there is a rhyme (i.e. "seis por cuatro es veinticuatro") are performed faster. Above and beyond these results, our study bares an important practical conclusion, as proof of concept, that participants can be motivated to perform substantial arithmetic training simply by presenting it in a gamified format.

El cerebro lector: últimas noticias de las neurociencias sobre la lectura, la enseñanza, el aprendizaje y la dislexia

Contenido: La nueva ciencia de la lectura. ¿Cómo leemos?. La "caja de letras" del cerebro. El simio lector. La invención de la lectura. Aprender a leer. El cerebro disléxico. La lectura y la simetría. Hacia una cultura de las neuronas. El futuro de la lectura

Education enhances the acuity of the nonverbal approximate number system.

All humans share a universal, evolutionarily ancient approximate number system (ANS) that estimates and combines the numbers of objects in sets with ratio-limited precision. Interindividual variability in the acuity of the ANS correlates with mathematical achievement, but the causes of this correlation have never been established. We acquired psychophysical measures of ANS acuity in child and adult members of an indigene group in the Amazon, the Mundurucú, who have a very restricted numerical lexicon and highly variable access to mathematics education. By comparing Mundurucú subjects with and without access to schooling, we found that education significantly enhances the acuity with which sets of concrete objects are estimated. These results indicate that culture and education have an important effect on basic number perception. We hypothesize that symbolic and nonsymbolic numerical thinking mutually enhance one another over the course of mathematics instruction.

Eye gaze reveals a fast, parallel extraction of the syntax of arithmetic formulas.

Mathematics shares with language an essential reliance on the human capacity for recursion, permitting the generation of an infinite range of embedded expressions from a finite set of symbols. We studied the role of syntax in arithmetic thinking, a neglected component of numerical cognition, by examining eye movement sequences during the calculation of arithmetic expressions. Specifically, we investigated whether, similar to language, an expression has to be scanned sequentially while the nested syntactic structure is being computed or, alternatively, whether this structure can be extracted quickly and in parallel. Our data provide evidence for the latter: fixations sequences were stereotypically organized in clusters that reflected a fast identification of syntactic embeddings. A syntactically relevant pattern of eye movement was observed even when syntax was defined by implicit procedural rules (precedence of multiplication over addition) rather than explicit parentheses. While the total number of fixations was determined by syntax, the duration of each fixation varied with the complexity of the arithmetic operation at each step. These findings provide strong evidence for a syntactic organization for arithmetic thinking, paving the way for further comparative analysis of differences and coincidences in the instantiation of recursion in language and mathematics.

The human Turing machine: a neural framework for mental programs.

In recent years much has been learned about how a single computational processing step is implemented in the brain. By contrast, we still have surprisingly little knowledge of the neuronal mechanisms by which multiple such operations are sequentially assembled into mental algorithms. We outline a theory of how individual neural processing steps might be combined into serial programs. We propose a hybrid neuronal device: each step involves massively parallel computation that feeds a slow and serial production system. Production selection is mediated by a system of competing accumulator neurons that extends the role of these neurons beyond the selection of a motor action. Productions change the state of sensory and mnemonic neurons and iteration of such cycles provides a basis for mental programs.

Flexible intuitions of Euclidean geometry in an Amazonian indigene group.

Kant argued that Euclidean geometry is synthesized on the basis of an a priori intuition of space. This proposal inspired much behavioral research probing whether spatial navigation in humans and animals conforms to the predictions of Euclidean geometry. However, Euclidean geometry also includes concepts that transcend the perceptible, such as objects that are infinitely small or infinitely large, or statements of necessity and impossibility. We tested the hypothesis that certain aspects of nonperceptible Euclidian geometry map onto intuitions of space that are present in all humans, even in the absence of formal mathematical education. Our tests probed intuitions of points, lines, and surfaces in participants from an indigene group in the Amazon, the Mundurucu, as well as adults and age-matched children controls from the United States and France and younger US children without education in geometry. The responses of Mundurucu adults and children converged with that of mathematically educated adults and children and revealed an intuitive understanding of essential properties of Euclidean geometry. For instance, on a surface described to them as perfectly planar, the Mundurucu's estimations of the internal angles of triangles added up to ~180 degrees, and when asked explicitly, they stated that there exists one single parallel line to any given line through a given point. These intuitions were also partially in place in the group of younger US participants. We conclude that, during childhood, humans develop geometrical intuitions that spontaneously accord with the principles of Euclidean geometry, even in the absence of training in mathematics.

