Ensemble statistics as units of selection

The current study investigated whether attentional mechanisms operate on ensembles as higher-order units for selection. In Experiment 1, we presented sets of circles and asked participants to compare the mean sizes of the sets while concurrently detecting a small probe appearing at a centroid of one of the sets. We found that, both with and even without the task instruction to favour larger mean sizes, people's mean size judgement was more accurate for the sets with larger mean sizes. In addition, detection of the probe appearing in the set with the largest mean size was facilitated by a matching task instruction. However, when the task instruction favoured smaller mean sizes, mean size judgement became more accurate for the sets with smaller mean sizes. These results suggest that attentional selection can be based on ensembles. In Experiment 2, we found further evidence that attention was directed towards the centroid of an ensemble, rather than towards an individual member of the ensemble. Together, these results suggest that attentional modulation can operate at the level of ensembles instead of selecting individuals separately and that the centroid of an ensemble can be the locus of selection based on an ensemble.     

The whole is indeed more than the sum of its parts: perceptual averaging in the absence of individual item representation

We tested Ariely's (2001) proposal that the visual system represents the overall statistical properties of sets of objects against alternative accounts of rapid averaging involving sub-sampling strategies. In four experiments, observers could rapidly extract the mean size of a set of circles presented in an RSVP sequence, but could not reliably identify individual members. Experiment 1 contrasted performance on a member identification task with performance on a mean judgment task, and showed that the tasks could be dissociated based on whether the test probe was presented before or after the sequence, suggesting that member identification and mean judgment are subserved by different mechanisms. In Experiment 2, we confirmed that when given a choice between a probe corresponding to the mean size of the set and a foil corresponding to the mean of the smallest and largest items only, the former is preferred to the latter, even when observers are explicitly instructed to average only the smallest and largest items. Experiment 3 showed that a test item corresponding to the mean size of the set could be reliably discriminated from a foil but the largest item in the set, differing by an equivalent amount, could not. In Experiment 4, observers rejected test items dissimilar to the mean size of the set in a member identification task, favoring test items that corresponded to the mean of the set over items that were actually shown. These findings suggest that mean representation is accomplished without explicitly encoding individual items.     

Can spatialisation be extended to episodic memory and open sets?

The SPoARC effect (Spatial Positional Associated Response Codes) has only been observed in working memory (WM) using closed sets. It is interpreted as showing that individuals spatialise to-be-remembered items in a left-to-right fashion, using spatialisation as context. Given that context is crucial for episodic memory (EM), we tested if this effect could be observed in EM by using 15-word lists taken from an open set. After each list, 30 probes were sequentially displayed to test recognition. The left/right-hand key assignment for yes/no answers was varied. No SPoARC effect was observed. However, as all previous SPoARC experiments had used short lists and closed sets, it was not possible to know if this absence of SPoARC was due to the open set feature or the length of the lists. A second experiment was thus run using open sets and short 5-word lists, which do not necessitate EM to be remembered. A SPoARC effect was observed indicating that Experiment 1 result was due to the involvement of supra-span lists and that SPoARC effects do not extend to EM with open sets. Experiment 2 also enabled us to generalise the SPoARC effect to open sets in WM for the first time.     

Comparing pluralities

What does it mean to compare sets of objects along a scale, for example by saying “the men are taller than the women”? We explore comparison of pluralities in two experiments, eliciting comparison judgments while varying the properties of the members of each set. We find that a plurality is judged as “bigger” when the mean size of its members is larger than the mean size of the competing plurality. These results are incompatible with previous accounts, in which plural comparison is inferred from many instances of singular comparison between the members of the sets (Matushansky &; Ruys, 2006). Our results suggest the need for a type of predication that ascribes properties to plural entities, not just individuals, based on aggregate statistics of their members. More generally, these results support the idea that sets and their properties are actively represented as single units.     

