Elsevier

Cognition

Volume 116, Issue 2, August 2010, Pages 217-241
Cognition

The long and the short of it: On the nature and origin of functional overlap between representations of space and time

https://doi.org/10.1016/j.cognition.2010.05.005Get rights and content

Abstract

When we describe time, we often use the language of space (The movie was long; The deadline is approaching). Experiments 1–3 asked whether—as patterns in language suggest—a structural similarity between representations of spatial length and temporal duration is easier to access than one between length and other dimensions of experience, such as loudness. Adult participants were shown pairings of lines of different length with tones of different duration (Experiment 1) or tones of different loudness (Experiment 2). The length of the lines and duration or loudness of the tones was either positively or negatively correlated. Participants were better able to bind particular lengths and durations when they were positively correlated than when they were not, a pattern not observed for pairings of lengths and tone amplitudes, even after controlling for the presence of visual cues to duration in Experiment 1 (Experiment 3). This suggests that representations of length and duration may functionally overlap to a greater extent than representations of length and loudness. Experiments 4 and 5 asked whether experience with and mastery of words like long and short—which can flexibly refer to both space and time—itself creates this privileged relationship. Nine-month-old infants, like adults, were better able to bind representations of particular lengths and durations when these were positively correlated (Experiment 4), and failed to show this pattern for pairings of lengths and tone amplitudes (Experiment 5). We conclude that the functional overlap between representations of length and duration does not result from a metaphoric construction processes mediated by learning to flexibly use words such as long and short. We suggest instead that it may reflect an evolutionary recycling of spatial representations for more general purposes.

Introduction

Central to human sophistication is the ability to engage in abstract thought—thought about things that we cannot directly perceive with our senses. Consider the ability to reason about time. The experience of time is fundamental—as Robert Ornstein (1969) has remarked, “…time is one of the continuing, compelling, and universal experiences of our lives, one of the primary threads which combine in the weave of our experience.” Yet there is no bodily organ specialized for temporal representation, nor any physical process in the world that gives rise to its experience. A challenge for cognitive science is to characterize the representations that underlie our experience of time and account for how they arise over evolution and ontogenesis.

The study of the nature and origin of abstract concepts has often taken representations in the domain of time—considered by many to be an example of an abstract domain par excellence—as a test case (e.g., Boroditsky, 2000, Boroditsky, 2001, Casasanto, 2008, Casasanto and Boroditsky, 2008, Gentner et al., 2002, McGlone and Harding, 1998). Some clues to the representation of time come from language. Linguists have noted that when we talk about temporal experience (and our experiences in other abstract domains), we co-opt the language of space, describing time as something we can actually see (Clark, 1973, Gruber, 1965, Jackendoff, 1983, Lakoff and Johnson, 1980, Langacker, 1987, Talmy, 1988). For example, in English, we speak of a ‘long meeting’, the ‘approaching deadline’, and the ‘future that lies ahead’ (see Table 1). The use of spatial language to describe time is also robust across languages (Alverson, 1994, Sweetser, 1991, Traugott, 1978).

These uses of language motivate a provocative proposal: we may use spatial language to describe time because we have adapted our cognitive faculties of spatial reasoning (for which we have richer perceptual experience) to the task of temporal reasoning, resulting in structural similarities and functional overlap among representations in the two domains (Casasanto, 2008, Casasanto and Boroditsky, 2008, Jackendoff, 1983, Lakoff and Johnson, 1980, Pinker, 1997, Murphy, 1996, Pinker, 2007). Of course, it would be hasty to draw sweeping conclusions about how we think from the presence of metaphorical language (cf. Murphy, 1996, Pinker, 1997). In order to gain new meanings, words were initially extended creatively (e.g., from using long to refer to not only space, but also to time). But over time, the initial motivation for these extensions could have faded, and could no longer be transparent to speakers today. This would suggest that, in these cases, metaphorical language is just an etymological relic (see Keysar, Shen, Glucksberg, & Horton, 2000; but see also Thibodeau & Durgin, 2008).

