Verification of algebra step problems: A chronometric study of human problem solving

A class of simple problem solving tasks requiring fast accurate solutions is introduced. In an experiment subjects memorized a mapping rule represented by lists of words labeled by cue words and made true/false decisions about conjunctions of propositions of the form “Y is in the list labeled by X”, written “X → Y”. Response times are analyzed using a “stage modeling” technique where problem solving algorithms are composed using a small set of psychological operations that have real time characteristics specified parametrically. The theoretical analysis shows that response time performance is adequately described in terms of the sequential application of elementary psychological operations. Unexpectedly, it was found that the proposition “X → YandX → Z” was verified as quickly as the apparently simpler “X → Y”. A case is presented for the modeling technique as applied to memory and problem solving tasks in terms of theoretical parsimony, statistical simplicity, and flexibility in investigative empirical research. Suggestions are made as to possible theoretical relations among fast problem solving, more complex and slower problem solving, and research in fundamental memory processes.     

The Multilevel Modality-Switch Effect: What Happens When We See the Bees Buzzing and Hear the Diamonds Glistening

Previous studies demonstrated that the sequential verification of different sensory modality properties for concepts (e.g., BLENDER-loud; BANANA-yellow) brings about a processing cost, known as the modality-switch effect. We report an experiment designed to assess the influence of the mode of presentation (i.e., visual, aural) of stimuli on the modality-switch effect in a property verification and lexical decision priming paradigm. Participants were required to perform a property verification or a lexical decision task on a target sentence (e.g., “a BEE buzzes”, “a DIAMOND glistens”) presented either visually or aurally after having been presented with a prime sentence (e.g., “the LIGHT is flickering”, “the SOUND is echoing”) that could either share both, one or none of the target’s mode of presentation and content modality. Results show that the mode of presentation of stimuli affects the conceptual modality-switch effect. Furthermore, the depth of processing required by the task modulates the complex interplay of perceptual and semantic information. We conclude that the MSE is a task-related, multilevel effect which can occur on two different levels of information processing (i.e., perceptual and semantic).     

Limited translation invariance of human visual pattern recognition

Visual object recognition is considered to be largely translation invariant. An earlier study (Foster & Kahn, 1985), however, has indicated that recognition of complex novel stimuli is partially specific to location in the visual field: It is significantly easier to determine the identity of two briefly displayed random patterns if both stimuli are presented at the same, rather than at different, locations. In a series ofsame/different discrimination tasks, we characterize the processes underlying this “displacement effect”: Horizontal and vertical translations are equally effective in reducing performance. Making the task more difficult by increasing pattern similarity leads to even higher positional specificity. The displacement effect disappears after rotation or contrast reversal of the patterns, indicating that positional specificity depends on relatively low levels of processing. Control experiments rule out explanations that are independent of visual pattern memory, such as spatial attention, eye movements, or retinal afterimages. Positional specificity of recognition is found only forsame trials. Our results demonstrate that position invariance, a widely acknowledged property of the human visual system, is limited to specific experimental conditions. Normalization models involving mental shifts of an early visual representation or of a window of attention cannot easily account for these findings.     

Biases of spatial attention in vision and audition

Neurologically normal observers misperceive the midpoint of horizontal lines as systematically leftward of veridical center, a phenomenon known as pseudoneglect. Pseudoneglect is attributed to a tonic asymmetry of visuospatial attention favoring left hemispace. Whereas visuospatial attention is biased toward left hemispace, some evidence suggests that audiospatial attention may possess a right hemispatial bias. If spatial attention is supramodal, then the leftward bias observed in visual line bisection should also be expressed in auditory bisection tasks. If spatial attention is modality specific then bisection errors in visual and auditory spatial judgments are potentially dissociable. Subjects performed a bisection task for spatial intervals defined by auditory stimuli, as well as a tachistoscopic visual line bisection task. Subjects showed a significant leftward bias in the visual line bisection task and a significant rightward bias in the auditory interval bisection task. Performance across both tasks was, however, significantly positively correlated. These results imply the existence of both modality specific and supramodal attentional mechanisms where visuospatial attention has a prepotent leftward vector and audiospatial attention has a prepotent rightward vector of attention. In addition, the biases of both visuospatial and audiospatial attention are correlated.     

