Elsevier

Cognition

Volume 120, Issue 1, July 2011, Pages 136-147
Cognition

Rapid parallel semantic processing of numbers without awareness

https://doi.org/10.1016/j.cognition.2011.03.005Get rights and content

Abstract

In this study, we investigate whether multiple digits can be processed at a semantic level without awareness, either serially or in parallel. In two experiments, we presented participants with two successive sets of four simultaneous Arabic digits. The first set was masked and served as a subliminal prime for the second, visible target set. According to the instructions, participants had to extract from the target set either the mean or the sum of the digits, and to compare it with a reference value. Results showed that participants applied the requested instruction to the entire set of digits that was presented below the threshold of conscious perception, because their magnitudes jointly affected the participant’s decision. Indeed, response decision could be accurately modeled as a sigmoid logistic function that pooled together the evidence provided by the four targets and, with lower weights, the four primes. In less than 800 ms, participants successfully approximated the addition and mean tasks, although they tended to overweight the large numbers, particularly in the sum task. These findings extend previous observations on ensemble coding by showing that set statistics can be extracted from abstract symbolic stimuli rather than low-level perceptual stimuli, and that an ensemble code can be represented without awareness.

Introduction

Given the huge amount of sensory information arising from visual perception, a question of great interest concerns how the human brain manages to selectively extract the relevant pieces of information and encode the “gist” of the scene. The visual system appears to be organized as a massive parallel system which processes many elements non-consciously at the same time. Only late in the process do one or very few objects or parameters gain access to conscious processing and slow serial scrutiny.

In particular, the visual system appears to possess cognitive mechanisms capable of representing a set of similar stimuli by means of coding only their overall statistical properties (summary or set statistic, also referred to as “ensemble coding”). For example, when participants are presented a set of spots with different sizes, they can accurately categorize the mean size of the set as smaller or larger than a test spot (Ariely, 2001). Similarly, discriminating the speed of dot stimuli which contain many different speeds is done by integrating the different speeds, producing an average global speed (Watamaniuk & Duchon, 1992).

Besides representing the average size (e.g., Ariely, 2001, Chong and Treisman, 2003), or speed (Watamaniuk & Duchon, 1992), the visual system can also represent other statistics like the average position of dots (Alvarez & Oliva, 2008), or the mean spatial frequency and orientation of stimuli (e.g., Alvarez and Oliva, 2009, Dakin and Watt, 1997). Furthermore, in a series of studies, Haberman and colleagues recently suggested that ensemble coding is not limited to low-level visual parameters. In their experiments participants automatically extracted the average emotion or gender from a set of faces (Haberman and Whitney, 2007, Haberman and Whitney, 2009, Haberman et al., 2009).

Obviously, for ensemble coding to be beneficial for processing visual information it needs to be highly efficient and automatic. In a recent study, attention to a set of stimuli was reduced by presenting them as a background, irrelevant for the experimental task. While participants were following the trajectory of dots on the screen, Gabor patches with different orientations on the background formed a spatial pattern. In a subsequent test phase, participants were able to match the spatial layout of the unattended background to a test stimulus indicating that the ensemble code of the spatial frequency and orientation was represented in the visual system (Alvarez & Oliva, 2009). In another study, the automatic extraction of ensemble coding was demonstrated using a priming paradigm. Here, the presentation of a set of spots on the screen increased the visibility of a single test spot if the mean size of the set of spots corresponded to the size of the test spot (Marchant & de Fockert, 2009). The representation of ensemble codes thus appears to be computed automatically and in parallel at a preattentive stage (Chong & Treisman, 2005).

In sum, statistical information can be extracted from a visual scene, and this can be done with reduced attention (for an alternative view see Myczek & Simons, 2008). The scope of these findings remains, however, largely unexplored. For example, to what extent can summary statistics be represented for more complex stimuli? Although low-level cues were distorted when participants were averaging faces (e.g., Haberman & Whitney, 2007) in this experiment, the potential contribution of feature-based information to the mean extraction might have been underestimated. Indeed, it is unclear how the recognition of gender or emotional expressions can occur without low-level cues.

In the present work, we investigate the possibility of ensemble coding for abstract yet highly familiar symbolic stimuli: Arabic numbers. The relation between the perceptual features of an Arabic digit and its magnitude is completely arbitrary. There have been many demonstrations of fast, subliminal encoding of the magnitude of a single Arabic digit (e.g., Dehaene et al., 1998b, Van Opstal et al., 2005). Demonstrating the representation of a set statistic for Arabic numerals would definitely prove that statistics extraction goes beyond the mere extraction of early visual parameters.

A second point that deserves further investigation is the relation between ensemble coding and conscious perception. Previous results demonstrating that ensemble coding can proceed with reduced or little attention lead us to formulate the hypothesis that awareness might be an unnecessary condition for ensemble coding. One way to clarify this is to study the effect of the ensemble code indirectly, and to present the set of stimuli subliminally, i.e. below the threshold of conscious perception. If the statistic of an ensemble that is subliminally presented affects a subsequent decision this would unequivocally demonstrate that ensemble coding can occur entirely outside of conscious intention.

