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Ask HN: Higher order derivatives in everyday life?

• rawgabbit 4y ago
  Agile Development 1. Story points 2. Velocity = user story points completed per iteration 3. Burn out = number of sick days per iteration due to unreasonable estimates 4. New hires = number of new developers you have to hire because the old ones quit
  • wiz21c 4y ago
    Although a fairly good approximation of that analytical version is a dice roll :-)
  • latchkey 4y ago
    At Pivotal, developers always gave the estimates (fib: 1,2,3,5,8 was most commonly used). If the story was > 3 points, it was broken into smaller stories. Thus, you were never working on stories that were more than 0-3 points and by then, most of the stories were pretty clearly defined, easily estimated units of work.
• laylower 4y ago
• AlDante2 4y ago
  Interest is not a derivative of a debt instrument such as an obligation. The most common example quoted is slowing the rise of the rate of increase in inflation. Inflation is change in price, i.e. first derivative.
  • soonerroadie 4y ago
    Similarly, finance people don’t consider interest rates/yields to be derivatives. So, on a bond “duration” is the first derivative of price with respect to yield, and “convexity” is the second derivative.
• jjgreen 4y ago
  They're rather important in roller-coaster rides, see for example https://iopscience.iop.org/article/10.1088/0143-0807/37/6/065008/pdf https://iopscience.iop.org/article/10.1088/0143-0807/37/6/06...
• mac3n 4y ago
  "sudden" acceleration 0: position 1: velocity 2: acceleration 3: jerk
  • skyyler 4y ago
    4, 5, and 6 also exist (but to my understanding aren't really used): https://en.wikipedia.org/wiki/Fourth,_fifth,_and_sixth_derivatives_of_position https://en.wikipedia.org/wiki/Fourth,_fifth,_and_sixth_deriv...
    • bigdict 4y ago
      Infinitely many exist if the function is infinitely differentiable (aka smooth).
    • Thrymr 4y ago
      They mostly exist so they can be called "snap", "crackle", and "pop". https://web.archive.org/web/20180626030437/https://info.aiaa.org/Regions/Western/Orange_County/Newsletters/Presentations%20Posted%20by%20Enrique%20P.%20Castro/AIAAOC_SnapCracklePop_docx.pdf https://web.archive.org/web/20180626030437/https://info.aiaa...
    • gojomo 4y ago
      I believe 4th (& possibly higher) is relevant in aeronautics/astronautics and robotics.
    • 532nm 4y ago
      The 4th derivative is quite important for good motion control where it is usually called 'snap'. Specifically, it is relevant both for feedforward control design [1] and trajectory planning [2]. As shown in the latter, it is advantageous to design trajectories based on segments of constant snap. Consequently, also including 'snap' in the feedforward signals makes the achieved position profiles notably smoother. [1] "Control for precision mechatronics" https://doi.org/10.1007/978-3-030-44184-5_100044 https://doi.org/10.1007/978-3-030-44184-5_100044 [2] "Trajectory planning and feedforward design for electromechanical motion systems" https://doi.org/10.1016/j.conengprac.2004.02.010 https://doi.org/10.1016/j.conengprac.2004.02.010
• mdcds 4y ago
  options trading when you calculate risk/exposure of your position, you want to consider Delta and its derivative, Gamma. But you also need to consider the rate of change of Gamma.
  • drexlspivey 4y ago
    More specifically, if you are a market maker and are in the business of selling options you want to hedge your portfolio. To do that you need to buy a certain amount of shares of the underlying that you sold calls on. As the price of the stock goes up you need to buy more stock (delta) but also the rate at which you need to keep buying stock increases (gamma). The fact that you keep buying stock as the price goes up further pushes the price up and can shoot the price to the moon (gamma squeeze)
• AnimalMuppet 4y ago
  Health. We care about our actual level of health, of course, and we care about the first derivative. But as I get older, I'm starting to keep an eye on the second derivative...
