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Listen here, Little Dicky

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Submitted ⁨⁨2⁩ ⁨weeks⁩ ago⁩ by ⁨fossilesque@mander.xyz⁩ to ⁨science_memes@mander.xyz⁩

https://mander.xyz/pictrs/image/c4583fa7-9329-4e99-9582-fd2d9b668888.png

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  • chortle_tortle@mander.xyz ⁨2⁩ ⁨weeks⁩ ago

    Mathematicians will in one breath tell you in one breath tell you they aren’t fractions, then in the next tell you dz/dx = dz/dy * dy/dx

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    • marcos@lemmy.world ⁨2⁩ ⁨weeks⁩ ago

      Have you seen a mathematician claim that? Because there’s entire algebra they created just so it becomes a fraction.

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    • lmmarsano@lemmynsfw.com ⁨2⁩ ⁨weeks⁩ ago

      Brah, chain rule & function composition.

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    • Koolio@hexbear.net ⁨2⁩ ⁨weeks⁩ ago

      Also multiplying by dx in diffeqs

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      • gandalf_der_12te@discuss.tchncs.de ⁨2⁩ ⁨weeks⁩ ago

        vietnam flashbacks meme

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    • Collatz_problem@hexbear.net ⁨2⁩ ⁨weeks⁩ ago

      This is until you do multivariate functions. Then you get for f(x(t), y(t)) this: df/dt = df/dx * dx/dt + df/dy * dy/dt

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    • RvTV95XBeo@sh.itjust.works ⁨2⁩ ⁨weeks⁩ ago

      (d/dx)(x) = 1 = dx/dx

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    • jsomae@lemmy.ml ⁨2⁩ ⁨weeks⁩ ago

      Not very good mathematicians if they tell you they aren’t fractions.

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  • benignintervention@lemmy.world ⁨2⁩ ⁨weeks⁩ ago

    I found math in physics to have this really fun duality of “these are rigorous rules that must be followed” and “if we make a set of edge case assumptions, we can fit the square peg in the round hole”

    Also I will always treat the derivative operator as a fraction

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    • bhamlin@lemmy.world ⁨2⁩ ⁨weeks⁩ ago

      I always chafed at that.

      “Here are these rigid rules you must use and follow.”

      “How did we get these rules?”

      “By ignoring others.”

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    • sepi@piefed.social ⁨2⁩ ⁨weeks⁩ ago

      is this how Brian Greene was born?

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  • rudyharrelson@lemmy.radio ⁨2⁩ ⁨weeks⁩ ago

    Derivatives started making more sense to me after I started learning their practical applications in physics class. d/dx was too abstract when learning it in precalc, but once physics introduced d/dt (change with respect to time t), it made derivative formulas feel more intuitive, like “velocity is the change in position with respect to time, which the derivative of position” and “acceleration is the change in velocity with respect to time, which is the derivative of velocity”

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    • Prunebutt@slrpnk.net ⁨2⁩ ⁨weeks⁩ ago

      Possibly you just had to hear it more than once.

      I learned it the other way around since my physics teacher was speedrunning the math sections to get to the fun physics stuff and I really got it after hearing it the second time in math class.

      But yeah: it often helps to have practical examples and it doesn’t get any more applicable to real life than d/dt.

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      • exasperation@lemmy.dbzer0.com ⁨2⁩ ⁨weeks⁩ ago

        I always needed practical examples, which is why it was helpful to learn physics alongside calculus my senior year in high school. Knowing where the physics equations came from was easier than just blindly memorizing the formulas.

        The specific example of things clicking for me was understanding where the “1/2” came from in distance = 1/2 (acceleration)(time)^2 (the simpler case of initial velocity being 0).

        And then later on, complex numbers didn’t make any sense to me until phase angles in AC circuits showed me a practical application, and vector calculus didn’t make sense to me until I had to actually work out practical applications of Maxwell’s equations.

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    • Lemmygradwontallowme@hexbear.net ⁨2⁩ ⁨weeks⁩ ago

      yea, essentially, to me, calculus is like the study of slope and a slope of everything slope, with displacement, velocity, acceleration.

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  • vaionko@sopuli.xyz ⁨2⁩ ⁨weeks⁩ ago

    Except you can kinda treat it as a fraction when dealing with differential equations

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    • prole@lemmy.blahaj.zone ⁨2⁩ ⁨weeks⁩ ago

      Oh god this comment just gave me ptsd

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    • JustAPenguin@lemmy.world ⁨2⁩ ⁨weeks⁩ ago

      Only for separable equations

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    • socsa@piefed.social ⁨2⁩ ⁨weeks⁩ ago

      And discrete math.

