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In this study, we ran a meta-analysis of neuroimaging studies to pinpoint the neural regions that are commonly activated across space, time, and numerosity, and we tested the existence of gradient transitions among these magnitude representations in the brain. Following PRISMA guidelines, we included in the meta-analysis 112 experiments (for space domain), 114 experiments (time domain), and 115 experiments (numerosity domain), and we used the activation likelihood estimation method. We found a system of brain regions that was commonly recruited in all the three magnitudes, which included bilateral insula, the supplementary motor area (SMA), the right inferior frontal gyrus, and bilateral intraparietal sulci. Gradiental transitions between different magnitudes were found along all these regions but insulae, with space and numbers leading to gradients mainly over parietal regions (and SMA) whereas time and numbers mainly over frontal regions. These findings provide evidence for the GradiATOM theory (Gradient Theory of Magnitude), suggesting that spatial proximity given by overlapping activations and gradients is a key aspect for efficient interactions and integrations among magnitudes., (© 2023. The Author(s).)

We are all used to drawing straight lines to represent time, and above them, we plot historical events or physical or economic data. What to us is a self-evident convention, is however of an astonishingly recent date: it emerged only in the second half of the eighteenth century. To us, this late date seems paradoxical and cries out for an explanation. How else did earlier periods measure change, if not as a function of time? it will be argued that since Antiquity, time was taken to measure change, and change to occur in space. 'Our' idea of representing time as an independent dimension would have seemed aberrant. But then, a second issue arises. Did not medieval natural philosophers employ timelines, Oresme's diagram of the mean speed theorem being the most famous case? However, as will be shown, our interpretation of his diagram is probably wrong. This insight, in turn, takes care of a third paradox, namely Galileo's initial inability to represent the law of free fall correctly. This article will document that the timeline first emerged in the late sixteenth century in works on chronology, made its first appearance in physics in Galileo's diagrams, and had its general breakthrough in the eighteenth century.

Dogs, the most common companion animal of humans, perform not only the auxiliary of an individual, but also contribute to the nations' crime and defence departments. Knowing the determinant-based disease status of dogs is imperative to keep them healthy by subsequent prevention and control of those diseases; however, such baseline epidemiological information is limited. Therefore, a retrospective cross-sectional study was conducted to estimate the proportional incidence of dog diseases to explore their magnitudes, and we compared them to different levels of intrinsic (age, gender, breed) and extrinsic determinants (season). Purposively, data of a total of 1,557 cases of different diseases were collected from the record book of the Central Veterinary Hospital (CVH), Dhaka, Bangladesh. The proportional incidence was calculated as the proportion of cases of a specific disease among total number of cases of all types of diseases attended the hospital during the study period. Diseases of dog were categorized into infectious, non-infectious, and non-specific. Results showed that the highest proportional incidence was noted in infectious diseases (53.8%) followed by non-infectious diseases (23.4%) and the lowest in non-specific (22.7%) cases. Among them, disease-specific proportional incidence was remarkable in case of mange (9.5%), parvovirosis (8.7%), lacerated wound (8.5%), ectoparasitism (8.3%), helminthiasis (7.8%), and fracture (5.7%). The occurrence of mange varied significantly (p < 0.05) among all studied determinants (age, gender, breed, and season); while significant discrepancies (p < 0.05) in magnitudes of lacerated wound, dystocia, abortion, and gastroenteritis were observed among various groups of age, gender, and breed. Accordingly, dermatitis and orchitis had significant differences (p < 0.05) in proportional incidence amid various levels of age, gender, and season; whilst the burden of parvovirosis and alopecia differed significantly (p < 0.05) amongst different categories of age, breed, and season. The magnitude of otorrhoea showed a significant (p < 0.05) variation among different groups of gender, breed, and season. The proportional incidence of other diseases also varied significantly (p < 0.05) amongst either one or two studied determinants. This study provides a valuable insight about important diseases in dogs, which may serve as useful baseline information for disease prioritization and subsequent planning of effective control and prevention measures against those diseases., Competing Interests: The authors declare no conflict of interest., (© 2021 The Author(s).)

Coins are physical representations of monetary values. Like mental or verbal representations of quantities, coins encode sums of money in formats shaped, in part, by cognitive and communicative needs. Studying the coins circulating today, we consider how their design, colour, and size reflect their value. We show that coin designs solve a trade-off between informativeness-the pressure to highlight distinct denominations-and simplicity-the pressure to limit the number of designs that coin users must memorise. Coinage worldwide is more likely to display distinctive graphic designs and distinct colours on pairs of coins with large differences in value, thus minimising the aggregate cost of mistaking one coin for another. Coin size differentials, in contrast, do not seem to indicate greater value differentials, although absolute coin sizes do reflect monetary values. Log-transformed values predict design and colour distinctiveness in coin pairs, as well as absolute coin sizes, better than raw values, consistent with research suggesting that monetary quantities may recruit the "numerosity system" for magnitude representations, thought to track quantities logarithmically. These results show that coins obey similar informational constraints as linguistic and mental representations., (Copyright © 2020 Elsevier B.V. All rights reserved.)

