There are theorems in chaos theory, but for most people chaos theory is a set of examples.
Not models per se, but cautionary tales.
You’re very unlikely to say “hey, my system is described by the logistic iteration too!” but to think “maybe small changes to my system can have large consequences, as in the logistic iteration.”
What is the application of chaos theory?
It is a source of useful metaphors and pretty images.
You don’t APPLY things like the butterfly effect per se, and books that claim to do so are often silly.
Instead you are HUMBLED by the butterfly effect, lowering your expectations of long range predictions.
The key to resolving an argument over percentage calculations is to insist that every time someone says “percent” they immediately follow it by “of.”
In grammatical lingo, the argument very likely boils down to ambiguous antecedents.
1/n
For example, what does 20% profit mean?
Does it mean the supplier adds 20% of the retail cost to his charge, or does it mean 20% of what the customer pays is the supplier’s profit?
2/n
To put it another way, does the supplier add 20 cents to every dollar of retail cost, or does the supplier keep 20 cents of every dollar paid by the customer?
(Notice I used “of” twice.)
Both are 20%, but they are 20% of different things.
3/n
Gell-Mann amnesia: This source is dead wrong about things I understand, but they’re probably right about everything else.
Gell-Mann memory: This source is dead wrong about things I understand, so my default assumption is they’re wrong about everything else.
Gell-Mann meets Bayes: This source was right (wrong) about what I can verify, and so I will update my prior probability in the direction of more (less) default trust.
Gell-Mann meets multi-level Bayes:
I have a hierarchical model of trustworthiness, and so confirmation in one area increases my prior probability of correctness in other areas, but not too much. Borrow strength but learn in each category somewhat independently.