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  • Worx@lemmynsfw.com ⁨2⁩ ⁨weeks⁩ ago

    It’s not even a fraction, you can just cancel out the two "d"s

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    • Worx@lemmynsfw.com ⁨2⁩ ⁨weeks⁩ ago

      "d"s nuts lmao

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  • callyral@pawb.social ⁨2⁩ ⁨weeks⁩ ago

    clearly, d/dx simplifies to 1/x

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  • bhamlin@lemmy.world ⁨2⁩ ⁨weeks⁩ ago

    If not fraction, why fraction shaped?

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  • moobythegoldensock@infosec.pub ⁨2⁩ ⁨weeks⁩ ago

    It was a fraction in Leibniz’s original notation.

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    • marcos@lemmy.world ⁨2⁩ ⁨weeks⁩ ago

      And it denotes an operation that gives you that fraction in operational algebra…

      Instead of making it clear that d is an operator, not a value, and thus the entire thing becomes an operator, physicists keep claiming that there’s no fraction involved. I guess they like confusing people.

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  • iAvicenna@lemmy.world ⁨2⁩ ⁨weeks⁩ ago

    Look it is so simple, it just acts on an infinite dimensional vector space of differentiable functions.

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    • gandalf_der_12te@discuss.tchncs.de ⁨2⁩ ⁨weeks⁩ ago

      fun fact: the vector space of differentiable functions (at least on a compact domain) is actually of countable dimension.

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      • iAvicenna@lemmy.world ⁨2⁩ ⁨weeks⁩ ago

        Doesn’t BCT imply that an infinite dimensional Banach spaces cannot have a countable basis

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  • Zerush@lemmy.ml ⁨2⁩ ⁨weeks⁩ ago

    When a mathematician want to scare an physicist he only need to speak about ∞

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    • corvus@lemmy.ml ⁨2⁩ ⁨weeks⁩ ago

      When a physicist want to impress a mathematician he explains how he tames infinities with renormalization.

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    • socsa@piefed.social ⁨2⁩ ⁨weeks⁩ ago

      Only the sith deal in ∞

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      • Zerush@lemmy.ml ⁨2⁩ ⁨weeks⁩ ago

        …and Buzz Lightyear

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  • Gladaed@feddit.org ⁨2⁩ ⁨weeks⁩ ago

    Why does using it as a fraction work just fine then?

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    • kogasa@programming.dev ⁨2⁩ ⁨weeks⁩ ago

      It doesn’t. Only sometimes it does, because it can be seen as an operator involving a limit of a fraction and sometimes you can commute the limit when the expression is sufficiently regular

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      • Gladaed@feddit.org ⁨2⁩ ⁨weeks⁩ ago

        Added clarifying sentence I speak from a physicists point of view.

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  • shapis@lemmy.ml ⁨2⁩ ⁨weeks⁩ ago

    This very nice Romanian lady that taught me complex plane calculus made sure to emphasize that e^j*theta was just a notation.

    Then proceeded to just use it as if it was actually eulers number to the j arg. And I still don’t understand why and under what cases I can’t just assume it’s the actual thing.

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    • frezik@lemmy.blahaj.zone ⁨2⁩ ⁨weeks⁩ ago

      Let’s face it: Calculus notation is a mess. We have three different ways to notate a derivative, and they all suck.

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      • JackbyDev@programming.dev ⁨2⁩ ⁨weeks⁩ ago

        Calculus was the only class I failed in college. It was one of those massive 200 student classes. The teacher had a thick accent and hand writing that was difficult to read. Also, I remember her using phrases like “iff” that at the time I thought was her misspelling something only to later realize it was short hand for “if and only if”, so I can’t imagine how many other things just blew over my head.

        I retook it in a much smaller class and had a much better time.

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    • zea_64@lemmy.blahaj.zone ⁨2⁩ ⁨weeks⁩ ago

      I’ve seen e^{d/dx}

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    • jsomae@lemmy.ml ⁨2⁩ ⁨weeks⁩ ago

      e^iθ^ is not just notation. You can graph the entire function e^x + iθ^ across the whole complex domain and find that it matches up smoothly with both the version restricted to the real axis (e^x^) and the imaginary axis (e^iθ^)

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      • shapis@lemmy.ml ⁨2⁩ ⁨weeks⁩ ago

        I’m aware of that identity. There’s a good chance I misunderstood what she said about it being just a notation.

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    • sabin@lemmy.world ⁨2⁩ ⁨weeks⁩ ago

      It legitimately IS exponentiation. Romanian lady was wrong.

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    • carmo55@lemmy.zip ⁨2⁩ ⁨weeks⁩ ago

      It is just a definition, but it’s the only definition of the complex exponential function which is well behaved and is equal to the real variable function on the real line.

      Also, every identity about analytical functions on the real line also holds for the respective complex function (excluding things that require ordering). They should have probably explained it.

