Available online
Description
The programme looks at catastrophe theory and examines two areas in which it is currently being used, the study of light rays and in the study of behaviour in prisons.
The programme looks at catastrophe theory and examines two areas in which it is currently being used, the study of light rays and in the study of behaviour in prisons.
| Module code and title: | M101, Mathematics: a foundation course |
|---|---|
| Item code: | M101; 32 |
| First transmission date: | 11-06-1978 |
| Published: | 1978 |
| Rights Statement: | |
| Restrictions on use: | |
| Duration: | 00:24:00 |
| + Show more... | |
| Producer: | David Saunders |
| Contributors: | Michael Berry; Mike Crampin; E.C.Zeeman; Jonathan Rosenhead; Peter Shapland |
| Publisher: | BBC Open University |
| Keyword(s): | Gartree prison; Riots; Catastrophe theory |
| Footage description: | The programme begins with shots of a prison riot, a graph showing catastrophe theory and the Maths Institute, University of Warwick. Professor Zeeman, of Warwick, explains the ideas behind catastrophe theory which he describes as a method of modelling discontinuous phenomena. He uses a small model to illustrate his ideas. A computer animation shows why Zeeman's model behaves differently at different times. He then describes the mathematics which explain the behaviour of the model. He obtains a formula which describes a cubic surface in a three dimensional space. Computer animations show how this surface is arrived at from the formula, and then Zeeman describes the surface, using a three dimensional model. Computer animations show the surface from above, highlighting the cusp points, analysed by the mathematician Rene Thorn. Professor Zeeman uses a cusp point diagram on his model to demonstrate the significance of the cusp. The use of catastrophe theory in the study of light rays is now considered. Michael Berry describes his work using Thorn's theorem and cusp points to describe focal patterns arising from refracting and reflecting objects found in nature. Shots of a prison. Peter Shapland, prison psychologist, describes how catastrophe theory was used to study the riots at Gartree prison in 1972. Zeeman explains how the theory was adapted for studying the behaviour of the prisoners. Johnathan Rosenhead, of L.S.E., criticises the use of the theory on technical grounds, implying that the assumptions made, made the catastrophe result inevitable. Shapland replies to this criticism, arguing that any measurement in such a complex organisation as a prison will be extremely difficult. Rosenhead expresses his concern about the use of mathematics as a tool for social control. Shapland argues that the theory will not be used for controlling prisoners. |
| Master spool number: | DOU2878 |
| Production number: | FOUM432R |
| Videofinder number: | 450 |
| Available to public: | no |
