User talk:Ozob/Archive 6

Audie Murphy edits
Ozob, thank you for asking about this at RFC PC/2. Over at Audie Murphy, we have been trying to get it cleaned up to nominate for A-class. I began researching the edit history for patterns on one thing or another. i.e., the redlink editor Audiesdad (May 7 2013) is a repeater in the history who was getting reverted for spamming, and given what he was spamming I suspect COI with the Texas government. Prior to 2013 was where it was worse. My raw results can be found in descending chron order tables at User:Maile66/Murph/Arb2 for 2013-2010, and User:Maile66/Murph/Arb3 for 2009-2003. It was too large to compile on one page. Ideally, it would be better to have this semi-protected permanently. But, of course, that all depends on which admin decides that. Some might say, "...not enough in recent history...." and decline. Since Feb 2013 when we began the cleanup, a small core of recent volunteers have been trying to deter it. Semi-protected would not take care of a return of disruptive edits by YahwehSaves, but perhaps it could eliminate other issues that are almost sure to return. Your opinion is welcome on this. — Maile (talk) 12:06, 9 June 2013 (UTC)


 * My interest in Audie Murphy (besides its being an excellent article on an exceptional man) is limited to its relevance to the current PC2 discussion. I think the best way for us to help that discussion is for us to continue in public.  I hope you don't mind, but I'm about to copy your comment to the PC2 RFC page and reply there.  Ozob (talk) 03:30, 11 June 2013 (UTC)

Clarify comment
Re: Your reply.

I actually meant it by it's definition (http://www.thefreedictionary.com/bureaucrat #2), with regards to someone who wants to follow strict procedure (albeit regardless of official capacity). It wasn't meant to be a pejorative nor a complimentary remark, simply an observation that if the closing of the RfC isn't handled correctly, it could have repercussions; in short, I agreed with you that all closers should be non-partisan, and those who !voted in prior PC/2 RfC's should be exempt from closing due to implicit bias this time round. It made sense to me that with you Opposing PC/2 and distrusting Cyperpower as a closer, that someone Supporting PC/2 should also request a neutral conclusion of the RfC, in order that our views on the closure matter be mutual, even if our views on PC/2 are not. Hope that helps.  Ma &reg;&copy; usBr iti sh {chat} 04:14, 17 June 2013 (UTC)


 * I see. I'm surprised; I never thought that someone would take me for a bureaucrat in that sense.  I was wrong to assume that you meant it pejoratively.  Sorry, and thank you for requesting a neutral closure.


 * It seems that my discussions with you and Maile66 have not gone well. This is not what I wanted.  I really like what's been done to Audie Murphy, and—despite our disagreements—I think that both of you genuinely want what's best for WP.  If our paths cross again then I would look forward to working with you.  Ozob (talk) 04:38, 17 June 2013 (UTC)


 * No worries. A MILHIST Peer review of the article was conducted back in February. Since then it has reached GA status, which is a big step from where it was pre-review. Getting it up to FA is a much bigger milestone though, and there has been a lot of scuffling over the article regarding parts of Murphy's life, none of which I can comment on as I don't know that much about him, he's an American hero, us outsiders know him more for his movies, I imagine. Hopefully the dust will settle, and Maile66 will feel inclined to continue with his efforts to reach FA. As it stands now, there hasn't been much headway because of the aforementioned disruptions from editors who seem more inclined to inhibit progression than aid it constructively. Must be very frustrating. Cheers,  Ma &reg;&copy; usBr iti sh {chat} 04:50, 17 June 2013 (UTC)

Differential calculus
You mentioned that you "disagree with some of these changes, mostly as a matter of style", however, the changes are not meant to be stylistic, they are meant to be more accurate. Eg. saying that differential calculus is "concerned with the study of the rates at which quantities change" is rather vague, as it makes no mention of the interval over which the change is measured. Compare to, for example: http://mathworld.wolfram.com/Derivative.html. Any objections to reverting to my changes? AW94 (talk) 13:46, 2 July 2013 (UTC)