Nonmetric grouping: Clusters and cliques

A class of related nonmetric (“monotone invariant”) hierarchical grouping methods is presented. The methods are defined in terms of generalized cliques, based on a systematically varying specification of the degree of indirectness of permitted relationships (i.e., degree of “chaining”). This approach to grouping is shown to provide a useful framework for grouping methods based on ana priori specification of the properties of the desired subsets, and includes a natural generalization for “complete linkage” and “single linkage” clustering, such as the methods of Johnson [1967]. The central feature of the class of methods is a simple iterative matrix operation on the original disparities (“inverse-proximities” or “dissimilarities”) matrix, and one of the methods also constitutes a very efficient single linkage clustering procedure.     

On modeling the creativity and the concept of Chef-D’oeuvre

The problem of modeling the creativity is shown to be entirely connected with another mysterious challenge — the “Explanatory Gap” between the concepts of “Brain” and “Mind”. We use the Natural Constructive Cognitive Architecture, with its important feature being the combination of two subsystems, for generation of new information and for its conservation. “Brain” is considered as records of the raw images of real objects (individual objective information), while “Mind” refers to individual subjective information created inside the cognitive system (symbols). We argued that creativity can be treated as “an effort to bring a piece of personal “Brain” into the “Mind” and World”. Specific thinking mode (intellectual panic or throes of creativity) is shown to enhance the creative work resulting in over-mobilization and even enriching personal deep inside (“Brain”) experience. It is simulated by chaotic jumps of the noise amplitude around abnormally high value. The nature of Aesthetic Emotions and the concept of Chef-D’oeuvre are analyzed. It is shown that they are caused by the “recognition paradox”: an object seems both, familiar but unusual. This occurs if the “Brain” does see its subtle features, while the “Mind” does not realize. Bright aesthetic emotions (goosebumps) are caused by irregular excitation of implicit associations provided by weak (“gray”) connections of the halo neurons (simulating the subconsciousness). General formula for Chef-D’oeuvre in science and art could be expressed as “condensed capacity to see the invisible, to combine the incompatible”.     

Judgments of differences and ratios of numerals

Each subject performed two tasks, dividing a line segment so that either (a) theratio of subjective lengths corresponded to the ratio of the magnitudes of two numerals or (b) thedifference in length was proportional to the numerical difference. Had subjects actually performed two operations on the same scale, the responses would have been nonmonotonically related. Instead, data for the two tasks were nearly identical and ordinally compatible with either a ratio or a subtractive model. The ratio model implied scale values for numerals that were a positively accelerated function of numerical value, inconsistent with previous results. With a nonlinear response function for graphic length, the subtractive model fit well, yielding scale values that were a negatively accelerated function of numerical value and a linear function of previously obtained scales. These results, together with other recent findings, suggest that subjects may perform the same operation in spite of instructions to judge “ratios” or “differences” and that this operation can be best represented by a subtractive model.     

“In One”: The Bearer Issue and the Principles of Exemplification

Traditionally, the so-called exemplification or the relation between the particular and the universal has been one of the three central problems making up the classical problem of universals: (1) What is a particular? (2) What is a universal? (3) What is the relation between the particular and the universal? I used the expression “classical problem of universals” instead of “the problem of universals” since the classical formulation of the problem could be said to contain a questionable assumption, namely that substance should be the bearer “in” which are the entities of (other) categories. Under these circumstances, a neutral approach to the problem of universals could consist in reformulating the three problems of the classical problem as follows: (4) What is the fundamental bearer of categories? (5) What categories are there? (6) What is the relation between the fundamental bearer and the categories? My purpose in this paper is to answer the latter three questions. In order to accomplish this task, I shall discuss the views of two leading figures in substance-ontology, Aristotle and Jonathan Lowe, and the views of two leading figures in fact-ontology, Gustav Bergmann and Reinhardt Grossmann. I shall answer the first question by claiming that the fundamental bearer of categories is facts; the second, by pointing out that it depends on the answer to the previous one; and the third, by showing that the relation between the fundamental bearer and the categories is the one between facts and its constituents, not between a substance or particular and its accidents or properties. In this connection, I shall argue that the “in” of property exemplification should be categorially reconstructed in order for entities other than properties, say, particulars, relations, connectives, numbers, and even facts, to be “in” facts. This categorial reconstruction will also argued for with respect to the Principle of Exemplification.     

