Exponentiality/non-linearity

Element Descriptor

We are not taught nonlinearity, but it is all around us, and its consequences are surprise and lack of readiness. Having an understanding of how it works helps you and others do planning, get ready for the unexpected, communicate when it hits

Level descriptors

NovicePractitionerExpertNinja
You can explain exponential growth with reference to the two commonest stories – “the grain of rice on the first chess square two on the second.”.. also the lily pads on the pond, covered after 30 days…”You have multiple different stories that explain exponential growth and nonlinearity (and you know that this term is loaded, implying as it does that linearity is somehow a ‘normal’ thing). You can help people cut through the bullshit and see our predicament for what it is.You can come up with new resonant examples for people you are talking with at the drop of a hat, helping them see what is going on, even if/when they would really rather not…You are like an expert, only you can do this across cultures and in the face of wilful ignorance and heckling about how you are a defeatist luddite communist

Element Overview Essay

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The reason groups don’t understand exponentiality and its cousin, non-linearity, (those two things are distinct) is that it is often counter-intuitive and does not relate to how daily life works. We get older a day at a time, hair doesn’t suddenly turn white overnight. I can’t think about the good examples.

Relatedly, people have to be trained in how to think about how to study exponentially in maths class or physics or whatever, most life is dominated by negative feedback loops homeo-dynamic systems or homeostatic systems as they used to be called incorrectly, nothing static about them.

The consequences are that we fail to explain to ourselves and other people, the depths of the crises that we are in. And therefore, we end up being satisfied with the kind of reformist, piecemeal, inadequate, reformist action that is proposed and then, less frequently delivered.

The solution is to come up with several easily understood, explanations of how exponentiality and non-linearity “work”, especially in the natural world. These could be around the chessboard and the grains of rice or the pond, which is covered with lilies and 30 days having doubled in size from the first day or the growth of a human baby that stops. This is related to questions around whether endless growth is a good thing or not. And these simple stories, almost fables, analogies, have to be in easily digested format, cartoons, means etc. That can be deployed at the drop of a hat.

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