User talk:Ozob

Thank you...

...for your improvements to the problem of Apollonius! :)

Welcome to Wikipedia, by the way! I hope that you like it here, and if I can help you, I'll do my best. I like your name; perhaps it's Bozo spelled backwards? ;) A friendly hello from Willow (talk) 23:22, 14 May 2008 (UTC)

....for helping me understand partitions and riemman integrals... —Preceding unsigned comment added by 69.116.88.176 (talk) 23:40, 14 July 2009 (UTC)

Empty product

I appreciate the compromise at empty product. The difficulty is that the material about 0^0 isn't particularly relevant to the article on empty products, except for the case where 0^0 is viewed as an empty product. That's why all the material you added is already in the exponentiation article, with a pointer from the empty product article. I hope you'll look through the talk archives of those pages to see that Bo Jacoby has made the same arguments before, but didn't find consensus. The previous round of discussion about the topic is what led to the consolidation in the exponentiation article. — Carl (CBM · talk) 22:06, 12 June 2008 (UTC)

Hi Carl,

Yes, I agree that the material's not relevant. I did read part of the talk page, and I agree that there's no consensus. And I, too, would prefer that the material be on the exponentiation page. But I saw a war starting, and I was hoping I could pacify both sides. I actually like the article better the way you've left it (because, as you say, the article is about empty products and not about 0^0); but I thought that by including the other side's arguments, I would make everyone happy. I just want the discussion to be peaceful. Ozob (talk) 17:49, 13 June 2008 (UTC)

If you feel a discussion is more appropriate somewhere else, the usual thing to do is to direct people there and copy material over. People leave messages to bring matters to community attention so at least Trovatore's request should not have been removed. You can't expect people to watch this page religiously. I almost missed seeing the request because of your removal. In general, you should not remove other people's comments unless they violate some serious policies. Even then, it may be preferable to archive them (see Wikipedia:Talk_page_guidelines). --C S (talk) 23:54, 12 June 2008 (UTC)

Hi C S,

I'm puzzled. Just as you suggested, I left a notice [1] redirecting people to Talk:Empty_product#Moved from WikiProject talk where I had moved the discussion [2]. Trovatore's original comment didn't provide any context except for a mention of Bo Jacoby (I had to look at the article history to know what was going on), so I thought my notice was no worse. So I'm wondering how I might have done better. I see that you would have preferred if I had left Trovatore's original comment, and now that I think about it, that would have been the right thing to do. Do you have any other ideas on better ways to move a discussion? Thanks. Ozob (talk) 17:49, 13 June 2008 (UTC)

Well, as you've figured out, without knowing the context, it's more prudent just to leave things the way they were said. Trovatore could have phrased it better but this is like the umpteenth time, so he probably was too exasperated to do so. To learn about Bo Jacoby you have to go through a lot more than one article history (you can try searching the WP:Math archives). Except for the removal of the original request, moving the other comments wasn't a bad idea. But it's unusual. It's not uncommon for the discussion to sometimes become a little article specific before someone advocates moving the focus of discussion elsewhere. Even then, the comments themselves are not expunged. I personally think it's just best to leave things as they are. The bot will archive them anyway. Also, sometimes people want to make a comment to the general community and not get involved on the article discussion page (which they may not even watch). --C S (talk) 21:01, 13 June 2008 (UTC)

Oh, I've seen Bo Jacoby at work before, and I realize that he's part of the problem. (But I also see User:Michael Hardy, User:JRSpriggs, and User:Kusma on his side.) Counting from the first reply (which was also the first to mention the issue at hand rather than plea for help) at 15:07 UTC to 21:02 UTC when I moved it, it generated ten posts totaling about 7,000 bytes, all of which simply repeated arguments that could be found on the talk page. My real concern was that the thread was pure noise, no signal, and a lot of noise at that (for that page, at least). I felt entirely justified in moving it away, "to a better place", as I put in my edit summary, and I meant that not only in a literal but also a more figurative way. I know that it's unusual, but I strongly feel that it was (and still is) the right thing to do. Ozob (talk) 00:28, 14 June 2008 (UTC)

Apollonius

Hi Ozob, I’ve replied to your points at: Talk:Problem_of_Apollonius#Oldest_significant_result_in_enumerative_geometry.3F

Sorry for the delay!

