this makes me think about how 'rate of change' stats are inherently infinitely nested
hold on i promise this is interesting
so, you have position. that's where you are. we figured that one out early by being places.
then you have velocity, which is how fast you go from where you are to somewhere else. we figured that one out too the first time somebody had to run away from a bear.
the rate of change of velocity is acceleration, which is a thing that presumably got coined the first time somebody stumbled upon the bear from a standing start still and suddenly it matters a lot how fast they could get fast.
but what about the rate of change of acceleration? this was something that didn't matter for the majority of human history, because the rate was never really fast enough in any situation where somebody was going to sit down and do math about it. wagons and trains can get by knowing just their acceleration rate. most situations where rate of change of acceleration mattered were usually terminal, i.e. falling off a thing and very suddenly experiencing deceleration at the bottom.
but then we invented planes, and planes go fast and turn fast. so fast than when you rapidly change direction, it emulates the effects of gravity and pulls the blood in your body in unexpected ways. World War 1 pilots (as in, canvas biplanes with motorcycle engine motherfuckers, people who rarely broke 200 kilometres an hour) started noticing that if they held a hard turn for a while at speed, they'd started to get dizzy. if they pulled hard out of a dive and their wings stayed on, their vision would start to go grey. and if they nosed down quickly, it fucking sucked 1
through the interwar period, we learned a bunch of stuff about acceleration and the effects on the human body. using this cool information, we invented things like autopilots that pull people out of dives that might knock them out (through GLOC, g-induced-loss-of-consciousness caused by the blood flowing into your feet when you pull up super hard) or masks that use air pressure to make it easier to breathe when you weigh eight times more than you should.
That all makes sense and is cool.
then planes started to get real fast, and some fucking asshole invented the jet fighter. during and after WW2 we started doing a bunch of very, very detailed testing into g-forces because now a pilot can literally kill themselves if they pull the stick too hard.
it doesn't take long before somebody points out that how quickly the onset of gs occur is important to the survival of pilots; slow gs are way different than fast gs. so you need a stat for the rate of change. so we coined 'jerk', the rate of change of acceleration. physicists knew about it as a concept, but had never really needed to care about it before this
then, when we started doing rocketry and fucking around with ejection seats, which subject the pilot to tremendous forces in the course of yeeting the pilot out of the plane with a barely controlled explosion, somebody in the big science lab presumably asked
'hey boss, what do i call the rate of change of jerk?'
so after sighing and probably pinching the bridge of their nose in frustration, the king of science or whatever was like, okay we're doing this, that's snap now. then, some smartass asked what the rate of change of snap is. and some even smarter ass went "its crackle. and before you ask, the rate of change of crackle is called pop."
so, to recap, pop is the rate of change of crackle which is the rate of change of snap which is the rate of change of jerk which is the rate of change of acceleration which is the rate of change of velocity which is the rate of change of position
we have not yet formerly defined what the rate of change of pop is, presumably because whenever somebody tries all the physicists and engineers get together to draw and quarter them
1 yes this post has footnotes. this distinction is positive gs (blood going to your feet) and negative gs (blood going to your head). human beings can handle shocking amounts of positive gs before passing out from lack of blood (and thus, tasty oxygen) in the thinking zone. by contrast, a very small amount of negative gs can just mcfucking kill you as the blood pressure in your brain spikes and all the delicate tissue take issue with that
ever stand up too fast and get dizzy? positive gs. wonder why being upside down for too long kinda sucks a lot? negative gs.
this is why planes always roll over onto one wing and turn 'up' into turns. turning 'down' into turns with any real force can literally make your eyeballs explode.
if you enjoyed learning about this distinction you will love reading my roleplaying games because its basically the only thing i ever talk about