"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.

@jokepp

11 ай бұрын

"...and it is higher order derivatives"? ;-)

@joseandresthuel623

10 ай бұрын

Should be a T-shirt slogan 😄

@squaddiepete

10 ай бұрын

""I feel the need for jerk...."" @@joseandresthuel623

@kaylor87

10 ай бұрын

Wish I could say the same -- I legitimately laughed out loud much harder than I'd like to admit 😂

@01but02

10 ай бұрын

its*

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

@JWQweqOPDH

11 ай бұрын

Reverse-click-bait! Click-scarecrow?

@SupercriticalSnake

11 ай бұрын

@@JWQweqOPDHClick-hate?

@danielroder830

11 ай бұрын

Oh snap! What a jerk!

@Prof1337

11 ай бұрын

Clearly Clickbait Video definitely wasn't unexciting. I hate it

@krzysiek1918

11 ай бұрын

Yeah, disgusting

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 ❤

Distance integrals are also fun to think about. I was crossing a canal lock recently, and there was a sign which read “limit 8kmh”. Sure, they may have just forgot the “/“ in there, but I prefer to think that they were putting an upper limit on the the integral of your position. “You can go a 8 kilometres downstream for an hour, or one kilometre for 8 hours, but then you need to get back in the lock”

@gsurfer04

11 ай бұрын

en.wikipedia.org/wiki/Absement

@aiocafea

11 ай бұрын

@@gsurfer04not relevant but *oh my god* a link in the youtube comments usually youtube quietly takes them in the back room

@gsurfer04

11 ай бұрын

@@aiocafea Absement is the product of distance and time

@petergerdes1094

11 ай бұрын

@@aiocafeaMy experience has been that Wikipedia links get special treatment. I dunno if they have a hard coded whitelist or if it's just their ML recognizing that Wikipedia links aren't indicitive of spam.

@petergerdes1094

11 ай бұрын

So you're stuck living right next to the lock trying to invent faster and faster modes of transit to visit farther off places within the limit?

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

@uganasilverhand

10 ай бұрын

Yeah, he's not a sportsman..... I find more fun in prime numbers than gladiatorial athletic displays

@kasroa

10 ай бұрын

What's your point? Are you trying to suggest that a lickle bikey wikey is more exciting than a spreadsheet? How cute.

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

@Phriedah

11 ай бұрын

Matt can spread my sheets any day

@benwisey

11 ай бұрын

Oh, snap! Me too.

@mikeallison5549

11 ай бұрын

Too bad it was all clickbait. I feel like I have only one choice for breaking my trust……. Unsubscribing

@EtienneBotek

11 ай бұрын

​@@mikeallison5549you're being a jerk.

@imightbebiased9311

11 ай бұрын

No snap! I think the data's too noisy.

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!

@AlanTheBeast100

11 ай бұрын

Kalman filters are not generic. They have to be designed according to the suite of sensors in use.

@mohammedfahmy6715

10 ай бұрын

@@AlanTheBeast100 True. Alpha-beta filters are a good optimization for the gh parameters for most non-accelerating systems though.

@codahighland

10 ай бұрын

​@@mohammedfahmy6715This... is most definitely an accelerating system. XD

@mohammedfahmy6715

10 ай бұрын

@@codahighland I'm sorry I misspoke. I meant systems that have a consistent change of acceleration. And even if they do I believe it should be possible to account for that.

@henrikoldcorn

10 ай бұрын

@@codahighlandsooo…constant jerk? But we want to see those higher orders, not assume they’re zero!

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.

@kleingrrmpf

10 ай бұрын

The way I imagine jerk is how fast you are pulling Gs. That is something that still makes sense to me. But everything above jerk, I can't really imagine. Sure, I know intellectually what the derivative means but it's hard to visualize it...

@TheAngelsHaveThePhoneBox

10 ай бұрын

I also always think in those modern elevators where you can barely feel any forces as it gets moving and stops, how many orders of the distance derivatives did the engineers need to smooth out in the elevator motion control to deceive our vestibular system to such a degree.

@ClementinesmWTF

10 ай бұрын

@@TheAngelsHaveThePhoneBox they probably had to minimize at least the first three derivatives. Hell, just use exp(-1/x^2) or exp(-1/abs(x)) as a basis function for the velocity and you’ve got a really great start for maximizing total displacement over time/average velocity while minimizing subsequent derivatives.

@benemenhall4215

10 ай бұрын

Really appreciate this description

@carrots1550

10 ай бұрын

Nice explanation! I think the easiest way to experience jerk is when you're standing on a bus ready to get off, and you find yourself being thrown *backwards* at any point. The bus's deceleration will push you forwards, so you brace your legs and lean into it, but suddenly that acceleration stops and your brace is inappropriate so you stagger. It can't be acceleration pushing you back, because that would mean the bus is speeding up, which it's not, so you know it must be jerk. (I notice this when I'm driving as well, so if I have passengers, I try to ease off the brake as I'm slowing down to reduce jerk when the vehicle finally comes to a stop. If you just keep your foot in the same position on the pedal, there can be uncomfortable jerk right at that moment.) I think most people in most contexts would struggle to identify snap, but I think jerk is easy enough.

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.