 * I realize that they are intended to be more accurate, but I am not convinced that they're helpful. Let me walk you through my thinking on each of the changes that I reverted:
 * "concerned with the study of the rates at which quantities change" &rarr; "concerned with differentials". This is the very first sentence of the article, so it needs to be in terms that an average person can understand.  A differential is a technical concept; someone who knows what a differential is and who is comfortable enough with them to use them as a definition of differential calculus probably doesn't need to look up "differential calculus" in an encyclopedia.  So while the original text is more vague, it is more likely to be helpful to an average reader.
 * "The derivative of a function at a chosen input value describes the rate of change of the function near that input value." &rarr; "The derivative of a function at a chosen value can be thought of as describing the rate of change of the function near that value." There are two changes in this sentence.  One is "input value" &rarr; "value".  I think this is confusing; a beginner might read "value" as "output value", especially since we so often use phrases like "the value of f at x is f(x)".  The other is "describes" &rarr; "can be thought of as describing".  We're still very early in the article (sentence #4), and this is the first sentence in the article that attempts to describe a derivative.  While the derivative admits many interpretations, I think this is the most basic and the most important to grasp, since it is always true (for real and complex variables, at least) and since it implies some of the other interpretations (such as velocity being the derivative of position).  I don't think that waffling on this point will make derivatives clearer to the average person (unlike the first sentence of the article, where I thought it did).  That said, I am not entirely happy about the phrase "rate of change", which I think is more of a slogan than something intuitive.
 * "Equations involving derivatives are called differential equations" &rarr; "Equations involving differentials are called differential equations". From most people's perspective, this is simply not true.  The average engineer, say, always formulates differential equations in terms of derivatives.  While I think it would be a great thing to introduce differential forms to the masses, this is not how things are generally done.  Since Wikipedia is an encyclopedia, not a vehicle for change, I think we are obligated to stick to what is standard.
 * "and are fundamental in describing natural phenomena." &rarr; "and are useful in describing natural phenomena." I think "fundamental" is entirely justified here: All of physics can be formulated in terms of variations of Lagrangians.  If anything, "useful" understates the importance of derivative.
 * So that's what I was thinking. I'm still open to discussion and to suggestions; and don't forget WP:BOLD.  Ozob (talk) 14:20, 3 July 2013 (UTC)

Chain rule
In Leibniz' notation, if one has a function 'f' and writes df/dx, this simply means "the derivative of f." In this context, 'x' is a dummy variable of sorts; for a function of a single variable it serves no actual purpose in the formal definition, and for a function of n variables it serves only to point at a specific spot in a n-tuple. That we write "dx" is more a product of historical accident than a meaningful mathematical notation, and is one of the reasons that Leibniz' notation in general is rather lousy, so far as correctness and consistency in notation are concerned.

With this in mind, "d(f ∘ g)/dg" is meaningless without further definition, since "f ∘ g" is simply a function of one variable, in the same way as f. For that notation to be meaningful, one must *define* it to mean (df/dx) ∘ g.  Functions do not have arguments when they are functions; as soon as you give a function an argument, it ceases to be a function and becomes an element in the image of the function.

If you can find any standard Analysis text which disagrees, feel free to cite it. — Preceding unsigned comment added by 129.2.129.149 (talk) 13:56, 25 October 2013 (UTC)


 * I will be extremely surprised if you can find an analysis textbook that agrees with your claim that the x in df/dx is a dummy variable. That is, quite frankly, wrong.  If y = g(x) and z = f(y) = f(g(x)), then df/dx is the derivative of the composite of f and g and df/dy is the derivative of f alone.  Moreover, since y = g(x), one can write df/dg to mean df/dy.


 * You should think carefully about the statement of the chain rule given further down in the article,


 * If y = f(u) and u = g(x), then this abbreviated form is written in Leibniz notation as:


 * $$\frac{dy}{dx} = \frac{dy}{du} \cdot \frac{du}{dx}.$$


 * Think about what this would mean if x were a dummy variable.


