
Walter Bradley Center Fellow Discovers Longstanding Flaw in Elementary Calculus - johnnyb_61820
https://mindmatters.ai/2019/04/walter-bradley-center-fellow-discovers-longstanding-flaw-in-elementary-calculus/
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jimm
The article's title is misleading. The mathematician has suggested an
improvement or clarification to the notation used to describe a second
derivative which makes it easier to manipulate formulaically.

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johnnyb_61820
Well, I guess that's debatable. However, the way I see it, the old version was
presented as a fraction, but couldn't be used as a fraction. The new version
is also presented as a fraction _and_ can be used as a fraction.

Perhaps it is due to my old-school nature, but if I wrote a fraction in school
that _didn 't_ work as a fraction, that would be a mistake, would it not?
Especially if it was possible to write it correctly? I couldn't go to my
professor and just say, "well, actually, while it looks like a fraction, it
was actually just a piece of notation that needed future clarification."

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EdwardCoffin
> Well, I guess that's debatable.

What part of it is debatable? The article clearly states that it is _just_ a
notational improvement: there was really no flaw in calculus, it was more a
wart in notation. This change would not result in different answers unless the
original calculations were done incorrectly.

I'd regard the current notation more like an irregular verb, or something that
is spelled differently from how it is pronounced: it's inconvenient to deal
with, but everyone adept at calculus knew about it and how to deal with it.
This article is just describing a notational improvement that would make it
_easier_ to get right.

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johnnyb_61820
The fact that there was a well-known kludge to get around the problems
inherent in the notation doesn't make the notation right. As the paper pointed
out, the new notation didn't drop magically from the sky, it is literally the
application of the quotient rule to the derivative. The reason that no one
noticed this notation before, is that they didn't think to apply the quotient
rule to the quotient dy/dx.

If I had a problem, and my solution involved forgetting to apply the quotient
rule to a prominent quotient, it would still be wrong, even if I also came out
with a set of kludges that allowed me to get right answers in the most common
cases.