@Steeyuv

11 ай бұрын

Good point well made. But given the choice between a video of ‘Matt sitting on a swing’ and ‘Matt tearing round Silverstone on a MotoGP bike’…

@catmacopter8545

11 ай бұрын

@@Steeyuv i think a 42 year old man who had just bought 27 lottery tickets recording himself sitting at a swing while strangers watch is worth something, at least

@pneumaniac14

11 ай бұрын

I mean you wouldn't sit on a swing for all eternity, and sin(t) is an approximation. I wonder if it's possible this is incorrect. 2 orbiting particles have infinite non-zero derivatives, but even that is an approximation. I highly doubt that the position of everything in the world can be written as a finite polynomial, but I can't find a fundemental reason why not. I guess because polynomials are unbounded either above or below, as time tends to infinity, the positions and velocities of everything approach infinity, but also we can't assume that time will last forever.

@radonato

11 ай бұрын

Release would be a parabolic with initial vector tan(t)?

@harper5128

11 ай бұрын

matt must not be having a lot of fun on the swing given that modelling position as a sinusoid is only true for small amplitudes of displacement

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

@ps.2

11 ай бұрын

Well, and spoken like a true Matt Parker. He has a long history of presenting a problem and encouraging his viewers to give it a go.

@lucasdasilva23

11 ай бұрын

Legit Parker teaching moment

@grutarg2938

10 ай бұрын

Every achievement in the world begins with someone giving it a go.

@coryman125

Ай бұрын

We need some sort of symbol for giving things a go, perhaps one that's to do with math, and named after Matt Parker in some way..... Ah well, no ideas!

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.

@Keldor314

10 ай бұрын

You get jerk every time you stop. It's that lurch at the end where you transition from decellerating to having come to a complete stop. Snap is what you feel at a stop sign when you start to let off the brakes at the end because coming to a complete stop like the law requires is just too much trouble.

@nicholasvinen

10 ай бұрын

Braking through turns isn't necessarily bad, it puts more weight over the front wheels that do the steering. Obviously you need to do most of the braking before you turn but it doesn't have to be all of it.

@beepbop6697

8 ай бұрын

"if you're still braking after you start to turn, you'll go wide in the turn". False. Braking into the curve is called "trail braking" and is the technique specifically used to *prevent going wide* in the curve. Cornering radius reduces as speed reduces, hence slowing down while turning let's you turn sharper. You'll go wide by not reducing speed enough or getting on the accelerator too early.

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

@Oaisus

11 ай бұрын

That should just be a mistake

@dopwop553

11 ай бұрын

it's a Parker's derivative

@angryapplebombs914

11 ай бұрын

I was just about to comment this but yeah I would assume that’s a mistake for jerk and snap too

@stevewithaq

11 ай бұрын

@@dopwop553 My favorite feature of Parker's derivatives is how the d's slowly mutate into a's.

@Games_and_Music

11 ай бұрын

That could explain why he made the worst 3 in his life. Because it looks like he was going to make the left "c" shape of the x but turned it into a 3 halfway, starting the Parker streak onward. EDIT: Actually, nevermind, he clearly makes a deliberate "3" movement with his hand, it just came out weird, even though the other 3 looks much worse in my opinion, as for his x's, it looks more like "doc" to me than dx.

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].

@aceman0000099

10 ай бұрын

Ahhh... this noise, it's music to my audio-recognition algorithms

@gcewing

10 ай бұрын

At least he didn't get a copyright strike!

@Xatzimi

10 ай бұрын

​@@gcewingI'm pretty sure Harley once attempted to copyright their distinctive engine sound... So that isn't too far off

@henrikoldcorn

10 ай бұрын

I spent a while wondering what “subtle writing software” was, before rereading more closely.

@tuxino

10 ай бұрын

@@henrikoldcorn There was a subtle difference that you missed, I guess? 😎

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)

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.

One minute in and I'm already learning something! I always thought GAS means "Genuinely approachable Sudoku"! Thank you Matt!

@rzezzy1

11 ай бұрын

After learning that the 5th derivative of position was "Crackle," did you think the next one was "The Cryptic?"

@GoldAmal

11 ай бұрын

Man of culture, I see

@user-cq4nq8dd3e

11 ай бұрын

I thought GAS means gas

@schizophrenicenthusiast

11 ай бұрын

Small world we live in. Hope they'll title the next one "Greater Automobile Speed"

@PiersCawley

11 ай бұрын

Same 😂

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.

@AttilaAsztalos

11 ай бұрын

This is how I like to think of it, referencing everything to how "pushed back into your seat" you feel: as we know, there is no sensation associated with constant speed - if the road wasn't bumpy, you couldn't tell that you're moving at constant speed and zero acceleration. There is no jerk or snap, there is no feeling of being pushed back. If your speed starts changing at a non-zero acceleration, you feel pushed back into your seat a fixed amount, depending on how high your acceleration is - but as long as it's constant, there's no jerk or snap and no change in feeling. If you experience non-zero constant jerk that means your acceleration is now increasing too, and you feel gradually pushed into your seat harder and harder - but as long as there's no snap, the process is gradual at a fixed rate. Finally, if you have non-zero constant snap, that means your jerk is now steadily increasing too and your acceleration is started increasing more and more sharply - you're getting pushed into the seat harder and harder at an accelerating rate... The thing to understand is that none of this necessarily involves what we think of as "being jerked around" in a daily sense - for instance, hitting a brick wall and stopping instantly (in an idealized scenario) involves all of the above in a negative direction, yet none of them "constant" but an abrupt spike...