  • e9 4y ago
    For a second I thought you are referring to kids(first derivative) and grand kids(second derivative) haha
• deleted 4y ago
  [deleted]
• andy81 4y ago
  Card games. e.g. MtG or LoR. You've got to deal X damage to win. You could directly cast spells at an opponent each turn. Or instead you can play units or destroy enemy units to affect the amount of damage being done each turn. Certain cards even increase the amount you can increase your damage each turn, e.g. by reducing costs, drawing cards on future turns, or improving deck contents.
  • thom 4y ago
    This is an interesting one. Obviously the fundamental theory of MtG is that cards have value roughly proportional to their mana cost, and the player that deploys more value overall will usually win. It’s a valid strategy to attack your opponent’s ability to deploy value (hand/land disruption, cheap permission/removal etc) but it’s often missed that aggro decks are in a sense using temporal denial. If you don’t get your fifth turn, all the card draw and mana in the world doesn’t matter, in the same way a 10 year bond isn’t useful to you if you have no money to eat today. So MtG offers valid strategies that match all sorts of different second and third order curves. Aggro cares about immediate liquid assets above all. Control cares about compound interest. Mid range balances the two.
• armchairhacker 4y ago
  Bezier curves. Cubic bezier curves (generally the most common type) are represented by cubic polynomials x(t) and y(t) (or just one polynomial P(t) where the coefficients are vectors). The first derivative gives you the tangent and normal. The second derivative gives you the direction the normal will gradually become as t increases. The third derivative gives you the change in this change (the fourth derivative is zero). Curvature is also computed from the first and second derivatives: K = det(P', P'')/||P'||^3 Other kinds of bezier curves are similar. In quadratic ones the first and second derivatives are normal and normal change but the third derivative is zero. In higher-polynomial bezier curves the third derivative changes over time as the fourth is non-zero, and so on. Source is a really interesting video on bezier curves which I highly recommend: https://www.youtube.com/watch?v=aVwxzDHniEw https://www.youtube.com/watch?v=aVwxzDHniEw.
  • _nhynes 4y ago
    And these are common in everyday life due to screensavers, right?
    • krallja 4y ago
      Fonts, vector graphics, interpolation for animation and video games
      • Someone 4y ago
        I think that, nowadays, it’s more likely that fonts use quadratic Bézier curves (as in TrueType and its derivatives), rather than cubic ones (as in PostScript and Adobe’s Type 1 fonts), but since OpenType supports both (https://en.wikipedia.org/wiki/OpenType#Description https://en.wikipedia.org/wiki/OpenType#Description) I may be wrong. Similarly, SVG supports both quadratic and cubic Bézier curves.
    • iainmerrick 4y ago
      And cars. Curves with higher-order continuity is why modern cars have such interesting smoothly curved surfaces.
• abxytg 4y ago
  driving is higher order derivative thinking (speed, rates of change in speed, relative rates of change in speed) and this is why most people suck at it.
  • deleted 4y ago
    [deleted]
• brian-armstrong 4y ago
  The universal speed limit applies to the 1st derivative of position, and we have nerve endings that can "feel" the second derivative, which seems to be a pretty important one!
  • TuringNYC 4y ago
    more crudely, i'd say..."you feel the second derivative in your gut"
    • dqft 4y ago
      And race car drivers with their butt.
• antegamisou 4y ago
  Everyday life may be a stretch, however some higher-end quadrotors are able to navigate safely in complex indoor environments by generating trajectories that minimize the snap, the second derivative of acceleration.
  • lake_vincent 4y ago
    Wait, meaning the third derivative of the what is already the second derivative of position - so snap = 5th derivative of position? Is there an intuitive explanation for this? Just checking my understanding.
    • flobosg 4y ago
      Snap, or jounce, is the fourth derivative of position.
      • jdougan 4y ago
        I thought that was called "jerk".
        • marcianx 4y ago
          0th derivative = position 1st derivative = velocity 2nd derivative = acceleration 3rd derivative = jerk 4th derivative = snap 5th derivative = crackle 6th derivative = pop I just learned the last 3 due to this discussion and Wikipedia[1][2]. [1]: https://en.wikipedia.org/wiki/Fourth,_fifth,_and_sixth_derivatives_of_position https://en.wikipedia.org/wiki/Fourth,_fifth,_and_sixth_deriv... [2]: https://en.wikipedia.org/wiki/Snap,_Crackle_and_Pop https://en.wikipedia.org/wiki/Snap,_Crackle_and_Pop
          • jdougan 4y ago
            Thanks! Very enlightening.
