Nonlinearity - Revision history

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energy>Ethan.boechler at 19:39, 10 September 2021

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	[[Category:Done 2018-06-15]]		[[Category:Done 2018-06-15]]
			[[Category:Translated to French]]
			[[fr:Non-linéarité]]
	[[File:nonlinearity3.png\|400px\|thumb\|right\|Figure 1. The above plot shows a variety of nonlinear relationships in comparison to a linear relationship, shown in yellow.<ref>Wikimedia Commons. (November 15, 2015). ''Resistor VI Graph'' [Online]. Available: https://upload.wikimedia.org/wikipedia/commons/2/20/Resistor_v-i_graph_(nonlinear).svg</ref>]]		[[File:nonlinearity3.png\|400px\|thumb\|right\|Figure 1. The above plot shows a variety of nonlinear relationships in comparison to a linear relationship, shown in yellow.<ref>Wikimedia Commons. (November 15, 2015). ''Resistor VI Graph'' [Online]. Available: https://upload.wikimedia.org/wikipedia/commons/2/20/Resistor_v-i_graph_(nonlinear).svg</ref>]]
	<onlyinclude>'''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.</onlyinclude> 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 scale\|logarithmic]] or based on a power relationship.<ref name="OED">Oxford English Dictionary, online: http://www.oed.com/view/Entry/127994?redirectedFrom=nonlinear#eid Accessed October 17th, 2017.</ref> Nonlinearity in a relationship is the opposite of [[linearity]].		<onlyinclude>'''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.</onlyinclude> 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 scale\|logarithmic]] or based on a power relationship.<ref name="OED">Oxford English Dictionary, online: http://www.oed.com/view/Entry/127994?redirectedFrom=nonlinear#eid Accessed October 17th, 2017.</ref> Nonlinearity in a relationship is the opposite of [[linearity]].

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	[[Category:Done ~~2016~~-01-15]]		[[Category:Done 2018-06-15]]
	[[File:nonlinearity3.png\|400px\|thumb\|right\|Figure 1. The above plot shows a variety of nonlinear relationships in comparison to a linear relationship, shown in yellow.<ref>Wikimedia Commons. (November 15, 2015). ''Resistor VI Graph'' [Online]. Available: https://upload.wikimedia.org/wikipedia/commons/2/20/Resistor_v-i_graph_(nonlinear).svg</ref>]]		[[File:nonlinearity3.png\|400px\|thumb\|right\|Figure 1. The above plot shows a variety of nonlinear relationships in comparison to a linear relationship, shown in yellow.<ref>Wikimedia Commons. (November 15, 2015). ''Resistor VI Graph'' [Online]. Available: https://upload.wikimedia.org/wikipedia/commons/2/20/Resistor_v-i_graph_(nonlinear).svg</ref>]]
	<onlyinclude>'''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.</onlyinclude> 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 scale\|logarithmic]] or based on a power relationship.<ref name="~~RE1~~">~~Investopedia. (November 15~~, ~~2015). ''Nonlinearity Definition'' [Online]. Available~~: http://www.~~investopedia~~.com/~~terms~~/n/~~nonlinearity~~.~~asp~~</ref> Nonlinearity in a relationship is the opposite of [[linearity]].		<onlyinclude>'''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.</onlyinclude> 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 scale\|logarithmic]] or based on a power relationship.<ref name="OED">Oxford English Dictionary, online: http://www.oed.com/view/Entry/127994?redirectedFrom=nonlinear#eid Accessed October 17th, 2017.</ref> Nonlinearity in a relationship is the opposite of [[linearity]].

	One of the biggest concerns about [[climate change]] is that some responses to increased [[greenhouse gas]]es 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.		One of the biggest concerns about [[climate change]] is that some responses to increased [[greenhouse gas]]es 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.
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	==Types==		==Types==
	Some simple examples of nonlinear relationships are logarithmic relationships (<m>log(x)</m>), exponential relationships (<m>e^x</m>), and power relationships (<m>x^n</m>). Often times it is useful to generalize nonlinear relationships to a power law relationship, wherein every time you double one quantity you increase the other quantity by some number that is not two, but is always the same number.<ref name="RE2"/>		Some simple examples of nonlinear relationships are logarithmic relationships (<math>log(x)</math>), exponential relationships (<math>e^x</math>), and power relationships (<math>x^n</math>). Often times it is useful to generalize nonlinear relationships to a power law relationship, wherein every time you double one quantity you increase the other quantity by some number that is not two, but is always the same number.<ref name="RE2"/>
	==References==		==References==
	{{reflist}}		{{reflist}}
			[[Category:Uploaded]]

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[[Category:Done 2016-01-15]]
[[File:nonlinearity3.png|400px|thumb|right|Figure 1. The above plot shows a variety of nonlinear relationships in comparison to a linear relationship, shown in yellow.<ref>Wikimedia Commons. (November 15, 2015). ''Resistor VI Graph'' [Online]. Available: https://upload.wikimedia.org/wikipedia/commons/2/20/Resistor_v-i_graph_(nonlinear).svg</ref>]]
<onlyinclude>'''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.</onlyinclude> 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 scale|logarithmic]] or based on a power relationship.<ref name="RE1">Investopedia. (November 15, 2015). ''Nonlinearity Definition'' [Online]. Available: http://www.investopedia.com/terms/n/nonlinearity.asp</ref> Nonlinearity in a relationship is the opposite of [[linearity]].

One of the biggest concerns about [[climate change]] is that some responses to increased [[greenhouse gas]]es 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.<ref name="RE2">New England Complex Systems Institute. (November 15, 2015). ''Concepts: Linear and Nonlinear''</ref> 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 (<m>log(x)</m>), exponential relationships (<m>e^x</m>), and power relationships (<m>x^n</m>). Often times it is useful to generalize nonlinear relationships to a power law relationship, wherein every time you double one quantity you increase the other quantity by some number that is not two, but is always the same number.<ref name="RE2"/>
==References==
{{reflist}}