Math has a hierarchy built-in.
The 3 can be derived from the 1+2, but the 1+2 cannot be derived from the 3.
The = is not = but establishes a hierarchy that nearly always requires one side to carry more complexity than the other., except in cases where 3=3 for example.
This is a flaw in the Turing terms, which tests for computability from L to R but not from R to L.
You cannot derive sources from final product.
This is the power of studying chaotic systems over solely the final effects of chaotic systems which are simple results. An integer. A fact. A fraction. A statement – is usually lacking that which makes it up.
Order arises from chaos. Order imposed “from above” meets resistance because chaos leading to order is the norm while artificial order does not usually reflect properly “what makes up the 3″.
My question is: How can this be taught well so that it becomes a natural understanding, rather than an exotic thing?
Chaotic systems in the narrower sense I was intending but did not specify refers to systems that are very sensitive to initial conditions.
The final product of a chaotic system can’t always be predicted properly, especially as complexity grows and more and more variables of changing values impact the system.
Yet there is order in the chaos. There is order in the complexity. You’re right that the limitations are perceptual, technological, comprehension limitations.
I think it’s a study that despite almost 40 years of amazing work in it, the surface of its power is barely tapped.
I’m not much for videos but I got the name, did some quick research and I see what you mean.
People who work in https://en.wikipedia.org/wiki/Ecology see things from a complexity minded, systemic POV and I approve.
Also, he seems like an amazing man who has done amazing work in a field that might otherwise be but a niche biology field.