Time and number: the privileged status of small values in the brain

Is the scalar property of interval timing preserved after hippocampus lesions?

Time perception is fundamental for decision-making, adaptation, and survival. In the peak-interval (PI) paradigm, one of the critical features of time perception is its scale invariance, i.e., the error in time estimation increases linearly with the to-be-timed interval. Brain lesions can profoundly alter time perception, but do they also change its scalar property? In particular, hippocampus (HPC) lesions affect the memory of the reinforced durations. Experiments found that ventral hippocampus (vHPC) lesions shift the perceived durations to longer values while dorsal hippocampus (dHPC) lesions produce opposite effects. Here we used our implementation of the Striatal Beat Frequency (SBFML) model with biophysically realistic Morris-Lecar (ML) model neurons and a topological map of HPC memory to predict analytically and verify numerically the effect of HPC lesions on scalar property. We found that scalar property still holds after both vHPC and dHPC lesions in our SBFML-HPC network simulation. Our numerical results show that PI durations are shifted in the correct direction and match the experimental results. In our simulations, the relative peak shift of the behavioral response curve is controlled by two factors: (1) the lesion size, and (2) the cellular-level memory variance of the temporal durations stored in the HPC. The coefficient of variance (CV) of the behavioral response curve remained constant over the tested durations of PI procedure, which suggests that scalar property is not affected by HPC lesions.

Discrimination of ordinal relationships in temporal sequences by 4-month-old infants

The ability to discriminate the ordinal information embedded in magnitude-based sequences has been shown in 4-month-old infants, both for numerical and size-based sequences. At this early age, however, this ability is confined to increasing sequences, with infants failing to extract and represent decreasing order. Here we investigate whether the ability to represent order extends to duration-based sequences in 4-month-old infants, and whether it also shows the asymmetry signature previously observed for number and size. Infants were tested in an order discrimination task in which they were habituated to either increasing or decreasing variations in temporal duration, and were then tested with novel sequences composed of new temporal items whose durations varied following the familiar and the novel orders in alternation. Across three experiments, we manipulated the duration of the single temporal items and therefore of the whole sequences, which resulted in imposing more or less constraints on infants' working memory, or general processing capacities. Results showed that infants failed at discriminating the ordinal direction in temporal sequences when the sequences had an overall long duration (Experiment 1), but succeeded when the duration of the sequences was shortened (Experiments 2 and 3). Moreover, there was no sign of the asymmetry signature previously reported for number and size, as successful discrimination was present for infants habituated to both increasing and decreasing sequences. These results suggest that sensitivity to temporal order is present very early in development, and that its functional properties are not shared with other magnitude dimensions, such as size and number.

The effect of multimodal information on children's numerical judgments

Although much research suggests that adults, infants, and nonhuman primates process number (among other properties) across distinct modalities, limited studies have explored children's abilities to integrate multisensory information when making judgments about number. In the current study, 3- to 6-year-old children performed numerical matching or numerical discrimination tasks in which numerical information was presented either unimodally (visual only), cross-modally (comparing audio with visual), or bimodally (simultaneously presenting audio and visual input). In three experiments, we investigated children's multimodal numerical processing across distinct task demands and difficulty levels. In contrast to previous work, results indicate that even the youngest children (3 and 4 years) performed above chance across all three modality presentations. In addition, the current study contributes two other novel findings, namely that (a) children exhibit a cross-modal disadvantage when numerical comparisons are easy and that (b) accuracy on bimodal trial types led to even more accurate numerical judgments under more difficult circumstances, particularly for the youngest participants and when precise numerical matching was required. Importantly, findings from this study extend the literature on children's numerical cross-modal abilities to reveal that, like their adult counterparts, children readily track and compare visual and auditory numerical information, although their abilities to do so are not perfect and are affected by task demands and trial difficulty.