          • shric 4y ago
• jules 4y ago
  "In the fall of 1972 President Nixon announced that the rate of increase of inflation was decreasing. This was the first time a sitting president used the third derivative to advance his case for reelection." -- http://www.ams.org/notices/199610/page2.pdf http://www.ams.org/notices/199610/page2.pdf
  • emerged 4y ago
    Sounds like a real jerk.
  • ironSkillet 4y ago
    First and only time maybe...
  • inasio 4y ago
    During the Covid pandemic health officials occasionally used similar language: The rate of increase in new cases was increasing/decreasing...
    • tunesmith 4y ago
      Oh, right! Yeah, in an Rt graph, any time the upward slope starts getting more gentle.
    • deleted 4y ago
      [deleted]
    • BrandoElFollito 4y ago
      During the COVID pandemic, I saw some truly magical statistics in our government (I am French). I tried to understand some of their data but it was beyond my capacities - despite having access to some raw data. I do not think that the general population cared (the concern was rather on how to calculate 1 km from their house) but for someone who is allergic to bad statistics creating crappy results it was torture.
      • inasio 4y ago
• lynndotpy 4y ago
  Roller coaster curves are so you experienced a gentle change in acceleration, i.e. the fourh derivative of position. We also see this for car brakes (and is responsible for the "elevator feeling".)
• nl 4y ago
  Changes in health insurance premiums. Age (base) -> Health (a large amount of the premium is based on age) (1st derivative) -> Premium (2nd derivative) -> Change in Premium (3rd derivative)
• valbaca 4y ago
  In terms of an real-time strategy (RTS) game, like Starcraft: 1. base: how many Marines you have 2. dx: how many Marine-producers you have = X Marines / sec 3. d2x: how many Marine-producer-producers you have, your harvesting units = (X Marines / sec) / sec 4. d3x: how many harvester-producers you have, your bases 5. d4x: how many base-producers you have Idle games also fall in this category: first you chop wood with a crap axe, then you use wood to upgrade to a better axe, eventually you assemble an axe factory. Inverted pendulums use such advanced math as well: https://en.wikipedia.org/wiki/Inverted_pendulum https://en.wikipedia.org/wiki/Inverted_pendulum
  • mirker 4y ago
    StarCraft mineral mining is interesting. 50 minerals per worker + 100 minerals per supply depot at some amortized rate. You have a dampening term on workers/mineral patch which saturates between 2-3 workers. It’s pretty linear till then. Then you get a new base and do it again. The problem is you have both time and minerals (and supply, gas) as resources, which means there are multiple competing derivatives. I’d be interested in seeing if you can approximate the economy with derivatives alone but I think you’d have to have some discrete simulation.
    • navane 4y ago
      You purposefully over-saturate (to 3/patch) your existing base before you create a new base. Then when the new base becomes operational, you can "maynard" a chunk of workers to the new base and have it be immediately productive at ~1 worker / patch.
  • nurettin 4y ago
    Number of base producers you have isn't correlated to the rate at which you produce bases.
    • valbaca 4y ago
      My memory is fuzzy, but I think it depends on faction. For zerg, your drones can turn into bases and drones come from bases. Within a game, the "derivatives" start looping on themselves to keep the game balanced and interesting.
• vagab0nd 4y ago
  Haha, I actually think about this a lot. There are mechanical g-force meters you use when driving. The position of the needle is the acceleration (2nd derivative of position). The velocity of the needle would be the 3rd derivative. The acceleration of the needle would be the 4th.
