Counting While Talking: Different Signatures for Verbal and Nonverbal Counting (original) (raw)
The perception of number from long-term memory
Abstract The perception of numerosity is supported by two systems: an exact system for small quantities, and an approximate system for large quantities. Two properties arise from the combination of these two systems: the accuracy of numerosity judgments changes qualitatively above the capacity limit for exact representations, and the ability to discriminate two quantities depends on the numerical distance between the quantities and the relationship of this distance to the absolute magnitudes.
Nonverbal Counting in Humans: The Psychophysics of Number Representation
Psychological Science, 1999
In non-verbal counting tasks derived from the animal literature, adult human subjects repeatedly attempted to produce target numbers of key presses at rates that made vocal or subvocal counting difficult or impossible. In a second task, they estimated the number of flashes in a rapid, randomly timed sequence. Congruent with the animal data, mean estimates in both tasks were proportional to target values, as was the variability in the estimates. Converging evidence makes it unlikely that subjects used verbal counting or time durations to perform these tasks. The results support the hypothesis that adult humans share with non-verbal animals a system for representing number by magnitudes that have scalar variability (a constant coefficient of variation). The mapping of numerical symbols to mental magnitudes provides a formal model of the underlying non-verbal meaning of the symbols (a model of numerical semantics).
A memory-based account of automatic numerosity processing
Memory & Cognition, 2005
We investigated the mechanisms responsible for the automatic processing of the numerosities represented by digits in the size congruity effect (Henik & Tzelgov, 1982). The algorithmic model assumes that relational comparisons of digit magnitudes (e.g., larger than {8,2}) create this effect. If so, congruity effects ought to require two digits. Memory-based models assume that associations between individual digits and the attributes "small" and "large" create this effect. If so, congruity effects ought only to require one digit. Contrary to the algorithmic model and consistent with memory-based models, congruity effects were just as large when subjects judged the relative physical sizes of small digits paired with letters as when they judged the relative physical sizes of two digits. This finding suggests that size congruity effects can be produced without comparison algorithms.
The averaging of numerosities: A psychometric investigation of the mental line
Attention, perception & psychophysics, 2020
Humans and animals are capable of estimating and discriminating nonsymbolic numerosities via mental representation of magnitudes-the approximate number system (ANS). There are two models of the ANS system, which are similar in their prediction in numerosity discrimination tasks. The log-Gaussian model, which assumes numerosities are represented on a compressed logarithmic scale, and the scalar variability model, which assumes numerosities are represented on a linear scale. In the first experiment of this paper, we contrasted these models using averaging of numerosities. We examined whether participants generate a compressed mean (i.e., geometric mean) or a linear mean when averaging two numerosities. Our results demonstrated that half of the participants are linear and half are compressed; however, in general, the compression is milder than a logarithmic compression. In Experiments 2 and 3, we examined averaging of numerosities in sequences larger than two. We found that averaging precision increases with sequence length. These results are in line with previous findings, suggesting a mechanism in which the estimate is generated by population averaging of the responses each stimulus generates on the numerosity representation.
Psychonomic Bulletin & Review
There is an ongoing, vibrant debate about whether numerical information in both nonsymbolic and symbolic notations would be supported by different neurocognitive systems or rather by a common preverbal approximate number system, which is ratio dependent and follows Weber's law. Here, we propose that the similarities between nonsymbolic and symbolic number processing can be explained based on the principle of efficient coding. To probe this hypothesis we employed a new empirical approach, by predicting the behavioural performance in number comparison tasks with symbolic (i.e., number words) and nonsymbolic (i.e., arrays of dots) information not only from numerical ratio, but for the first time also from natural language data. That is, we used data extracted from vector-space models that are informative about the distributional pattern of numberwords usage in natural language. Results showed that linguistic estimates predicted the behavioural performance in both symbolic and nonsymbolic tasks. However, and critically, our results also showed a task-dependent dissociation: linguistic data better predicted the performance in the symbolic task, whereas real numerical ratio better predicted the performance in the nonsymbolic task. These findings indicate that efficient coding of environmental regularities is an explanatory principle of human behavior in tasks involving numerical information. They also suggest that the ability to discriminate a stimulus from similar ones varies as a function of the specific statistical structure of the considered learning environment.
