Book contents
- Frontmatter
- Contents
- Preface
- 1 INTRODUCTION
- 2 APPLYING PROBABILITY THEORY TO PROBLEMS IN SOCIOLOGY AND PSYCHOLOGY
- 3 FROM PHYSICS TO PERCEPTION
- 4 WHEN SYSTEMS EVOLVE OVER TIME
- 5 NON-LINEAR AND CHAOTIC SYSTEMS
- 6 DEFINING RATIONALITY
- 7 HOW TO EVALUATE EVIDENCE
- 8 MULTIDIMENSIONAL SCALING
- 9 THE MATHEMATICAL MODELS BEHIND PSYCHOLOGICAL TESTING
- 10 HOW TO KNOW YOU ASKED A GOOD QUESTION
- 11 THE CONSTRUCTION OF COMPLEXITY
- 12 CONNECTIONISM
- 13 L'ENVOI
- References
- Index of Names
- Index of Subjects
4 - WHEN SYSTEMS EVOLVE OVER TIME
Published online by Cambridge University Press: 04 May 2010
- Frontmatter
- Contents
- Preface
- 1 INTRODUCTION
- 2 APPLYING PROBABILITY THEORY TO PROBLEMS IN SOCIOLOGY AND PSYCHOLOGY
- 3 FROM PHYSICS TO PERCEPTION
- 4 WHEN SYSTEMS EVOLVE OVER TIME
- 5 NON-LINEAR AND CHAOTIC SYSTEMS
- 6 DEFINING RATIONALITY
- 7 HOW TO EVALUATE EVIDENCE
- 8 MULTIDIMENSIONAL SCALING
- 9 THE MATHEMATICAL MODELS BEHIND PSYCHOLOGICAL TESTING
- 10 HOW TO KNOW YOU ASKED A GOOD QUESTION
- 11 THE CONSTRUCTION OF COMPLEXITY
- 12 CONNECTIONISM
- 13 L'ENVOI
- References
- Index of Names
- Index of Subjects
Summary
SYSTEMS OF VARIABLES
The social and behavioral sciences often deal with situations in which many variables interact over time. The term system is used to refer to such situations. Systems are ubiquitous. In psychotherapy, poor health may be a cause for depression, and the physiological effects of depression may, in turn, produce poor health. In economics price, production cost, and consumer demand vary together over time. In evolutionary biology, the rabbit and the fox evolved together. Time lags may be introduced. In manufacturing, production costs at time t fall as a result of capital investment at time t − k. When system behavior is being studied, the object of the game is to find how the simplest process that can describe the system is evolving. To do this, we develop a mathematical description of the process and compare the resulting numbers to the data. The mathematical description is called a (model) system, an idea that will now be described.
Imagine a system that consists of variables x, y, and z and in which the change in each variable over time depends entirely upon the values of the other variables. This sort of system is called a closed system. The solar system, for example, can be treated as a (nearly) closed system because the positions and motions of the Sun and the planets are almost entirely determined by their current position and motion.
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- Information
- The Mathematics of Behavior , pp. 67 - 103Publisher: Cambridge University PressPrint publication year: 2006