• ACow_Adonis 4y ago
  Pandemics, disease control, and epidemiology :) i.e. infected = base. New infection rate, spread, R0 etc = 1st derivative. R0 increasing or decreasing = 2nd derivative. Environment, Metereology and Climate. Climate/phenomenon (i.e. global warming) = base. Is it increasing/decreasing = 1st derivative. Is the rate of change increasing or decreasing (i.e. as carbon emissions start to enter the atmosphere after the industrial revolution) = 2nd derivative. You could get really fancy and say that climate is a statistical function on localised individual weather observations which follow the above pattern. And that you can take a derivative on the numbers generated by these individual observations themselves measuring localised 1st/2nd derivatives. Does that make it a third derivative? Exercise left for the reader :) Economics, Finance, Risk and Regulation. Closely related to interest rates and equilibrium funnily enough. Lets take mortgage stock/book cause it's easy. A percentage of mortages go into default. 1st derivative. Are the rate of defaults (or adverse events) increasing or decreasing: 2nd derivative. (am i right on that, i haven't thought too hard, just whipped it out). Indeed, I imagine it would come up in a lot of places where things can transition between states of equilibrium. To observe equilbrium and transition to another state, you may need to first measure 1st derivative. 2nd derivative may then inform on whether the system is transitioning to a new equilibrium/state or not. Sorry if that's too abstract. Engineering I presume higher derivatives would come up anywhere there's possibly of feedback loops. 2nd derivative can tell you if the system is heading towards catastrophic failure. Which brings us to... Anything (or at least a lot) of fields that invovle practical or empirical measurements or estimations of exponential effects. Since in the real world most exponential effects have a natural limit or regulator, we're often interested in knowing when the phenomenon hits its natural limit. And this means observing the rate of change (2nd derivative) on the rate of change (1st derivative) to pinpoint where and when the exponential behaviour is breaking down.
• di456 4y ago
  Disk space = base, change in disk space = 1st derivative, rate of change = 2nd derivative. Useful as a monitor for the rate of change in data intensive applications that sometimes spill to disk. Spikiness is okay if it reverts towards the base within a certain timeframe, but not okay if the rate of change persists or increases over same timeframe.
• randycupertino 4y ago
  Drug derivatives are pretty common in chemistry and pharma. First-order derivatives are drugs that are created from the parent drug via just one chemical reaction. there are derivatives of derivatives which create (fun, lol) headaches for pharma licensing and marketing regulatory authorities. Ecgonine is a tropane derivative from coca leaves and is convertible 2-carbomethoxytropinone and then cocaine. Another example is making buprenorphine from thebaine which is used for making oxycodone, oxymorphone, buprenorphine, naloxone and other opiate agonists. US Controlled substances act in 1986 spelled out the number of steps was irrelevant. https://pubs.acs.org/doi/10.1021/acsomega.0c00282 https://pubs.acs.org/doi/10.1021/acsomega.0c00282 Another area we're seeing twice and third derivatives to get around regulatory & consumer purview is perfluoroalkyl chemicals ie PFOAs, PFAS, PFOS. Consumers and regulators start avoiding or banning some of them, let's just spin up some derivatives of the perfluorooctane sulfonic acids that they haven't cracked down on yet and put that in everything until the people become savvy and then we'll move on to newer harmful unbanned things!
• marshallward 4y ago
  We use biharmonic diffusion operators in oceanography as a basic turbulence model, which is effectively a fourth order derivative in space. It is like an accelerated diffusion which aggressively dissipates small scales but preserves the large physical scales more robustly than normal diffusion.
  • boppo1 4y ago
    Maybe you can help me: what is it about turbulence that remains mathematically 'unsolved'? How is turbulence different than navier-stokes applied to a really fast moving medium with directional randomness?
    • lutorm 4y ago
      My understanding is that it's "solved" in the sense you say, we know that the solution obeys the NS equations. The problem is that we can't actually solve them on a sufficient range of scales to actually make that knowledge useful for making predictions, so we have to resort to approximations.
    • dhdc 4y ago
      Turbulence is unsolved because Navier-Stokes is unsolved.
