The dynamics of insight: Mathematical discovery as a phase transition

Memory and Cognition

Volumn 37, Issue 8, 2009, Pages 1132-1149

  Stephen, Damian G ^a   Boncoddo, Rebecca A ^a   Magnuson, James S ^a,b   Dixon, James A ^a,b  

^a UNIVERSITY OF CONNECTICUT   (United States)

^b HASKINS LABORATORIES   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ARTICLE; BEHAVIOR; COGNITION; DYNAMICS; ENTROPY; EYE MOVEMENT; FEMALE; HUMAN; HUMAN EXPERIMENT; MALE; MATHEMATICAL ANALYSIS; NEUROTRANSMISSION;

ALGORITHMS; ATTENTION; AWARENESS; ENTROPY; EYE MOVEMENTS; HUMANS; IMAGINATION; MATHEMATICS; NEURAL NETWORKS (COMPUTER); NONLINEAR DYNAMICS; ORIENTATION; PATTERN RECOGNITION, VISUAL; PROBLEM SOLVING; PSYCHOMOTOR PERFORMANCE; PSYCHOPHYSICS;

EID: 72449211751     PISSN: 0090502X     EISSN: None     Source Type: Journal    
DOI: 10.3758/MC.37.8.1132     Document Type: Article

References (72)

