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Re:Ask HN: Higher order derivatives in everyday life? by p1esk on Thursday July 28, 2022 @02:13AM (#32260984)
I only see a 3rd derivative here. 1st: labor productivity, 2nd: rate of labor productivity growth, 3rd: acceleration of a rate of labor productivity growth.

The quote in Russian also describes a 3rd derivative.

Re:Ask HN: Higher order derivatives in everyday life? by garrybelka on Thursday July 28, 2022 @03:08AM (#32261310)
Acceleration - d2t

Rate - dt

Labor - dt

Productivity - dt

Growth - dt

Altogether d6(Work)/dt

The quote in Russian is an example of a 6th derivative.

It was often mentioned next to a proof that the party line was straight (каждая точка - точка перегиба).

Re:Ask HN: Higher order derivatives in everyday life? by p1esk on Thursday July 28, 2022 @11:33AM (#32265735)
Let’s say “labor” refers to building houses, and “labor productivity” refers to how many houses are build in a year. This is the first rate of change (1st derivative). For example, “in 2019 one house was built, in 2020 one house was built, in 2021 one house was built”, and the 1st derivative is 1 house per year.

“Labor productivity growth rate” is how much the first rate of change changes (2nd derivative): for example, “in 2019 one house was built, in 2020 two houses were built, in 2021 three houses were built”, the second derivative is 1 house per year per year. This is the second rate of change in that statement.

Finally, “acceleration of labor productivity growth rate” describes how the growth changes (the third rate of change): “in 2019 one house was built, in 2020 two houses were built, in 2021 four houses were built”. The 3rd derivative is 1 house per year per year per year. No other rates of change are mentioned in your statement.

Does this make sense?

Re:Ask HN: Higher order derivatives in everyday life? by penteract on Thursday July 28, 2022 @05:40AM (#32262268)
I don't know Russian, but I'd read the English quote as referring to a third derivative - the units of "labour productivity" are work/time; so growth of that is a second derivative. Also if someone said "acceleration of speed" I would assume they meant acceleration, so that only adds one derivative.