The dynamics of insight: Mathematical discovery as a phase transition

Stephen, Damian G.; Boncoddo, Rebecca; Magnuson, James S.; Dixon, James A.

doi:10.3758/mc.37.8.1132

Cited by 113 publications

(104 citation statements)

References 60 publications

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“…In a visual search task requiring participants to identify an upright "T" amid rotated "Ts," both one-dimensional gaze distance measures exhibited fractal fluctuations, and the distance measure exhibited fractal ranges over longer time scales (Aks et al, 2002). Given static images of interlocking gears, for participants determining the turning direction of the final gear, angular change of gaze exhibited fractal fluctuations (Stephen, Boncoddo, Magnuson, & Dixon, 2009). Our first prediction (Hypothesis 1) is that angular change of gaze exhibits fractal fluctuations during visual search.…”

Section: Inhibition Of Return and Hyperdiffusivitymentioning

confidence: 99%

“…Furthermore, fractal fluctuations in angular change of gaze have precedence for predicting individual differences in visual-cognitive performance. In the gear task described above, trial-by-trial changes in fractality of angular change of gaze predicted individual differences in how soon (over trials) participants discover the parity rule relating even-/oddness of gear number and final turning direction (Stephen, Boncoddo, et al, 2009). It may be that fractal fluctuations in angular change will similarly predict how soon (within trials) participants can decide whether or not a target stimulus is present on the screen.…”

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confidence: 99%

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Fractal fluctuations in gaze speed visual search

Stephen

Anastas

2010

Atten Percept Psychophys

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Visual search involves a subtle coordination of visual memory and lower-order perceptual mechanisms. Specifically, the fluctuations in gaze may provide support for visual search above and beyond what may be attributed to memory. Prior research indicates that gaze during search exhibits fractal fluctuations, which allow for a wide sampling of the field of view. Fractal fluctuations constitute a case of fast diffusion that may provide an advantage in exploration. We present reanalyses of eye-tracking data collected by Stephen and Mirman (Cognition, 115, 154-165, 2010) for single-feature and conjunction search tasks. Fluctuations in gaze during these search tasks were indeed fractal. Furthermore, the degree of fractality predicted decreases in reaction time on a trial-by-trial basis. We propose that fractality may play a key role in explaining the efficacy of perceptual exploration.

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Section: Inhibition Of Return and Hyperdiffusivitymentioning

confidence: 99%

mentioning

confidence: 99%

Fractal fluctuations in gaze speed visual search

Stephen

Anastas

2010

Atten Percept Psychophys

Self Cite

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“…For instance, explicit categorization tasks can be presented as "diagnoses" (Castro & Wasserman, 2007;Wasserman & Castro, 2005), and implicit categorization tasks can be presented as the detection of "secret code words" embedded in artificial grammars (Sallas, Mathews, Lane, & Sun, 2007). Causal reasoning has been presented as a scientist uncovering the workings of a "black box" with light rays and atoms (Johnson & Krems, 2001), or using electrical circuits (Johnson & Mayer, 2010), or many other back stories (Dixon & Banghert, 2004;Dixon & Dohn, 2003;Ozubko & Joordens, 2008;Stephen, Boncoddo, Magnuson, & Dixon, 2009). The detection and prediction of change has been investigated in a "tomato processing factory" (Brown & Steyvers, 2009).…”

Section: Gaming-up Experimentsmentioning

confidence: 99%

Gamelike features might not improve data

et al. 2012

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Many psychological experiments require participants to complete lots of trials in a monotonous task, which often induces boredom. An increasingly popular approach to alleviate such boredom is to incorporate gamelike features into standard experimental tasks. Games are assumed to be interesting and, hence, motivating, and better motivated participants might produce better data (with fewer lapses in attention and greater accuracy). Despite its apparent prevalence, the assumption that gamelike features improve data is almost completely untested. We test this assumption by presenting a choice task and a change detection task in both gamelike and standard forms. Response latency, accuracy, and overall task performance were unchanged by gamelike features in both experiments. We present a novel cognitive model for the choice task, based on particle filtering, to decorrelate the dependent variables and measure performance in a more psychologically meaningful manner. The model-based analyses are consistent with the hypothesis that gamelike features did not alter cognition. A postexperimental questionnaire indicated that the gamelike version provided a more positive and enjoyable experience for participants than the standard task, even though this subjective experience did not translate into data effects. Although our results hold only for the two experiments examined, the gamelike features we incorporated into both tasks were typical of-and at least as salient and interesting as those usually used by-experimental psychologists. Our results suggest that modifying an experiment to include gamelike features, while leaving the basic task unchanged, may not improve the quality of the data collected, but it may provide participants with a better experimental experience.

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“…Another problem is the experimental task as such: Especially experiments that contrast distinct groups of treatments with a between-participant design do not allow to trace effects of time or influences of task-changes that could lead to different interpretations of similar tasks (see the problem described in ''Interaction effects and the general linear model''). The first step would be to use repeated measures designs more frequently, and to either use them in a way that one can observe the unfolding performance to investigate when and where a re-organization of the cognitive systems takes place, and what this means for putative cognitive components that participate in such tasks (e.g., Stephen et al 2009)-or to continuously manipulate independent variables in an experiment, in order to observe whether this continuous manipulation actually leads to continuous effects, of qualitative changes in task performance, that are indicative of a change of the component-architecture (Kelso 1995).…”

Section: Interaction-dominant Dynamicsmentioning

confidence: 99%

Interaction-Dominant Causation in Mind and Brain, and Its Implication for Questions of Generalization and Replication

Wallot

Kelty-Stephen

2017

Minds & Machines

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The dominant assumption about the causal architecture of the mind is, that it is composed of a stable set of components that contribute independently to relevant observables that are employed to measure cognitive activity. This view has been called component-dominant dynamics. An alternative has been proposed, according to which the different components are not independent, but fundamentally interdependent, and are not stable basic properties of the mind, but rather an emergent feature of the mind given a particular task context. This view has been called interaction-dominant dynamics. In this paper, we review evidence for interaction-dominant dynamics as the causal architecture of the mind. We point out, that such an architecture is consistent with problems of convergence in research on the level of results and theorizing. Moreover, we point out that if interactiondominant dynamics as the causal architecture of the mind were to be true, this would naturally lead to (some degree of) problems with generalization and replicability in sciences of the mind and brain, and would probably warrant changes in the scientific practice with regard to study-design and data analysis.

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The dynamics of insight: Mathematical discovery as a phase transition

Cited by 113 publications

References 60 publications

Fractal fluctuations in gaze speed visual search

Fractal fluctuations in gaze speed visual search

Gamelike features might not improve data

Interaction-Dominant Causation in Mind and Brain, and Its Implication for Questions of Generalization and Replication

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