Cognitive Algebra in Intuitive Physics

Abstract Intuitive or commonsense physics concerns physical knowledge that operates in everyday actions, especially in sports and other motor behavior. Intuitive physics typically requires integration of several stimulus factors, a problem to which the theory of information integration may be applied. The hypothesis that the stimulus integrations of intuitive physics follow algebraic rules can be tested with the parallelism theorem and the linear fan theorem of functional measurement. Preliminary results with Galileo's inclined plane and a collision task support the hypothesis of a cognitive algebra of intuitive physics, in agreement with previous results on intuitive mathematics. In this approach, analysis is entirely cognitive, with no essential reliance on physical metrics or physical relations. The problem of learning of intuitive physics is discussed in terms of patterning, both of the response and of the information-reinforcement schedule.

[1]  S. S. Stevens.  Chapter 11 – PERCEPTUAL MAGNITUDE AND ITS MEASUREMENT , 1974 .

[2]  James Shanteau,et al.  5 – AN INFORMATION-INTEGRATION ANALYSIS OF RISKY DECISION MAKING , 1975 .

[3]  Berndt Brehmer,et al.  Learning complex rules in probabilistic inference tasks , 1976 .

[4]  Ola Svenson,et al.  Intuitive extrapolation of a growth function , 1977 .

[5]  N. Anderson.  Test of a model for number-averaging behavior , 1964 .

[6]  M. Leon.  Extent, multiplying, and proportionality rules in children's judgments of area. , 1982, Journal of experimental child psychology.

[7]  James G. Greeno,et al.  Psychology of learning, 1960–1980: One participant's observations. , 1980 .

[8]  J. Carroll,et al.  Learning on a response continuum: Comparison of a linear change and a functional learning model , 1976 .

[9]  Berndt Brehmer,et al.  Subjects' ability to find the parameters of functional rules in probabilistic inference tasks , 1976 .

[10]  M. Lindahl.  THE IMPORTANCE OF STRATEGY IN A COMPLEX LEARNING TASK , 1964 .

[11]  N. Anderson.  Note on functional measurement and data analysis , 1977 .

[12]  Paul Slovic,et al.  Information Integration in Multiple-Cue Judgments. , 1980 .

[13]  M. Lindahl.  Concept learning and the intradimensional spread of the relevant values of the instances I. Effects of intraclass variability , 1974 .

[14]  C. E. SHANNON,et al.  A mathematical theory of communication , 1948, MOCO.

[15]  D. Cuneo,et al.  Children's judgments of numerical quantity: A new view of early quantification , 1982, Cognitive Psychology.

[16]  N. Anderson,et al.  The height?+?width rule seems solid: Reply to Bogartz , 1978 .

[17]  Lola L. Lopes.  Model-based decision and inference in stud poker. , 1976 .

[18]  O. Svenson.  A functional measurement approach to intuitive estimation as exemplified by estimated time savings. , 1970 .

[19]  N. Anderson.  Algebraic Rules in Psychology Measurement , 1979 .

[20]  W. R. Garner,et al.  Perceptual independence: definitions, models, and experimental paradigms. , 1969, Psychological bulletin.

[21]  D. Klahr,et al.  The representation of children's knowledge. , 1978, Advances in child development and behavior.

[22]  H. Eisler,et al.  ON THE SIGN OF SLOPE IN THE LEARNING OF LINEAR FUNCTIONS , 1970 .

[23]  Lennart Sjöberg,et al.  Delay of Outcome and Preference for Different Courses of Action , 1979 .

[24]  Han Timmers,et al.  Extrapolation of exponential time series is not enhanced by having more data points , 1978 .

[25]  Norman H. Anderson,et al.  Linear models for responses measured on a continuous scale. , 1964 .

[26]  M. Birnbaum.  Intuitive Numerical Prediction , 1976 .

[27]  N. Anderson.  Application of a model for numerical response to a probability learning situation. , 1969 .

[28]  N. Anderson,et al.  The height?+?width rule in children's judgments of quantity , 1978 .

[29]  Irwin P. Levin,et al.  Information integration in numerical judgments and decision processes. , 1975 .

[30]  N. Anderson.  Chapter 8 – ALGEBRAIC MODELS IN PERCEPTION* , 1974 .

[31]  T. R. Stewart,et al.  10 – SOCIAL JUDGMENT THEORY , 1975 .

[32]  R. Bogartz.  Comment on Anderson and Cuneo's "The Height + Width Rule in Children's Judgments of Quantity.". , 1978 .

[33]  N. Anderson,et al.  Comparison of two rule-assessment methodologies for studying cognitive development and knowledge structure. , 1982 .

[34]  K. Norman.  Rule learning in a stimulus integration task. , 1974 .

[35]  M. Björkman.  Studies in predictive behavior. Explorations into predictive judgments based on functional learning and defined by estimation, categorization, and choice. , 1965, Scandinavian journal of psychology.

[36]  R. Bogartz,et al.  A functional measurement analysis of the development of dimensional coordination in children. , 1978, Journal of experimental child psychology.

[37]  J. Piaget,et al.  The Growth Of Logical Thinking From Childhood To Adolescence: An Essay On The Construction Of Formal Operational Structures , 1958 .

[38]  D. Cuneo,et al.  A general strategy for quantity judgments: the height width rule. , 1980, Child development.

[39]  F. Wilkening.  Integrating velocity, time, and distance information: A developmental study , 1981, Cognitive Psychology.

[40]  W. Friedman.  The Developmental psychology of time , 1982 .

[41]  W. R. Garner,et al.  Chapter 2 – ATTENTION: THE PROCESSING OF MULTIPLE SOURCES OF INFORMATION* , 1974 .

[42]  N. Anderson.  Averaging of space and number stimuli with simultaneous presentation. , 1968, Journal of experimental psychology.