But while metaphorical language need not reveal relationships among concepts, a compelling body of evidence suggests that spatial and temporal representations are intimately related in the mind (Boroditsky, 2000, Boroditsky, 2001, Casasanto, 2008, Casasanto and Boroditsky, 2008, Gentner et al., 2002, McGlone and Harding, 1998, Xuan et al., 2007). A first contribution of the present experiments is to add another phenomenon in support of this position, which demonstrates that magnitude representations of space and time more spontaneously engage with and align with one another than do other structurally similar representations. We suggest that spatial and temporal representations functionally overlap to a large extent, perhaps due to a shared neural substrate. A second contribution of these experiments is to elucidate the role of ontogenetic and evolutionary processes in establishing this functional overlap. On the one hand, it is possible that spatial representations have been recycled, over evolutionary time (see Gould & Vrba, 1982), for the purpose of representing time, resulting in an innate, generalized representation for both space and time. Alternatively, functionally overlapping representations of space and time could result from a metaphorical construction process over development that is motivated by learning to use spatial words such as long and short to metaphorically describe temporal experience (see Boroditsky, 2000). We test whether this type of linguistic experience is necessary for the creation of functional overlap among spatial and temporal representations and provide evidence that it is not.

In the present studies, we focus on one aspect of the representation of time: namely, the representation of temporal duration, as invoked in phrases such as “a long tone” or “this tone is longer than that one.” The structurally similar representations of space we consider are representations of spatial length, as invoked in phrases such as “a long line” or “this line is longer than that one.”

Two representational systems are structurally similar if they can be relationally aligned as follows: symbols (a, b, c, …) and relations (P, Q, …) in one system are mapped to symbols (a′, b′, c′, …) and relations (P′, Q′, …) in the other such that if a given relation holds among symbols in the first system, a mapped relation among mapped symbols holds in the second, structurally similar system. This is a fairly weak sense of structural similarity and it describes many systems of representation. Under this definition, for example, dimensions in which symbols are serially ordered (e.g., numbers, days of the week, and letters of the alphabet) are structurally similar and can be aligned by virtue of that relation (e.g., 1 = Monday, 2 = Tuesday, 3 = Wednesday, etc.). However, structurally similar representations can have even richer relational mappings. Consider the case of analog magnitude representations, which include representations of numerosity as well as other continuous quantities and intensities such as area, spatial length, duration, brightness, temperature, and loudness (Brannon et al., 2007, Feigenson, 2007, Meck and Church, 1983). The structural similarity among these dimensions goes beyond the fact that each is characterized by a serial order. First, each has an analog format—each dimension of experience is represented by a physical magnitude that is proportional to the quantity it depicts. Second, in virtue of their analog formats, these representations are inherently noisy, such that representations of increasing values are increasingly more variable. This ensures that comparison of different values along a particular dimension is subject to Weber’s law, where discriminability is a function of the ratio of two values, rather than their absolute difference. Third, locating individual values along each of these continua depends upon a contextually defined standard, as evidenced by the semantic congruity effect (Banks et al., 1975, Holyoak and Walker, 1976, Petrusic, 1992).

Analog magnitude representations meet the basic conditions of structural similarity: a pair of dimensions can be relationally aligned such that the ratio between a pair of values on a first dimension is the same as that between a pair of mapped values on a second dimension (e.g., 1 = a line one inch long, 2 = a line two inches long, etc.). Classic work in psychophysics on cross-modal matching demonstrates that people can access this structural similarity when they are instructed to do so (Stevens, 1975, Stevens and Guirao, 1963, Stevens and Marks, 1965). Participants are presented with successive pairs of stimuli that differ along some dimension (e.g., tones of different durations). For each stimulus pair presented in this first dimension, participants are asked to adjust the stimuli from a second dimension (e.g., lines of different lengths) until the difference between them seems to match that of those of the first dimension (such that the lengths of lines differ by the same ratio as the lengths of tones). Adults and even young children find this a meaningful task and provide consistent and systematic responses. In particular, one can predict matching responses from the discriminability of each matched dimension on its own. Many dimensions of experience are represented by analog magnitudes, and all participate in cross-modal matching (Stevens, 1975).