1. Abarbanel, H. D. I. (1996). Analysis of observed chaotic data. New York: Springer.
2. Aks, D. J. (2005). 1/f dynamic in complex visual search: Evidence for self-organized criticality in human perception. In M. A. Riley & G. C. Van Orden (Eds.), Tutorials in contemporary nonlinear methods for the behavioral sciences (pp. 326-359). Arlington, VA: National Science Foundation. Retrieved March 1, 2006, from www.nsf.gov/sbe/ bcs/pac/nmbs/nmbs.jsp.
3. Aks, D. J., Zelinsky, G. J., & Sprott, J. C. (2002). Memory across eyemovements: 1/f dynamic in visual search. Nonlinear Dynamics, Psychology, & Life Sciences, 6, 1-25. doi:10.1023/A:1012222601935
4. Anderson, J. R., & Schooler, L. J. (1991). Reflections of the environment in memory. Psychological Science, 2, 396-408. doi:10.1111/j .1467-9280.1991.tb00174.x
5. Ashby, F. G., Ennis, J. M., & Spiering, B. J. (2007). A neurobiological theory of automaticity in perceptual categorization. Psychological Review, 114, 632-656. doi:10.1037/0033-295X.114.3.632
6. Bressler, S. L., & Kelso, J. A. S. (2001). Cortical coordination dynamics and cognition. Trends in Cognitive Sciences, 5, 26-36. doi:10.1016/ S1364-6613(00)01564-1573
7. Chronicle, E. P., MacGregor, J. N., & Ormerod, T. C. (2004). What makes an insight problem? The roles of heuristics, goal conception, and solution recoding in knowledge-lean problems. Journal of Experimental Psychology: Learning, Memory, & Cognition, 30, 14-27. doi:10.1037/0278-7393.30.1.14
8. Cohen, L. B., Chaput, H. H., & Cashon, C. H. (2002). A constructivist model of infant cognition. Cognitive Development, 17, 1323-1343. doi:10.1016/S0885-2014(02)00124-7
9. Dale, R., Roche, J., Snyder, K., & McCall, R. (2008). Exploring action dynamics as an index of paired-associate learning. PLoS One, 3, e1728. doi:10.1371/journal.pone.0001728 (Pubitemid 351903229)
10. Dixon, J. A., & Bangert, A. S. (2004). On the spontaneous discovery of a mathematical relation during problem solving. Cognitive Science, 28, 433-449. doi:10.1016/j.cogsci.2003.12.004 (Pubitemid 38670707)
11. Dixon, J. A., & Kelley, E. A. (2006). The probabilistic epigenesis of knowledge. In R. V. Kail (Ed.), Advances in child development and behavior (Vol. 34, pp. 323-361). New York: Academic Press.
12. Dixon, J. A., & Kelley, E. A. (2007). Theory revision and redescription: Complementary processes in knowledge acquisition. Current Directions in Psychological Science, 16, 111-115. doi:10.1111/j.1467 -8721.2007.00486.x
13. Edwards, A. M., Phillips, R. A., Watkins, N. W., Freeman, M. P., Murphy, E. J., Afanasyev, V., et al. (2007). Revisiting Lévy flight search patterns of wandering albatrosses, bumblebees and deer. Nature, 449, 1044-1048. doi:10.1038/nature06199
14. Fodor, J. A. (2000). The mind doesn't work that way: The scope and limits of computational psychology. Cambridge, MA: MIT Press.
15. Gentner, D., Loewenstein, J., & Hung, B. (2007). Comparison facilitates children's learning of names for parts. Journal of Cognition & Development, 8, 285-307. doi:10.1080/15248370701446434 (Pubitemid 47490678)
16. Gentner, D., & Namy, L. L. (1999). Comparison in the development of categories. Cognitive Development, 14, 487-513. doi:10.1016/S0885 -2014(99)00016-17
17. Gilden, D. L. (2001). Cognitive emissions of 1/f noise. Psychological Review, 108, 33-56. doi:10.1037/0033-295X.108.1.33
18. Graepel, T., Burger, M., & Obermayer, K. (1997). Phase transitions in stochastic self-organizing maps. Physical Review, 56E, 3876-3890. doi:10.1103/PhysRevE.56.3876
19. Grebogi, C., Ott, E., Romeiras, F., & Yorke, J. A. (1987). Critical exponents for crisis-induced intermittency. Physical Review, 36A, 5365-5380. doi:10.1103/PhysRevA.36.5365
20. Hadley, R. F., & Cardei, V. C. (1999). Language acquisition from sparse input without error feedback. Neural Networks, 12, 217-235. doi:10.1016/S0893-6080(98)00139-7
21. Handy, T. C. (2004). Event-related potentials: A methods handbook. Cambridge, MA: MIT Press.
22. Harrison, L. G., & Hillier, N. A. (1985). Quantitative control of Acetabularia morphogenesis by extracellular calcium: A test of kinetic theory. Journal of Theoretical Biology, 114, 177-192. doi:10.1016/ S0022-5193(85)80261- 80267