Effects of practice on task architecture: combined evidence from interference experiments and random-walk models of decision making.

Does extensive practice reduce or eliminate central interference in dual-task processing? We explored the reorganization of task architecture with practice by combining interference analysis (delays in dual-task experiment) and random-walk models of decision making (measuring the decision and non-decision contributions to RT). The main delay observed in the Psychologically Refractory Period at short stimulus onset asynchronies (SOA) values was largely unaffected by training. However, the range of SOAs over which this interference regime held diminished with learning. This was consistent with an overall shift observed in single-task performance from a highly variable decision time to a reliable (non-decision time) contribution to response time. Executive components involved in coordinating dual-task performance decreased (and became more stable) after extensive practice. The results suggest that extensive practice reduces the duration of central decision stages, but that the qualitative property of central seriality remains a structural invariant.

How learning to read changes the cortical networks for vision and language.

Does literacy improve brain function? Does it also entail losses? Using functional magnetic resonance imaging, we measured brain responses to spoken and written language, visual faces, houses, tools, and checkers in adults of variable literacy (10 were illiterate, 22 became literate as adults, and 31 were literate in childhood). As literacy enhanced the left fusiform activation evoked by writing, it induced a small competition with faces at this location, but also broadly enhanced visual responses in fusiform and occipital cortex, extending to area V1. Literacy also enhanced phonological activation to speech in the planum temporale and afforded a top-down activation of orthography from spoken inputs. Most changes occurred even when literacy was acquired in adulthood, emphasizing that both childhood and adult education can profoundly refine cortical organization.

The brain's router: a cortical network model of serial processing in the primate brain.

The human brain efficiently solves certain operations such as object recognition and categorization through a massively parallel network of dedicated processors. However, human cognition also relies on the ability to perform an arbitrarily large set of tasks by flexibly recombining different processors into a novel chain. This flexibility comes at the cost of a severe slowing down and a seriality of operations (100-500 ms per step). A limit on parallel processing is demonstrated in experimental setups such as the psychological refractory period (PRP) and the attentional blink (AB) in which the processing of an element either significantly delays (PRP) or impedes conscious access (AB) of a second, rapidly presented element. Here we present a spiking-neuron implementation of a cognitive architecture where a large number of local parallel processors assemble together to produce goal-driven behavior. The precise mapping of incoming sensory stimuli onto motor representations relies on a "router" network capable of flexibly interconnecting processors and rapidly changing its configuration from one task to another. Simulations show that, when presented with dual-task stimuli, the network exhibits parallel processing at peripheral sensory levels, a memory buffer capable of keeping the result of sensory processing on hold, and a slow serial performance at the router stage, resulting in a performance bottleneck. The network captures the detailed dynamics of human behavior during dual-task-performance, including both mean RTs and RT distributions, and establishes concrete predictions on neuronal dynamics during dual-task experiments in humans and non-human primates.

Neurophysiological bases of exponential sensory decay and top-down memory retrieval: a model.

Behavioral observations suggest that multiple sensory elements can be maintained for a short time, forming a perceptual buffer which fades after a few hundred milliseconds. Only a subset of this perceptual buffer can be accessed under top-down control and broadcasted to working memory and consciousness. In turn, single-cell studies in awake-behaving monkeys have identified two distinct waves of response to a sensory stimulus: a first transient response largely determined by stimulus properties and a second wave dependent on behavioral relevance, context and learning. Here we propose a simple biophysical scheme which bridges these observations and establishes concrete predictions for neurophsyiological experiments in which the temporal interval between stimulus presentation and top-down allocation is controlled experimentally. Inspired in single-cell observations, the model involves a first transient response and a second stage of amplification and retrieval, which are implemented biophysically by distinct operational modes of the same circuit, regulated by external currents. We explicitly investigated the neuronal dynamics, the memory trace of a presented stimulus and the probability of correct retrieval, when these two stages were bracketed by a temporal gap. The model predicts correctly the dependence of performance with response times in interference experiments suggesting that sensory buffering does not require a specific dedicated mechanism and establishing a direct link between biophysical manipulations and behavioral observations leading to concrete predictions.

Limits on introspection: distorted subjective time during the dual-task bottleneck.