Neural Correlates of Interval Timing Deficits in Schizophrenia

Previous research has shown that schizophrenia (SZ) patients exhibit impairments in interval timing. The cause of timing impairments in SZ remains unknown but may be explained by a dysfunction in the fronto-striatal circuits. Although the current literature includes extensive behavioral data on timing impairments, there is limited focus on the neural correlates of timing in SZ. The neuroimaging literature included in the current review reports hypoactivation in the dorsal-lateral prefrontal cortex (DLPFC), supplementary motor area (SMA) and the basal ganglia (BG). Timing deficits and deficits in attention and working memory (WM) in SZ are likely due to a dysfunction of dopamine (DA) and gamma-aminobutyric acid (GABA) neurotransmission in the cortico-striatal-thalamo-cortical circuits, which are highly implicated in executive functioning and motor preparation.

A divergence of sub- and supra-second timing abilities in childhood and its relation to academic achievement

Work with adult humans and nonhuman animals provides evidence that the processing of sub-second (<1 s) and supra-second (>1 s) durations are modulated via distinct cognitive and neural systems; however, few studies have explored the development of these separate systems. Moreover, recent research has identified a link between basic timing abilities and academic achievement, yet it is unclear whether sub-second and supra-second temporal processing may play independent roles in this relation. In the current study, we assessed the development of sub- and supra-second timing across middle childhood and examined how each ability may relate to academic achievement. Child participants (6- to 8-year-olds, n = 111) completed reading and math assessments and a temporal discrimination task that included comparisons in both the sub- and supra-second ranges. Results revealed that younger children performed comparably across the sub- and supra-second ranges, whereas 8-year-olds and adults (n = 72) were relatively better at discriminating durations in the supra-second range. Although discrimination performance in these distinct duration ranges did not uniquely predict math or reading achievement, overall timing abilities were related to math, but not reading, when controlling for age. Together, these data provide evidence for a divergence in timing abilities across sub- and supra-second durations emerging around 8 years of age; however, at least during this stage of development, the relation between children's timing and math achievement is unrelated to this divergence.

Cognitive Load Affects Numerical and Temporal Judgments in Distinct Ways

Prominent theories suggest that time and number are processed by a single neural locus or a common magnitude system (e.g., Meck and Church, 1983; Walsh, 2003). However, a growing body of literature has identified numerous inconsistencies between temporal and numerical processing, casting doubt on the presence of such a singular system. Findings of distinct temporal and numerical biases in the presence of emotional content (Baker et al., 2013; Young and Cordes, 2013) are particularly relevant to this debate. Specifically, emotional stimuli lead to temporal overestimation, yet identical stimuli result in numerical underestimation. In the current study, we tested adults’ temporal and numerical processing under cognitive load, a task that compromises attention. Under the premise of a common magnitude system, one would predict cognitive load to have an identical impact on temporal and numerical judgments. Inconsistent with the common magnitude account, results revealed baseline performance on the temporal and numerical task was not correlated and importantly, cognitive load resulted in distinct and opposing quantity biases: numerical underestimation and marginal temporal overestimation. Together, our data call into question the common magnitude account, while also providing support for the role of attentional processes involved in numerical underestimation.

Oscillation patterns of local field potentials in the dorsal striatum and sensorimotor cortex during the encoding, maintenance, and decision stages for the ordinal comparison of sub- and supra-second signal durations

Ordinal comparison of successively presented signal durations requires (a) the encoding of the first signal duration (standard), (b) maintenance of temporal information specific to the standard duration in memory, and (c) timing of the second signal duration (comparison) during which a comparison is made of the first and second durations. Rats were first trained to make ordinal comparisons of signal durations within three time ranges using 0.5, 1.0, and 3.0-s standard durations. Local field potentials were then recorded from the dorsal striatum and sensorimotor cortex in order to investigate the pattern of neural oscillations during each phase of the ordinal-comparison process. Increased power in delta and theta frequency ranges was observed during both the encoding and comparison stages. Active maintenance of a selected response, "shorter" or "longer" (counter-balanced across left and right levers), was represented by an increase of theta and delta oscillations in the contralateral striatum and cortex. Taken together, these data suggest that neural oscillations in the delta-theta range play an important role in the encoding, maintenance, and comparison of signal durations.

