The Roles of Internal Representation and Processing in Problem Solving Involving Insight: A Computational Complexity Perspective

Abstract

In human problem solving, there is a wide variation between individuals in problem solution time and success rate, regardless of whether or not this problem solving involves insight. In this paper, we apply computational and parameterized analysis to a plausible formalization of extended representation change theory (eRCT), an integration of problem solving by problem space search and insight as problem restructuring which proposes that this variation may be explainable by individuals having different problem representations and search heuristic choices. Our analyses establish not only the intractability of eRCT in general, but also sets of restrictions under which eRCT-based problem solving can and cannot be done quickly. As such, our analyses both prove that several conjectures about what makes problem solving under eRCT possible in practice are incomplete, in the sense that not all factors in the model whose restriction is responsible for efficient solvability are part of the explanation, and provide several new explanations that are complete.

Theory Before the Test: How to Build High-Verisimilitude Explanatory Theories in Psychological Science

“…Tractability/intractability analyses apply widely, not just to simple examples such as the ones above. The approach has been used to assess constraints that render tractable/intractable computational accounts for various capacities relevant for psychological science that span across domains and levels ( Table 1 ), such as coherence-based belief updating ( van Rooij et al, 2019 ), action understanding and theory of mind ( Blokpoel et al, 2013 ; van de Pol et al, 2018 ; Zeppi & Blokpoel, 2017 ), analogical processing ( van Rooij et al, 2008 ; Veale & Keane, 1997 ), problem-solving ( Wareham, 2017 ; Wareham et al, 2011 ), decision-making ( Bossaerts & Murawski, 2017 ; Bossaerts et al, 2019 ), neural-network learning ( Judd, 1990 ), compositionality of language ( Pagin, 2003 ; Pagin & Westerståhl, 2010 ), evolution, learning or development of heuristics for decision-making ( Otworowska et al, 2018 ; Rich et al, 2019 ), and evolution of cognitive architectures generally ( Rich et al, 2020 ). This existing research (for an overview, see Compendium C in van Rooij et al, 2019 ) shows that tractability is a widespread concern for theories of capacities relevant for psychological science and moreover that the techniques of tractability analysis can be fruitfully applied across psychological domains.…”

Theory before the test: How to build high-verisimilitude explanatory theories in psychological science

“…≤ max ( c ( s , s' )) + ; see Blokpoel et al 2013;Bourgin et al, 2017, (Blokpoel et al, 2013;Zeppi and Blokpoel, 2017;van de Pol et al 2018), analogical processing (Veale & Keane, 1997;van Rooij et al, 2008), problem solving (Wareham, 2017;Wareham, Evans, & van Rooij, 2011), decision-making (Bossaerts & Murawski, 2017;Bossaerts, Yadav, & Murawski, 2019), neural network learning (Judd, 1990), compositionality of language (Pagin, 2003;Pagin & Westerståhl, 2010), evolution, learning or development of heuristics for decision-making (Otworowska et al, 2018, Rich et al, 2019) and evolution of cognitive architectures generally (Rich et al, 2020). This existing research shows that tractability is a widespread concern for theories of capacities relevant for psychological science, and moreover that the techniques of tractability analysis can be fruitfully applied across psychological domains.…”