Encoding Numbers in the Context of Multiple Overlapping Cues: Evidence from a Chinese Finger Number Cognition Study

How people encode numbers in the context of multiple overlapping encoded cues remains unclear. In this study, we explored Chinese finger numbers, which contain both a numerical magnitude cue and a left-right hand cue offered by the expressing hand, to investigate the number encoding mechanism in the context of multiple overlapping cues. Chinese finger numbers expressed by the left or right hand were randomly and centrally presented on a computer screen to participants who were asked to perform a hand classification task (Experiment 1), a magnitude classification task (Experiment 2), a parity classification task (Experiment 3) and a magnitude classification or ring classification task (Experiment 4). We discovered (a) only an association effect between the pressed key and the expressing hand in hand classification and parity classification tasks, (b) the SNARC effect only on the magnitude classification task, (c) the association effect between the pressed key and the expressing hand on the larger, Chinese finger number, magnitude classification task in Experiment 2, and (d) the SNARC effect and the association between the pressed key and the expressing hand were reversed on the ring classification task. From these results, we concluded that people can flexibly choose appropriate number encoding cues and how numbers are encoded in the context of multiple overlapping cues depending on (a) which cognition task individuals perform and (b) the character of the numbers involved.

Numerosities and Other Magnitudes in the Brains: A Comparative View

The ability to represent, discriminate, and perform arithmetic operations on discrete quantities (numerosities) has been documented in a variety of species of different taxonomic groups, both vertebrates and invertebrates. We do not know, however, to what extent similarity in behavioral data corresponds to basic similarity in underlying neural mechanisms. Here, we review evidence for magnitude representation, both discrete (countable) and continuous, following the sensory input path from primary sensory systems to associative pallial territories in the vertebrate brains. We also speculate on possible underlying mechanisms in invertebrate brains and on the role played by modeling with artificial neural networks. This may provide a general overview on the nervous system involvement in approximating quantity in different animal species, and a general theoretical framework to future comparative studies on the neurobiology of number cognition.

Characterising ontogeny of numerosity discrimination in zebrafish reveals use of multiple, numerical and non- numerical mechanisms

Non-symbolic number cognition based on an approximate sense of magnitude has been documented in adult zebrafish. Here we investigated the ontogeny of this ability using a group size preference task in juvenile zebrafish. Fish showed group size preference from 26 days post fertilization (dpf) and from 27 dpf fish reliably chose the larger group when presented with discrimination ratios from 1:8 to 2:3. When the ratio between the number of conspecifics in each group was maintained at 1:2, fish could discriminate between 1 vs. 2 individuals and 3 vs. 6, but not when given a choice between 2 vs. 4 individuals. These findings suggest that the systems involved in numerosity representation in fish do not operate separately from other cognitive mechanisms. Rather they suggest numerosity processing is the result of an interplay between attentional, cognitive and memory-related mechanisms that orchestrate numerical competence both in humans and animals. Our results emphasise the potential of the use of zebrafish to explore the genetic and neural processes underlying the ontogeny of number cognition.

Unwarranted philosophical assumptions in research on ANS

Clarke and Beck import certain assumptions about the nature of numbers. Although these are widespread within research on number cognition, they are highly contentious among philosophers of mathematics. In this commentary, we isolate and critically evaluate one core assumption: the identity thesis.

Neurons in the dorso-central division of zebrafish pallium respond to change in visual numerosity

Non-symbolic number cognition based on an approximate sense of magnitude has been documented in zebrafish. Here we investigated for the first time its neural bases. Zebrafish were habituated to a set of three or nine small dots associated with food reward. During habituation trials, the dots changed in their individual size, position and density maintaining their numerousness and overall surface area. In the dishabituation test, zebrafish faced a change (i) in number (from three to nine or vice versa with the same overall surface), (ii) in shape (with the same overall surface and number), or (iii) in size (with the same shape and number); in a control group (iv) zebrafish faced the same familiar stimuli as during the habituation. Using qPCR to measure modulation of the expression of the immediate early genes c-fos and egr-1 and in-situ hybridization to count egr1-positive cells we found a specific and selective activation of the caudal part of the dorso-central (Dc) division of the zebrafish pallium upon change in numerosity. As pallial regions are implicated in number cognition in mammals and birds, these findings support the existence of an evolutionarily conserved mechanism for approximate magnitude and provide an avenue for exploring the underlying molecular correlates.

The Neuropsychology of Acquired Number and Calculation Disorders

Acalculia is an acquired disorder of number and/or calculation skills following cerebral damage (Henschen, 1919) which affects about 20% of patients with left hemisphere injury. The inability to use numbers can be very incapacitating as it interferes with several everyday activities such as shopping and using bank accounts and telephones (Butterworth, 1999; Dehaene, 1997). After introducing the main cognitive and anatomical features of the normal number system, this chapter will discuss the main historical and contemporary achievements in the neuropsychology of number cognition. These achievements concern: understanding that the number system is fractionated in distinct subcomponents; characterizing the relation between number and other cognitive skills; defining the role of the brain regions that cause number and calculation disorders or that allow maintenance of residual number skills; and identifying tools for the assessment and the possible rehabilitation of acalculia.