Novel Inversions in Auditory Sequences Provide Evidence for Spontaneous Subtraction of Time and Number

Animals, including fish, birds, rodents, non-human primates, and pre-verbal infants are able to discriminate the duration and number of events without the use of language. In this paper, we present the results of six experiments exploring the capability of adult rats to count 2–6 sequentially presented white-noise stimuli. The investigation focuses on the animal’s ability to exhibit spontaneous subtraction following the presentation of novel stimulus inversions in the auditory signals being counted. Results suggest that a subtraction operation between two opposite sensory representations may be a general processing strategy used for the comparison of stimulus magnitudes. These findings are discussed within the context of a mode-control model of timing and counting that relies on an analog temporal-integration process for the addition and subtraction of sequential events.

Transcranial Magnetic Stimulation Studies of Human Time Perception: A Primer

The study of the neural basis of time perception has seen a resurgence of interest within the past decade. A variety of these studies have included the use of transcranial magnetic stimulation (TMS), a noninvasive technique for stimulating discrete regions of the surface of the brain. Here, the results of these studies are reviewed and their conclusions are interpreted within a context-dependent framework. However, the use of TMS as an investigatory technique has much unexplored potential that may be particularly beneficial to the study of time perception. As such, considerations are made regarding the design of TMS studies of time perception and future directions are outlined that may be utilized to further elucidate the neural basis of timing in the human brain.

Comparative judgments of symbolic and non-symbolic stimuli yield different patterns of reaction times

Are different magnitudes, such as Arabic numerals, length and area, processed by the same system? Answering this question can shed light on the building blocks of our mathematical abilities. A shared representation theory suggested that discriminability of all magnitudes complies with Weber's law. The current work examined this suggestion. We employed comparative judgment tasks to investigate different types of comparisons - conceptual comparison of numbers, physical comparison of numbers and physical comparison of different shapes. We used 8 different size ratios and plotted reaction time as a function of these ratios. Our findings suggest that the relationship between discriminability and size ratio is not always linear, as previously suggested; rather, it is modulated by the type of comparison and the type of stimuli. Hence, we suggest that the representation of magnitude is not as rigid as previously suggested; it changes as a function of task demands and familiarity with the compared stimuli.

Numerical cognition in bees and other insects

The ability to perceive the number of objects has been known to exist in vertebrates for a few decades, but recent behavioral investigations have demonstrated that several invertebrate species can also be placed on the continuum of numerical abilities shared with birds, mammals, and reptiles. In this review article, we present the main experimental studies that have examined the ability of insects to use numerical information. These studies have made use of a wide range of methodologies, and for this reason it is striking that a common finding is the inability of the tested animals to discriminate numerical quantities greater than four. Furthermore, the finding that bees can not only transfer learnt numerical discrimination to novel objects, but also to novel numerosities, is strongly suggestive of a true, albeit limited, ability to count. Later in the review, we evaluate the available evidence to narrow down the possible mechanisms that the animals might be using to solve the number-based experimental tasks presented to them. We conclude by suggesting avenues of further research that take into account variables such as the animals' age and experience, as well as complementary cognitive systems such as attention and the time sense.

Time-scale invariance as an emergent property in a perceptron with realistic, noisy neurons

In most species, interval timing is time-scale invariant: errors in time estimation scale up linearly with the estimated duration. In mammals, time-scale invariance is ubiquitous over behavioral, lesion, and pharmacological manipulations. For example, dopaminergic drugs induce an immediate, whereas cholinergic drugs induce a gradual, scalar change in timing. Behavioral theories posit that time-scale invariance derives from particular computations, rules, or coding schemes. In contrast, we discuss a simple neural circuit, the perceptron, whose output neurons fire in a clockwise fashion based on the pattern of coincidental activation of its input neurons. We show numerically that time-scale invariance emerges spontaneously in a perceptron with realistic neurons, in the presence of noise. Under the assumption that dopaminergic drugs modulate the firing of input neurons, and that cholinergic drugs modulate the memory representation of the criterion time, we show that a perceptron with realistic neurons reproduces the pharmacological clock and memory patterns, and their time-scale invariance, in the presence of noise. These results suggest that rather than being a signature of higher order cognitive processes or specific computations related to timing, time-scale invariance may spontaneously emerge in a massively connected brain from the intrinsic noise of neurons and circuits, thus providing the simplest explanation for the ubiquity of scale invariance of interval timing.