Nbarth (email) (talk) 11:49, 22 June 2008 (UTC)

With thanks

Mmmm, gratitude...

I'd like to thank you for your contributions to Emmy Noether. As a total mathematics moron, I feel infinitely indebted to number-smart folks like you and WillowW. I appreciate your support and the many edits you've made. Have a donut. – Scartol • Tok 00:03, 23 June 2008 (UTC)

Emmy Noether

I saw that you have almost entirely reverted an IP's edit, which I'm not that happy about. The person obviously knew what s/he was talking about. Missing citations is bad, but one cannot make everything perfect in one go. Please reconsider your revert. Thank you, Randomblue (talk) 19:13, 30 June 2008 (UTC).

I have discussed this privately with the user over email, and I hope we are both satisfied with the situation. I'm actually looking forward to their contributions, since (as you said) they seem to know what they're talking about. If there's something you'd like to rescue from the edit in question, please go ahead and change the article. I'm not infallible, after all, and as I said initially, I'm probably being a little overprotective. Ozob (talk) 22:31, 30 June 2008 (UTC)

The footnote to Einstein's letter to the New York Times links to a Web page that claims Einstein's letter appeared on May 5, 1935. However, one can retrieve the actual letter from the New York Times archive, and see that the letter appeared in the Times on May 4, 1935. Therefore, the Web page cited in the footnote has the date wrong. I corrected the date recently, but just discovered that my correction was reverted on the grounds that my change was incorrect. I invite you to check for yourself that the letter appeared on May 4, 1935. —Preceding unsigned comment added by 66.108.13.221 (talk) 00:23, 4 July 2009 (UTC)

expert point of view

Hi Ozob. I just wanted to point out that Moon Duchin, one of the sources in the Noether article, has kindly accepted to review the article. I see she has left a message on the talk page today discussing various issues. There is still room for improvement! Best, Randomblue (talk) 10:22, 9 July 2008 (UTC).

RFC at St. Petersburg paradox

As you have contributed to an earlier related discussion at Wikipedia talk:Manual of Style (mathematics)#Punctuation of block-displayed formulae, you may be interested in Talk:St. Petersburg paradox#Request for comments: punctuation after displayed formula.  --Lambiam 18:18, 8 August 2008 (UTC)

Thanks!

Yes, \textstyle{} is much better. Thanks for fixing it up! siℓℓy rabbit (talk) 15:18, 9 August 2008 (UTC)

Common interests, clearly

You're right, we've been chasing same articles all over the place for the past weeks. I just ended up reverting your IPA guide to étale (see the talk page). I accidentally got more involved in fixing articles related to algebraic geometry (just back from vacation so I really should not have time for this!), so it's very good to have some company doing this. I think we've had some good progress on many topics. A lot remains to be done to AG-related topics — one example is just adding the maths rating template to many (majority of) articles on important topics. With things getting busier at work by the day, I'm afraid my contributions will slow down from now on, but let's see. Cheers, Stca74 (talk) 09:13, 10 August 2008 (UTC)

Ozob's proposed deletion of "Non-Newtonian calculus"

The article "Non-Newtonian calculus" provides a brief description about a subject of interest to scientists, engineers, and mathematicians. The omission of this subject from Wikipedia would be a huge disservice to those people. The article is coherent, meaningful, and unbiased. Exactly what do you object to? Shouldn't an encyclopedia contain as much pertinent knowledge as possible? Please reconsider your decision. Thank you.

Sincerely, Michael Grossman —Preceding unsigned comment added by Smithpith (talk • contribs) 19:48, 12 September 2008 (UTC)

Citation, reviews, and comments re "Non-Newtonian Calculus"

"Non-Newtonian Calculus" is cited by Professor Ivor Grattan-Guinness in his book "The Rainbow of Mathematics: A History of the Mathematical Sciences" (ISBN 0393320308). Please see pages 332 and 774.

"Non-Newtonian Calculus" has received many favorable reviews and comments:

The [books] on non-Newtonian calculus ... appear to be very useful and innovative.

                       Professor Kenneth J. Arrow, Nobel-Laureate 
                       Stanford University, USA 

Your ideas [in Non-Newtonian Calculus] seem quite ingenious.

