Verbal interference suppresses exact numerical representation

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Abstract

Language for number is an important case study of the relationship between language and cognition because the mechanisms of non-verbal numerical cognition are well-understood. When the Pirahã (an Amazonian hunter-gatherer tribe who have no exact number words) are tested in non-verbal numerical tasks, they are able to perform one-to-one matching tasks but make errors in more difficult tasks. Their pattern of errors suggests that they are using analog magnitude estimation, an evolutionarily- and developmentally-conserved mechanism for estimating quantities. Here we show that English-speaking participants rely on the same mechanisms when verbal number representations are unavailable due to verbal interference. Followup experiments demonstrate that the effects of verbal interference are primarily manifest during encoding of quantity information, and—using a new procedure for matching difficulty of interference tasks for individual participants—that the effects are restricted to verbal interference. These results are consistent with the hypothesis that number words are used online to encode, store, and manipulate numerical information. This linguistic strategy complements, rather than altering or replacing, non-verbal representations.

Highlights

► With no words for numbers, Amazonian tribes cannot perform numerical tasks. ► When prevented from counting, English speakers also fail on these tasks. ► Our results support a view of language as a tool aiding online information encoding.

Introduction

How does knowing a language affect the way you perceive, act, and reason? Do differences between languages cause systematic differences in the cognition of their speakers? Questions about the relationship between language and thought are among the most controversial in cognitive science (Boroditsky, 2001, Davidoff et al., 1999, Gentner and Goldin-Meadow, 2003, Gumperz and Levinson, 1996, Levinson et al., 2002, Li and Gleitman, 2002, Pinker, 1994, Rosch Heider, 1972). Theoretical proposals concerning the nature of this relationship run the gamut from suggestions that individual languages strongly influence their speakers cognition (Davidoff et al., 1999, Levinson, 2003, Whorf, 1956) to suggestions that there is no causal relationship between speakers’ language and their cognition (Fodor, 1975, Li and Gleitman, 2002, Pinker, 1994), with a number of more moderate proposals falling between these extremes (Gentner, 2003, Kay and Kempton, 1984, Slobin, 1996).

Recently, across the domains of color, number, navigation, theory of mind, and object individuation, there has been a convergence of empirical results addressing this question. In each of these domains, meaningful cognitive differences have been demonstrated between people who have words for particular concepts and those who do not, either because their language does not encode those concepts (Frank et al., 2008, Gordon, 2004, Pica et al., 2004, Pyers and Senghas, 2009, Winawer et al., 2007) or because they have not yet learned the relevant words (de Villiers and de Villiers, 2000, Le Corre et al., 2006). These group differences are mitigated or disappear entirely when the people who do know the relevant words cannot access these words (for example, when they are required to occupy their verbal resources with interfering material or when tasks are speeded) (Hermer-Vazquez et al., 1999, Ratliff and Newcombe, 2008, Newton and de Villiers, 2007, Winawer et al., 2007).

These similarities across domains point towards a unified account of the relationship between language and cognition that falls midway between the two theoretical extremes of strong interaction and no interaction. On the one hand, the data suggest that languages do change the cognition of their speakers: they help their speakers accomplish difficult cognitive tasks by creating abstractions for the efficient processing and storage of information. On the other hand, the data also suggest the hypothesis that these abstractions complement rather than replace pre-existing non-verbal representations. When linguistic abstractions are temporarily inaccessible, language users seem to fall back on the representations used by other animals, children, and speakers of languages without those abstractions.

This relationship—the use of language online for encoding—has been referred to in a number of ways in the previous literature. Kay and Kempton (1984) follow Whorf (1956) in describing cognition as having two tiers: “one, a kind of rock-bottom, inescapable seeing-things-as-they are (or at least as human beings cannot help but see them) and a second, in which the metaphors implicit in the grammatical and lexical structures of language cause us to classify things in ways that could be otherwise (and are otherwise for speakers of different languages).” Gentner and Goldin-Meadow, 2003, Frank et al., 2008, emphasizing the way that linguistic representations augment cognition, refer to this view as “language as a toolkit” or “cognitive technology.” Dessalegn and Landau (2008) refer to this as the “momentary” hypothesis, emphasizing that the role of language is online rather than permanent. All of these accounts posit that tasks like verbal interference temporarily disable this second tier, leading speakers to perform tasks in ways that are shared cross-culturally. The goal of the current experiments is to test this prediction for numerical cognition: that experienced number users under verbal interference should perform numerical tasks in the same way as people with no number words.