Capacity limit of ensemble perception of multiple spatially intermixed sets

The visual system is remarkably efficient at extracting summary statistics from the environment. Yet at any given time, the environment consists of many groups of objects distributed over space. Thus, the challenge for the visual system is to summarize over multiple groups. The current study investigates the capacity and computational efficiency of ensemble perception, in the context of perceiving mean sizes of multiple spatially intermixed groups of circles. In a series of experiments, participants viewed an array of one to eight sets of circles. Each set contained four circles in the same colors, but with different sizes. Participants estimated the mean size of a probed set. The set that would be probed was either known before onset of the array (pre-cue condition) or afterwards (post-cue condition). By comparing estimation error in the pre-cue and post-cue conditions, we found that participants could reliably estimate mean sizes for approximately two sets (Experiment 1). Importantly, this capacity was robust against attention bias toward individual objects in the sets (Experiment 2). Varying the exposure time to stimulus arrays did not increase the capacity limit, suggesting that ensemble perception could be limited by an internal resource constraint, rather than the speed of information encoding (Experiment 3). Moreover, we found that the visual system could not encode and hold more individual items than ensemble representations (Experiment 4). Taken together, these results suggest that ensemble perception provides an efficient way of information processing but with constraints.     

Quantity judgments of auditory and visual stimuli by chimpanzees (Pan troglodytes)

Many species can choose between two visual sets of stimuli on the basis of quantity. This is true when sets are both visible, or are presented one set at a time or even one item at a time. However, we know comparatively little about how well nonhuman animals can compare auditory quantities. Here, three chimpanzees (Pan troglodytes) chose between two sets of food items when they only heard each item fall into different containers rather than seeing those items. This method prevented the chimpanzees from summing the amount of visible food they saw because there were no visual cues. Chimpanzees performed well, and their performance matched that of previous experiments with regard to obeying Weber's law. They also performed well with comparisons between a sequentially presented auditory set and a fully visible set, demonstrating that duration of presentation was not being used as a cue. In addition, they accommodated empty sets into these judgments, although not perfectly. Thus, chimpanzees can judge auditory quantities in flexible ways that show many similarities to how they compare visual quantities.     

Accepting or Rejecting Medical Treatment: A Comparison of Decisions Made for Self Versus Those Made for a Significant Other1

College students (N= 52) made sets of hypothetical decisions concerning whether to accept or withhold medical treatment for oneself as well as for a significant other. Two sets of decisions were made for the significant other: a set representing what the significant other would want for himself or herself, and a set representing what the potential surrogate would want for the significant other. Results revealed consistent sets of decisions within each decision frame, considerable individual differences in mean judgments, an emphasis on the levels of mental and physical functioning, self‐reported decision weights that differed across the decision frames, and considerable self‐insight into the decision policy used when deciding for oneself.     

Rapid averaging? Not so fast!

Previous research suggests that sets of similar items are represented using a rapid averaging mechanism that automatically extracts statistical properties within 50 ms. However, typically in these studies, displays are not masked, so it is possible that the sets are available for longer than this duration. In the present study, using masked displays, we (a) tested a newly proposed strategy for extracting the mean size of a set of circles, and (b) more precisely evaluated the time course of rapid averaging. The results indicate that when viewing conditions are poor, performance can be explained by assuming that observers rely on information from previous trials. In this study, observers required at least a 200-ms exposure time in order to derive the average size of a set of circles without relying on information from previously-viewed sets, suggesting that rapid averaging is not as fast as previously assumed and, therefore, that it may not be an automatic process.     

Exploration and exploitation during sequential search

When we learn how to throw darts we adjust how we throw based on where the darts stick. Much of skill learning is computationally similar in that we learn using feedback obtained after the completion of individual actions. We can formalize such tasks as a search problem; among the set of all possible actions, find the action that leads to the highest reward. In such cases our actions have two objectives: we want to best utilize what we already know (exploitation), but we also want to learn to be more successful in the future (exploration). Here we tested how participants learn movement trajectories where feedback is provided as a monetary reward that depends on the chosen trajectory. We mathematically derived the optimal search policy for our experiment using decision theory. The search behavior of participants is well predicted by an ideal searcher model that optimally combines exploration and exploitation.     