    • btrettel 4y ago
      Turbulence can be accurately solved by simulating the Navier-Stokes equations on powerful enough computers. [0] The problem is that the computational complexity is enormous. Even relatively simple turbulent flows may exceed the capabilities of a supercomputer 50 years from now. This is pretty easy to show mathematically using the Kolmogorov scales [1] combined with the CFL condition [2] to estimate the computational complexity of unbounded turbulence. (But it's an incomplete estimate. Adding boundaries or other complexities will increase the computational cost.) The real turbulence problem is figuring out ways to get around the computational complexity with cheaper models. Accurately modeling turbulence without using the full Navier-Stokes equations is really hard. Also, contrary to what the science media says, the Navier-Stokes existence and uniqueness problem doesn't have anything to do with turbulence being hard aside from that both involve the Navier-Stokes equations. [3, 4] 2D Navier-Stokes, where existence and uniqueness has been proved, still has turbulence. [0] Given accurate initial and boundary conditions. [1] https://en.wikipedia.org/wiki/Kolmogorov_microscales https://en.wikipedia.org/wiki/Kolmogorov_microscales [2] https://en.wikipedia.org/wiki/Courant%E2%80%93Friedrichs%E2%80%93Lewy_condition https://en.wikipedia.org/wiki/Courant%E2%80%93Friedrichs%E2%... [3] https://news.ycombinator.com/item?id=31227133 https://news.ycombinator.com/item?id=31227133 [4] https://news.ycombinator.com/item?id=31049535 https://news.ycombinator.com/item?id=31049535
• tough 4y ago
  It's funny because NFT 10k collections is all derivs of punks for example lol
  • abxytg 4y ago
    .......not that type of derivative
• venachescu 4y ago
  While it's mostly a phenomenological observation (and not a natural law), many types of movements in humans and animals are well described by a "minimum jerk trajectory" [1]. There's a ton of debate about whether or not the brain is actually computing or optimizing the 'jerk' of your arm at all - or if it just happens to be the consequence of minimizing the effects of noisy neurons and muscles. [1] https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6565116 https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6565116
• kalid 4y ago
  y(t) = bank balance y'(t) = income y''(t) = raises
  • kamaal 4y ago
    y'''(t) = job hopping(rate of increase of raises) Perfectly explains grifters.
• quickthrower2 4y ago
  There was a HN submission about the G forces in roller coasters. G force is acceleration, so a second derivative. Early looping roller coasters had big spikes in G force rather than a steady G force. This made them horrible to ride on, so no one did, and was a problem to be solved (later solved by a different loop shape). Measure how spikey G forces are is the 3rd derivative.
  • pflanze 4y ago
    "Why roller coaster loops aren’t circular anymore", https://news.ycombinator.com/item?id=32005421 https://news.ycombinator.com/item?id=32005421
• omarhaneef 4y ago
  Agree with whomever said options but it should be noted that the higher derivatives “lurk” in the lower ones in real life. Example: a simple change in position means that the object had to move or experience two changes in velocity (starting and stopping). And to change its velocity it had to accelerate, and in order to do that it had to change its acceleration (from 0 to whatever) and so on. So it is with all deltas that require basically many derivatives to happen at the edges.
• bilsbie 4y ago
  Change in acceleration is one. I always wondered if we could feel that.
  • onos 4y ago
    It’s called jerk and it’s what gives you a whiplash feeling.
    • bloudermilk 4y ago
      Fun fact: the derivatives of position after velocity, acceleration, and jerk are snap (or jounce), crackle, and pop. Source: https://en.m.wikipedia.org/wiki/Fourth,_fifth,_and_sixth_derivatives_of_position https://en.m.wikipedia.org/wiki/Fourth,_fifth,_and_sixth_der...
    • Schroedingersat 4y ago
      It's also what makes you fall over on the bus or train. You can handle a surprising amount of lateral acceleration if the jerk is low. 0.5g is pretty much like standing on a steep hill.
• onos 4y ago
  Reads to me like op’s example is a fourth derivative as they are slowing the pace!
• gigatexal 4y ago
  This is such a cool thread and why I keep coming to HN. I think that if I had friends like this that nerded out on such things and made such escoteric things like second and third derivatives of things I’d not have bombed calculus.
• seanhunter 4y ago
  Not exactly an answer to your question but also from finance. A fun moment after the 2008 financial crisis came when a lot of pundits were trying to call the bounce. Everyone kept going on MSNBC and the like saying that “the second derivative was positive” and saying that was a sign the economy was about to turn around. I was watching one day and yet another person said that for some indicator (maybe nonfarm payrolls?) the second derivative was positive and therefore things were about to get better when Mohammed El-Erian (who was also on the program) said dryly “There are lots of analytic functions where the second derivative is consistently positive and the first derivative is consistently negative”. There was a stunned silence.