@syriuszb8611

11 ай бұрын

When I was often in car for work, I started thinking about that when the driver stops lifts his foot from the gas pedal, you get thrown to front a little. When I was thinking about it, my first thought, and people with whom I discussed it, seemed to think that it was deceleration of a car. But it didn't make sense to me, since it is very noticeable for a short amount of time, no matter the speed. So I came up with the idea that the reason for that is probably elastic reaction of the seat foam (and probably reaction from your body and other elements). The foam is compressed during acceleration, and when acceleration stops, it releases this energy like a spring, throwing you in the opposite direction. That's why jerk is so noticeable in cars, you basically lay on a spring that is ready to push you when it has opportunity. Harder, stiffer backrest should decrease the jerk feeling.

@seedmole

11 ай бұрын

Check out the video on Spline Continuity floating around out there, it gets into some neat applications of higher order derivatives like these, but in the context of smoothness of surfaces. The higher orders come into factor when considering things like how light would reflect off a given surface -- engineers of smooth shiny real world objects (like car door handles for example) have to conform to these factors to keep reflections from looking wrong.

In this video, Matt discovers integrator drift and the noise emphasizing properties of differencing.

@RubenMoor

9 ай бұрын

Weird that he doesn't point it out himself. I suppose there are ways to get meaningful values for the higher order derivatives after acceleration... ideally that would be by measurement, though.

Oh, snap! Edit: It has occurred to me, as a result of watching this video, that English lacks a useful word for the _scalar_ of acceleration. We have displacement vs distance, and velocity vs speed, but when we reach acceleration...nothing. I hereby nominate "haste" as the term for the magnitude of acceleration. Haste cannot be negative--haste means you are changing speed somehow. It's a clean, convenient, existing English word with more or less the right meaning (it implies specifically _positive_ acceleration, but I'm okay with that small wrinkle). Jerk, snap, crackle, and pop can all just stay as they are, since those magnitudes are much less relevant than distance, speed, and haste.

@leonsteed606

9 ай бұрын

Acceleration is the rate of change of velocity and the magnitude of that acceleration is not the same as the rate of change of speed. I.e. The magnitude of the rate of change of velocity is not necessarily the same as the rate of change of the magnitude of velocity. For example, an object moving in a circle at constant speed has an acceleration directed towards the centre - the magnitude of that acceleration is constant and non-zero, yet the speed is not changing, so the rate of change of speed *is* zero. As you say "haste means you are changing speed somehow", I think you mean to define haste as rate of change of speed. If this is the case, your haste would be negative when you are reducing your speed. This being so, I think a better word for it might be "quickening"?

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.

@slkjvlkfsvnlsdfhgdght5447

11 ай бұрын

i like to think of it as the "amount of openness" in a gate for example

@yeepyorp

10 ай бұрын

then there's absity, abseleration, abserk there is some use for them in fluid flow too

@3Ppaatt

10 ай бұрын

Very interesting!

@aceman0000099

10 ай бұрын

You could also use it as a metric for "likelihood your relationship will break up"... If you spend 3 years away from your partner, but only 1200m away, you're as likely to break up as spending 10 days on a trip 130km away. Or maybe your partner went to serve in the army 600km away for a year, which would make you 166 times more likely to break up! Try not to get caught cheating...

@abserk

10 ай бұрын

As a crude example, absement may be used, very approximately, to model the cost of a long-distance phone call as the product of distance and time. A short-duration call over a long distance might, for example, represent the same quantity of absement (and hence the cost) as a long-duration call over a shorter distance.

circuit distance is also calculated at the mid-point of the track the racing line will be different, probably shorter, so your measurement is even more accurate

@DJejbarros

11 ай бұрын

Also, he may have started or ended from the box

@AshleyFrankland

11 ай бұрын

I can't speak for Moto GP but I know in F1 the Racing line optimises for speed carried through a corner, not distance travelled, so the racing line may not be that far off the mid-point distance in length, and could actually be longer.

@custard131

11 ай бұрын

@@AshleyFrankland for some sections of the track the racing line might be a little longer than the official distance but i would expect over an entire track the racing line to be somewhere between the center line and the shortest route for a single corner the racing line would be wide on entry, hit the apex, wide on exit which is further than the shortest path and i expect likely pretty close to the center line distance depending on the exact corner (i think a hairpin would be a bigger difference to the center line than a shallow kink) when there is a series of closely linked corners / a chicane the racing line and the shortest line are going to be pretty close i cant really think of any situations where the racing line is going to be noticeably longer than the center line just for the benefit of being able to carry more speed through the corner, the only ones i can think of really its to avoid bumps on street circuits, like the "straight" between Casino and Mirabeau in monaco that has a virtual chicane 1/2 way along it which afaik is just to avoid a bump on the left side of the track

@cfgp

11 ай бұрын

@@custard131 yeah, that's why i said probably shorter there might be some instances where it is faster to go the long way, but usually the faster path with be shorter

@petehiggins33

11 ай бұрын

@@custard131 I would have thought that the racing line is sure to be longer than the centre line distance because it effectively zig-zags along the track. At each corner It swings from the outside edge on entry to the inside edge at the apex and then back to the outside edge. Also, if the next corner is in the opposite direction then it needs to cross the centre line again before entry.

You should take a look into Kalman filters. That is one main way that GPS measurements are merged with accelerometer data to combine the accuracy of the GPS with the precision of the accelerometers.

@jasonosmond6896

11 ай бұрын

The history of inertial navigation systems would be a highly relevant and interesting followon topic.

@digitig

11 ай бұрын

@@jasonosmond6896Of course, GPS is not inertial, though Kalman filters are used in both and their interaction is interesting because they complement each other well - inertial is very accurate short-term, but tends to drift, whereas GPS is not so accurate short-term but doesn't drift. Feed *both* into a suitably weighted Kalman filter and you can get the best of both worlds.

