
Tulsa Teacher discovers calculus flaw - Buttons840
http://www.tulsatoday.com/2019/04/11/tulsa-teacher-discovers-flaw-in-calculus/
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gmiller123456
Unfortunately the article is kind of idiotic, the actual paper [1] has nothing
to do with discovering a newly discovered flaw. As the paper's author even
says, many students find the same "flaw" themselves.

[1]
[http://online.watsci.org/abstract_pdf/2019v26/v26n3a-pdf/4.p...](http://online.watsci.org/abstract_pdf/2019v26/v26n3a-pdf/4.pdf)

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XaspR8d
Joke's on you -- the article helped me find a flaw in the theory of
journalism!

(Paper is much better yes. I always had trouble with that notation.)

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lyctc
"Extending the Algebraic Manipulability of Differentials"
[https://arxiv.org/pdf/1801.09553.pdf](https://arxiv.org/pdf/1801.09553.pdf)

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tathougies
If you're attempting to manipulate the infinitesimals in a derivative
notation, it's your understanding of calculus that's flawed, not calculus.

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epicwhaleburger
I do understand where the confusion is stemming from, but taking the time to
properly learn the clash between Leibniz and Lagrange is very important. It
makes a lot of sense to use one versus the other in specific cases. You might
be able to protest by saying there are certain cases where the differential
operator is treated like a fraction, but not only would I call this a rarity
but also a cheat to what is really happening (the chain rule comes to mind). I
do think it's cool to think of analogies that could include notation changes
for students in early calculus classes though.

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burfog
Fixing the notation would be great, saving numerous future generations from
confusion.

Getting agreement to do this is difficult. Short of laying it down in the law
as part of a treaty (throw it in with WTO or Berne copyright?) there doesn't
seem to be a way to make the change happen. Nobody wants to buy the calculus
book with weird non-standard notation. It would be like a trigonometry book
with the symbols Feynman invented in high school.

We're more likely to get serious mathematicians calling equations "math
sentences".

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dvt
The article is dumb, but the paper is actually pretty interesting.

Intuitively, I never treated differentials as "algebraic units" \-- even
though I can see why it might be tempting to do so. In other words, I never
thought that dx^2/dy^2 = (dx/dy)^2. From my experience, most teachers and
professors _do_ hint that "something funky" is happening when you say "dBLAH."

Further, (and more to the root of the problem), as far as higher-order
derivatives are concerned, I always held a firm belief that something like
"d^nx" was not really a manipulatable statement and was just shorthand for
"the nth derivative" and certainly not the "first derivative raised to the nth
power."

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a1369209993
The main point seems to be that:

    
    
            / d\²   d²
      D²ₓ = |−−| ≠ −−−
            \dx/   dx²
      because
      (1/dx)*d*(1/dx)*d ≠ (1/dx)*(1/dx)*d*d
      or just
      d*(1/dx) ≠ (1/dx)*d
    

In other words, the "algebraic units" are fine, but multiplication on them is
noncommutative.[0]

0: Like multiplication on damn near everything else that isn't really a
number.

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al2o3cr

        When writing a ratio that works like a ratio is too cumbersome, we
        prefer simply avoiding the ratio notation altogether, to prevent
        making unwarranted leaps based on notation that may mislead the intuition.
    

Yeah, would definitely be a shame if somebody misunderstood some notation and
leapt into writing a paper about it.

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lidHanteyk
The paper is interesting. I think that dual numbers provide a better basis for
algebraic manipulations of expressions with derivatives.

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DangBigot
Realizing that mathematical notional is inconsistent and contextual, and
potentially confusing if inappropriately generalized, is a common frustrating
learning experience, and it's nice to consider alternatives.

But it is not a "calculus flaw".

Also, the sidebars beside this article are filled with unrelated low-quality
political clickbait, so perhaps we shouldn't give this site more traffic.

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commandlinefan
I was definitely hoping for a lot more based on the title. I'm also not sure I
agree with the phrasing that he "discovered" an alternative notation.
Invented, maybe, but not discovered.

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csours
That's one of the fundamental questions of mathematics. Are you discovering or
inventing?

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kadendogthing
Here's an exercise for the reader:

* Why is this coming from "tulsatoday"

* Why is the article written in a particular manner?

* What biases and agenda is the publication attempting to platform here?