Stop—reaction time and the internal clock

In astop-reaction-time (stop-RT) task, a subject is presented with a regular, isochronous sequence of brief signals separated by a constant time interval, orstimulus onset asynchrony (SOA). His/her task is to press a response key as fast as possible when the sequence stops. As the sequence unfolds, an internal representation of the SOA duration builds up. Stop-RT is assumed to be triggered when aninternal clock, operating as an “alarm clock,” reaches a time criterion. Criterion setting is contingent upon variability in the SOA’s internal representation. In Experiment 1A, stop-RT was measured for isochronous sequences of brief tones, light flashes, and also sequences of tones and flashes presented in regular alternation (tone-light-tone…). Stop-RT was a linear function of SOA duration (ranging from 250 to 1,000 msec), regardless of modality, supporting a “central-clock” hypothesis. On the other hand, taken together, the results of Experiments 1A, 1B, 2, and 3 suggest that no internal representation of thebimodal (tone-light) SOA of alternating sequences builds up. Indeed, an alternating sequence is physically equivalent to two interlaced isochronous subsequences, one auditory and one visual. So,two internal representations, one for the auditory (tone-tone) and one for the visual (light-light) SOA, could build up, andtwo time criteria running “in parallel” could thus support stop-RT. To provide a critical test of parallel timing, stop-RT was measured for bimodal 5∶3 polyrhythms formed by the superposition of auditory and visual isochronous sequences that haddifferent SOA durations (Experiment 4). Parallel timing accounted for a large proportion of variance in polyrhythmic stop-RT data. Overall findings can be accounted for by assuming a functional architecture of an internal clock in which pulses emitted by acentral pacemaker are available in parallel with twomodality-specific switch-accumulator “timing modules.”     

Artifact and Essence

An essential property is a property that an object possesses in every possible world in which that object exists. An individual essence is a property (or set of properties) that an object possesses in every world in which that object exists, and that no other object possesses in any possible world. Call the claim that some artifacts possess an individual essence ‘artifactual essentialism’. I will argue that artifactual essentialism is true. In doing so, I will be responding to two recent arguments by Penelope Mackie against artifactual essentialism (Mackie (2006), esp. ch. 3.). In “Individual Essence Properties”, I will rehearse the qualifications that any property must meet if it is to constitute an individual essence, and in “Artifacts and the Recycling Problem” and “Artifacts and the Tolerance Problem”, I will rehearse Mackie’s arguments against artifactual essentialism. In “Artifacts and Weak Unshareability?” and “Artifacts and Strong Unshareability?”, I will show why both of these arguments fail. In “Mona Lisa’s Essence”, I will defend the interesting claim that some artifacts possess an individual essence. In the final section I will entertain some objections to my proposal.     

Accidental Communities: Race,Emergency Medicine,and the Problem of PolyHeme®

This article focuses on emergency medical care in black urban populations, suggesting that the classification of a “community” within clinical trial language is problematic. The article references a cultural history of black Americans with pre-hospital emergency medical treatment as relevant to contemporary emergency medicine paradigms. Part I explores a relationship between “autonomy” and “community.” The idea of community emerges as a displacement for the ethical principle of autonomy precisely at the moment that institutionalized medicine focuses on diversity. Part II examines a clinical trial for the blood substitute PolyHeme^® (Northfield Laboratories, Inc., Evanston, IL). It illustrates the ways in which bias in research paradigms and Institutional Review Board decisions attach to the notion and utility of the language of “community.” The conclusion's contemporary anecdote makes apparent the vitality of the issues of prehospital emergency medical care and the ways in which decisions and practices fall too easily into a narrative of culturally biased treatment.     