As a case study of the relationship between language and thought, number has a key advantage over other domains: the pre-linguistic mechanisms for representing numerical information are relatively well-understood (Cantlon et al., 2009, Carey, 2009, Dehaene, 1997). Numerical cognition in infants and non-human animals is characterized by two distinct systems (Feigenson, Dehaene, & Spelke, 2004). The parallel-individuation (“object file”) system is used to track the identity of a few (up to three or four) discrete objects. In contrast, the analog magnitude system is used to represent large, approximate quantities. Analog magnitude estimation operates over arbitrarily large quantities, but the error in the estimate increases in proportion to the size of the set being estimated (resulting in a constant coefficient of variation, or COV; see Appendix) (Shepard, 1975, Whalen et al., 1999).

In the absence of words for numbers, even human adults appear to rely on these core numerical systems. For example, adults’ estimates of quantity show the same systematic errors as those of infants and pigeons when the sets are presented too rapidly to be counted (Whalen et al., 1999). When a culture has no words for number, the same profile is observed even for slower presentation rates, as documented in two Amazonian groups, the Pirahã (Gordon, 2004) and the Mundurukú (Pica et al., 2004). Evidence from the Pirahã has been used to support a further claim, as well. Gordon reported that the Pirahã language had only three numerical words, roughly corresponding to the concepts of “one,” “two,” and “many,” and that Pirahã participants were unable to perform simple numerical matching tasks, including creating a set that was the same size as a target set using one-to-one correspondence. He interpreted these results as evidence for a strong Whorfian claim: without language for number, he argued, the Pirahã have no concept of exact quantity.

Our own recent results slightly alter this picture. We reported that Pirahã actually has no words for exact quantities; the words previously glossed as exact numerals (“one” and “two”) apparently are comparative or relative terms (Frank et al., 2008). In addition, we showed that the Pirahã were able to succeed in simple one-to-one matching tasks, suggesting that they did understand the principle of exact, one-to-one correspondence, even for large sets. However, our results were similar to those reported by Gordon in that the Pirahã made systematic errors on matching tasks that required memory for exact quantities. Thus, current evidence from the Pirahã suggests that the ability to remember and manipulate exact quantities, but not the concept of exact correspondence, relies on language.

Another set of recent results seems to conflict with this account, however. Butterworth, Reeve, Reynolds, and Lloyd (2008) investigated a group of numerical tasks with children ages 4–7 who had grown up speaking Warlpiri or Anindilyakwa, two native Australian languages. Both languages have some number morphology (e.g. singular, dual, plural in Warlpiri) and Anindilyakwa has a base-5 number system, though it is not in heavy use. To test for effects of language on numerical cognition, Butterworth and colleagues compared data from tasks on cross-modal matching, addition, and number memory (as well as a sharing task in which performance depended on learned strategies) to control data from 4–5 year-old English-speaking children from an urban environment. They found that all three groups performed comparably in all tasks, with age emerging as the major factor driving performance. A second study suggested that spatial grouping strategies might provide a non-linguistic alternative to exact enumeration (Butterworth & Reeve, 2008). Across both studies, the authors interpreted this lack of a language effect as suggesting that language was not the key factor in the development of enumeration abilities, contra work with the Pirahã and Mundurukú.

One salient issue in comparing these data to the previous Amazonian results is the pattern of errors shown by the English-speaking participants. In two out of three tasks in Butterworth et al. (2008), the young English-speaking children—like the Warlpiri and Anindilyakwa children—made responses consistent with approximate number use. In fact, across both sets of studies performance by the English-speakers in all tasks was strikingly low: for example, performance in simple addition problems like 3 + 1 was below 50%, and it dropped to about 20% in problems like 5 + 3. This pattern suggests that even if the children had mastered the count list, they were not using their exact number knowledge to succeed and may even have had trouble understanding the tasks. The Australian data thus do not provide a strong test of what role language plays in establishing exact number concepts because even numerate participants in their study failed to use exact number concepts.

Nevertheless, the Butterworth et al. account makes a strong prediction that contradicts the theoretical accounts of the online role of language in cognition that are described above. If language is not crucial in establishing exact number concepts either developmentally or in the moment, adult speakers of English should be able to perform exact numerical tasks under verbal interference. In contrast, if language is necessary for online storage of exact numbers, English speakers should rely on analog magnitude estimation when they cannot use linguistic resources. Our experiments evaluate this prediction.

