t’s how a simple rule of behavior is not enough to predict results.

It’s not randomness : It’s theoretically predictable but not from the rules of behavior alone because they don’t capture everything. This is why weather prediction is so difficult: What _seems_ to follow simple rules, isn’t simple at all.

Non-linear isn’t necessarily non-deterministic – just REALLY difficult because as the formula returns to itself, the “pinch” in phase space has infinite dimensionality : that is, non-linear. It can extend to 2D, 3D, 18D – orthogonal to the original formulas by ? dimensions.

Yet, it’s not random. Just difficult.

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Quite true. Modeling chaos on a computer is easier because all variables are controlled. But real-world chaotic systems are extremely difficult to model well for exactly the reason you state.

I can understand the appeal of “randomness” over “chaotic systems” but it’s not random just really hard to figure out.

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agree 100% Besides, random on a computer is just pseudo-random. Did you know the National Institute of Standards in the USA broadcasts a new “random number” set on a regular basis?

I just learned about it the other day Our chips on our PCs are limited in their abilities to generate “random” numbers. But even the random numbers generated by NIST aren’t random, but chaotic.

I like having knobs to tweak and a little structure. Butterfly effect may be exaggerated but I like the imagery.

Or think of a seed. We may have a general idea what the oak tree will look like but when we get into the “how precisely?” to where we can see exactly how the rings will be, where all of the branches will form from the seed? I’d consider that chaotic in some sense.

A DNA researcher could tweak one of the bits of DNA, plant the seed, and watch a tree grow in unexpected ways.

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I honestly think that eventually chaos will overtake statistical analysis. Statistics depends on a backdrop of “random” – which is based on an idealized perfect gas in a perfect container, which we only emulate somewhat. I don’t think we’ll ever get to the point that all chaotic systems will be identified, but it’ll be nice to have fewer things being measured against a backdrop of a mythical randomness, although random is a good enough shorthand for chaos for most people I suppose.

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Ok. Here’s an example: Starting with a multicolored ball of clay, predict precisely where all of the colors will fall when pulled and folded 7 times by a small child. Now do it 27 times by an athletic adult.

Now do it 12 times by a machine with a bit of grit in one of the ball bearings.

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It’s ok. I appreciate the questions as answering them helps me clarify my own understanding of it.

[I’m never certain what I know until challenged – so thank you!]

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In 2D, that would generate a beautiful pattern of lines. Now that you’ve said it, I can see it too.

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