The structural similarities among analog magnitude representations are important in explaining how it is that different dimensions could be described using the same language: if metaphorical extensions of words are to be understood, people must be able to align elements and relations between the source and target domains (Gentner, 1983). However, the use of spatial language to describe time across languages suggests a stronger relationship between representations of space and time than the mere possibility of relationally aligning them. That is, although all magnitude representations are alignable with representations of duration in the sense defined here, we do not use the language of loudness, brightness, temperature, or pain to describe duration.

Some structural similarities among systems of representation may reflect an even stronger relationship—a functional overlap in processing that allows these representations to automatically engage one another, leading to spontaneous access of their structural similarity (Cantlon et al., 2009, Walsh, 2003). Psychological evidence for functional overlap of many of the dimensions discussed above dates back to the ‘congruity’ tasks of Paivio (1975). In these Stroop-like paradigms, participants are shown two stimuli on a computer screen, such as two numerical digits. Participants are told to attend to one dimension of the stimuli (e.g., their cardinal value) and choose which of the two stimuli is larger on this dimension, while ignoring variation in an irrelevant dimension (e.g., physical size). The two dimensions are varied such that the stimuli are either relationally congruent (the numerically larger digit is also physically larger), neutral (the two digits are of the same size), or incongruent (the numerically larger digit is the physically smaller one). These studies find a facilitative effect of congruent pairings (they are responded to faster than neutral pairings), and an inhibitory effect of incongruent pairings (they are responded to slower than neutral pairings) and have been observed in the interactions between number, size, and luminance (Cohen Kadosh and Henik, 2006, Henik and Tzelgov, 1982, but see Pinel, Piazza, Le Bihan, & Dehaene, 2004, who do not find behavioral interference between number and luminance). Automatic effects of congruence on processing have also been observed in the SNARC effect, in which participants are faster to make judgments about larger numbers on the right side of space and smaller numbers on the left side of space (Dehaene et al., 1993, Fias, 2001). These effects demonstrate a spontaneous, intrinsic mapping between number and space, and similar effects have also been observed for pitch and space (Rusconi, Kwan, Giordano, Umlita, & Butterworth, 2006).

Studies on the processing of temporal duration also suggest that its representations functionally overlap with spatial representations. For instance, Xuan and colleagues (2007) had participants judge which of two stimuli were presented for a longer duration, and found that participants were affected by variation in irrelevant properties of the stimuli presented (e.g., their numerosity, size, and luminance), such that when these were of a “larger” magnitude, stimuli were judged to last longer. Casasanto and Boroditsky (2008) also suggested that representations of duration are spontaneously aligned with representations of spatial length. Participants were presented a line for some amount of time, and were then asked to reproduce its duration by indicating the beginning and end of the interval with mouse clicks. The spatial length of the line interfered with duration estimates—longer lines were estimated to last for longer periods of time, and shorter lines for shorter periods.

Just as structural similarity is graded, so too is functional overlap—representations of different dimensions may engage with and align with one another to different degrees. For example, Casasanto (2008) found that irrelevant variation in spatial length interfered with estimates of temporal duration for English and not Greek speakers, while irrelevant variation in quantity interfered with estimates of duration for Greek speakers and not English speakers. These effects are consistent with linguistic patterns in English and Greek—while the dominant spatial metaphor for duration in English is length (a long meeting), the dominant metaphor in Greek involves quantity (a big meeting). This result suggests that language learning may play a role in the degree to which representations functionally overlap, an issue to which we will later return.

