Electrophysiological Measures of Time Processing in Infant and Adult Brains: Weber's Law Holds

Behavioral studies have demonstrated that time perception in adults, children, and nonhuman animals is subject to Weber's Law. More specifically, as with discriminations of other features, it has been found that it is the ratio between two durations rather than their absolute difference that controls the ability of an animal to discriminate them. Here, we show that scalp-recorded event-related electrical brain potentials (ERPs) in both adults and 10-month-old human infants, in response to changes in interstimulus interval (ISI), appear to obey the scalar property found in time perception in adults, children, and nonhuman animals. Using a timing-interval oddball paradigm, we tested adults and infants in conditions where the ratio between the standard and deviant interval in a train of homogeneous auditory stimuli varied such that there was a 1:4 (only for the infants), 1:3, 1:2, and 2:3 ratio between the standard and deviant intervals. We found that the amplitude of the deviant-triggered mismatch negativity ERP component (deviant-ISI ERP minus standard-ISI ERP) varied as a function of the ratio of the standard to deviant interval. Moreover, when absolute values were varied and ratio was held constant, the mismatch negativity did not vary.

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The role of Weber’s law in human time perception

Attention Perception & Psychophysics ◽

10.3758/s13414-020-02128-6 ◽

2020 ◽

Author(s):

Andrew Haigh ◽

Deborah Apthorp ◽

Lewis A. Bizo

Keyword(s):

Time Perception ◽

Weber’S Law ◽

Weber's Law

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The failure of Weber's law in time perception and production

Behavioural Processes ◽

10.1016/j.beproc.2005.11.006 ◽

2006 ◽

Vol 71 (2-3) ◽

pp. 201-210 ◽

Cited By ~ 57

Author(s):

Lewis A. Bizo ◽

Josey Y.M. Chu ◽

Federico Sanabria ◽

Peter R. Killeen

Keyword(s):

Time Perception ◽

Weber’S Law ◽

Weber's Law

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The Neural Representation of Time: An Information-Theoretic Perspective

Neural Computation ◽

10.1162/neco_a_00280 ◽

2012 ◽

Vol 24 (6) ◽

pp. 1519-1552 ◽

Cited By ~ 16

Author(s):

Joachim Hass ◽

J. Michael Herrmann

Keyword(s):

Stochastic Processes ◽

Time Perception ◽

Temporal Information ◽

Neural Representation ◽

Weber’S Law ◽

Information Theoretic ◽

Weber's Law ◽

Timing Errors ◽

Temporal Correlations ◽

Neuronal Mechanisms

A prominent finding in psychophysical experiments on time perception is Weber's law, the linear scaling of timing errors with duration. The ability to reproduce this scaling has been taken as a criterion for the validity of neurocomputational models of time perception. However, the origin of Weber's law remains unknown, and currently only a few models generi- cally reproduce it. Here, we use an information-theoretical framework that considers the neuronal mechanisms of time perception as stochastic processes to investigate the statistical origin of Weber's law in time perception and also its frequently observed deviations. Under the assumption that the brain is able to compute optimal estimates of time, we find that Weber's law only holds exactly if the estimate is based on temporal changes in the variance of the process. In contrast, the timing errors scale sublinearly with time if the systematic changes in the mean of a process are used for estimation, as is the case in the majority of time perception models, while estimates based on temporal correlations result in a superlinear scaling. This hierarchy of temporal information is preserved if several sources of temporal information are available. Furthermore, we consider the case of multiple stochastic processes and study the examples of a covariance-based model and a model based on synfire chains. This approach reveals that existing neurocomputational models of time perception can be classified as mean-, variance- and correlation-based processes and allows predictions about the scaling of the resulting timing errors.

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Induced Alpha-band Oscillations Reflect Ratio-dependent Number Discrimination in the Infant Brain

Journal of Cognitive Neuroscience ◽

10.1162/jocn.2008.21162 ◽

2009 ◽

Vol 21 (12) ◽

pp. 2398-2406 ◽

Cited By ~ 25

Author(s):

Melissa E. Libertus ◽

Laura B. Pruitt ◽

Marty G. Woldorff ◽

Elizabeth M. Brannon

Keyword(s):