  • tartakovsky 4y ago
    Hi @seanhunter, any chance you have a source for this?
  • gordaco 4y ago
    As a simple example, one can look at f(x)=1/x in R+. The derivative is f'(x)=-1/x^2 and the second derivative is f''(x)=2/x^3. In general, every function of the form f(x)=1/x^n with odd n will have this behaviour, and if n is even the behaviour is the opposite. And yes, many more examples can be found. More generally, this is why I'm wary of indirect indicators. They never tell the whole story, and because of that they're used disingenuously in order to muddy the waters. You see this a lot in big scale PR campaings, such as climate change denialism, and pro-sugar and pro-alcohol disinformation (we had a lot of pro-tobacco as well, but it has subsided in the last two decades or so, at least in the West).
    • seanhunter 4y ago
      Yes exactly. There are folks who would ride that positive second derivative all the way down to f(x) = 0 and believe every step of the way that the indirect indicator is telling them that we're going to turn around any second now.
    • adament 4y ago
      For those who find the existence of such analytic functions intuitively "wrong", note that it is essential to this example that though the second derivative is positive, it is positive and decreasing towards 0. If the second derivative is bounded from below by some positive value, then eventually the first derivative will become positive and it will diverge towards positive infinity and thus the function itself will diverge towards positive infinity. More precisely suppose that f is twice continuously differentiable and f'(x) < 0 and f''(x) ≥ 0 for all x greater than some K (for example K=0 in the examples given) then λ( (f'')^-1((a, ∞)) ∩ (K, ∞) ) < ∞ for all a > 0 where λ is the Lebesque measure.
• alted 4y ago
  A fun one with easy visualization is mechanical engineering statics, in which one calculates how much something deforms from a force (e.g., a bookshelf or bridge sags, a spring stretches, or an elastic tire or sponge or pillow squishes). The standard example is simple beam bending [1]. If you hold a thin beam (say, a ruler or a stiff piece of paper) horizontally in the air by one end, and press down on the free end, it bends from a straight line into a third-order (cubic) polynomial. To calculate this, one considers the beam as a number of little segments connected to one another. The vertical force on each segment due to the force pressing down is constant over the beam. The first integral of this is the torque ("moment") on each segment. The second integral is the slope of the beam, and the third integral is the actual shape of the bent beam. If you consider it the other way around, the force is the third derivative of the resulting beam shape. This is often visualized in a "shear force and bending moment diagram". The best part is there's a stupidly simple approximation to calculate how much bending you get from a single force (Hooke's law [2]): the distance the beam moves is proportional to the force (by some constant you can get either with these derivative calculations or by experiment). [1] https://en.wikipedia.org/wiki/Bending https://en.wikipedia.org/wiki/Bending [2] https://en.wikipedia.org/wiki/Hooke%27s_law https://en.wikipedia.org/wiki/Hooke%27s_law
  • Too 4y ago
    Someone else pointed out Bézier curves. What is interesting is such are same as the bending equation! Back in the pre-cad days, designers would bend a piece of thin, elastic spline-wood to draw curves. From the side it looks exactly like a Bézier curve, this is not a coincidence, Beziers are more or less same as the physical bending equation for such a spline.
• c_o_n_v_e_x 4y ago
  CNC machining relies on motion controls with higher order derivatives. https://tenmilesquare.com/resources/iot-connected-hardware/a-big-advance-in-desktop-manufacturing-jerk-controlled-motion-explained/ https://tenmilesquare.com/resources/iot-connected-hardware/a... "Note: In the past TinyG used 3rd-order “constant jerk” motion planning, similar to a form of controlled-jerk motion planning that is found in some commercial products. TinyG has since moved on to even smoother motion control that uses further derivatives “snap” (4th derivative), “crackle” (5th derivative), and “pop” (6th derivative). As far as we know, no commercial CNC products advertise that they use 6th-order motion planning."