Testing n-stimuli bisymmetry

In the seventies bisection, a kind of observational averaging of two stimuli, came to be studied and empirically investigated in measurement theory and corresponding psychophysical experiments. Since 1993, Münnich, Maksa and Mokken (Aggregating evaluations of multi-attribute stimuli. 31st International Symposium on Functional Equations, Debrecen, 2000) developed the formal framework and theory for a more general type of bisection of more than two variables. A core assumption for this generalization of 2-stimuli bisection to that of n-stimuli, is that of n-variable bisymmetry. After an introduction of this concept, the validity of its assumption is tested and demonstrated with four experiments. Experiment 1 was a computer-aided task in which input modalities were different line lengths presented on computer screen. Experiments 1, 3 and 4 included field experiments of the paper and pencil type, in which numbers served as input modalities, but in different contexts.     

Specifically objective stochastic latency mechanisms

A two parameter additive model for psychological response latencies f_vi(t) = (θ_v + ?_i) exp(?(θ_v + ?_i)t) is suggested. Conditional inference procedures are derived for the psychometric latency model. If the model is considered as a theory for speed test construction the unrestricted comparability of measurements obtained under “speed” and “power” conditions is an attractive feature of the model. An extension of the parametric structure gives the “linear exponential model” f_vi(t) = (θ_v + Σ_ι^ma_iιη_ι) exp(?(θ_v + Σ_ι^ma_iιη_ι)t), where the time constants of the latencies are conceived as linear combinations of “basic parameters” corresponding to the experimental conditions of the latency situations. The linear exponential model includes as special cases some well known series latency mechanisms. Some generalizations of the distributional assumptions are discussed, especially the Weibull distributions. The estimation of parameters by conditional inference procedures and the evaluation of the fit of the model by conditional likelihood ratio tests is illustrated by means of the numerical data from a free recall experiment.     

“Girls Are as Good as Boys at Math” Implies That Boys Are Probably Better: A Study of Expressions of Gender Equality

Although “Girls are as good as boys at math” explicitly expresses equality, we predict it could nevertheless suggest that boys have more raw talent. In statements with this subject‐complement structure, the item in the complement position serves as the reference point and is thus considered more typical and prominent. This explains why “Tents are like houses,” for instance, sounds better than “Houses are like tents”—people generally think of houses as more typical. For domains about ability, the reference point should be the item that is typically more skilled. We further propose that the reference point should be naturally more skilled. In two experiments, we presented adults with summaries of actual scientific evidence for gender equality in math (Experiment 1) or verbal ability (Experiment 2), but we manipulated whether the reference point in the statements of equality in the summaries (e.g., “Boys’ verbal ability is as good as girls’”) was girls or boys. As predicted, adults attributed more natural ability to each gender when it was in the complement rather than subject position. Yet, in Experiment 3, we found that when explicitly asked, participants judged that such sentences were not biased in favor of either gender, indicating that subject‐complement statements must be transmitting this bias in a subtle way. Thus, statements such as “Girls are as good as boys at math” can actually backfire and perpetuate gender stereotypes about natural ability.     

Representational Pseudoneglect: A Review

Pseudoneglect, the tendency to be biased towards the left-hand side of space, is a robust and consistent behavioural observation best demonstrated on the task of visuospatial line bisection, where participants are asked to centrally bisect visually presented horizontal lines at the perceived centre. A number of studies have revealed that a representational form of pseudoneglect exists, occurring when participants are asked to either mentally represent a stimulus or explore a stimulus using touch in the complete absence of direct visuospatial processing. Despite the growing number of studies that have demonstrated representational pseudoneglect there exists no current and comprehensive review of these findings and no discussion of a theoretical framework into which these findings may fall. An important gap in the current representational pseudoneglect literature is a discussion of the developmental trajectory of the bias. The focus of the current review is to outline studies that have observed representational pseudoneglect in healthy participants, consider a theoretical framework for these observations, and address the impact of lifespan factors such as cognitive ageing on the phenomenon.     