Spectral Power ◽

Brain Activity ◽

Human Life ◽

Alpha Band ◽

Weber’S Law ◽

Weber's Law ◽

Ratio Dependence ◽

Number Discrimination ◽

Behavioral Studies ◽

Ratio Dependent

Behavioral studies show that infants are capable of discriminating the number of objects or events in their environment, while also suggesting that number discrimination in infancy may be ratio-dependent. However, due to limitations of the dependent measures used with infant behavioral studies, the evidence for ratio dependence falls short of the vast psychophysical datasets that have established ratio dependence, and thus, adherence to Weber's Law in adults and nonhuman animals. We addressed this issue in two experiments that presented 7-month-old infants with familiar and novel numerosities while electroencephalogram measures of their brain activity were recorded. These data provide convergent evidence that the brains of 7-month-old infants detected numerical novelty. Alpha-band and theta-band oscillations both differed for novel and familiar numerical values. Most importantly, spectral power in the alpha band over midline and right posterior scalp sites was modulated by the ratio between the familiar and novel numerosities. Our findings provide neural evidence that numerical discrimination in infancy is ratio dependent and follows Weber's Law, thus indicating continuity of these cognitive processes over development. Results are also consistent with the idea that networks in the frontal and parietal cortices support ratio-dependent number discrimination in the first year of human life, consistent with what has been reported in neuroimaging studies in adults and older children.

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Analytical Calculation of Errors in Time and Value Perception Due to a Subjective Time Accumulator: A Mechanistic Model and the Generation of Weber’s Law

Neural Computation ◽

10.1162/neco_a_00792 ◽

2016 ◽

Vol 28 (1) ◽

pp. 89-117 ◽

Cited By ~ 5

Author(s):

Vijay Mohan K. Namboodiri ◽

Stefan Mihalas ◽

Marshall G. Hussain Shuler

Keyword(s):

Decision Making ◽

Time Perception ◽

Experimental Testing ◽

Mechanistic Model ◽

Analytical Calculation ◽

Temporal Discounting ◽

Subjective Time ◽

Weber’S Law ◽

Weber's Law ◽

Accumulator Model

It has been previously shown (Namboodiri, Mihalas, Marton, & Hussain Shuler, 2014 ) that an evolutionary theory of decision making and time perception is capable of explaining numerous behavioral observations regarding how humans and animals decide between differently delayed rewards of differing magnitudes and how they perceive time. An implementation of this theory using a stochastic drift-diffusion accumulator model (Namboodiri, Mihalas, & Hussain Shuler, 2014a ) showed that errors in time perception and decision making approximately obey Weber’s law for a range of parameters. However, prior calculations did not have a clear mechanistic underpinning. Further, these calculations were only approximate, with the range of parameters being limited. In this letter, we provide a full analytical treatment of such an accumulator model, along with a mechanistic implementation, to calculate the expression of these errors for the entirety of the parameter space. In our mechanistic model, Weber’s law results from synaptic facilitation and depression within the feedback synapses of the accumulator. Our theory also makes the prediction that the steepness of temporal discounting can be affected by requiring the precise timing of temporal intervals. Thus, by presenting exact quantitative calculations, this work provides falsifiable predictions for future experimental testing.

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Corrigendum to “The failure of Weber's law in time perception and production” [Behav. Process. 71 (2–3) (2006) 201–210]

Behavioural Processes ◽

10.1016/j.beproc.2013.08.014 ◽

2014 ◽

Vol 106 ◽

pp. 193

Author(s):

Lewis A. Bizo ◽

Josey Y.M. Chu ◽

Federico Sanabria ◽

Peter R. Killeen

Keyword(s):

Time Perception ◽

Weber’S Law ◽

Weber's Law

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Weber’s Law and the Scalar Property of Timing: A Test of Canine Timing

Animals ◽

10.3390/ani9100801 ◽

2019 ◽

Vol 9 (10) ◽

pp. 801

Author(s):

Jessica Cliff ◽

Surrey Jackson ◽

James McEwan ◽

Lewis Bizo

Keyword(s):

Stimulus Pair ◽

Light Stimulus ◽

Geometric Mean ◽

Domestic Dogs ◽

Weber’S Law ◽

Scalar Property ◽

Weber's Law ◽

Research Reporting ◽

Temporal Bisection ◽

Bisection Procedure

Domestic dogs completed a temporal bisection procedure that required a response to one lever following a light stimulus of short duration and to another lever following a light stimulus of a longer duration. The short and long durations across the four conditions were (0.5–2.0 s, 1.0–4.0 s, 2.0–8.0 s, and 4.0–16.0 s). Durations that were intermediate, the training durations, and the training durations, were presented during generalization tests. The dogs bisected the intervals near the geometric mean of the short and long-stimulus pair. Weber fractions were not constant when plotted as a function of time: A U-shaped function described them. These results replicate the findings of previous research reporting points of subjective equality falling close to the geometric mean and also confirm recent reports of systematic departures from Weber’s law.

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