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Teaching and Learning Resource (TLR)

1. Title

Chaos without Confusion

2. Keywords

Chaos, determinism, free-will, phase space, prediction, attractor.

3. Introduction

The science of chaos could revolutionise many disciplines, from economics to meteorology. It raises important questions about the nature of knowledge, and its history provides a good illustration of the role of paradigms in constraining research. Chaos theory reveals that many patterns thought of as random may be deterministic, implying that, in some respects, nature might be more ordered than we previously thought. However, it also suggests that the scientific goal of predicting these systems may be impossible. This could affect many aspects of the environmental sciences, such as the management of wild populations (e.g. in fisheries) and the prediction of future climate trends. It is important, therefore, that students have a basic understanding of the ideas and language of chaos. However, much of the terminology and mathematics is obscure and difficult for environmental science and ecology students. This package will introduce students to chaos and some of the related issues using a simple model of population growth. It will encourage students to reflect on how this new approach might influence our attempts to understand, predict and manage the natural world. The dream of perfect prediction, based on the assumption of an entirely deterministic, clock-work universe, has underpinned most of western science for three centuries, and given theologians, philosophers and champions of free-will many sleepless nights. This TLR will raise the question of how chaos might relate to scientific determinism and free-will.

4. Aim

To provide an introduction to chaos using a simple CAL package.

If you wish to receive the CAL package, contact June Balshaw and the package will be sent to you via e-mail as an attachment.

5. Learning outcomes

After studying this package, students will be able to:

1. Explain the difference between random and deterministic systems.
2. Describe, graphically and with words, the meaning of the phrase 'phase space'.
3. Illustrate three different types of attractor.
4. Critically evaluate the main implications of chaos for our understanding of natural systems, and for the possbility of perfect predictability and free-will.

6. Pre-requisites

No pre-requisites necessary.

7. How to use TLR

This is designed as a two hour tutorial, with students working in pairs. The optimum group size is probably around 10-12 students per member of staff. All the instructions for students are contained on the tutorial sheet.

8. Stimulus Material

Written tutorial sheet, Chaos Without Confusion, provided with the TLR, and CAL package.

If you wish to receive the CAL package, contact June Balshaw and the package will be sent to you via e-mail as an attachment.

10. Degree stage

Years 2 and 3.

11. Resource requirements

PCs with Microsoft Excel 5.0 or later, ideally at least 1 PC between two students, graph paper.

12. Preparation

None required, although a discussion of the difference between linear and non-linear systems might be useful.

13. Links with other TLRs

The aims and/or learning outcomes of this TLR are related to those of other TLRs listed in the following 'thematic cluster':

• Contested science

14. Follow-up activities

Exploration of fractals - can the students think of any examples of fractal geometry in the natural world? What might be the implications of fractals for science (for example, what does an appreciation of fractals mean for how much 'room' there is for populations of small organisms?).

15. Recommended reading

For a good general overview: Gleick, James. Chaos. Making a New Science. Abacus. 1987.

For more detail: Williams, G. Chaos Theory Tamed, Taylor and Francis, 1997.