• raverbashing 4y ago
  Elevators. You want to keep the 3rd derivative of position (jerk) limited, to have a smooth ride
• QuadrupleA 4y ago
  Steering an airplane is a fun one - you the pilot want to set the compass direction of the plane. The derivative of that is the rate of turn, corresponding to bank angle. But what the yoke / stick actually controls is the derivative of that, the bank angle rate / roll speed. So pilots have to sort of double-integrate to set their heading.
  • isametry 4y ago
    Huh, this is interesting! So to put that into context, driving a car is only the 1st derivative right? The steering wheel angle corresponds (although nowadays non-linearly) to that of the wheels, a function of which is the driving direction. Do you know whether the “angle rate” behavior is unique to airliners, or does it apply to other aircraft as well? Because my assumption (based mostly on imagination and videogame controls) would be that f''(x) handling can’t be reactive enough for the real-time type of flying done in helicopters or fighter jets…?
    • QuadrupleA 4y ago
      Yeah, car is one step simpler, steering wheel sets the derivative of direction (turn rate). Fighter jets definitley have that same double-integration, although they can handle super fast control inputs, roll speeds etc. Not as familiar but I think helicopters too - the cyclic stick controls bank angle and pitch, which you'd use along with the pedals during turns in moving flight. But while hovering in place you could rotate with just the pedals (tail rotor) more like steering a car.
    • BrandoElFollito 4y ago
      > The steering wheel angle corresponds (although nowadays non-linearly) to that of the wheels This is interesting, I always thought that it was linear. I was wondering about how speed impacts this (if at all) and now I will have to dig deeper :)
• garrybelka 4y ago
  "Acceleration of a rate of labor productivity growth" - 6th derivative. Not found in English, but in original Russian - "ускорение темпов роста производительности труда" - about 4,090 results in Google. "The acceleration of labor productivity growth" in English - about 11,700 results. But that's only a 5th derivative.
  • p1esk 4y ago
    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.
    • garrybelka 4y ago
      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).
      • penteract 4y ago
        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.
      • p1esk 4y ago
        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?
• freahsteaksauce 4y ago
  Jerk is the feeling you get when you change acceleration, for example in a car when you go from a little gas pedal to flooring it. That abrupt change is jerk. The third derivative of position with respect to time.
• gnicholas 4y ago
  PG, who built up YC, which builds up startups, which build up products/services. OTOH, I have never encountered PG in everyday life, so perhaps this doesn't count!
• ur-whale 4y ago
  Jerk (derivative of acceleration, so 3rd derivative of position) matters when planning drone trajectories: https://www.coursera.org/lecture/robotics-flight/supplementary-material-solving-for-coefficients-of-minimum-jerk-trajectories-W4Y3w https://www.coursera.org/lecture/robotics-flight/supplementa... https://www.youtube.com/watch?v=8RILnqPxo1s https://www.youtube.com/watch?v=8RILnqPxo1s
• bradwood 4y ago
  Hardly everyday life, but "The Greeks" are used often in (financial) options pricing and market risk analysis. Delta, Gamma, Theta, Rho. And then some more obscure ones like Vega and even a thing called Vanna.
• gitgud 4y ago
  Fuel prices (1st order) Affect people's decisions to go on longer trips to the country (2nd order) Which affects growth and tourism of outlying towns in the country (3rd order)
• jbay808 4y ago
  Carbon emissions is a big one. Since the climate is far from equilibrium, temperature goes as something like the time-integral of excess carbon concentration. CO2 concentration goes with the integral of total emissions. So emissions is roughly the second derivative of temperature. But public policy discussions are often taking place on the level of slowing the rate of emissions growth. Which is about four derivatives up from temperature.
• rakoo 4y ago
  Music ? A sound wave at a specific frequency is a cyclical difference in air pressure, so there's an infinite number of derivatives here. But let's take the Fourier Transform to keep it simple: a specific frequency is a constant. Music is made by having different frequencies together, ie multiple constants, and changing them over time ie first derivatives. You also want that change of rate to be smooth, which means there is an impact on the second derivative. I'm not sure what the third derivative would be, but I guess it would be the change in rhythm, tone, or even changing music.