Perceptions of sexual harassment as a function of sex of rater and incident form and consequence

The purpose of this study was to investigate differences in perceptions of two “severity dichotomies” present in the Equal Employment Opportunity Commission Guidelines on sexual harassment. Alale and female undergraduates (N = 198), from a predominately white midwestern university, were given one of four statements based on these guidelines, varying “form” (physical/verbal) and “consequence” (economic injury/hostile environment) of the behavior. Analysis of variance results showed females rated the incident as more definitely sexual harassment and as affecting perfonnance more than did males. Participants reading “economic injury” statements rated them as having more effect on the victim’s job status than did those reading “hostile environment” statements. A multivariate analysis of variance revealed significant “consequence” and “sex” effects on several factors: A significant three-way interaction showed that males rated statements less negatively than did females, especially when the statement described “physical” behavior with “hostile environment“ consequences. Cluster analysis results are also presented.     

The logic of viewpoints

In this paper a propositional logic of viewpoints is presented. The language of this logic consists of the usual modal operatorsL (of necessity) andM (of possibility) as well as of two new operatorsA andR. The intuitive interpretations ofA andR are “from all viewpoints” and “from some viewpoint”, respectively. Semantically the language is interpreted by using Kripke models augmented with sets of “viewpoints” and with a new alternativeness relation for the operatorA. Truth values of formulas are evaluated with respect to a world and a viewpoint. Various axiomatizations of the logic of viewpoints are presented and proved complete. Finally, some applications are given.     

Can Multimodal and Rational Emotive Behavior Therapy be Reconciled?

The purpose of this article is to determine whether two distinct modes of cognitive-behaviour therapy—Rational Emotive Behaviour Therapy (REBT) and Multimodal Therapy (MMT)—can be reconciled. This quest in the spirit of integrationism is pursued along three lines of inquiry: Do we talk about schools, approaches, or techniques? A reconciliation between MMT and REBT as systems seems not to be feasible, just because of the simple fact that MMT is not a new school with an idiosyncratic theory, whereas REBT is. However, REBT is also a congenial approach consisting of various eclectic techniques, as is MMT. It is explained how the A-B-C format and firing orders of the BASICI.D. modalities stem from an S-O-R model. Furthermore, the circular character of the various modalities (thinking, feeling, and behaving) is recognised both in MMT and in REBT. The techniques used in REBT and MMT overlap for 65–80%, according to a comparative perusal of Ellis's and Lazarus's presentations of preferred techniques. This means that MMT and REBT, as an approach with distinct techniques, “must” be very similar in practice. The conclusion is that philosophically Ellis and Lazarus see eye-to-eye and that MMT and REBT overlap a great deal. But a fusion is not yet at hand. At best the two can be described as two sides of one coin. “When you wake up in the morning, Pooh,” said Piglet at last, “what's the first thing you say to yourself?” “What's for breakfast?” said Pooh. “What do you say, Piglet?” “I say, I wonder what's going to happen exciting today?” said Piglet. Pooh nodded thoughtfully. “It's the same thing,” he said. “What's that?” the Unbeliever asked. “Wisdom from a Western Taoist,” I said. “It sounds like something from Winnie-the Pooh,” he said. “It is,” I said. From The Tao of Pooh Benjamin Hoff (1982)     

Single-word predictions of upcoming language during comprehension: Evidence from the cumulative semantic interference task

Comprehenders predict upcoming speech and text on the basis of linguistic input. How many predictions do comprehenders make for an upcoming word? If a listener strongly expects to hear the word “sock”, is the word “shirt” partially expected as well, is it actively inhibited, or is it ignored? The present research addressed these questions by measuring the “downstream” effects of prediction on the processing of subsequently presented stimuli using the cumulative semantic interference paradigm. In three experiments, subjects named pictures (sock) that were presented either in isolation or after strongly constraining sentence frames (“After doing his laundry, Mark always seemed to be missing one …”). Naming sock slowed the subsequent naming of the picture shirt – the standard cumulative semantic interference effect. However, although picture naming was much faster after sentence frames, the interference effect was not modulated by the context (bare vs. sentence) in which either picture was presented. According to the only model of cumulative semantic interference that can account for such a pattern of data, this indicates that comprehenders pre-activated and maintained the pre-activation of best sentence completions (sock) but did not maintain the pre-activation of less likely completions (shirt). Thus, comprehenders predicted only the most probable completion for each sentence.