Cognition is both empowered and limited by representations. The matrix lens model explicates tasks that are based on frequency counts, conditional probabilities, and binary contingencies in a general fashion. Based on a structural analysis of such perspective on representational accounts of cognition that recognizes representational isomorphs as opportunities, rather than as problems.
The shared structural construct of a 2×2 matrix supports a set of generic tasks and semantic mappings that provide a tasks, the model links several problems and semantic domains and provides a new unifying framework for understanding problems and defining scientific measures. Our model’s key explanatory mechanism is the adoption of particular perspectives on a 2×2 matrix that categorizes the frequency counts of cases by some condition, treatment, risk, or outcome factor. By the selective steps of filtering, framing, and focusing on specific aspects, the measures used in various semantic domains negotiate distinct trade-offs between abstraction and specialization. As a consequence, the transparent communication of such measures must explicate the perspectives encapsulated in their derivation.
To demonstrate the explanatory scope of our model, we use it to clarify theoretical debates on biases and facilitation effects in Bayesian reasoning and to integrate the scientific measures from various semantic domains within a unifying framework. A better understanding of problem structures, representational transparency, and the role of perspectives in the scientific process yields both theoretical insights and practical applications.
|The solution to a problem changes the problem.|
[Copyright neth.de, 2008]:
Hans Neth and Thomas Mueller (2008). Thinking by doing and doing by thinking: A taxonomy of actions. Paper presented at CogSci 2008.
Hansjörg Neth, Thomas Müller
From the introduction: Although human thought may be possible in those floatation tanks that are used to encourage meditative states, in by far the majority of instances thought occurs in the context of some physical task environment. The physical environment can be as simple as a light and book. It can be as complex as the face of a mountain and the equipment of the climber. It may be as dynamic as the cockpit of an F-16 in supersonic flight and as reactive as a firefight in Iraq or as heated as an argument between lovers.
|There is a co-ordination of senses and thought, and also
a reciprocal influence between brain activity and material creative activity.
In this reaction the hands are peculiarly important. It is a moot point whether
the human hand created the human brain, or the brain created the hand.
Certainly the connection is intimate and reciprocal.
|A.N. Whitehead, Technical Education and its Relation to Science and Literature, p. 78.|
[Copyright neth.de, 1999–2014]
Hans Neth and Steve Payne (2002): Thinking by doing: Epistemic actions in the ToH, paper presented at CogSci 2002.
Hansjörg Neth, Stephen J. Payne
Abstract: This article explores the concept of epistemic actions in the Tower of Hanoi (ToH) problem. Epistemic actions (Kirsh & Maglio, 1994) are actions that do not traverse the problem space toward the goal but facilitate subsequent problem solving by changing the actor’s cognitive state. We report an experiment in which people repeatedly solve ToH tasks. An instructional manipulation asked participants to minimize moves either trial by trial or only on the last three of six trials. This manipulation did not have the predicted effect on the trial-by-trial move counts. A second, device manipulation provided some participants with an “exploratory mode” in which move sequences could be tried then undone without affecting the criterion move count. Participants effectively used this mode to reduce moves on each trial, but there was no clear evidence that they used it to learn about the problem across trials. We conclude that there is strong evidence for one sub-type of epistemic action (acting-to-plan) but no evidence for a second sub-type (acting-to-learn).