Functional overlap may in some cases also reflect shared neural substrate. Information processing of many of the different dimensions under discussion here appears to involve the same brain areas, including inferior parietal areas and the intraparietal sulcus (IPS). For example, the level of behavioral interference observed in congruity tasks is correlated with level of activity in the IPS, suggesting that it may be the site of integration of information from different dimensions, including number, size, and luminance into a generalized magnitude system (Cohen Kadosh et al., 2008, Fias et al., 2003, but see Pinel et al., 2004, who suggest a different locus for representations of luminance). Neuropsychological data from non-human primates also support this possibility, as individual neurons in posterior parietal areas simultaneously code for both line length and numerical value (Tudusciuc & Nieder, 2007).

There are also indications that the IPS and other inferior parietal areas may include representations of duration, in addition to representations of space, numerosity, luminance, and other magnitudes. First, these areas have been shown to be active during the encoding of temporal intervals (Rao, Meyer, & Harrington, 2001). Second, damage to inferior parietal areas often results in temporal disorientation—and also often results in deficits in spatial and numerical abilities (Critchley, 1953). Finally, application of trans-cranial magnetic stimulation to the IPS can cause deficits in spatial tasks, number comparison, and temporal discrimination (Bjoertomt et al., 2002, Cohen Kadosh et al., 2007, Rushworth et al., 2001, Walsh and Pascual-Leone, 2003).

Thus, inferior parietal areas and the IPS may be responsible for representations and computations that are general to a variety of quantities and intensities including numerosity, size, length, duration, and brightness (Cantlon et al., 2009, Walsh, 2003), although these representations could share neural circuitry to different extents (cf. Pinel et al., 2004). This functional and neural overlap could reflect a recycling, over evolutionary time, of representations and processes for more general purposes (e.g., from a system that once computed only spatial length, to one that computed length, duration, numerosity, and other magnitudes) (Cantlon et al., 2009). Environmental, cultural, and linguistic experience could also play a role in creating functional overlap among different quantities and intensities over ontogeny (Berch et al., 1999, Boroditsky, 2000, Casasanto, 2008, Lakoff and Johnson, 1980, Lakoff and Johnson, 1999, Zebian, 2005).

Due to their functional overlap, the representations of different magnitudes could automatically engage with one another, making their relational correspondences transparent. To the extent that functional overlap is graded, those correspondences that are the easiest for people to notice might also be reflected in flexible word use, as the same words (e.g., long, short, big, high, etc.) come to be applied to functionally overlapping dimensions. Thus, while a structural similarity among different representations is necessary to explain how different dimensions could be relationally aligned and described using the same words, a large degree of functional overlap could explain why some dimensions, such as spatial length and temporal duration, receive common expression in many of the world’s languages.

Evidence from human infants’ discrimination of values in different domains provides unequivocal evidence that infants deploy analog magnitude representations for a variety of quantities, including temporal duration. Like human adults and non-human animals, human infants discriminate numerosity, length, duration, and other continuous quantities and intensities according to Weber’s law. For example, 6-month-old infants can discriminate numerosity at a 1:2 ratio (but fail at a 2:3 ratio), independent of whether sets are presented as dots (Xu & Spelke, 2000), sounds (Lipton & Spelke, 2003), or actions (Wood & Spelke, 2005), and independently of the absolute size of the sets (success at 4 vs. 8 but not 4 vs. 6; success at 16 vs. 32 but not 16 vs. 24). Discrimination of duration, area, and length also depend on ratio, and interestingly, at 6 months of age the critical Weber ratio for these dimensions is also 1:2 (Brannon et al., 2006, Huttenlocher et al., 2002, VanMarle and Wynn, 2006). Discrimination of numerosity increases in precision by 9 months of age, when infants succeed at a 2:3 ratio (Lipton and Spelke, 2003, Wood and Spelke, 2005). The discrimination of duration also shows increasing precision at the same age (Brannon et al., 2007).

