Categories of insight and their correlates: An exploration of relationships among classic-type insight problems, rebus puzzles, remote associates and esoteric analogies.

A central question in creativity concerns how insightful ideas emerge. Anecdotal examples of insightful scientific and technical discoveries include Goodyear's discovery of the vulcanization of rubber, and Mendeleev's realization that there may be gaps as he tried to arrange the elements into the Periodic Table. Although most people would regard these discoveries as insightful, cognitive psychologists have had difficulty in agreeing on whether such ideas resulted from insights or from conventional problem solving processes. One area of wide agreement among psychologists is that insight involves a process of restructuring. If this view is correct, then understanding insight and its role in problem solving will depend on a better understanding of restructuring and the characteristics that describe it. This article proposes and tests a preliminary classification of insight problems based on several restructuring characteristics: the need to redefine spatial assumptions, the need to change defined forms, the degree of misdirection involved, the difficulty in visualizing a possible solution, the number of restructuring sequences in the problem, and the requirement for figure-ground type reversals. A second purpose of the study was to compare performance on classic spatial insight problems with two types of verbal tests that may be related to insight, the Remote Associates Test (RAT), and rebus puzzles. In doing so, we report on the results of a survey of 172 business students at the University of Waikato in New Zealand who completed classic-type insight, RAT and rebus problems

Stochastic lattice models for the dynamics of linear polymers

Linear polymers are represented as chains of hopping reptons and their motion is described as a stochastic process on a lattice. This admittedly crude approximation still catches essential physics of polymer motion, i.e. the universal properties as function of polymer length. More than the static properties, the dynamics depends on the rules of motion. Small changes in the hopping probabilities can result in different universal behavior. In particular the cross-over between Rouse dynamics and reptation is controlled by the types and strength of the hoppings that are allowed. The properties are analyzed using a calculational scheme based on an analogy with one-dimensional spin systems. It leads to accurate data for intermediately long polymers. These are extrapolated to arbitrarily long polymers, by means of finite-size-scaling analysis. Exponents and cross-over functions for the renewal time and the diffusion coefficient are discussed for various types of motion.Comment: 60 pages, 19 figure

Enabling spontaneous analogy through heuristic change

Despite analogy playing a central role in theories of problem solving, learning and education, demonstrations of spontaneous analogical transfer are rare. Here, we present a theory of heuristic change for spontaneous analogical transfer, tested in four experiments that manipulated the experience of failure to solve a source problem prior to attempting a target problem. In Experiment 1, participants solved more source problems that contained an additional financial constraint designed to signal the inappropriateness of moves that maximized progress towards the goal. This constraint also led to higher rates of spontaneous analogical transfer to a superficially similar problem. Experiments 2 and 3 showed that the effects of this constraint extend to superficially and structurally different analogs. Experiment 4 generalized the finding to a non-analogous target problem that also benefitted from inhibiting maximizing moves. The results indicate that spontaneous transfer can arise through experience during the solution of a source problem that alters the heuristic chosen for solving both analogical and non-analogical target problems

Complete spectrum of the infinite-UU Hubbard ring using group theory

We present a full analytical solution of the multiconfigurational strongly-correlated mixed-valence problem corresponding to the $N$-Hubbard ring filled with $N-1$ electrons, and infinite on-site repulsion. While the eigenvalues and the eigenstates of the model are known already, analytical determination of their degeneracy is presented here for the first time. The full solution, including degeneracy count, is achieved for each spin configuration by mapping the Hubbard model into a set of Huckel-annulene problems for rings of variable size. The number and size of these effective Huckel annulenes, both crucial to obtain Hubbard states and their degeneracy, are determined by solving a well-known combinatorial enumeration problem, the necklace problem for $N-1$ beads and two colors, within each subgroup of the $C_{N-1}$ permutation group. Symmetry-adapted solution of the necklace enumeration problem is finally achieved by means of the subduction of coset representation technique [S. Fujita, Theor. Chim. Acta 76, 247 (1989)], which provides a general and elegant strategy to solve the one-hole infinite-$U$ Hubbard problem, including degeneracy count, for any ring size. The proposed group theoretical strategy to solve the infinite-$U$ Hubbard problem for $N-1$ electrons, is easily generalized to the case of arbitrary electron count $L$, by analyzing the permutation group $C_L$ and all its subgroups.Comment: 31 pages, 4 figures. Submitte