# Nonlinearity

**Nonlinearity** is a property that is used to describe a relationship that is not linear - essentially it is a term used to describe a relationship that cannot be plotted as a straight line on a graph, but rather has a curved or angular shape. The term however usually implies that the relationship will yield surprising results. More specifically non-linearity is a type of relationship that cannot be explained as a simple linear combination or sum of its variable inputs, instead it has some other relationship that could be logarithmic or based on a power relationship.^{[2]} Nonlinearity in a relationship is the opposite of linearity.

One of the biggest concerns about climate change is that some responses to increased greenhouse gases will be linear for a while, but will then have a sudden jump. These sudden jumps are often irreversible. This kind of relationship is shown with the grey line in Figure 1. Other relationships shown here are power relationships - shown in red - which is more than linear, as well as logarithmic in blue. This relationship shows a potential situation wherein more greenhouse gases being added to the atmosphere has comparatively less impact than a strictly linear relationship.

## Importance

Nonlinearity can sometimes be an issue when cause and effect relationships are investigated as they cannot be predicted and modelled as easily as linear relationships. Instead, nonlinear cause-effect relationships require complex modeling and predictions to be able to explain some events.^{[3]} Many nonlinear relationships are **monotonic**, meaning they always increase or decrease. These monotonic increases or decreases may be smooth or abrupt, again contributing to the difficulty in modelling nonlinear relationships.

## Types

Some simple examples of nonlinear relationships are logarithmic relationships (^{[3]}

## References

- ↑ Wikimedia Commons. (November 15, 2015).
*Resistor VI Graph*[Online]. Available: https://upload.wikimedia.org/wikipedia/commons/2/20/Resistor_v-i_graph_(nonlinear).svg - ↑ Oxford English Dictionary, online: http://www.oed.com/view/Entry/127994?redirectedFrom=nonlinear#eid Accessed October 17th, 2017.
- ↑
^{3.0}^{3.1}New England Complex Systems Institute. (November 15, 2015).*Concepts: Linear and Nonlinear*