                       Professor Dirk J. Struik 
                       Massachusetts Institute of Technology, USA 

There is enough here [in Non-Newtonian Calculus] to indicate that non-Newtonian calculi ... have considerable potential as alternative approaches to traditional problems. This very original piece of mathematics will surely expose a number of missed opportunities in the history of the subject.

                       Professor Ivor Grattan-Guinness 
                       Middlesex University, England 

The possibilities opened up by the [non-Newtonian] calculi seem to be immense.

                       Professor H. Gollmann
                       Graz, Austria 

This [Non-Newtonian Calculus] is an exciting little book. ... The greatest value of these non-Newtonian calculi may prove to be their ability to yield simpler physical laws than the Newtonian calculus. Throughout, this book exhibits a clarity of vision characteristic of important mathematical creations. ... The authors have written this book for engineers and scientists, as well as for mathematicians. ... The writing is clear, concise, and very readable. No more than a working knowledge of [classical] calculus is assumed.

                       Professor David Pearce MacAdam
                       Cape Cod Community College, USA

... It seems plausible that people who need to study functions from this point of view might well be able to formulate problems more clearly by using [bigeometric] calculus instead of [classical] calculus.

                       Professor Ralph P. Boas, Jr.
                       Northwestern University, USA

We think that multiplicative calculus can especially be useful as a mathematical tool for economics and finance ... .

                       Professor Agamirza E. Bashirov
                       Eastern Mediterranean University, Cyprus/
                       Professor Emine Misirli Kurpinar
                       Ege University, Turkey/
                       Professor Ali Ozyapici
                       Ege University, Turkey

Non-Newtonian Calculus, by Michael Grossman and Robert Katz is a fascinating and (potentially) extremely important piece of mathematical theory. That a whole family of differential and integral calculi, parallel to but nonlinear with respect to ordinary Newtonian (or Leibnizian) calculus, should have remained undiscovered (or uninvented) for so long is astonishing -- but true. Every mathematician and worker with mathematics owes it to himself to look into the discoveries of Grossman and Katz.

                       Professor James R. Meginniss
                       Claremont Graduate School and Harvey Mudd College, USA

Note 3. The comments by Professors Grattan-Guinness, Gollmann, and MacAdam are excerpts from their reviews of the book Non-Newtonian Calculus in Middlesex Math Notes, Internationale Mathematische Nachrichten, and Journal of the Optical Society of America, respectively. The comment by Professor Boas is an excerpt from his review of the book Bigeometric Calculus: A System with a Scale-Free Derivative in Mathematical Reviews.

Thank you.

Sincerely, Michael Grossman —Preceding unsigned comment added by Smithpith (talk • contribs) 01:03, 13 September 2008 (UTC)

Dab page

The dab page is at Janko; why did you redirect the other dab page (Janko_group_(disambiguation)) to the aricle Janko group instead of the correct dab page ? SandyGeorgia (Talk) 00:02, 14 September 2008 (UTC)

"Janko group" on its own is ambiguous. Shouldn't Janko group (disambiguation) disambiguate Janko group rather than Janko?

I agree that the present Janko group article is not a proper disambiguation page, but I'll fix that. Ozob (talk) 00:08, 14 September 2008 (UTC)

Janko group is now a "proper" article, as it should be. Which page is going to be the dab page, and the other (duplicate) dab page should direct to it. SandyGeorgia (Talk) 00:10, 14 September 2008 (UTC)

Janko group is incapable of containing actual content since it could refer to any of four separate objects. I've made it a disambiguation page. Janko group (disambiguation) points there. It's worth pointing out that I created Janko group (disambiguation) because Template:Group navbox pointed to Janko group but clearly intended to refer to all four groups. Ozob (talk) 00:18, 14 September 2008 (UTC)

This was an article. OK, you'll need to sort this with the folks at the Group Math FAC, as the article will now show as incorrectly linked. I did what I could to try to help. SandyGeorgia (Talk) 00:21, 14 September 2008 (UTC)

I have this feeling that we're both trying to do the right thing, and somehow we're not communicating.