Do children learn number words by associating them with perceptual magnitudes? Recent studies argue that approximate numerical magnitudes play a foundational role in the development of integer concepts. Against this, we argue that approximate number representations fail both empirically and in principle to provide the content required of integer concepts. Instead, we suggest that children's understanding of integer concepts proceeds in two phases. In the first phase, children learn small exact number word meanings by associating words with small sets. In the second phase, children learn the meanings of larger number words by mastering the logic of exact counting algorithms, which implement the successor function and Hume's principle (that one-to-one correspondence guarantees exact equality). In neither phase do approximate number representations play a foundational role., (Copyright © 2019 Elsevier Ltd. All rights reserved.)

A current intense discussion in numerical cognition concerns the relationship between the processing of numerosity and other non-numerical quantities. In particular, it is a matter of debate whether number and other quantities (e.g., size, length) are represented separately in the brain or whether they share a common generalized magnitude representation. We acquired high-resolution functional MRI data while adult subjects engaged in a magnitude comparison task involving either numerosity (i.e., which of the two sets has more elements?) or line length (i.e., which of the two lines is longer?). We compared the activation evoked by the two different types of quantity and observed a common recruitment of a vast portion of occipital and parietal cortices. Using MVPA, we demonstrated that some of the commonly activated regions represented the discrete and continuous quantities via a similar distance-dependent magnitude code. However, we found no effect of distance across the two quantity representations, failing to support the existence of a common, dimension invariant, generalized quantity code. Taken together, these findings indicate that although the processing of number and length is supported by partially overlapping neural resources, representations within these regions do not appear to be based on a common neural code., (Copyright © 2018 Elsevier Ltd. All rights reserved.)

The spatial numerical association of response code (SNARC) effect is characterized by low numbers mapped to the left side of space and high numbers mapped to the right side of space. In addition to numbers, SNARC-like effects have been found in non-numerical magnitude domains such as time, size, letters, luminance, and more, whereby the smaller/earlier and larger/later magnitudes are typically mapped to the left and right of space, respectively. The purpose of this systematic and meta-analytic review was to identify and summarise all empirical papers that have investigated horizontal (left-right) SNARC-like mappings using non-numerical stimuli. A systematic search was conducted using EMBASE, Medline, and PsycINFO, where 2216 publications were identified, with 57 papers meeting the inclusion criteria (representing 112 experiments). Ninety-five of these experiments were included in a meta-analysis, resulting in an overall effect size of d = .488 for a SNARC-like effect. Additional analyses revealed a significant effect size advantage for explicit instruction tasks compared with implicit instructions, yet yielded no difference for the role of expertise on SNARC-like effects. There was clear evidence for a publication bias in the field, but the impact of this bias is likely to be modest, and it is unlikely that the SNARC-like effect is a pure artefact of this bias. The similarities in the response properties for the spatial mappings of numerical and non-numerical domains support the concept of a general higher order magnitude system. Yet, further research will need to be conducted to identify all the factors modulating the strength of the spatial associations.

Space and time are intimately coupled dimensions in the human brain. Several lines of evidence suggest that space and time are processed by a shared analogue magnitude system. It has been proposed that actions are instrumental in establishing this shared magnitude system. Here we provide evidence in support of this hypothesis, by showing that the interaction between space and time is enhanced when magnitude information is acquired through action. Participants observed increases or decreases in the height of a visual bar (spatial magnitude) while judging whether a simultaneously presented sequence of acoustic tones had accelerated or decelerated (temporal magnitude). In one condition (Action), participants directly controlled the changes in bar height with a hand grip device, whereas in the other (No Action), changes in bar height were externally controlled but matched the spatial/temporal profile of the Action condition. The sign of changes in bar height biased the perceived rate of the tone sequences, where increases in bar height produced apparent increases in tone rate. This effect was amplified when the visual bar was actively controlled in the Action condition, and the strength of the interaction was scaled by the magnitude of the action. Subsequent experiments ruled out that this was simply explained by attentional factors, and additionally showed that a monotonic mapping is also required between grip force and bar height in order to bias the perception of the tones. These data provide support for an instrumental role of action in interfacing spatial and temporal quantities in the brain., (© 2015 The Author(s) Published by the Royal Society. All rights reserved.)