KNOWING OURSELVES AS EMBODIED,EMBEDDED, AND RELATIONALLY EXTENDED

What does it mean to know oneself, and what is the self that one hopes to know? This article outlines the implications of an embodied understanding of persons and some aspects of the “self” that are generally ignored when thinking about our selves. The Cartesian model of body–soul (or body–mind) dualism reinforces the idea that there is within us a soul, or self, or mind that is our hidden, inner, and real self. Thus, the path to self‐knowledge is introspection. The alternative view is that persons are embodied (entirely physical creatures), embedded (formed by our physical and social environment), and at times extended (cognitively soft‐coupled to artifacts or other persons). This article emphasizes the bodily, active, contextual, relational, often simulated, and sometimes extended nature of the selves that we are, and that we hope to know.     

Ensemble representations: Effects of set size and item heterogeneity on average size perception

Observers can accurately perceive and evaluate the statistical properties of a set of objects, forming what is now known as an ensemble representation. The accuracy and speed with which people can judge the mean size of a set of objects have led to the proposal that ensemble representations of average size can be computed in parallel when attention is distributed across the display. Consistent with this idea, judgments of mean size show little or no decrement in accuracy when the number of objects in the set increases. However, the lack of a set size effect might result from the regularity of the item sizes used in previous studies. Here, we replicate these previous findings, but show that judgments of mean set size become less accurate when set size increases and the heterogeneity of the item sizes increases. This pattern can be explained by assuming that average size judgments are computed using a limited capacity sampling strategy, and it does not necessitate an ensemble representation computed in parallel across all items in a display.     

Rapid extraction of mean identity from sets of faces

Recent evidence suggests that the notion that the visual system can rapidly extract summary statistics from complex scenes extends to representing sets of faces in terms of mean emotion or gender. Here we show that observers can also extract a mean identity from a set of faces with different identities. Observers first saw a set of four faces with different identities and were subsequently asked whether or not a single test face had been present in the preceding set. They were significantly more likely to respond that the test face had been present in the set if it was the morphed mean of all four set faces than when it was an actual set member. This finding suggests that representations based on summary statistics are available for face identity.     

What is learned in spatial contextual cuing— configuration or individual locations?

With the use of spatial contextual cuing, we tested whether subjects learned to associate target locations with overall configurations of distractors or with individual locations of distractors. In Experiment 1, subjects were trained on 36 visual search displays that contained 36 sets of distractor locations and 18 target locations. Each target location was paired with two sets of distractor locations on separate trials. After training, the subjects showed perfect transfer to recombined displays, which were created by combining half of one trained distractor set with half of another trained distractor set. This result suggests that individual distractor locations were sufficient to cue the target location. In Experiment 2, the subjects showed good transfer from trained displays to rescaled, displaced, and perceptually regrouped displays, suggesting that the relative locations among items were also learned. Thus, both individual target-distractor associations and configural associations are learned in contextual cuing.     

What is learned in spatial contextual cuing--configuration or individual locations?

With the use of spatial contextual cuing, we tested whether subjects learned to associate target locations with overall configurations of distractors or with individual locations of distractors. In Experiment 1, subjects were trained on 36 visual search displays that contained 36 sets of distractor locations and 18 target locations. Each target location was paired with two sets of distractor locations on separate trials. After training, the subjects showed perfect transfer to recombined displays, which were created by combining half of one trained distractor set with half of another trained distractor set. This result suggests that individual distractor locations were sufficient to cue the target location. In Experiment 2, the subjects showed good transfer from trained displays to rescaled, displaced, and perceptually regrouped displays, suggesting that the relative locations among items were also learned. Thus, both individual target-distractor associations and configural associations are learned in contextual cuing.     