23. Henderson, J. M., & Ferreira, F. (Eds.) (2004). The interface of language, vision, and action: Eye movements and the visual world. New York: Psychology Press.
24. Hilborn, R. C. (1994). Chaos and nonlinear dynamics: An introduction for scientists and engineers. New York: Oxford University Press.
25. Jensen, H. J. (1998). Self-organized criticality: Emergent complex behavior in physical and biological systems. Cambridge: Cambridge University Press.
26. Jones, G. (2003). Testing two cognitive theories of insight. Journal of Experimental Psychology: Learning, Memory, & Cognition, 29, 1017-1027. doi:10.1037/0278-7393.29.5.1017
27. Kelso, J. A. S. (1995). Dynamic patterns: The self-organization of brain and behavior. Cambridge, MA: MIT Press.
28. Knöblich, G., Ohlsson, S., Haider, H., & Rhenius, D. (1999). Constraint relaxation and chunk decomposition in insight problem solving. Journal of Experimental Psychology: Learning, Memory, & Cognition, 25, 1534-1555. doi:10.1037/0278-7393.25.6.1534
29. Knöblich, G., Ohlsson, S., & Raney, G. E. (2001). An eye movement study of insight problem solving. Memory & Cognition, 29, 1000-1009. (Pubitemid 34157978)
30. Kowler, E. (1990). Eye movements and their role in visual and cognitive processes. New York: Elsevier.
31. Kugler, P. N., Kelso, J. A. S., & Turvey, M. T. (1982). On the control and coordination of naturally developing systems. In J. A. S. Kelso & J. E. Clark (Eds.), The development of movement control and coordination (pp. 5-78). Chichester, U.K.: Wiley.
32. Kugler, P. N., & Turvey, M. T. (1987). Information, natural law, and the self-assembly of rhythmic movement. Hillsdale, NJ: Erlbaum.
33. Lee, F. J., & Anderson, J. R. (2001). Does learning a complex task have to be complex? A study in learning decomposition. Cognitive Psychology, 42, 267-316. doi:10.1006/cogp.2000.0747
34. Li, P., Zhao, X., & MacWhinney, B. (2007). Dynamic self-organization and early lexical development in children. Cognitive Science, 31, 581-612. doi:10.1080/15326900701399905
35. Lorenz, E. N. (1963). Deteministic nonperiodic flow. Journal of the Atmospheric Sciences, 20, 130-141. doi:10.1177/0309133308091948
36. Mandelbrot, B. B. (1982). The fractal geometry of nature. San Francisco: Freeman.
37. Marwan, N., Romano, M. C., Thiel, M., & Kurths, J. (2007). Recurrence plots for the analysis of complex systems. Physics Reports, 438, 237-329. doi:10.1016/j.physrep.2006.11.001
38. McClelland, J. L. (2006). How far can you go with Hebbian learning, and when does it lead you astray? In Y. Munakata & M. Johnson (Eds.), Processes of change in brain and cognitive development: Attention and performance XXI (pp. 33-69). Oxford: Oxford University Press.
39. McClelland, J. L., Rumelhart, D. E., & PDP Research Group (Eds.) (1986). Parallel distributed processing: Explorations in the microstructure of cognition (Vol. 1). Cambridge, MA: MIT Press.
40. Mirman, D., Dixon, J. A., & Magnuson, J. S. (2008). Statistical and computational models of the visual world paradigm: Growth curves and individual differences. Journal of Memory & Language, 59, 475-494. doi:10.1016/j.jml. 2007.11.006
41. Munakata, Y., & McClelland, J. L. (2003). Connectionist models of development. Developmental Science, 6, 413-429. doi:10.1111/1467 -7687.00296
42. Nadeau, R. L., & Kafatos, M. (1999). The non-local universe. Oxford: Oxford University Press.
43. Nicolis, G., & Prigogine, I. (1977). Self-organization in nonequilibrium systems: From dissipative structures to order through fluctuations. New York: Wiley.
44. Ormerod, T. C., MacGregor, J. N., & Chronicle, E. P. (2002). Dynamics and constraints in insight problem solving. Journal of Experimental Psychology Learning, Memory, & Cognition, 28, 791-799. doi:10.1037/0278-7393.28.4.791
45. Palmeri, T. J. (1999). Theories of automaticity and the power law of practice. Journal of Experimental Psychology: Learning, Memory, & Cognition, 25, 543-551. doi:10.1037/0278-7393.25.2.543
46. Prigogine, I., & Stengers, I. (1984). Order out of chaos. New York: Bantam.
47. Rickard, T. C. (1997). Bending the power law: A CMPL theory of strategy shifts and the automatization of cognitive skills. Journal of Experimental Psychology: General, 126, 288-311. doi:10.1037/0096 -3445.126.3.288
