photo: Randy Robertson
When I first read Chaos by James Gleick, some years ago, the only way to draw your own fractal was to write a computer program. The technology we had was more advanced that that used for the discovery of the butterfly effect (the class reading for this week). But now it is easy to draw fractals using websites. As computer power has increased the models they run have become more detailed and complicated. Compare the model that was running when the butterfly effect was discovered, to the models used by the Bureau of Meteorology to generate detailed seven-day forecasts. Computer power and the complexity of models will continue to increase. However, as we saw in Week 6, models need to be interpreted by people skilled in managing complexity.
Panel Reflection
The panel was presented by Prof. Michael Barnsley (see his SuperFractals website).
Since chaos science is a relatively young field, many of the people who developed it are still alive. Prof Barnsley was able to recount stories of encounters with some of these pioneers. These types of stories can add interest to many topics. As we have seen in previous weeks, stories are a powerful tool to show the practical application/consequences of complex issues.
Panel Question
There wasn’t much opportunity to ask questions today. The question I wrote down was: Were the Cascades of Bifurcations discovered using real data or computer simulations?
This is explained in the Life’s Ups and Downs chapter of Chaos. It was first simulated using computers, but later confirmed in physical systems, including dripping taps.
Tutorial Reflection
Bicycle racing (such as in the Tour de France) is a great example of a non-linear complex system. Peddling effort is not linearly related to speed, because riders drafting behind other riders experience less drag. This type of race is managed using technical tools like computer models. Another important aspect of competing in the race are the cultural values, a complex “code of ethics” based on many years of tradition. In analysing complex issues these other aspects need to be addressed as well as the more technical aspects.
Connections within this course
As I predicted in Week 4, we were told today that the length of the coastline of Britain is infinite. You can magnify sections of the coastline as much as you want, but it never becomes a simple straight line. Experts in one area need to seek assistance from experts in other areas to ensure the claims they make are correct. It would be an interesting exercise to get a historians view on the increased power of computers and computer models over time. Many people in the computer industry simply extrapolate forward to predict future increases in computer power. Based on the panel in Week 4, I suspect that the historians would say that you don’t know what will happen in the future based on what has happened in the past.
Connections to other courses
The idea of determining the future state of a system based on its current state is a topic we have been studying in Survival Models and Actuarial Techniques over the last couple of weeks. In the panel today it was described using the concept of a black box. According to Gleick (p76), research into chaos science started in the Soviet Union in the 1950s with the work of Kolmogorov. Just last week we were learning about Kolmogorov’s equations in Survival Models. The reason I mention this is that although chaos theory and survival modelling draw on the same historical background, I am not aware of any use of chaos theory in survival modelling. This could be an area for further research.
External Connections
Some of the ideas mentioned today sounded similar to control systems engineering. A recurring theme I have noticed during this course is that many disciplines are doing very similar work. For example, statistics is taught in psychology, mathematics, engineering and finance. New discoveries and techniques in one area do not necessarily get applied for the benefit of other fields. In some senses this sounds simple to solve, everyone should work together more, but as we have seen previously inter-disciplinary collaboration is complex in itself. One way of addressing this is by publishing research, on the Internet and in other forms. Another approach worth considering is peer review of research by experts from completely different disciplines. This approach may be particularly worthwhile in natural sciences where fractal type patterns are seen to occur (such as in the photo above).
The Questacon harmonograph is an example of a system with sensitive dependence on initial conditions.
Tools to Address Complexity
Chaos has lots of pictures throughout the book. A (perhaps unintended) consequence of this is that it is very easy to flick through the book to find a section about a certain topic. This book demonstrates the power of graphics/pictures to illustrate complex issues.
The panel presentation had a list of keywords at the end of each topic. This was an effective way of defining a common vocabulary.
Prof Barnsley advocated a possible problem solving technique: If it isn’t working do the opposite. The example he suggested was that rather than taxing carbon emission, people/countries should be paid to amass carbon and store it. He claimed this would probably result in a more stable system than a carbon tax. I’m not sure if this is a robust method to manage complexity. It seems to be on the same level as re-framing the question if you don’t like what is being asked.
Other tools mentioned above:
- stories