Reading Achievement and Science Proficiency: International Comparisons From the Programme on International Student Assessment

Students need to develop scientific literacy in order to participate fully as citizens, community members, and in the globalized economy. But what is the relationship between scientific literacy and reading literacy? Three international data sets from the Programme on International Student Assessment (PISA) were used to calculate correlations between scientific literacy and reading literacy for 15-year-old students. Mean correlations at the individual student level across countries were .840 for the PISA 2000 data set, .805 for the PISA 2003 data set, and .819 for the PISA 2006 data set. In all three data sets, this correlation varied among countries, and the reading-science relationship was weakest in countries with low country mean reading scores. Three possible interpretations are discussed, favoring the interpretation that knowledge and skills that drive higher reading comprehension also drive higher science achievement.     

The New Sacred Math

The individual soul is an ageless idea, attested in prehistoric times by the oral traditions of all cultures. But as far as we know, it enters history in ancient Egypt. I will begin with the individual soul in ancient Egypt, then recount the birth of the world soul in the Pythagorean community of ancient Greece, and trace it through the Western Esoteric Tradition until its demise in Kepler's writings, along with the rise of modern science, around 1600 CE. Then I tell of the rebirth of the world soul recently, in new branches of mathematics.     

Optimal test length for maximum battery validity

Having given a fixed amount of total testing time it is important to know how long each test in the battery should be so that the correlation of the battery with the criterion will be a maximum. The precise solution for the test lengths will depend on a particular set of conditions which may be specified. The writer has previously presented solutions for two sets of conditions. This article presents the solution for a third set of conditions. These are: (1) The total number of items or testing time is fixed. (2) The score is the total number of items correctly answered. (3) The test lengths are determined in such a way that the correlation of total score with the criterion is a maximum. The solutions for the two previous sets of conditions, together with the current set, are summarized. A set of experimental data is submitted to each solution and the three sets of results are compared.     

Disentangling encoding versus retrieval explanations of the bizarreness effect: Implications for distinctiveness

Recall effects attributed to distinctiveness have been explained by both encoding and retrieval accounts. Resolution of this theoretical controversy has been clouded because the typical methodology confounds the encoding and retrieval contexts. Using bizarre and common sentences as materials, we introduce a paradigm that decouples the nature of the encoding context (mixed vs. unmixed lists of items) from the retrieval set (mixed vs. unmixed retrieval sets). Experiment 1 presented unmixed lists for study, and Experiment 2 presented mixed lists for study. In both experiments, significant bizarreness effects were obtained in free recall when the retrieval set intermixed items but not when the retrieval set consisted of only one item type. Also, Experiment 1, using a repeated testing procedure, did not reveal evidence for more extensive encoding of bizarre sentences than of common sentences. The results support the idea that retrieval dynamics primarily mediate the bizarreness effect, and perhaps more generally, distinctiveness effects.     

From Bodo Ethics to Distributive Justice

Concern with material equality as the central form of distributive justice is a very modern idea. Distributive justice for Aristotle and many other writers for millennia after him was a matter of distributing what each ought to get from merit or desert in some sense. Many, such as Hume, thought material equality a pernicious idea. In the medieval village life of Bodo, villagers knew enough about each other to govern relations through norms, including, when necessary, a norm of charity. In more complex modern societies, economic destitution cannot so well be handled by individual charity, but now it can be handled by states. Hence, we begin to conceive of the idea of distributive justice as driven essentially by concern for material equality. The difference in state capacities is largely epistemological: states today can know much more about their citizens.     

You may look unhappy unless you smile: The distinctiveness of a smiling face against faces without an explicit smile

An expressionless face is often perceived as rude whereas a smiling face is considered as hospitable. Repetitive exposure to such perceptions may have developed stereotype of categorizing an expressionless face as expressing negative emotion. To test this idea, we displayed a search array where the target was an expressionless face and the distractors were either smiling or frowning faces. We manipulated set size. Search reaction times were delayed with frowning distractors. Delays became more evident as the set size increased. We also devised a short-term comparison task where participants compared two sequential sets of expressionless, smiling, and frowning faces. Detection of an expression change across the sets was highly inaccurate when the change was made between frowning and expressionless face. These results indicate that subjects were confused with expressed emotions on frowning and expressionless faces, suggesting that it is difficult to distinguish expressionless face from frowning faces.