@insouciantFox

11 ай бұрын

The missile knows where it is...

@blackbriarmead1966

11 ай бұрын

​@@insouciantFoxbecause it knows where it isn't, (but also where the nearest oil field is down to the mm)

@ps.2

11 ай бұрын

I think his main problem was, as he points out, the accelerometers were attached to a piston engine that produces vibrations at variable Hz. Worse, the engine cycles within the same order of magnitude as the accelerometer sampling frequency (100 Hz, equivalent to 6000 RPM). So it's an interesting idea, but doesn't solve the problem of noise in the accelerometer readings. More sensors! You could try noise cancellation between the accelerometers and recorded audio. I doubt that would work, though. But what you do get with recorded audio is a pretty good cross-check of velocity, if you know the gear ratios.

This is why you have to bandwidth-limit derivative data in many control theory applications, taking the derivative increases noise markedly unless you've got a high quality sensor with very low noise to start with. And if you think about it a lot of the actual jerk and snap will be vibration to start with.

There's a suspicious, fairly consistent interval between all the peaks in the snap plot. They're even too regular for gear changes. It's probably some slight periodic discontinuity that's been introduced in the data at some point. Possibly even be an inherent limitation of the accelerometer, where it periodically does some extra processing, or some kind of correction. Would be interesting to do the same data processing in some other scenarios, including being stationary.

@johnharrisson5207

10 ай бұрын

I noticed that too. Periodicity seems to be about every 3 seconds. It could be from the measurement device, or the post processing?

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

@olivier2553

11 ай бұрын

I had a teacher who was ambidextrous and could write with both hands, but at any given time, he was writing with only one hand! Very surprising to see him standing at the middle of the blackboard (yes, that's a long time ago) and start writing and continue writing on the full width without moving. I felt something was odd and it took me a few minutes to understand.

We're going to need a video calculating the derivative of the rate of change of Matt's d's into a's on the whiteboard

@AthAthanasius

11 ай бұрын

And some "x"s into nothings.

@PiersCawley

11 ай бұрын

The Parker D-celeration?

@Games_and_Music

11 ай бұрын

@@AthAthanasius dx turning into 'doc', and the "s" turning into 8's, and the t's turning into + .

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

What an amazing experience it must have been for you to get to go on that ride. I was really surprised to see that it was a real racing bike. I was really really surprised to see that you actually rode on my cousin Nicky's bike. Nicky Hayden aka the Kentucky Kid was MotoGP champion in 2006. We tragically lost him in an accident (not related to racing) in 2017.

As humans, we are more sensitive to jerk than to acceleration. When you are in an elevator and feel it jerk, it is the jerk, not the acceleration, that you are noticing.

@pneumaniac14

11 ай бұрын

humans don't feel acceleration or force at all, instead what we feel is the derivative of force across distance. Treating gravity as a force, because its close enough, you feel weightless, that because the force is generally uniform across the body. The reason you can notice an elevator accelerating, is because we have inertia and so our feet feel a compression.

@qwqeqrqtqz

11 ай бұрын

@pneumaniac14 This is really interesting, however the feeling of weightless in orbit alone might not be enough to demonstrate the idea. Let's assume there was some way to feel force directly. In low earth orbit (assuming your body is pointing in the same direction the whole time) this would be a 360° rotation of the force direction over about two hours which would be really hard to notice. You could however spin your body around the head-feet axis at 90° to the down direction. You would feel the centrifugal force, but that would be constant over time. The direction of earth's gravitational pull would change by 360° relative to your body for each revolution around your axis. If force could be felt directly you should be able to tell the direction of earth. For an example with no extra forces felt I think you would need to be in a pretty tight orbit around a neutron star.

@fghsgh

11 ай бұрын

Oh, this matches how I drive. I always try to minimise jerk when e.g. braking. Relatives complain that it looks like I am going to hit the car in front of me because I'm not braking fast enough, but they also compliment me on driving really smoothly.

@andrewsnow7386

11 ай бұрын

@@pneumaniac14 I would have do disagree with the statement that we don't feel acceleration at all. We are actually very good at defecting the direction of an acceleration, but we are less sensitive to its magnitude. Sensing the direction of an acceleration is why we can tell which way is "up" fairly accurately. It's also why full-motion flight simulators feel so realistic for airliner pilot training -- we sense the direction of the acceleration (as well as the jerk), but aren't sensitive to the accelerations being off by 10% or 20% from what they would be on a real airplane.

@pneumaniac14

11 ай бұрын

@andrewsnow7386 we can only tell which way is up because of the normal force of the ground. We also aren't accelerating when we're on the ground. Contact forces provide a difference in force across the body, so thats why we can feel contact forces, and hence we can feel gravity when standing, an elevator that accelerates, a plane that has turbulence. But strictly speaking it isn't the force that we feel, but the variability in force. Assuming you are standing, and the force is being applied to your feet, then every bone bar the arms accelerates almost as a rigid structure, blood lags behind so you can feel that, your flesh and arms also lag behind. What I'm getting at, is if you applied an acceleration, or a jerk, or any derivative of force for that matter, to every atom in the human body uniformly, so long as there is no reference point, ie the ground, or the air, you would never feel a thing.

This is similar to how it was explained to me 20 years ago. Speed, acceleration, jerk, etc. are the easiest conceptual representation of calculus - in both directions.