These studies of human infants suggest that numerosity, duration, length, area, and other continuous quantities and intensities have a common representational format, as mental analog magnitudes, and so are structurally similar to each other in the sense defined above. But in addition, the fact that the Weber ratio for numerosity and duration is the same at 6 months, and improves equivalently at 9 months suggests that the representations of these dimensions, and perhaps others (such as area and length, which are also discriminated at a 1:2 ratio at 6 months), may be more intimately related. Rather than merely drawing on a common type of representation, these dimensions may draw on functionally overlapping, generalized representations. However, the common and increasing precision in discrimination seen with numerosity and duration could also reflect an increase in precision of the common magnitude comparison process, which could in principle operate over distinct representations from different domains (Cantlon et al., 2009, Feigenson, 2007). In order to establish whether infants, like adults, have functionally overlapping representations of different dimensions, studies are needed to explore whether infant representations of different dimensions can automatically engage with and relationally align with one another.

Given the ubiquity of analog magnitude representations in the animal kingdom as well as their early presence in infancy (e.g., Cantlon et al., 2009, Feigenson, 2007, Gallistel, 1990, Meck and Church, 1983), it is unlikely that a metaphorical construction process over ontogeny is necessary for the creation of structurally similar representations of space and time. Nonetheless, it is an open question as to whether such a process plays a role in creating functional overlap between representations of temporal duration and spatial length. Indeed, the results of Casasanto (2008) suggest that experience using the spatial metaphors of one’s language may play an important role in creating or strengthening functional overlap between these dimensions. The present studies begin to explore these issues.

The experiments reported here make use of a novel paradigm to explore the degree of functional overlap between the representation of spatial length, on the one hand, and other representations—of temporal duration (Experiments 1 and 3) and loudness (Experiment 2)—on the other. Because a form of this paradigm was to be used with pre-linguistic infants (Experiments 4 and 5), it could not, like Paivio’s congruity paradigm, explicitly direct participants to attend to certain dimensions of the stimuli and ignore others. Instead, the task measured participants’ spontaneous tendencies to relationally align the values of two dimensions. The task was simple—participants were asked to attend to a randomly presented array of lines of different lengths. Each line was paired with a tone, the tones differing from one another on a second dimension (duration in Experiments 1 and 3; loudness in Experiment 2). In familiarization, one group of participants saw a relationally congruent set of pairings in which the two magnitudes that constituted the stimuli were related by a positive linear function (e.g., longer lines paired with longer tones). The other group of participants saw an incongruent set of stimuli where the two magnitudes were related by a negative linear function (e.g., longer lines paired with shorter tones). In test, both groups were shown pairings from both the congruent and incongruent sets and were asked whether they remembered seeing each one in familiarization.

Because any given magnitude (e.g., a line or a tone) would appear, during familiarization, in the context of other magnitudes (other lines or tones), each could be encoded in relative terms, as having a certain relative “quantity”. Pairings from the congruent set could consequently be seen to consist of two magnitudes that stand in the same relations to other magnitudes from their respective domains (e.g., a line that is x times longer than the shortest line and y times shorter than the longest line would be paired with a tone that is x times longer than the shortest tone and y times shorter than the longest tone). As previous studies have shown, if participants access a structural similarity among dimensions and recognize relational equivalence in a pairing, it can be encoded and processed more efficiently and precisely (Dehaene et al., 1993, Paivio, 1975). This could then yield an asymmetry whereby participants receiving a congruent familiarization are better able than participants receiving an incongruent familiarization to process those stimuli, and to later differentiate between them and the novel test stimuli. Of interest to us was the degree to which participants receiving a congruent familiarization would spontaneously construct a relational mapping among the stimuli from the paired dimensions, given that they could approach this task without doing so. For instance, participants could instead make arbitrary associations between the lines and tones presented during familiarization, in which case performance would not differ between the two groups of participants. Participants could also formulate an explicit, general rule to describe the pairings they see—the longer the line, the longer the tone, or the longer the line, the shorter the tone—in which case performance would also not differ between the groups.

While a structural similarity between representations is necessary and sufficient for the recognition of relational equivalence in pairings from the congruent set (as shown by cross-modal matching phenomena, Stevens, 1975, Stevens and Guirao, 1963, Stevens and Marks, 1965), a functional overlap between representations could make participants more likely to access that structural similarity and construct a relational mapping between those representations. Thus, conceptually, functional overlap between two dimensions is suggested if those dimensions are more spontaneously and precisely aligned than other, equally alignable pairs of dimensions. Experiments 1–3 present evidence for such a dissociation, demonstrating that, within this task, congruence affects the binding of values of spatial length and temporal duration but not of values of length and loudness.

