The infancy of the human brain

The human infant brain is the only known machine able to master a natural language and develop explicit, symbolic, and communicable systems of knowledge that deliver rich representations of the external world. With the emergence of non-invasive brain imaging, we now have access to the unique neural machinery underlying these early accomplishments. After describing early cognitive capacities in the domains of language and number, we review recent findings that underline the strong continuity between human infants’ and adults’ neural architecture, with notably early hemispheric asymmetries and involvement of frontal areas. Studies of the strengths and limitations of early learning, and of brain dynamics in relation to regional maturational stages, promise to yield a better understanding of the sources of human cognitive achievements.This work was supported by the Center for Brains, Minds and Machines (CBMM), funded by NSF STC award CCF – 1231216

The role of right and left parietal lobes in the conceptual processing of numbers

Neuropsychological and functional imaging studies have associated the conceptual processing of numbers with bilateral parietal regions (including intraparietal sulcus). However, the processes driving these effects remain unclear because both left and right posterior parietal regions are activated by many other conceptual, perceptual, attention, and response-selection processes. To dissociate parietal activation that is number-selective from parietal activation related to other stimulus or response-selection processes, we used fMRI to compare numbers and object names during exactly the same conceptual and perceptual tasks while factoring out activations correlating with response times. We found that right parietal activation was higher for conceptual decisions on numbers relative to the same tasks on object names, even when response time effects were fully factored out. In contrast, left parietal activation for numbers was equally involved in conceptual processing of object names. We suggest that left parietal activation for numbers reflects a range of processes, including the retrieval of learnt facts that are also involved in conceptual decisions on object names. In contrast, number selectivity in right parietal cortex reflects processes that are more involved in conceptual decisions on numbers than object names. Our results generate a new set of hypotheses that have implications for the design of future behavioral and functional imaging studies of patients with left and right parietal damage

Number-space associations in synaesthesia are not influenced by finger-counting habits

In many cultures, one of the earliest representations of number to be learned is a finger-counting system. Although most children stop using their fingers to count as they grow more confident with number, traces of this system can still be seen in adulthood. For example, an individual's finger-counting habits appear to affect the ways in which numbers are implicitly associated with certain areas of space, as inferred from the spatial–numerical association of response codes (SNARC) effect. In this study, we questioned the finger-counting habits of 98 participants who make explicit, idiosyncratic associations between number and space, known as number-space synaesthesia. Unexpectedly, neither handedness nor finger-counting direction (left-to-right or right-to-left) was associated with the relative positions of 1 and 10 in an individual's number-space synaesthesia. This lack of association between finger-counting styles and number-space synaesthesia layout may result from habitual use of synaesthetic space rather than fingers when learning to count; we offer some testable hypotheses that could assess whether this is the case

A comparison of the entanglement measures negativity and concurrence

In this paper we investigate two different entanglement measures in the case of mixed states of two qubits. We prove that the negativity of a state can never exceed its concurrence and is always larger then $\sqrt{(1-C)^2+C^2}-(1-C)$ where $C$ is the concurrence of the state. Furthermore we derive an explicit expression for the states for which the upper or lower bound is satisfied. Finally we show that similar results hold if the relative entropy of entanglement and the entanglement of formation are compared

Spatially Invariant Coding of Numerical Information in Functionally Defined Subregions of Human Parietal Cortex

Macaque electrophysiology has revealed neurons responsive to number in lateral (LIP) and ventral (VIP) intraparietal areas. Recently, fMRI pattern recognition revealed information discriminative of individual numbers in human parietal cortex but without precisely localizing the relevant sites or testing for subregions with different response profiles. Here, we defined the human functional equivalents of LIP (feLIP) and VIP (feVIP) using neurophysiologically motivated localizers. We applied multivariate pattern recognition to investigate whether both regions represent numerical information and whether number codes are position specific or invariant. In a delayed number comparison paradigm with laterally presented numerosities, parietal cortex discriminated between numerosities better than early visual cortex, and discrimination generalized across hemifields in parietal, but not early visual cortex. Activation patterns in the 2 parietal regions of interest did not differ in the coding of position-specific or position-independent number information, but in the expression of a numerical distance effect which was more pronounced in feLIP. Thus, the representation of number in parietal cortex is at least partially position invariant. Both feLIP and feVIP contain information about individual numerosities in humans, but feLIP hosts a coarser representation of numerosity than feVIP, compatible with either broader tuning or a summation cod

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.Psycholog

Exact Equality and Successor Function: Two Key Concepts on the Path Towards Understanding Exact Numbers

Humans possess two nonverbal systems capable of representing numbers, both limited in their representational power: the first one represents numbers in an approximate fashion, and the second one conveys information about small numbers only. Conception of exact large numbers has therefore been thought to arise from the manipulation of exact numerical symbols. Here, we focus on two fundamental properties of the exact numbers, as prerequisites to the concept of exact numbers: the fact that all numbers can be generated by a successor function, and the fact that equality between numbers can be defined in an exact fashion. We discuss some recent findings assessing how speakers of Mundurucu (an Amazonian language), and young western children (3-4 years old) understand these fundamental properties of numbers.Psycholog

Response to Comment on “Log or Linear? Distinct Intuitions of the Number Scale in Western and Amazonian Indigene Cultures

The performance of the Mundurucu on the number-space task may exemplify a general competence for drawing analogies between space and other linear dimensions, but Mundurucu participants spontaneously chose number when other dimensions were available. Response placement may not reflect the subjective scale for numbers, but Cantlon et al.’s proposal of a linear scale with scalar variability requires questionable additional hypotheses.Psycholog