2 ms·
IMHO, the figure of speech "n-th order" generally comes from Taylor series approximation, where n-th term is indeed expressed using n-th derivative. Also, if th
by js8 4y ago
IMHO, the figure of speech "n-th order" generally comes from Taylor series approximation, where n-th term is indeed expressed using n-th derivative. Also, if the series converges, the higher order terms will become smaller, thus the practice of approximating the reality up to n-th order term.
Also, it's often practical to ignore 2nd order and higher terms, because then you have a linear function - something really easy to work with. Therefore, "2nd order effects" have effectively become synonymous to "non-linear effects".
- thrown_22 4y agoHigher order functions have nothing to do with derivatives however.
- earleybird 4y agoHowever, regular types do: "The Derivative of a Regular Type is its Type of One-Hole Contexts" [0] http://strictlypositive.org/diff.pdf http://strictlypositive.org/diff.pdf
- sanderjd 4y agoI really doubt this is where "nth order" comes from colloquially.
- bee_rider 4y agoThis is what I've always assumed as well. The feeling of "things that usually don't matter but may explode (if it turns out the series doesn't converge)" seems to fit the expression pretty well.
- cbm-vic-20 4y agoE = mc^2 is a notable example.