You could say that acceleration is the rotational position of the driver's wrist (or foot on the break), jerk is the rotational speed, and snap is the acceleration of that speed. This makes it easier to imagine it, one derivation up, I think. So I think the snap basically corresponds to a very quick acceleration/breaking done by an imperfect human being that is trying but is not able to immediately accelerate the rotation of their wrist/foot. So I believe your snap is believable as a graph of trying harder.

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!

Numerical second derivatives are extremely sensitive to noise. Before and between derivations you should smooth the data just to get meaningful results. You should be able to do that as you have 100 samples per second and the changes on the bike are slower than that.

@jupa7166

11 ай бұрын

YES!

@konstaConstant

11 ай бұрын

Yeah, this! I think a 0,1s resolution would be interesting enough, because a moment of experience can't be much shorter than that. We'd get plenty precise data even with 10x smoothing.

@DudeWhoSaysDeez

11 ай бұрын

I'm surprised he didn't smooth the initial data. He could have worked with a nice curve the whole time.

What you describe with the different pros and cons of accelerometers and GPS is precisely the reason Kalman filters are used. You could run your data through that for the best of both worlds.

@AlanTheBeast100

11 ай бұрын

A Kalman filter needs to know a lot of characteristics (statistics) about the sensors in use. On that note, getting a GPS that runs 25 Hz or so would be a fine start. Airline INS' accelerometers are integrated at well over 2000 Hz. For this sort of thing, you also want the accelerometers and gyros "strapped down" pretty tight.

Oh snap! I can't believe that my favorite math educator has decided to experience my favorite hobby. This is the best day of my life.

" ..Jerk, snap, crackle, pop" - never to be forgotten. Thanks.

Jerk is rate of change of acceleration, so I'd guess that the moment you were at minimum Jerk was when the bike went from accelerating as hard as possible, to breaking as hard as possible. The acceleration would have gone from a big positive to a big negative in a short amount of time. The other largest Jerk moments would be similarly placed at the boundary of braking and acceleration zones. EDIT: As to the question of whether you experienced Snap, you definitely did. The issue is whether it is recorded accurately, but you definitely changed the rate at which you were changing the rate at which you were changing the rate at which you were changing position. I'd say it's damn near impossible to be a human and NOT do that.

@Dansl05

11 ай бұрын

One other consideration is gear changing. When you shift up under acceleration the acceleration momentarily stops before returning when the engine is reengaged. I suspect this would also produce noticable jerk and even snap

@FirstNameLastName-mw1pj

11 ай бұрын

What you said for snap can also be applied to infinitely higher derivatives of speed as well. They just get a lot harder to accurately record.

@beepbop6697

11 ай бұрын

Don't discount the sharp left/right accelerations through the slaloms -- though forward speed can remain near constant.

@SpeedcoreDancecore

11 ай бұрын

In free fall (neglecting air) you have no jerk or snap or crackle or pop

@robinw77

11 ай бұрын

@@SpeedcoreDancecore nice observation. Although I guess at the start of your fall from the high building, you go from 0 acceleration to 9.81 so at that point it must have some rate of change. So I guess the only potential jerk etc comes from whether you calmly side-step off the building, or launch yourself from a springy diving board? (Again like you said, this is all happening with no air).

The large values of snap look like they're occurring regularly, so it's possible that this is an artefact introduced by whatever filter Dom used, and/or some low-frequency artefact from the accelerometer itself. Otherwise, I think you're right that this signal is just noise

i just want to mention that numerical derivative is extremely sensitive to noise, the high derivative you go the less reliable it is. coming from a control background

I love how effectively titled/thumbnailed this is; I didn't believe you when you said there was nothing exciting, so you thus perfectly matched my expectations. I love the honesty, ie. lack of clickbait.

Oh snap! I really like how with each derivative you can see it hone in on and highlight the "most notable" sections. When it got to Snap basically the only things on the graph were a few lines relating to the greatest change of pretty much everything.

You know you are becoming a mathematician (studying at uni) when this video made you well excited and happy

I need an episode about Euler's brick. I am not expecting success in the matter, but it would bring about the same level of entertainment/joy as the annual PI-episodes.

4:44 Hannah Fry spotted

My country's economy (Argentina) must be the only one in the world where the inflation rate has Jerk

I love a nice, quiet explanation in a room with a whiteboard. No need for an "oh snap" moment!

Just to add a note, a negative jerk does not imply you are slowing down. In fact it doesn't tell you anything about whether your speed is increasing, decreasing or staying the same. It just means your acceleration is decreasing, whether it is positive, negative or zero.

Was hoping to see the crackle and pop plots, even if they would have just been noise.

@karolakkolo123

11 ай бұрын

They would have even more spikes than snap, but that could just be due to noise because every small rapid change in dataset amounts to an extremely high slope/derivative

@ThomasWinget

11 ай бұрын

To be fair, snap, crackle, and pop are *all* just noise(s).

Latitude and longitude are not what you should be using if you want your plot to have the correct shape. You should convert them to cartesian coordinates, and then rotate the points so their center lands on on the z axis. Then you can scatter plot the x/y components, and it should be much closer to the actual shape of the circuit...

@stargazer7644

11 ай бұрын

Other than a slight aspect ratio difference between lat and long (which he corrected for by stretching the image), none of that will make any difference over a couple of kilometers. He would have been far better off to have logged the output of a proper GPS receiver instead of the pseudo GPS that a phone gives you.

@stephaneduhamel7706

11 ай бұрын

@@stargazer7644 the aspect ratio difference is not slight. And using cartesian coordinates would also allow him to use actual units of length, which could be derived over time to get speed, acceleration, and so on.