 * I'll concede that df/dg is perhaps not a very common notation, but it does appear in places. I have seen people write df/d(log x).  There is nothing wrong with it.  Ozob (talk) 14:09, 25 October 2013 (UTC)


 * What you have to understand here is that formally, if we declare
 * $$f:\mathbb{R}\rightarrow \mathbb{R}$$, and
 * $$ \frac{df}{dx}:\mathbb{R}\rightarrow \mathbb{R}$$ such that
 * $$\frac{df}{dx}(x) = \lim_{t\rightarrow 0} \frac{f(x+t) - f(x)}{t}$$,
 * then the "dx" does not enter meaningfully into the formal definition of df/dx. We could call that "variable" anything we want, and the definition would be precisely the same.  The function 'f' does not have anything to do with the argument 'x', and f(x) does not refer to a function, it refers to an element in the image of f.  Similarly, df/dx has nothing to do with 'x.'  It is simply a function; it is defined uniquely by a set of 2-tuples.  The mathematical object of a function does not have an argument.  A function evaluated at an argument is no longer a function.


 * To clarify, it helps to realize that if we define
 * $$g:\mathbb{R}^{2}\rightarrow \mathbb{R}$$ such that
 * $$g(x,y) = x^{2} + y^{3}$$, and define
 * $$\frac{\partial g}{\partial x}: \mathbb{R}^{2}\rightarrow \mathbb{R}$$ such that
 * $$\frac{\partial g}{\partial x}(x,y) = \lim_{t\rightarrow 0} \frac{g(x+t,y) - g(x,y)}{t}$$,
 * then it is provably true that
 * $$\frac{\partial g}{\partial x}(y,x) = 2y$$.
 * By our formal definition, $$\frac{\partial g}{\partial x}$$ refers only to the *first* variable, regardless of what it is called; that we call it 'x' is a matter of convenience, not of definition; we cannot have it behave otherwise without either our notation being inconsistent or defining some sort of metalanguage for producing new formal definitions of the derivative based on what we happen to be calling the point at which we're evaluating it (which is overwhelmingly silly).


 * The notation df/d(log(x)) is overwhelmingly sloppy; you might see physicists or engineers do it, but it's not something you will ever see in well-posed mathematics, because it does not follow from the formal definition of the derivative. Strictly in terms of the limit expression, it is completely meaningless. 129.2.129.149 (talk) 15:26, 25 October 2013 (UTC)


 * I think the first time I saw something like df/d(log x) was in Fisher and Tippett, Limiting forms of the frequency distribution of the largest or smallest member of a sample, Mathematical Proceedings of the Cambridge Philosophical Society, Volume 24, Issue 2, April 1928, pp. 180–190. I found a scanned copy at  for you; it's right there on page 186.  If you doubt the authors' credentials then you can read about them at Ronald Fisher and L. H. C. Tippett.  Ozob (talk) 03:13, 26 October 2013 (UTC)

Integral Calculus
Ozob, Thanks for the positive feedback on my Integral Calculus edits. I'm relearning Calculus, and I think I will have more to add in terms of lucid explanations for the layman. I'm curious about your Math and professional background, but am not sure of the right forum to discuss that. Mathaholicsidsoni (talk) 15:59, 24 November 2013 (UTC)


 * Well, I don't much like to talk about myself on the Internet, but I'm a professional research mathematician. While my specialty is not related to calculus (I'm an algebraic geometer by training) I have a soft spot for it, because it was the first math that I ever really got interested in.  I've now not only taught calculus, I've even said in lecture the same thing that you put into the article—I think it's important for students to hear (because they often think of integrals as complicated, when in fact they're closely related to things they already understand).  For some reason I never thought to write it down here, but I liked it when you did.


 * I too am curious about your mathematical and professional background. Your edit sounded like you understand these things, not like you're relearning calculus.  Usually people put personal facts about themselves on their user page, though I won't be offended if you prefer to be as cryptic about your identity as I am about mine.  Ozob (talk) 17:09, 24 November 2013 (UTC)

Talkback
Over a hundred days later, I think I've found a way to eliminate those error terms. Jasper Deng (talk) 18:01, 20 December 2013 (UTC)