• njkleiner 4y ago
  I suppose it depends on how you define "everyday life", but in digital image processing, derivatives can be used as a relatively simple method for edge detection. For example, the Sobel and Prewitt operators (1st derivative) and the Laplacian operator (2nd derivative) can be used as filter kernels to detect edges in images.
• an1sotropy 4y ago
  Many other comments have noted "jerk", the derivative of acceleration that you can feel in a car; but here's maybe a way to make that a little more concrete. Suppose you're driving, and you keep your speed constant (no change in the accelerator or "gas" pedal). Keeping the steering wheel at a fixed orientation then moves you uniformly along a fixed circle == constant acceleration == constant force (you feel from car) to the left or right. But when you move the steering wheel, you're changing the circle radius, and changing acceleration, which changes the force you feel. To a first order approximation (I think), the rate of change of steering wheel position is the rate of change of acceleration, or 3rd derivative of position. It's not a surprise that a car ride feels smoother when move the steering wheel slower, but the speed of steering wheel motion is the simplest tangible example I can think of for controlling and experiencing a third derivative.
  • globular-toast 4y ago
    The accelerator and brake pedals are the same. Although in many cars the maximum jerk via the accelerator seems quite limited. Jerk is also what triggers car/motion sickness. So for the comfort of your passengers, move the controls slowly. Roller coaster designers know this well and I think they even consider fourth and fifth derivatives when designing coasters.
    • anonym29 4y ago
      See: snap, crackle, pop https://en.m.wikipedia.org/wiki/Fourth,_fifth,_and_sixth_derivatives_of_position https://en.m.wikipedia.org/wiki/Fourth,_fifth,_and_sixth_der...
  • hanche 4y ago
    I have read that for this reason, the Euler spiral (a.k.a. Cornu spiral) is commonly used in the design of modern roads. Its defining characteristic is that the curvature changes at a constant rate with respect to arc length. So a curve in the road is typically composed of three parts: First, a section of an Euler spiral starting with zero curvature, joined by a circular arc, then a new Euler spiral ending once more at zero curvature. When I first learned about this, I tried it on some recently built roads. And indeed, entering the curve I can move the steering wheel at a constant rate, hold it still through the middle of the curve, t’en move it back at a constant rate until I am once more traveling in a straight line.
• yobbo 4y ago
  When you "scroll" on smart phones, the scroll speed is calculated a bit like a physical simulation with an instantaneous acceleration (second order) by a "flick" on the screen and then set to slowly decrease the scroll speed (first order).
• eternityforest 4y ago
  Jerk is the 3rd derivative of position after velocity and acceleration, and has real effects on people.
• dmurray 4y ago
  This confused me more than it should have, thinking through "is the interest rate really the time derivative of the amount of money outstanding on my loan?" It might be easier to think of it in terms of a bank deposit. If I put $100 in a bank account and the rate of interest is 5%/year, after a year my balance has grown by $5. Of course, a loan works the exact same way in reverse. But as consumers normally we think of a loan as being paid off over a fixed length of time, so the rate of change is the rate at which you pay it off, and only second-order influenced by the interest rate.
  • ironSkillet 4y ago
    I see your point. The interest rate in isolation is not the derivative (an exponential function is), but it does uniquely parameterize the derivative.
• mathattack 4y ago
  Recently when I wasn’t merging into traffic fast enough I was told “More acceleration.”
• anonym29 4y ago
  base = location 1st = velocity (location/time AKA speed) 2nd = acceleration (location/time/time AKA rate of change of speed) 3rd = jerk (location/time/time/time AKA rate of change of acceleration) If you've ever rode in (or drove) a Model S P85D, P90D, P100D, Performance AWD, or Plaid, you'll understand "jerk".
• GeorgeChiesa 4y ago
  see "Derivative Thinking with George Chiesa [Just for Jerks]" https://vimeo.com/GeorgeChiesa/Just4Jerks https://vimeo.com/GeorgeChiesa/Just4Jerks
• deleted 4y ago
  [deleted]
• GeorgeChiesa 4y ago
  You can read the book The JERK by my dear friend Chris Surdak...