@stargazer7644

11 ай бұрын

@@stephaneduhamel7706 The aspect ratio at his lat/lon is all of 1.62:1 and once again, he easily corrected for that. If it really bothers you, you can simply scale the lat or lon axis for it in an area this small. What difference does it make? You don't need Cartesian coordinates to calculate distances, as I didn't in calculating that aspect ratio. He didn't use the GPS coordinate data for speed or acceleration and he explained why. It is too low in temporal resolution, and as I mentioned and he showed, phones don't generate very good GPS data to start with.

@stephaneduhamel7706

11 ай бұрын

@@stargazer7644 I don't understand why you are against the idea of plotting GPS coordinates the correct way. Calculating the local aspect ratio is a nice approximation for smaller scale objects, but doing the reprojection properly isn't that hard and doesn't deform the shapes no matter the GPS coordinates.

@stargazer7644

11 ай бұрын

@@stephaneduhamel7706 My objection is precisely because of your insistence that it is the "correct" way. You keep going on about distortion but you don't seem to realize any projection of spherical coordinates onto a flat surface will ALWAYS result in distortion of one type or another. Again not that it would matter the slightest in an area this small, but you don't seem to realize that either.

The most obvious moment you can feel jerk is when a vehicle stops. It was decelerating, so you felt like there was a force pushing you forward, so you adapted by resisting that force. But when the speed reaches 0, it suddenly stops decelerating, so you're thrown back into your seat because of your own force. In that situation, you have an instant change of acceleration, so you have infinite jerk. And infinite snap.

@mojeimja

10 ай бұрын

its not infinite, nothing in real world is (except for people stupidity). the car isnt rigid, you have suspension with springs, shocks, you have a soft seat - everything works to compensate sudden accels and jerks.

@lucasbrelivet5238

10 ай бұрын

@mojeimja OK, the jerk might not be infinite, but it's really big, at least for the wheels, though for the passengers, it is dampened by everything between the wheels and them. And the snap might not be infinite, but it's even bigger. And the more you derive, the bigger it can get, because the more you derive, the less physical sense it has. And the less physical sense it has, the less it is constrained by physical laws such as "nothing is infinite"

@mojeimja

10 ай бұрын

@@lucasbrelivet5238 its big but it is very short. and the more you derive, the shorter it gets, so it can be felt less and less

@ZandarKoad

9 ай бұрын

But there is no end to the derivatives. To affect even the slightest change in position requires an infinite derivative derivative derivative chain... My mind bleeds thinking about this stuff.

@mojeimja

8 ай бұрын

@@lucasbrelivet5238 yes

The huge jerk comes from tracing a rough, relatively small circle to another one but in the other direction in a really short time! Acceleration is going from very big and roughly constant to your right to very big and roughly constant to your left, so of course that means you experience a huge jerk, very localized in time (ideally, Dirac delta-like), and its subsequent derivatives only get larger and larger, but more and more localized in time. So I don't think it's data noise/error. It is simply huge because it lasts very shortly but its high order integral must be finite to ensure the change in acceleration!

@mynameisben123

10 ай бұрын

But I thought that Dom normalised the data in the direction of travel?

Fingers crossed for rice krispies memes🤞 Edit: rice krispy memes are satisfactory

15:40 I'd have thought that this might be due to misalignment of the accelerometer and the gyroscope. If you can't precisely eliminate the gravitational component, you'll naturally have a linear increase of the velocity over time. 🤔

@iskierka8399

11 ай бұрын

This would be the case, so most likely the conversion was simply calibrated wrong the whole time. You should be able to identify the gravitational axis by using gyro to convert the accelerations all into one (arbitrary) uniform axis set, and then integrating that from start to finish, with the end point being the direction of gravity (and its magnitude multiplied by time). With that calibrated and subtracted out you would then have in the integration a plot of your horizontal velocity over time, and with some simple knowledge of the track you could use that to determine a "forward" orientation for the phone over time also.

@jonasdaverio9369

11 ай бұрын

Cheap accelerometers typically have drift, even if you calibrate them. They simply are bad for measuring absolute position and velocity.

@stiansoiland-reyes2548

11 ай бұрын

Likewise by forcing the acceleration etc to be 1-dimensional along the track, large lateral changes in the turns will add more noise in normalising for bike frame of reference - do you subtract vectors from before or after the time spot? This mini-integration will accumulate more error the higher the snap.

@stargazer7644

11 ай бұрын

All accelerometers drift. The more money you pay for them, the less they drift, but they all drift over time. And you didn't pay much for the ones in your cell phone .

Thank you Matt. Disappointingly interesting.

Can't help but admire the Parker penchant for pushing mathematical ideas beyond their real-world ability to be meaningful. In this one, we see the perils of over-differentiating a dataset with a coarse time increment. 4th (time) derivative of position? My immediate thought was, "Here comes some random noise!" This is just the sort of thing I've come to love about this channel! A random observation, at around 7min: The "aspect ratio" mismatch between the curve from the map and your plotted GPS positions, looks like it resulted from not correcting your longitude-line spacings by the factor cos(latitude). Fred

@stargazer7644

11 ай бұрын

Well actually he took the first (jerk) and second (snap) derivative of acceleration from an accelerometer.

@ffggddss

10 ай бұрын

@@stargazer7644 Yes, I'm sure he foresaw what would happen if he took 3 or 4 derivatives of velocity or position data. Still, accelerometers are subject to drift, and . . . but the "Parkerness" of this quest is in the sort of extreme that going after 4th derivatives entails. Love it!

