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Where 2+2=5 and we're not sure why
Topic: Non-linearity
by Nick, 2019 Cohort
“Non-Linearity means that the act of playing the game has a way of changing the rules…”- James Gleick
We are often confounded by the nature of relationships between things. A linear relationship is relatively easy to understand because it is a relationship with constant proportions; in other words, they are a product of direct cause and effect interactions. For centuries, science and mathematics have focused on these simple linear interactions which can be described in compact equations, not because that’s the way the world is, but because it’s easier to encode in our language of mathematics and science. Non-linear relationships, by contrast, appear much more chaotic and counter- intuitive. Unfortunately for us, the world we inhabit is inherently non-linear, and the changeability of non- linear systems subvert our expectations, forcing us to confront the complexity of the
Non-linear systems can ‘simply’ be defined as systems which defy the principles that characterise linear systems; known as the Superposition principles of Additivity and Homogeneity. The Additivity principle states that when two or more components are combined, the resulting combination will be no more or less than the simple addition of those components’ properties in isolation. An example of this would be the simple formula of 1+1=2. However, in non-linear systems, the things combined affect the interactions that make the overall product of the combination more or less than a simple additive function; encapsulated in the phrase ‘the whole is more than the sum of its parts’. For example, the distinguishing properties of water, that being its liquid form and non-flammability, are the exact opposite of the properties of its component gases- hydrogen and oxygen- in isolation. This process of unique system properties emerging from individual components interacting with each other in unexpected ways is known as
Non-linearity also arises when the Homogeneity principle breaks down. The Homogeneity principle essentially states that the change in the output of a system is proportional to the change in input- two times as much in, two times as much out. Four times as much in, four times as much out etc. However, this principle ignores the effect that the current actions of a system will have on its environment, and how it will in turn feedback to affect future input variables to the system. In other words, this linear model does not account for negative feedback loops. For example, uprooting natural vegetation to make room for crops can work for a while, but eventually uprooting enough natural vegetation will cause the water table to rise, increasing soil salinity and making it impossible to grow crops. Moreover, wildfires thankfully cannot grow exponentially forever, because the environmental effect- say the depletion of the forest that fuels it- will inevitably feedback to constrain the state of the
Non-linearities are important to understand when confronting the complexities of world, not only because they confound our expectations of relationships between cause and effect, but because they can flip the function of a system from one mode of behaviour to another.
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“Non-Linearity means that the act of playing the game has a way of changing the rules…”- James Gleick
We are often confounded by the nature of relationships between things. A linear relationship is relatively easy to understand because it is a relationship with constant proportions; in other words, they are a product of direct cause and effect interactions. For centuries, science and mathematics have focused on these simple linear interactions which can be described in compact equations, not because that’s the way the world is, but because it’s easier to encode in our language of mathematics and science. Non-linear relationships, by contrast, appear much more chaotic and counter- intuitive. Unfortunately for us, the world we inhabit is inherently non-linear, and the changeability of non- linear systems subvert our expectations, forcing us to confront the complexity of the
Non-linear systems can ‘simply’ be defined as systems which defy the principles that characterise linear systems; known as the Superposition principles of Additivity and Homogeneity. The Additivity principle states that when two or more components are combined, the resulting combination will be no more or less than the simple addition of those components’ properties in isolation. An example of this would be the simple formula of 1+1=2. However, in non-linear systems, the things combined affect the interactions that make the overall product of the combination more or less than a simple additive function; encapsulated in the phrase ‘the whole is more than the sum of its parts’. For example, the distinguishing properties of water, that being its liquid form and non-flammability, are the exact opposite of the properties of its component gases- hydrogen and oxygen- in isolation. This process of unique system properties emerging from individual components interacting with each other in unexpected ways is known as
Non-linearity also arises when the Homogeneity principle breaks down. The Homogeneity principle essentially states that the change in the output of a system is proportional to the change in input- two times as much in, two times as much out. Four times as much in, four times as much out etc. However, this principle ignores the effect that the current actions of a system will have on its environment, and how it will in turn feedback to affect future input variables to the system. In other words, this linear model does not account for negative feedback loops. For example, uprooting natural vegetation to make room for crops can work for a while, but eventually uprooting enough natural vegetation will cause the water table to rise, increasing soil salinity and making it impossible to grow crops. Moreover, wildfires thankfully cannot grow exponentially forever, because the environmental effect- say the depletion of the forest that fuels it- will inevitably feedback to constrain the state of the
Non-linearities are important to understand when confronting the complexities of world, not only because they confound our expectations of relationships between cause and effect, but because they can flip the function of a system from one mode of behaviour to another.