48. Schwartz, D. L., & Black, J. B. (1996). Shuttling between depictive models and abstract rules: Induction and fallback. Cognitive Science, 20, 457-497. doi:10.1016/S0364-0213(99)80012-3
49. Schyns, P. G. (1991). A modular neural network model of concept acquisition. Cognitive Science, 15, 461-508. doi:10.1016/0364 -0213(91)80016-X
50. Shannon, C. E. (1948). A mathematical theory of communication. Bell System Technical Journal, 27, 379-423, 623-656.
51. Shlesinger, M. F., Zaslavsky, G. M., & Klafter, J. (1993). Strange kinetics. Nature, 363, 31-37. doi:10.1038/363031a0
52. Siegler, R. S., & Araya, R. (2005). A computational model of conscious and unconscious strategy discovery. In R. V. Kail (Ed.), Advances in child development and behavior (Vol. 33, pp. 1-42). Oxford: Elsevier.
53. Silberman, Y., Bentin, S., & Miikkulainen, R. (2007). Semantic boost on episodic associations: An empirically-based computational model. Cognitive Science, 31, 645-671. doi:10.1080/15326900701399921
54. Simon, H. A. (2002). Near decomposability and the speed of evolution. Industrial & Corporate Change, 11, 587-599. doi:10.1093/icc/ 11.3.587
55. Sims, D. W., Southall, E. J., Humphries, N. E., Hays, G. C., Bradshaw, C. J. A., Pitchford, J. W., et al. (2008). Scaling laws of marine predator search behavior. Nature, 451, 1098-1102. doi:10.1038/ nature06518
56. Singer, J. D., & Willett, J. B. (2003). Applied longitudinal data analysis. New York: Oxford University Press.
57. Siri, B., Quoy, M., Delord, B., Cessac, B., & Berry, H. (2007). Ef- fects of Hebbian learning on the dynamics and structure of random networks with inhibitory and excitatory neurons. Journal of Physiology, 101, 136-148. doi:10.1016/j.jphysparis.2007.10.003
58. Sparrow, C. (1982). Lorenz equations: Bifurcations, chaos, and strange attractors. New York: Springer.
59. Spivey, M. J. (2007). The continuity of mind. New York: Oxford University Press.
60. Spivey, M. J., & Dale, R. (2006). Continuous dynamics in real-time cognition. Current Directions in Psychological Science, 15, 207-211. doi:10.1111/j.1467-8721.2006.00437.x
61. Spivey, M. J., & Geng, J. J. (2001). Oculomotor mechanisms activated by imagery and memory: Eye movements to absent objects. Psychological Research, 65, 235-241. doi:10.1007/s004260100059
62. Stephen, D. G., Dixon, J. A., & Isenhower, R. W. (in press). Dynamics of representational change: Entropy, action, and cognition. Journal of Experimental Psychology: Human Perception & Performance.
63. Stewart, I., & Golubitsky, M. (1992). Fearful symmetry: Is God a geometer? Oxford: Blackwell.
64. Sullivan, T. J., & de Sa, V. R. (2006). Homeostatic synaptic scaling in self-organizing maps. Neural Networks, 19, 734-743. doi:10.1016/j .neunet.2006.05.006 (Pubitemid 44148946)
65. Takens, F. (1981). Detecting strange attractors in turbulence. In D. Rand & L. S. Young (Eds.), Lecture notes in mathematics: Dynamical systems and turbulence (Vol. 898, pp. 366-381). Berlin: Springer.
66. Thornton, T. L., & Gilden, D. L. (2005). Provenance of correlations in psychological data. Psychonomic Bulletin & Review, 12, 409-441.
67. van Gompel, R. P. G., Fischer, M. H., Murray, W. S., & Hill, R. L. (Eds.) (2007). Eye movements: A window on mind and brain. Oxford: Elsevier.
68. Van Orden, G. C., Holden, J. G., & Turvey, M. T. (2003). Self- organization of cognitive performance. Journal of Experimental Psychology: General, 132, 331-350. doi:10.1037/0096-3445.132.3.331
69. Webber, C. L., Jr., & Zbilut, J. P. (1994). Dynamical assessment of physiological systems and states using recurrence plot strategies. Journal of Applied Physiology, 76, 965-973.
70. Webber, C. L., Jr., & Zbilut, J. P. (2005). Recurrence quantification analysis of nonlinear dynamical systems. In M. A. Riley & G. C. Van Orden (Eds.), Tutorials in contemporary nonlinear methods for the behavioral sciences (pp. 26-94). Arlington, VA: National Science Foundation. Retrieved March 1, 2006, from www .nsf.gov/sbe/bcs/pac/nmbs/nmbs.jsp.
71. Webster, G., & Goodwin, B. (1996). Form and transformation: Generative and relational principles in biology. Cambridge: Cambridge University Press.
72. West, G. B., Brown, J. H., & Enquist, B. J. (1999). The fourth dimension of life: Fractal geometry and allometric scaling of organisms. Science, 284, 1677-1679. doi:10.1126/science.284.5420.1677