Love the slow dishevelled walk after you get off the MotoGP pillion ride

@cosmicshambles

11 ай бұрын

You should've seen him for the next hour or so! Some of it is in the documentary.

The big indication for me that there was an issue with the snap data was the even spacing. Something with the filtering caused an artifact every 3 seconds.

@tunefix

11 ай бұрын

I think that might be the gear-changes.

@edwardbarton1680

11 ай бұрын

@@tunefix Gear changes wouldn't be that consistent

Loved this video, I didn't know that you could actually make sense of all these derivatives

absolutely brilliant

17:20 On the original speed plot, the central peak seems to have been clipped to 50 m/s by the same gps error you observed in the position plot. Since the integrated acceleration plot shows higher speeds through that portion, it suggests the first speed plot would underestimate your total distance. We can't know how much of the discrepancy that error accounts for, but it would move your estimate toward the actual circuit length.

I think a third data set is required to rule on snap v.s. jerk. Perhaps the audio track allows recovery of engine RPM, assuming the max jerk and snap aren't taking place during clutch use where engine RPM does not match with RPM of the rear wheel?

What a video. Niche physics units that I've been fascinated by for years, motorcycles, and a reverse psychology click-bait title. Bravo Matt and a big GG

Distance, speed, acceleration, jerk, snap, crackle, pop... That sounds fun.

Came here for snap, crackle, and pop and was not disappointed.

I remember an old Open University video on this topic. They were taking the data from a roller coaster ride and they called the time derivate of jerk jolt, rather than snap. Memory tells me that the conclusion was that jolt (or snap) was an essential part of the roller coaster experience.

@jaapsch2

11 ай бұрын

Yes, a constant acceleration is not very exciting as you experience it as a constant force that you can brace against. The jerk/jolt is what throws you around, where the force changes direction and you have to change which muscles to use to counteract this.

@Nerdule

11 ай бұрын

"Jounce" is also sometimes used, as another name for snap/jolt: in which case, instead of snap, crackle, and pop, they're instead known as jounce, flounce, and pounce. (The names aren't terribly standardized because it comes up so rarely in practical use; snap/jounce does actually come up when designing roller coasters and railways, but as far as I'm aware, crackle/flounce and pop/pounce pretty much never show up at all, which is why they're allowed to have silly names.)

@guest_informant

11 ай бұрын

I commented something similar above. Zach Starr (I think) made a video about Jerk, Snap, Crackle, and Pop, and in the comments a rollercoaster engineer said he commonly used Snap in his work.

@robertpearce802

11 ай бұрын

@@Nerdule You have got me thinking that I have may have mis-remembered and that "jounce" was the term used in the old OU video.

Awesome video Matt! The thing is, that while most everyone would assume racing would give the most jerk and snap, the fastest racer is probably the one who minimizes those quantities. Smooth is fast is an old racing adage, and after all, smooth and jerk are inversely proportional!

This is the awesomest video yet. I use data from my Gopro's GPS, accel and gyro all the time to try and learn where i could be improving in my track riding. I had never thought about derivating the accelerometer data to find additional inputs. Now i wonder if this can help me understand things like smoothness of throttle application!

Sizes of bikes apparently changed drastically between 2007 and 2012.

@cosmicshambles

11 ай бұрын

07-11 the bikes were 800cc, went up to 1000cc in 2012 onwards.

@vigilantcosmicpenguin8721

11 ай бұрын

Actually, Matt is a giant, and that bike was made specifically for him.

I think for the calculation of the jerk and snap you experienced, it might be better to calculate based on the general magnitude of acceleration, not just the component along the bike axis. That corner is a really snappy corner, and this might be clearer when considering the speed rather than velocity as a starting point (or, the scalar rather than vector acceleration)

As a massive maths, physics and motorsport fan, I really loved this video. I'm sure I wasn't the only person watching to be naming all of the corners of the Silverstone circuit while watching the footage - that corner with the 'oh snap' moment is called The Loop by the way. There is such a lot of maths and physics involved in motorsport, which is one of the reasons why I love it (though I prefer 4 wheels to 2).

Oh snap, that was a very interesting watch!

I saw this and I trust Matt is such an honest person my gut instinct was “Oh ok I guess this one isn’t that interesting, maybe I should skip it.”

Derivatives amplify noise creating all the spikes, so you should use something like cubic spline interpolation on the acceleration graph before computing jerk and snap.

@jupa7166

11 ай бұрын

YES, this ^^^

@MarcusCactus

11 ай бұрын

Nope! The derivative would essentially record this 3d degree curves.

@DudeWhoSaysDeez

11 ай бұрын

He could've smoothed the data initially. That would have helped.

Great concept for a video.

Oh snap! I sat on this for 3 weeks. I would have watched it sooner had I known it was a good one!

I really thought the catch was that the room was sideways when i saw the permanent markers trying to roll to the right and how careful Matt was to put the caps back on. I thought the (presumably) calculator was glued-down to hold them in-place. 😂

This video has been up for 20 minutes and nobody has commented on what number bike it was? for shame, KZread. Oh yeah, nice video Matt.

@mrosskne

11 ай бұрын

why would anyone comment on that?

@theloganator13

11 ай бұрын

@@mrosskne it was number 69, a very famous and important number in the math community.

@cosmicshambles

11 ай бұрын

Fun Fact: The bike in the picture is of the late Nicky Hayden who ran with #69 so his bike read the same even if it was upside down after a crash.