The use of subliminally presented symbolic stimuli further allows us to investigate the relation between consciousness and parallel and serial processing. Earlier work found that information coming from an unattended stimulus can build up in parallel with information from an attended stimulus (Posner & Snyder, 1975). In a dichotic listening task, for example, a word presented on the unattended ear can elicit a galvanic skin response the same size as when it is presented in the attended ear (Von Wright, Anderson, & Stenman, 1975). The unattended word is processed in parallel with the attended word without the participants’ awareness. On the other hand, the processing of a target stimulus that is presented during a rapid serial visual presentation impairs the processing of a subsequent stimulus, and makes it inaccessible for conscious awareness (the attentional blink; Broadbent and Broadbent, 1987, Raymond et al., 1992). Dual-stage models of conscious access (e.g., Chun and Potter, 1995, Sergent et al., 2005) propose that this is caused because of a capacity limitation of central processing. According to the theory of the global neuronal workspace (Baars, 1988, Baars, 2002, Dehaene et al., 2006, Dehaene et al., 1998a), multiple parallel processors can operate non-consciously, but the serial execution of multiple cognitive operations requires conscious access. This hypothesis was recently tested in a study where two successive operations had to be performed on a subliminal or supraliminal number. When the input number was subliminal, it was shown that participants could perform each individual operation better than chance, but were unable to perform the two operations serially in close succession without conscious access (Sackur & Dehaene, 2009). Translated to the present context, this would mean that the integration of multiple items into a serial computation should be impossible for subliminally presented stimuli. Only ensemble statistics that can rely on the parallel extraction of information should be extracted subliminally.

In the present case, we investigate the possibility that addition and averaging dissociate with respect to subliminal priming. Addition of several Arabic numbers, at least when performed in an exact, arithmetically rigorous manner, seems to be a typically serial and controlled process where one number is added to another number, and the next number is then added to this sum, etc. Approximate averaging, on the other hand, essentially amounts to finding the typical value of a set, and could be accomplished by a parallel process where all magnitudes are simultaneously weighted and their votes used to converge to a single attractor value on the internal number line, representing the entire set. Indeed, the above examples of ensemble coding with non-symbolic stimuli indicate that finding the mean of some parameter in a set can be done in a fast parallel manner.

Several factors might however mitigate the proposed dissociation between serial addition and parallel averaging. Summing and averaging are similar operations, and in the experiments below, they amount to performing exactly the same task, with the sole difference lying in the instructions given to subjects. Furthermore, human participants appear to have a capacity for fast approximate calculation, including addition, which may bypass serial symbolic processing (Dehaene et al., 1999, El Yagoubi et al., 2003). When participants are trained in approximate calculation, performance generalizes without cost to neighboring addition problems and to problems present in a second language (Dehaene et al., 1999, Spelke and Tsivkin, 2001). These results could indicate that approximate addition might rely on intuitive parallel computations, and indeed there is evidence for subliminal addition of just two digits (Lefevre et al., 1988, Sackur and Dehaene, 2009). From a computational point of view, it has been proposed that a neuron’s activity is determined by the weighted sum of different parallel input signals (McCullough & Pitts, 1943) suggesting that the neuronal architecture of the brain permits parallel addition. Conversely, it could be argued that averaging is composed of two serial calculation steps, summing and dividing – in which case we would expect averaging to be impossible under subliminal conditions. Given these uncertainties about the computational processes underlying addition and averaging, the present experiments were exploratory in nature and merely examined if these tasks would dissociate under subliminal conditions.

To address these points empirically, a numerical subliminal priming experiment was designed in which participants were presented with a target display consisting of four Arabic digits (the target set). Different groups of participants were explicitly asked to extract either the mean or the sum of the digits and to compare it to a reference value (five for the mean task, and 20 for the sum task; note that with four target digits, these tasks are formally identical). Unbeknownst to the participants, a prime display, sandwiched between two mask displays, presented four additional digit primes unrelated to the targets, shortly before the target display (the prime set). The automatic extraction of an ensemble code for symbolic stimuli could thus be investigated by looking at the influence of the four-digit prime display on the responses to the four-digit target display.

Section snippets

Participants

22 university students (one male, aged between 18–21) took part in the experiment for course credits. None of the participants was aware of the purpose of the experiment.

Apparatus and stimuli

A 60 Hz monitor was used with stimulus presentation synchronized to the refresh rate (16.7 ms). Key presses were registered with a response box. Each trial was announced by a fixation cross (500 ms) followed by the presentation of a premask (67 ms), a prime display (33 ms), a postmask (67 ms), and a target display. The target display

Experiment 2

To further investigate this issue, we designed another experiment in which we discouraged subjects from adopting similar strategies in the sum and mean task. We achieved this result by changing the number of stimuli presented on a trial. Each set now comprised 3, 4 or 5 digits. Because the sum or mean of the target set still had to be compared to 20 or 5 respectively, participants were now forced to use the instructed calculation (mean or sum) in order to respond correctly. For example, when

General discussion

The results of these experiments extend previous findings on ensemble statistics by showing that an ensemble code can be extracted from a set of abstract symbolic stimuli that are presented without the participant’s awareness. Because Arabic numerals bear absolutely no resemblance to the magnitude they represent the current study clearly demonstrates that ensemble coding can go beyond surface perception and applies also to a higher level of analysis. These results extend those of Haberman and

Acknowledgments

FVO is a Postdoctoral Fellow of the Research Foundation – Flanders (FWO-Vlaanderen).

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