Several previous studies have investigated numerical tasks under conditions designed to suppress or circumvent the use of language, but they used paradigms that were at least partially verbal in nature. Logie and Baddeley (1987) conducted a detailed investigation of the effects of interference tasks on verbal counting. They found that verbal suppression via rapid repetition of the word “the” caused participants to make errors in counting, while simply tapping a finger or listening to speech caused far fewer. They concluded that the articulatory-phonological loop (Baddeley, 1987) was strongly implicated in counting. In a followup study, Trick (2005) investigated the effects of simple and complex verbal suppression and motor interference tasks (repeating one letter/tapping one finger or alternating between two letters/two fingers) and found substantial effects of both complex verbal and complex motor tasks on enumeration. Because neither of these studies provided evidence about the variability of participants’ errors, it is not possible to determine whether participants were making use of analog magnitude estimation (as would have been tested by an analysis of COV).

Two studies have investigated the relationship between counting and COV. Whalen et al. (1999) showed participants Arabic numerals and then asked them to press a key so quickly that they could not verbally enumerate the number of times they did so. Cordes, Gelman, Gallistel, and Whalen (2001) used a similar task but asked participants either to perform a verbal suppression task (repeating “the”) or to count as fast as they could. These studies found that participants showed a constant COV under speeded response and verbal suppression, signaling a reliance on analog magnitude estimation. In contrast, when counting they showed a decreasing COV, suggesting a pattern of binomial errors (caused by errors in the correspondence between the verbal count list and their key presses; see the Appendix for more details on how different COV trends can be derived from different numerical mechanisms or strategies).

These studies provide direct evidence that verbal suppression affects counting performance. However, they investigated explicitly verbal tasks (either counting a quantity or translating a numeral into a set of actions). It is still unknown whether participants from a numerate culture who are under verbal interference will rely on analog magnitude estimation in completely non-verbal tasks. To evaluate this question, we conducted three experiments. Experiment 1 tests English speakers’ performance under verbal interference when tested in completely non-verbal tasks identical to those used with the Pirahã. We find that, while English speakers primarily use ad-hoc non-linguistic strategies in simpler matching tasks, in the most demanding tasks they rely exclusively on analog magnitude estimation. Experiment 2 investigates how verbal resources facilitate the storage and manipulation of quantity information, testing whether verbal interference impairs verbal encoding of quantity information, or whether it has an equal effect on retrieving quantity information once it is encoded. We find that encoding, as opposed to retrieval, is differentially affected by verbal interference. Finally, by comparing the effects of matched verbal and spatial interference tasks, Experiment 3 tests whether it is specifically the inaccessibility of linguistic resources that forces a reliance on the approximate number system. We find that language interference produces both a greater degree and a different pattern of impairment in numerical performance.

Section snippets

Experiment 1

In our first experiment, we compared the previously-reported matching task performance of Pirahã participants—who lack words for exact numbers entirely—to new data from English-speakers under verbal interference—for whom number words were temporarily unavailable. We performed the same set of tasks that we used with the Pirahã with English-speaking participants in Boston, MA while these participants verbally shadowed radio news broadcasts (repeating words out loud as they were heard over

Experiment 2

Our next experiment focused in on the nuts-in-a-can task. As discussed above, we believe this task provides the cleanest test of performance, since participants cannot rely on other visual strategies to succeed. Because the finding of a constant COV for English speakers in this task was the most important result of Experiment 1, we were interested in replicating this finding. In addition, we were interested in whether verbal interference differentially affected encoding (creating a mental

Experiment 3

Our goal in our final experiment was to test whether verbal interference specifically—rather than cognitive load more generally—was responsible for the use of the approximate number system in the nuts-in-a-can task in Experiments 1 and 2.

Because the results of Experiment 2 suggested that the effect of verbal interference was primarily manifest during encoding, and because the manual nature of the tasks used in Experiments 1 and 2 limited the number of trials we could conduct (setting up each

General discussion

The goal of our experiments was to test whether, when access to number words was impaired via verbal interference, participants would use analog magnitudes to keep track of approximate quantities. Experiment 1 showed that, like the Pirahã, who have no words for numbers, numerically-savvy English speakers will also rely on analog magnitude estimation when they are prevented from using linguistic resources—though they do this only in tasks where it is difficult to use other ad-hoc strategies.

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