@theloganator13

11 ай бұрын

@@cosmicshambles That's clever I suppose. I hadn't heard of him before this. Imagine driving motorbikes for a living and dying in a bicycle accident. 😣

This really made me mis Nicky Hayden a true legend. Super nice you got to ride his bike, very jealous.

I love all the little motorcycle references in the set.

Missed a couple of x's at the 3rd and 4th derivatives on the white board...

This unexciting video is still better then most of live TV.

the data collection was awesome

"That's how you define things in physics, you take a vote." *Pluto demoters looking around nervously*

Prime entertainment, now only available in non-multiples

My physics lecturer liked this example of jerk: when you brake in a car, the lurching effect you feel when you stop is the jerk. This is because when your velocity hits 0, your acceleration isn't yet at 0, causing you to begin moving backwards. During this time period after you begin to move is when you experience jerk, as the car begins to accelerate forward

@svhb1000

11 ай бұрын

Indeed. But the car itself is not really moving backwards (the brakes prevent this). It's just because you are rather loose sitting in the car.

@Teslaling101

11 ай бұрын

​@@svhb1000 Related, the car is somewhat loosely positioned as well due to the suspension. The differential loading of the front and rear suspension can cause a brief acceleration of the car body backwards, relative to the locked wheels. When I was a teen driving a manual car (and you know, being a teen), I got pretty good at releasing the brake just as the car came to a stop such that it would roll backwards a foot or two!

This is such a derivative video. Love it!

Oh snap! I wasn't expecting Matt to do something as crazy as data collection.

I'd be curious to take this the other way, try to have skme kind of calibrated track/apparatus that could move at sustained velocity, acceleration, jerk, and so forth (though a constant pop would presumably run out of track _very_ quickly).

@blumoogle2901

11 ай бұрын

I think that constant pop would just be a very high vibration. You shouldn't run out of track if the movement is back and forth, as in acceleration changing direction very rapidly around 0, oscillating + to - and back.

I'm curious as to how exactly you're doing numerical differentiation, for instance if the time in between data points is Δt, and you use 3 data points for the derivative of the middle point (central difference scheme), then the error on the first derivative is on the order of Δt³, and the error of the second derivative is on the order Δt².

I thought for a moment i had been duped by the promise of a video about derivatives, but, when it was disrupted by something duller, i was reassured.

That snap graph was exactly what I was expecting

Great video, I would've loved a deep dive into the math of how to convert the gyroscopic data of accelerations in three directions to the one-dimensional acceleration while accounting for gravity.

When you apply a compressive force to a mass to get an acceleration we call it push. If you apply a tensile force it’s called a pull. But if you increase the compressive force to get a jerk we call that a yeet, and if we do it with a tensile force we get a yoink. Thank you for coming to my TED talk.

Maths is exciting enough without tarting it up

@qfz2112

11 ай бұрын

Yeah, right? What a jerk

@SupercriticalSnake

11 ай бұрын

Tell me you're a pure mathematician without telling me you're a pure mathematician.

@cosmicshambles

11 ай бұрын

MotoGP is exciting enough without tarting it up with maths you mean ;)

@Andrew_Fernie

11 ай бұрын

@@cosmicshambles I was going to say that

Sick video!

This is one of those videos where the math is so exciting I just can't help but yell "oh snap" when this charts pop on screen

Is there a mathematical way to determine how many data points per second you need in order to reliably calculate the n-th derivative?

@alimanski7941

11 ай бұрын

You could model the noise statistically, and then solve for n such that the difference between the true derivative and the approximation is smaller than some epsilon in probability. No reason that the approximated derivative can’t be treated as any other estimator.

Oh snap! It is disappointing that Matt switched from a spreadsheet to Google to do the units conversion. I mean, I'd do it but I expected more from a more experienced spreadsheet user such as Matt! 😂

When I was often in car for work, I started thinking about that when the driver stops lifts his foot from the gas pedal, you get thrown to front a little. When I was thinking about it, my first thought, and people with whom I discussed it, seemed to think that it was deceleration of a car. But it didn't make sense to me, since it is very noticeable for a short amount of time, no matter the speed. So I came up with the idea that the reason for that is probably elastic reaction of the seat foam (and probably reaction from your body and other elements). The foam is compressed during acceleration, and when acceleration stops, it releases this energy like a spring, throwing you in the opposite direction. That's why jerk is so noticeable in cars, you basically lay on a spring that is ready to push you when it has opportunity. Harder, stiffer backrest should decrease the jerk feeling.

@jonathanjohnson2427

10 ай бұрын

I’m not so sure of that. We are very sensitive to jerk. In fact at constant velocity we don’t really experience any difference as a sensation. At constant acceleration the only feeling is a constant unchanging slight push into your seat. Almost imperceptible. (Basically higher gravity but not changing - that is can you tell if you weigh 2% more?). Jerk is totally different your gravity changes back and forth you weigh less then in an instant you weigh more. ….

@syriuszb8611

10 ай бұрын

@@jonathanjohnson2427 Well, when the car stops accelerating you not only feel it, but you are physically thrown forward (in relation to the car), and sometimes you can see it on inanimate objects resting on seat backrest too. I think it may be the other way- we feel the jerk so much, because it changes the "resting state of our bodies". Meaning, during acceleration your body accommodates to it, and after jerk happens, it needs to adapt it. Imagine your head, not resting on the headrest in car during acceleration- your muscles need to keep head in place, but when jerk happens, the muscles need rebalance forces or your head will start moving.

The most special part of this whole vid is that he got to ride on Nicky Hayden's bike. What a special honor. R.I.P. Kentucky Kid. We miss you.