Book contents
- Frontmatter
- Contents
- Preface
- 1 Introduction
- 2 Background
- 3 The seven elementary catastrophes
- 4 The geometry of the seven elementary catastrophes
- 5 Applications in physics
- 6 Applications in the social sciences
- 7 Applications in biology
- 8 Morphogenesis
- 9 Conclusions
- Exercises
- Appendix. Elementary catastrophes of codimension ≦ 5
- References
- Author index
- Subject index
6 - Applications in the social sciences
Published online by Cambridge University Press: 05 June 2012
- Frontmatter
- Contents
- Preface
- 1 Introduction
- 2 Background
- 3 The seven elementary catastrophes
- 4 The geometry of the seven elementary catastrophes
- 5 Applications in physics
- 6 Applications in the social sciences
- 7 Applications in biology
- 8 Morphogenesis
- 9 Conclusions
- Exercises
- Appendix. Elementary catastrophes of codimension ≦ 5
- References
- Author index
- Subject index
Summary
The applications in this chapter represent the opposite end of the spectrum to the physical systems of Chapter 5. When we are trying to analyse the behaviour of an individual, or of a group, we cannot write down a set of equations of motion for the system based on known quantitative laws, and then look to see what catastrophe theory has to say about the solutions of these equations. What we must do is quite different. If we observe in a system some or all of the features which we recognize as characteristic of catastrophes – sudden jumps, hysteresis, bimodality, inaccessibility and divergence – we may suppose, at least as a working hypothesis, that the underlying dynamic is such that catastrophe theory applies. We then choose what appear to be appropriate state and control variables and attempt to fit a catastrophe model to the observations.
Right from the start, we see one of the advantages of catastrophe theory in this sort of problem. The data which are available are often not quantifiable. We can generally order our observations; for example, we can tell whether a person has become more angry or less angry. And we can usually say whether or not a variable is continuous and whether it changes smoothly. On the other hand, algebraic concepts such as addition and multiplication generally have no meaning: it makes little real sense to say that someone has become twice as angry.
- Type
- Chapter
- Information
- An Introduction to Catastrophe Theory , pp. 83 - 97Publisher: Cambridge University PressPrint publication year: 1980