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# Deterministic or Chaos?

Topic: Chaos

by Hannah, 2020 Cohort

Chaos:

- a state of utter confusion
- the inherent unpredictability in the behaviour of a complex natural system

Chaos theory is the science of predicting behaviour in fundamentally unpredictable systems. It is mathematical approach to extracting order from what may initially appear as disorder. The definitions above exemplify the contradiction; chaos is both utterly confusing, as well as systematic.

As the natural world does not often exhibit linearity, chaos theory can be used to solve natural, and therefore inherently nonlinear, problems. However, nonlinear processes are often unsolvable in a traditional sense. Due to the butterfly effect, which states small inputs can create vast changes overtime, chaotic problems are deterministic over short periods. For example, we can only forecast the weather accurately for up to 10 days. Nonetheless, a 10-day forecast is a solvable segment of what initially appeared to be a chaotic system. It is deterministic, as well as chaotic.

#### The Father of Chaos Theory#

The father of chaos theory is considered to be Henri Poincar?, a French mathematician. Whilst orbiting had been explored by scientists such as Isaac Newton, there was much to be understood about the solar system in the late 19th century.

In 1885, King Oscar II of Sweden offered a prize for anyone who could establish the stability of the solar system. Poincar? chose a simplified orbiting example and presented equations that established stability through pathways arbitrarily close to consistent. Unfortunately, upon winning the prize, he realised he had made an error. Consequently, he actually proved that stability could not be established.

*“… it may happen that small differences in the initial conditions produce very great ones in the final phenomena. A small error in the former will produce an enormous error in the latter. Prediction becomes impossible, and we have the fortuitous phenomenon”- Poincare,

Similarly to weather forecasting, solar system trajectory is deterministic. Today, it is accurate to about 5 million years.

#### 3 Tips for Applying Chaos Theory#

- Find the patterns. Complex problems inherently have multiple components that make them difficult to solve. Chaotic problems are likely to have multiple components, but they will also be unpredictable. Chaos theory asks you to move passed utter confusion and consider whether or not there are patterns within the complexity, regardless of how short the periods of determinism are.
- Consider various inputs. As a tool, chaos theory encourages a holistic analysis. Ask yourself: ‘What has contributed to this chaos?’. There are going to be multiple inputs, the more you identify the more likely you are to discover interactions and patterns.
- Remember that chaos is valid. Proving a system is chaotic is a valid result. Poincar?’s most famous work was proving the solar system was
*not*stable and it was an important development in our understanding of natural systems.

#### Disclaimer#

This content has been contributed by a student as part of a learning activity.

If there are inaccuracies, or opportunities for significant improvement on this topic, feedback is welcome on how to improve the resource.

You can improve articles on this topic as a student in "Unravelling Complexity", or by including the amendments in an email to: Chris.Browne@anu.edu.au