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      • shapis@lemmy.ml ⁨2⁩ ⁨weeks⁩ ago

        She did. She spent a whole class on about the fundamental theorem of algebra I believe? I was distracted though.

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  • olafurp@lemmy.world ⁨2⁩ ⁨weeks⁩ ago

    The thing is that it’s legit a fraction and d/dx actually explains what’s going on under the hood. People interact with it as an operator because it’s mostly looking up common derivatives and using the properties.

    Take for example ∫f(x) dx to mean "the sum (∫) of supersmall sections of x (dx) multiplied by the value of x at that point ( f(x) ). This is why there’s dx at the end of all integrals.

    The same way you can say that the slope at x is tiny f(x) divided by tiny x or d*f(x) / dx or more traditionally (d/dx) * f(x).

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    • kogasa@programming.dev ⁨2⁩ ⁨weeks⁩ ago

      The other thing is that it’s legit not a fraction.

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      • jsomae@lemmy.ml ⁨2⁩ ⁨weeks⁩ ago

        it’s legit a fraction, just the numerator and denominator aren’t numbers.

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  • LovableSidekick@lemmy.world ⁨2⁩ ⁨weeks⁩ ago

    Having studied physics myself I’m sure physicists know what a derivative looks like.

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  • corvus@lemmy.ml ⁨2⁩ ⁨weeks⁩ ago

    Chicken thinking: “Someone please explain this guy how we solve the Schroëdinger equation”

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  • SaharaMaleikuhm@feddit.org ⁨2⁩ ⁨weeks⁩ ago

    I still don’t know how I made it through those math curses at uni.

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    • filcuk@lemmy.zip ⁨2⁩ ⁨weeks⁩ ago

      Calling them ‘curses’ is apt

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  • Daft_ish@lemmy.dbzer0.com ⁨2⁩ ⁨weeks⁩ ago

    1/2 <-- not a number. Two numbers and an operator.

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    • jsomae@lemmy.ml ⁨2⁩ ⁨weeks⁩ ago

      In Comp-Sci, operators mean stuff like >>, *, /, + and so on. But in math, an operator is a (possibly symbollic) function, such as a derivative or matrix.

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      • Daft_ish@lemmy.dbzer0.com ⁨2⁩ ⁨weeks⁩ ago

        Youre not wrong, distinctually, but even in mathematics “/” is considered an operator.

        en.m.wikipedia.org/wiki/Operation_(mathematics)

        Image

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  • justme@lemmy.dbzer0.com ⁨2⁩ ⁨weeks⁩ ago

    Division is an operator

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  • KTJ_microbes@mander.xyz ⁨2⁩ ⁨weeks⁩ ago

    Little dicky? Dick Feynman?

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  • devilish666@lemmy.world ⁨2⁩ ⁨weeks⁩ ago

    Is that Phill Swift from flex tape ?

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  • socsa@piefed.social ⁨2⁩ ⁨weeks⁩ ago

    The world has finite precision. dx isn't a limit towards zero, it is a limit towards the smallest numerical non-zero. For physics, that's Planck, for engineers it's the least significant bit/figure. All of calculus can be generalized to arbitrary precision, and it's called discrete math. So not even mathematicians agree on this topic.

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  • Mubelotix@jlai.lu ⁨2⁩ ⁨weeks⁩ ago

    We teach kids the derive operator being ’ or ·. Then we switch to that writing which makes sense when you can use it properly enough it behaves like a fraction

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  • BoxOfFeet@lemmy.world ⁨2⁩ ⁨weeks⁩ ago

    What is Phil Swift going to do with that chicken?

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    • ArsonButCute@lemmy.dbzer0.com ⁨2⁩ ⁨weeks⁩ ago

      The will repair it with flex seal of course

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      • BoxOfFeet@lemmy.world ⁨2⁩ ⁨weeks⁩ ago

        To demonstrate the power of flex seal, I SAWED THIS CHICKEN IN HALF!

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  • someacnt@sh.itjust.works ⁨2⁩ ⁨weeks⁩ ago

    But df/dx is a fraction, is a ratio between differential of f and standard differential of x. They both live in the tangent space TR, which is isomorphic to R.

    What’s not fraction is \partial f / \partial x, but likely you already know that. This is akin to how you cannot divide two vectors.

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  • Zerush@lemmy.ml ⁨2⁩ ⁨weeks⁩ ago

    Headache for mathematicians

    youtube.com/shorts/WSFkDNXOpMk

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  • voodooattack@lemmy.world ⁨2⁩ ⁨weeks⁩ ago

    Software engineer: 🫦

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  • Kolanaki@pawb.social ⁨2⁩ ⁨weeks⁩ ago

    De dix, boss! De dix!

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