1 < 2 and 2 < 3: non-linguistic appreciations of numerical order

Ordinal understanding is involved in understanding social hierarchies, series of actions, and everyday events. Moreover, an appreciation of numerical order is critical to understanding number at a highly abstract, conceptual level. In this paper, we review findings concerning the development and expression of ordinal numerical knowledge in preverbal human infants in light of literature about the same cognitive abilities in non-human animals. We attempt to reconcile seemingly contradictory evidence, provide new directions for prospective research, and evaluate the shared basis of ordinal knowledge among non-verbal organisms. Our review of the research leads us to conclude that both infants and non-human animals are adapted to respond to monotonic progressions in numerical order, consonant with mathematical definitions of numerical order. Further, we suggest that patterns in the way that infants and non-human animals process numerical order can be accounted for by changes across development, the conditions under which representations are generated, or both.

Impaired interval timing and spatial-temporal integration in mice deficient in CHL1, a gene associated with schizophrenia

Interval timing is crucial for decision-making and motor control and is impaired in many neuropsychiatric disorders, including schizophrenia - a neurodevelopmental disorder with a strong genetic component. Several gene mutations, polymorphisms or rare copy number variants have been associated with schizophrenia. L1 cell adhesion molecules (L1CAMs) are involved in neurodevelopmental processes, and in synaptic function and plasticity in the adult brain. Mice deficient in the Close Homolog to L1 (CHL1) adhesion molecule show alterations of hippocampal and thalamo-cortical neuroanatomy as well as deficits in sensorimotor gating and exploratory behavior. We analyzed interval timing and attentional control of temporal and spatial information in male CHL1 deficient (KO) mice and wild type (WT) controls. In a 20-s peak-interval timing procedure (standard and reversed), KO mice showed a maintained leftward shift of the response function relative to WT, indicative of a deficit in memory encoding/decoding. In trials with 2, 5, or 10-s gaps, KO mice shifted their peak times less than WT controls at longer gap durations, suggesting a decreased (attentional) effect of interruptions. In the spatial-temporal task, KO mice made more working and reference memory errors than controls, suggestive of impaired use of spatial and/or temporal information. When the duration spent on the central platform of the maze was manipulated, WT mice showed fewer spatial errors at the trained duration than at shorter or longer durations, indicative of discrimination based upon spatial-temporal integration. In contrast, performance was similar at all tested durations in KO mice, indicative of control by spatial cues, but not by temporal cues. These results suggest that CHL1 KO mice selectively attend to the more relevant cues of the task, and fail to integrate more complex spatial-temporal information, possibly as a result of reduced memory capacity related to hippocampal impairment, and altered temporal-integration mechanisms possibly due to thalamo-cortical anomalies.

Time-sharing in rats: effect of distracter intensity and discriminability

Interruptions (gaps) and unfamiliar events (distracters) during a timed signal delay the timed response of humans and other animals. To explore this phenomenon, we manipulate the intensity of auditory distracters (Experiment 1), and we dissociate the role of distracter intensity, distracter similarity with the intertrial interval, and dissimilarity from the timed auditory signal (Experiment 2). When the intertrial interval and the timed signal were silent, the delay in response after an auditory distracter increased with its intensity: Rats ignored (ran through) a 40-dB distracter, stopped timing during a 75-dB distracter, and reset after a 100-dB distracter. However, when timing was signaled by a 70-dB noise, rats reset both for 40- and 100-dB distracters, stopped for both 55- and 85-dB distracters, and run for the 70-dB distracter. Data are accounted for by a time-sharing model assuming 2 concurrent processes-time accumulation and memory decay controlled by the discriminability of the interrupting event-whose interplay results in a continuum of responses, from run to reset.

Developmental neuroscience of time and number: implications for autism and other neurodevelopmental disabilities

Estimations of time and number share many similarities in both non-humans and man. The primary focus of this review is on the development of time and number sense across infancy and childhood, and neuropsychological findings as they relate to time and number discrimination in infants and adults. Discussion of these findings is couched within a mode-control model of timing and counting which assumes time and number share a common magnitude representation system. A basic sense of time and number likely serves as the foundation for advanced numerical and temporal competence, and aspects of higher cognition-this will be discussed as it relates to typical childhood, and certain developmental disorders, including autism spectrum disorder. Directions for future research in the developmental neuroscience of time and number (NEUTIN) will also be highlighted.