Electrophysiological evidence for differential processing of numerical quantity and order in humans
Cognitive Brain Research, 2004
Numbers convey different meanings when used in different contexts . In a cardinal context, a number will tell us how many entities are in a set and convey quantity meaning. In an ordinal context, a number will refer to the relative position (or rank) of one element within a sequence; non-numerical ordered series (e.g. the letters of the alphabet) can also be used to provide meaningful order information. Because quantity and order are linked up with each other in the cognitive number domain (the larger the quantity a number refers to, the later it is located in the conventional number sequence), the question of whether they rely on some common or distinct underlying mechanism(s) is theoretically relevant and was addressed in the present thesis. Experimental studies showed evidence of both similarities (similar distance and SNARC effects, recruitment of parietal and frontal regions, and conjoint impairment or preservation after brain damage) and dissociations (different developmental course, dissociation after cerebral lesion, and specific behavioural markers) between quantity and order neuro-functional processes. The aim of the present thesis was to clarify the relationship between numerical quantity and order processing and to test the hypothesis that they rely on (at least partially) dissociated mechanisms. We tested this hypothesis in a single case study, an electrophysiological study and in two behavioural experiments. In the neuropsychological study, we reported the case of patient CO, who showed Gerstmann syndrome after bilateral parietal damage and beca...
Number and Continuous Magnitude Processing Depends on Task Goals and Numerosity Ratio
A large body of evidence shows that when comparing non-symbolic numerosities, performance is influenced by irrelevant continuous magnitudes, such as total surface area, density, etc. In the current work, we ask whether the weights given to numerosity and continuous magnitudes are modulated by top-down and bottom-up factors. With that aim in mind, we asked adult participants to compare two groups of dots. To manipulate task demands, participants reported after every trial either (1) how accurate their response was (emphasizing accuracy) or (2) how fast their response was (emphasizing speed). To manipulate bottom-up factors, the stimuli were presented for 50 ms, 100 ms or 200 ms. Our results revealed (a) that the weights given to numerosity and continuous magnitude ratios were affected by the interaction of top-down and bottom-up manipulations and (b) that under some conditions, using numerosity ratio can reduce efficiency. Accordingly, we suggest that processing magnitudes is not rigid and static but a flexible and adaptive process that allows us to deal with the ever-changing demands of the environment. We also argue that there is not just one answer to the question 'what do we process when we process magnitudes?', and future studies should take this flexibility under consideration.
Big and small numbers: Empirical support for a single, flexible mechanism for numerosity perception
The existence of perceptually distinct numerosity ranges has been proposed for small (i.e., subitizing range) and larger numbers based on differences in precision, Weber fractions, and reaction times. This raises the question of whether such dissociations reflect distinct mechanisms operating across the two numerosity ranges. In the present work, we explore the predictions of a single-layer recurrent on-center, off-surround network model of attentional priority that has been applied to object individuation and enumeration. Activity from the network can be used to model various phenomena in the domain of visual number perception based on a single parameter: the strength of inhibition between nodes. Specifically, higher inhibition allows for precise representation of small numerosities, while low inhibition is preferred for high numerosities. The model makes novel predictions, including that enumeration of small numerosities following large numerosities should result in longer reaction times than when a small numerosity trial following small numerosities. Moreover, the model predicts underestimation of number when a display containing a large number of items follows a trial with small numerosities. We behaviorally confirmed these predictions in a series of experiments. This pattern of results is consistent with a single, flexible object individuation system, which can be modeled successfully by dynamic on-center, off-surround network model of the attentional priority (saliency) map.
Non-verbal numerical cognition: from reals to integers
Trends in Cognitive Sciences, 2000
2 , F e b r u a r y 2 0 0 0 monkeys (Macaca mulatta). J. Comp. Psychol. 111, 286-293 44 Itakura, S. and Tanaka, M. (1998) Use of experimenter-given cues during object-choice tasks by chimpanzees (Pan troglodytes), an orangutan (Pongo pygmaeus), and human infants (Homo sapiens).
Psychophysical study of numbers
Psychological Research, 1975
Two experiments were conducted to study the number biases of subjects in situations not involving the usual psychophysical stimuli. In Exp. I subjects were asked to generate numbers (whithin boundary conditions) they thought other people would produce under the same conditions. In Exp. II only a single lower boundary (e.g., t, i0 or 100) was employed and subjects generated a set of numbers larger than the boundary. Results suggested that definite number biases exist. ~ultiples of 1, 10, t00 and to a lesser extent 5, 50 and 500 dominate and are appropriate to the log cycle. That is, multiples of i occur most often in the cycle 1--10, multiples of t0 in the cycle 10--t00, etc. The implications of these results are noted for several psychophysical theories.