What is Additivism? (part I of II)

Just watch this video, like I have 4 or 5 times, and ask yourself the question “what is additivism?”

The student of nonlinear dynamics immediately thinks of additivism as a conservative concept.

In a linear system, the total effect of the combined action of two or more operations is merely the additive superposition of the effects of each operation individually. So where additivism prevails, the principle of superposition holds, and the system in turn is restricted to a graduated, quantitatively lower or higher behavior, but at any rate is always qualitatively the same, it remains unchanged, viz. a change by degrees that does not produce a new change in kind.  And as Ed Lorenz often liked to observe, linear systems have two choices: they either remain locally-bound or they fly off to infinity.

By contrast, in a nonlinear system, the combined effect of two or more elementary operations can induce dramatic effects, disposing the system of new solutions whose availability were previously latent or unactualized. Here one observes perhaps even an incremental change by degrees, but which suddenly produces a new change in kind. The divergent evolutionary process of difference by way of repetition, topological folding and twisting, nonorientability -these are all the kinds of system-behaviors cooked into nonlinearity.

My sense is, after watching the video, thinking (which I like to do sometimes), and reading up on their cookbook project, that Additivism self-understands itself to be wagering on nonlinearity -and yet there’s that term, “additivism”.

So my question is, what, prey-tell (that’s not a typo -come on people let’s distribute a new meme!), is additivism?

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