Interesting post, abstractions are the few stable-ish quantities that weren’t eaten by chaotic noise.
Exponentially growing errors are not always chaotic. Suppose you have around 1000 starting cells, with a 1% error in the population size. The number of cells doubles in each hour. The absolute error of the population size can be 10.24 times larger than the initial population 10 hours later; however, the relative error remained 1%. (The billiard ball example is still chaotic, but the tilde character does the heavy lifting: 31.4 with 10% error is an imprecise but usable measurement, sin(31.4 +- 10%) is garbage.)
If the relative error of a quantity remains bounded as the elements of a system interact, then this value could be a useful abstraction.
Interesting post, abstractions are the few stable-ish quantities that weren’t eaten by chaotic noise.
Exponentially growing errors are not always chaotic. Suppose you have around 1000 starting cells, with a 1% error in the population size. The number of cells doubles in each hour. The absolute error of the population size can be 10.24 times larger than the initial population 10 hours later; however, the relative error remained 1%. (The billiard ball example is still chaotic, but the tilde character does the heavy lifting: 31.4 with 10% error is an imprecise but usable measurement, sin(31.4 +- 10%) is garbage.)
If the relative error of a quantity remains bounded as the elements of a system interact, then this value could be a useful abstraction.