Which cognitive processes are accessible to conscious report? To study the limits of conscious reportability, we designed a novel method of quantified introspection, in which subjects were asked, after each trial of a standard cognitive task, to estimate the time spent completing the task. We then applied classical mental-chronometry techniques, such as the additive-factors method, to analyze these introspective estimates of response time. We demonstrate that introspective response time can be a sensitive measure, tightly correlated with objective response time in a single-task context. In a psychological-refractory-period task, however, the objective processing delay resulting from interference by a second concurrent task is totally absent from introspective estimates. These results suggest that introspective estimates of time spent on a task tightly correlate with the period of availability of central processing resources.

Brain mechanisms of serial and parallel processing during dual-task performance.

The psychological refractory period (PRP) refers to the fact that humans typically cannot perform two tasks at once. Behavioral experiments have led to the proposal that, in fact, peripheral perceptual and motor stages continue to operate in parallel, and that only a central decision stage imposes a serial bottleneck. We tested this model using neuroimaging methods combined with innovative time-sensitive analysis tools. Subjects performed a dual-task visual-auditory paradigm in which a delay of 300 ms was injected into the auditory task either within or outside of the dual-task interference period. Event-related potentials indicated that the first approximately 250 ms of processing were insensitive to dual-task interference, and that the PRP was mainly reflected in a delayed global component. By a clustering analysis based on time-resolved functional magnetic resonance imaging, we identified networks with qualitatively different timing properties: sensory areas tracked the objective time of stimulus presentation, a bilateral parietoprefrontal network correlated with the PRP delay, and an extended bilateral network that included bilateral posterior parietal cortex, premotor cortex, supplementary motor area, anterior part of the insula, and cerebellum was shared by both tasks during the extent of dual-task performance. The results provide physiological evidence for the coexistence of serial and parallel processes within a cognitive task.

Log or linear? Distinct intuitions of the number scale in Western and Amazonian indigene cultures.

The mapping of numbers onto space is fundamental to measurement and to mathematics. Is this mapping a cultural invention or a universal intuition shared by all humans regardless of culture and education? We probed number-space mappings in the Mundurucu, an Amazonian indigene group with a reduced numerical lexicon and little or no formal education. At all ages, the Mundurucu mapped symbolic and nonsymbolic numbers onto a logarithmic scale, whereas Western adults used linear mapping with small or symbolic numbers and logarithmic mapping when numbers were presented nonsymbolically under conditions that discouraged counting. This indicates that the mapping of numbers onto space is a universal intuition and that this initial intuition of number is logarithmic. The concept of a linear number line appears to be a cultural invention that fails to develop in the absence of formal education.

Illusory displacement due to object substitution near the consciousness threshold.

A briefly presented target shape can be made invisible by the subsequent presentation of a mask that replaces the target. While varying the target-mask interval in order to investigate perception near the consciousness threshold, we discovered a novel visual illusion. At some intervals, the target is clearly visible, but its location is misperceived. By manipulating the mask's size and target's position, we demonstrate that the perceived target location is always displaced to the boundary of a virtual surface defined by the mask contours. Thus, mutual exclusion of surfaces appears as a cause of masking.

Core knowledge of geometry in an Amazonian indigene group.

Does geometry constitute a core set of intuitions present in all humans, regardless of their language or schooling? We used two nonverbal tests to probe the conceptual primitives of geometry in the Mundurukú, an isolated Amazonian indigene group. Mundurukú children and adults spontaneously made use of basic geometric concepts such as points, lines, parallelism, or right angles to detect intruders in simple pictures, and they used distance, angle, and sense relationships in geometrical maps to locate hidden objects. Our results provide evidence for geometrical intuitions in the absence of schooling, experience with graphic symbols or maps, or a rich language of geometrical terms.

Exact and approximate arithmetic in an Amazonian indigene group.

Is calculation possible without language? Or is the human ability for arithmetic dependent on the language faculty? To clarify the relation between language and arithmetic, we studied numerical cognition in speakers of Mundurukú, an Amazonian language with a very small lexicon of number words. Although the Mundurukú lack words for numbers beyond 5, they are able to compare and add large approximate numbers that are far beyond their naming range. However, they fail in exact arithmetic with numbers larger than 4 or 5. Our results imply a distinction between a nonverbal system of number approximation and a language-based counting system for exact number and arithmetic.