An unexciting video about distance derivatives

An exploration of distance, speed, acceleration and other members of the distance-derivatives family. With no need for any flashy gimmicks.

Huge thanks to Cas Visser, Dom Wilson, Jan Wolf and everyone else who had a look at my giant csv of data and tried to help wrangle it.

CORRECTIONS
- None yet, let me know if you spot anything!

Filming and editing by Trunkman Productions
Additional filming by Alice Degrassi and Ben Westaway
Written and performed by Matt Parker
Background extra by Hannah Fry
Produced by Nicole Jacobus
Music by Howard Carter
Design by Simon Wright and Adam Robinson

Special thanks to Trunkman Productions Ltd, The Cosmic Shambles Network, Two Wheels for Life and DornaSports for facilitating filming at the British Round of the MotoGP™ Championship. MotoGP™ is a registered trademark of DORNA SPORTS, S.L and all footage and images from the MotoGP™ championship are used with their permission and remain their © Copyright. Documentary footage is Copyright © 2023 Trunkman Productions Ltd and is used with permission.

MATT PARKER: Stand-up Mathematician

[shaunsaggers]

"I have a need for speed, and it's higher order derivatives" was literally so funny I forgot to laugh. I had to just sit back and appreciate such a great physics joke.

[wasteraer]

I love how this could have been so click baity with a sick MotoGP clip, but instead we get a whiteboard. True to his maths ❤

[infrabread]

I am not surprised that Matt can find more excitement in a spreadsheet than riding a 200 bhp motorbike.

[mohammedfahmy]

Your running into real-life drift errors is the first time I felt my engineering and automation degree wasn't useless. Please do a video on Kalman filters next it'd be so interesting. And I can do the filtering for you if you'd like!

[gordonwiley]

Oh snap! I love mundane videos where Matt sits in a quiet room and talks spreadsheets.

[ibonitog]

At 17:00 you say that one has a better long term accuracy (no drift) while the other has the better shape (smoother data). That rang a bell for me from an old uni class. This would be a perfect application for Kalman sensor fusion! Where multiple data sources are used to create one superior output that contains the best of both worlds without each side's drawbacks. First time I tried it, it's kinda magic, might be a cool video idea! (although not sure how engaging the maths is for an engineering topic :p)

[JWQweqOPDH]

Silly Matt! Simply sitting on a swing allows you to experience infinite speed derivatives! For simplicity let's say your position is sin(t), then your speed is cos(t), your acceleration is -sin(t), your jerk is -cos(t), your snap is sin(t), your crackle is cos(t), and your pop is -sin(t). This pattern repeats indefinitely.

[ClementinesmWTF]

You can actually translate higher order derivatives of displacement into a measurement of displacement to some extent. Acceleration is how far back into your seat you are pushed (ie you’ve translated it back into displacement into a soft squishy seat), jerk is roughly the speed you get pushed into it, and snap is the acceleration of you squishing into it. Of course, it’s only roughly linear at low “speeds” (accelerations) because the seat acts as a spring whose resistance increases as you go further into it. You could also do something similar by making your measure of acceleration into the displacement of the gas pedal, but that’s less of a feeling of forces of higher order derivatives and more of making those higher order derivatives.

And jerk as a measurement *is* truly what you mean whenever you saying you’re getting “jerked around”—the acceleration is usually fine, but lots of jerk can be extremely uncomfortable and that’s why there’s very few fields of engineering that actually both to deal with minimizing it. Namely roller coaster engineers put a lot of effort into minimizing jerk, snap, crackle, and sometimes pop if it becomes important enough.

[DesmondAltairEzio]

How could Matt do this to us with that blatant click-bait

[jeremyvoltoliniferrari]

To simplify a bit the higher derivatives :
Acceleration is (basically) at what angle your gas handle stay ;
Jerk is at what rotation speed your handle is turning ;
Snap is the acceleration of the speed of handle.

So high jerk is turning the gas fast but steadily, and snap is beginning slow and turning it faster and faster

[Nerdule]

Fun fact: There's also a name for the -1st derivative of position: the time *integral* of displacement, measured in units of meters *times* seconds! It's known as Absement. It's a measure of how far something's away from the origin, for how long. It doesn't come up much but it has some use in cases where there's a natural resting position for a thing. For instance, if a car's speed is a function of the displacement of the gas/brake pedal, then the distance traveled is a function of the absement of those pedals.

[isaacwalters]

"...and I appreciate everyone that gave it a go" Spoken like a true teacher, Matt!

[Sakkura]

1:42 It's actually very interesting, once you take the derivative for the third time, the distance variable disappears!

[tomtrask_YT]

The easiest way to get jerk or snap is to brake hard into a corner (because you always want to do all your braking before you turn - if you're still braking after you start to turn, you'll go wide on the turn) and then hit the throttle as you turn and exit the curve. This describes what you probably did in that pretty sharp turn on your diagram of the track.

[tuxino]

Matt Parker might not be the biggest motorcycle enthusiast, but the subtitle writing software seems to be. It labels the sound of an accelerating bike as [Music].

[Bobsmithgeorgette]

I teach engineering and do a lab exactly like this (with a mechanism, not a motorcycle) in 2nd year dynamics. Very cool seeing you frig around with this type of data. I might recommend my students watch this video before the lab next year! PS your content is excellent.

[johngranahan]

As a man with his own whiteboard, I fully appreciate the skills on show required to effectively and clearly write on one with one hand

[Geenimetsuri]

Hi! As a seismologist we often work between displacement – velocity – acceleration time series. One "trick" if you want to integrate is indeed linear detrending. Another one is high pass filtering, as there's usually a maximum period (i.e. a lowest frequency) a seismometer or accelerometer can reliably measure.

The whole process usually is: Detrend, taper (usually 5 % half-cosine) or pad with zeroes, filter, integrate, but just detrending the result can be enough for some purposes!

[jeffclarke]

Over thirty years ago I was tasked with driving a relative’s wedding cake about 40 miles, and although it was a nerve-wracking journey, I kept myself occupied in attempting to reduce all the derivatives that I could think of. The third derivative (the jerk) was to me equivalent to the change of pressure on the accelerator or brake pedal, but further derivatives were beyond what my brain could manage! Subsequently as a passenger I noted the least comfortable drives were when the driver failed to minimize this third derivative. I don’t think I have ever rationalised what the fourth derivative actually feels like. Ever since that wedding cake drive I still use this method of driving for any fragile cargo – particularly elderly relatives, and I haven’t had any complaints yet.

[johnquijote]

As a long time fan and ex- racer, this has immediately become my favorite episode! RIP, Champ.