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Beyond velocity and acceleration: jerk, snap and higher derivatives (2016)

(iopscience.iop.org)
181 points EndXA | 1 comments | 19 Jun 24 10:16 UTC | HN request time: 0.27s | source
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vinc ◴[19 Jun 24 11:26 UTC] No.40727212[source]▶
A long time ago I wrote an engine for a newspaper that was helping journalists discover what was happening on social media. I was counting the number of times an URL was posted on Twitter and Facebook. I started with velocity and acceleration, but after I while I discovered that I could go one level higher and use jerk to understand when an URL was shared by an influencer.

I have a hard time imagining another level above that.

replies(3): >>40727451 #>>40727471 #>>40733414 #
1. simpaticoder ◴[19 Jun 24 23:18 UTC] No.40733414[source]▶
When it comes to a measured time-series, the function is always discrete and arbitrary; there is no 'curve' like that generated by a function well-defined on the reals, and so there is no real closed-form derivative. In this context derivatives are not equations so much as derived data, reducing two points to one. And this process is recursive, such that you can take 4 points, reduce the two adjacent ones to 1 point, and then reduce those two into 1 point. In fact for 2^n points you can get the nth derivative in this way. The utility of this data is highly questionable in almost every context, but its available for every time-series. (One application that comes to mind is a kind of checksum, where you recursively derive a time series and stop when local neighbors go to 0, and you're left with a sparse list of high-order numbers that in some sense characterize the series.)