Abstract

During the last decade, both behavioraland neuroimaging studies suggested theidea of a common magnitude system fornon-symbolic estimation of time, space,and number, the so-called “A TheoryOf Magnitude” (ATOM, Walsh, 2003).To date, different approaches have beenadopted in cognitive psychology to testthe predictions of ATOM. The most com-monapproachisbasedonbehavioraldata and uses conflict paradigms (e.g.,stroop tasks) to explore the interactionsamong the three domains (Dormal et al.,2006; Vicario et al., 2008; Agrillo et al.,2010). For instance, in a task requiring toremember different arrays of lines associ-ated to congruent (e.g., small line-shorttone) or incongruent (e.g., small line-long tone) temporal information, partic-ipants proved able to remember betterthe spatial–temporal pairings when vari-ation in space and time was congruent(Srinivasan and Carey, 2010). Bisectiontasks are also used to study the interac-tionamongmagnitudes.Ithasbeenshownthat our accuracy in a temporal bisec-tion task is significantlyaffected by chang-ing the numerical size presented on thescreen, suggesting that the size of a num-ber influences the subjective midpoint ofaduration(Vicario, 2011). Alternatively,reproduction tasks are presented in whichparticipants are told to reproduce the esti-mateddurationofanevent(Lu et al.,2009; Chang et al., 2011), the numberof items or the length of a line, withthe assumption that non-relevant infor-mation (e.g., numbers presented on thescreen in a spatial task) should not affectthe estimation of the relevant informa-tionifdifferentsystemsareinvolved.Usingthis paradigm it has been shown thatthe reproduction of a spatial extensionis underestimated when delimited by twosmall numbers, while it is overestimated ifdelimited by two large numbers (de Heviaet al., 2008). Neuro-anatomical correlatesare also observed to explore the similar-ity of the three domains. Indeed if thethree dimensions are processed by thesame cognitive mechanism, similar neu-ral networks should be involved (CohenKadosh et al., 2008; Vicario and Martino,2010). Based on this evidence, severalauthors have referred to the possibilitythat we would represent numerical mag-nitudes using a spatial layout, the so-called “mental number line,” as well as wewould represent time flowusinga “mentaltime line” (Daar and Pratt, 2008; Bonatoet al., 2012), which again aligns with theidea of a common system for magnitudeprocessing.Comparative studies showed that tem-poral, spatial, and numerical abilities arenot only a human prerogative. Non-human species have been found to usetemporal, spatial and numerical informa-tion in both laboratory and field stud-ies (Breukelaar and Dalrymple-Alford,1999; Evans et al., 2009; Spence et al.,2011). Nonetheless, the debate surround-ing ATOM has been almost entirely con-fined to our species, and it is currentlyunknown whether the supposed commonmagnitude system is a recent evolutionarydevelopment (restricted to humans) or, incontrast, is more evolutionarily pervasive.However, even in the absence of studiesdirectly focused on testing the predictionsof ATOM, we believe that the hallmarkof ATOM can be tracked in comparativeliterature.First of all, time, space, and num-ber estimation obeys Weber’s law inmost species. The capacity to discriminatebetween two quantities (durations, areasor number of items) becomes increas-ingly accurate as the ratio between thesmaller and the larger quantity decreases(time: Gibbon, 1977;space:Cheng, 1990;number: Perdue et al., 2012). The univer-sality of Weber’s law reinforces the ideaof similar quantificational systems amongspecies (Beran, 2008) and highlights thesimilaritiesincognitive processes fortime,space, and number estimation, whichaligns with the idea of a common magni-tude system.More compelling evidence comes fromstudies directly presenting two differentmagnitudes and using contrast paradigmssimilar to those adopted in human liter-ature. For instance, both mammals (rats)and birds (pigeons) show number-timeinteraction. Meck and Church (1983) ini-tially trained rats to discriminate auditorystimuli varying in both number and dura-tion (i.e., 2 sounds in 2s or 8 soundsin 8s). Subsequently the subjects weretested in a transfer task, where novelstimuli varying in just one dimensionwere presented (2–8 tones in 4s or 4tones in 2–8s). The rats spontaneouslyencoded information about both time andnumber, thus showing an almost identi-cal psychophysical function for both timeand number (Meck and Church, 1983).Roberts and Mitchell (1994) obtainedsimilar results with pigeons trained todiscriminate between sequences of lightflashes differing in number and duration.Pigeons, like rats, were able to processboth number and time simultaneously.Apparently, both species cannot ignorethe non-relevant information (i.e., tem-poral information in a numerical task)in both temporal and numerical tasks.Glimpse of ATOM can be found also inresearch on time-space interactions. Intwo different experiments, Merritt et al.(2010) tested rhesus monkeys in contrastparadigms. In one of these tasks (dura-tion bisection), the subjects had to judgeseven durations (two anchors and fiveintermediatevalues)aslongorshortwhilethe length of different lines was orthog-onally varied between short, medium,and long values. The authors foundthatirrelevantspatialinformationaffectedtime judgments, and irrelevant temporal

Highlights

  • Comparative studies showed that temporal, spatial, and numerical abilities are a human prerogative

  • The debate surrounding ATOM has been almost entirely confined to our species, and it is currently unknown whether the supposed common magnitude system is a recent evolutionary development or, in contrast, is more evolutionarily pervasive

  • Even in the absence of studies directly focused on testing the predictions of ATOM, we believe that the hallmark of ATOM can be tracked in comparative literature

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Summary

Introduction

Comparative studies showed that temporal, spatial, and numerical abilities are a human prerogative. The universality of Weber’s law reinforces the idea of similar quantificational systems among species (Beran, 2008) and highlights the similarities in cognitive processes for time, space, and number estimation, which aligns with the idea of a common magnitude system.

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