Section snippets

Participants

The participants were 18 Harvard University students: two participants were excluded due to failure of a method check, which showed that these participants were responding randomly. All participants were undergraduate students, and were given course credit or a token gift for their participation.

Materials

Stimuli consisted of a visual stimulus (a solid line) and an auditory stimulus (a tone) presented simultaneously. In each exposure, the line appeared at the center of a screen with a white background as

Participants

The participants were 18 Harvard University students (a distinct group from Experiment 1): two participants were excluded due to failure of a method check. All participants were undergraduate students, and were given course credit or a token gift for their participation.

Materials

Solid lines and tones were presented simultaneously. The same 16 lines that appeared in Experiment 1 were used. 16 tones in A3 (220.0 Hz) were again used, but instead of varying in duration, they varied in loudness, while their

Participants

The participants were 37 Harvard University students (a distinct group from Experiments 1 and 2): three participants were excluded due to failure of a method check. We doubled our sample size from the previous experiments to ensure that we had enough statistical power to detect any differences from the pattern of effects found in Experiment 1. All participants were undergraduate students, and were given course credit or a token gift for their participation.

Materials

As in Experiment 1, stimuli consisted

The origin of functional overlap between representations of length and duration

How might functional overlap between representations of length and duration (as observed with the adult participants of Experiments 1–3) arise? One possibility is that it is innate, having resulted from a recycling, over evolutionary time, of spatial representations in the service of representing other dimensions. However, environmental, cultural, and linguistic experience could also play a role in creating functional overlap between representations of length and duration over development. This

Participants

The participants were 34 healthy full-term 9-month-old infants (mean age = 9 months 15 days, range: 9 months 0 days—10 months 0 days). Families were contacted based on information from birth records and received a token gift for participation. 16 infants formed the congruent group, and 18 infants formed the incongruent group. 21 infants were female. Data from an additional four infants were discarded because of fussiness resulting in failure to complete four test trials.

Apparatus

Infants were seated on a

Participants

The participants were 36 healthy full-term 9-month-old infants (a distinct group from Experiment 4; mean age = 9 months 16 days, range: 9 months 0 days—9 months 29 days). 16 infants formed the congruent group, and 16 infants formed the incongruent group. 16 infants were female. Data from an additional four infants were discarded because of fussiness resulting in failure to complete at least four test trials. Infants were recruited and compensated as in Experiment 4.

Apparatus

All aspects of the apparatus were the

General discussion

The use of spatial language to describe time across languages suggests that representations of space and time are intimately related, a possibility supported by prior research (Boroditsky, 2000, Boroditsky, 2001, Casasanto, 2008, Casasanto and Boroditsky, 2008, Gentner et al., 2002, McGlone and Harding, 1998, Xuan et al., 2007). The experiments reported here make two additional contributions to this literature. In doing so, they also introduce a new measure to assess overlap among

Conclusion and future directions

The studies reported here have provided evidence for a privileged relationship between representations of spatial length and temporal duration—in addition to sharing a common representational format, these representations may have functional overlap such that correspondences are easily and precisely computed (Experiments 1 and 3, contrasted with Experiment 2). This functional overlap is present in 9-month old infants (Experiment 4, contrasted with Experiment 5), and we argue that it is part of

Acknowledgements

We thank the members of Carey Lab and the Lab for Developmental Studies for discussion and comments on an earlier draft, and Leah Fey, Adrienne Scutellaro, Jeehye Kim, Jasmine Khamis, and Kristiana Laugen for assistance with stimuli construction, participant recruitment, and data collection. This research was supported by NIH Grant # 2 ROI HD038338-06A2 to S. Carey, and by an NSF Graduate Research Fellowship to M. Srinivasan.

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