I'm not sure what part of the MoS Janko group now violates; it does not give extended definitions as you stated in your edit summary, but only the simplest possible fact which could be used to distinguish the groups (besides their names), namely their order. I'll ask at the Group FAC and we'll sort it out there. Ozob (talk) 00:34, 14 September 2008 (UTC)

I'll wait for you all to sort it; the article was fine and did the job, now it's back to being a dab trying to be an article, and we have Group (mathematics) pointing to a dab, that easily could have been (was) an article. SandyGeorgia (Talk) 00:36, 14 September 2008 (UTC)

Janko

Hi Ozob,

before we are all going mad!!! (<- notice the complete anti-MOS-hly markup), I have replaced the Janko group link in the navbox by all four groups (which is, I believe, worse than having the link to J.gr. itself, but at least compliant to MOS). (I'm so tired by these nitpicking comments at FAC whose sole objective it seems to be to follow the guidelines mm per mm) Jakob.scholbach (talk) 10:06, 14 September 2008 (UTC)

Easy as pi?: Making mathematics articles more accessible to a general readership

The discussion, to which you contributed, has been archived, with very much additional commentary,
at Wikipedia:Village pump (proposals)/Archive 35#Easy as pi? (subsectioned and sub-subsectioned).
A related discussion is at
(Temporary link) Talk:Mathematics#Making mathematics articles more accessible to a general readership and
(Permanent link) Talk:Mathematics (Section "Making mathematics articles more accessible to a general readership"). Another related discussion is at
(Temporary link) Wikipedia talk:WikiProject Mathematics#Making mathematics articles more accessible to a general readership and
(Permanent link) Wikipedia talk:WikiProject Mathematics (Section "Making mathematics articles more accessible to a general readership").
-- Wavelength (talk) 01:38, 29 September 2008 (UTC)

Derivative with respect to a vector

Hi Ozob. On the talk page for Euclidean vector, you wrote that there is a section in the article called:

• Derivatives with respect to a vector (wrongly labeled the "derivative of a vector")

I don't want to sidetrack the discussion on that page, so I'm asking you here. Why do you believe it is incorrectly titled? Isn't

${\frac {\mathrm {d} \mathbf {v} }{\mathrm {d} t}}$

the derivative of the vector v with respect to the scalar t? MarcusMaximus (talk) 06:15, 5 October 2008 (UTC)

It should be "Derivative of a vector-valued function" or "Derivative with respect to a vector". I believe that the section is incorrectly titled because vectors are not functions, and therefore the idea of differentiation is meaningless. Ozob (talk) 01:23, 6 October 2008 (UTC)

What about the concepts of relative velocity as the derivative of displacement, and acceleration as the derivative of velocity? Is the displacement between two points not a vector, but rather a vector function? Is it worth making such a semantic distinction? The text says that the vector is a function of a scalar.

Also, I think it would be incorrect to title it "derivative with respect to a vector", because that is the phrasing typically used to refer to the quantity that appears in the "denominator" part when using the d/dt notation. Certainly there is nothing in there about taking the derivative of something with respect to a vector, in the sense of measuring the rate of change of a dependent function as an independent vector changes. MarcusMaximus (talk) 02:32, 6 October 2008 (UTC)

Displacement between two points is a vector. If one (or both) of those points is variable, then you get a function: Each choice of points determines a unique displacement vector. Functions have derivatives, so this makes sense. But to talk about the derivative of a vector—just a vector, not a vector-valued function—is meaningless. Derivatives are only defined for functions; even when we differentiate a constant (as in (d/dx)(1) = 0) we are really differentiating the constant function.

I think "derivative with respect to a vector" is an appropriate description of a directional derivative. It seems to me that it would be consistent with the usual notation to write the directional derivative in the direction v as d/dv, even though that's not usually done.

I have a question for you: You write d/dt where I would write d/dt. Surely you learned this notation somewhere. Where? The only place I've ever seen an upright d is on Wikipedia. Ozob (talk) 14:53, 6 October 2008 (UTC)

I understand your point about vector functions. In fact, the reference I was using refers to them as vector functions, so I agree that we should change the title to Derivative of a vector function. I've made the change.

The section we are talking about doesn't discuss the directional derivative, only the derivative a of vector with respect to scalars. Regardless, I don't believe that d/dv would be the correct notation for the directional derivative. The directional derivative in the direction of v is defined using the gradient function as

$\nabla _{\mathbf {v} }{f}(\mathbf {x} )=\nabla f(\mathbf {x} )\cdot \mathbf {v} .$

In contrast, the notation you are suggesting indicates that there is some vector-valued function that is dependent on v and we want to differentiate it with respect to v; in other words, find the rate of change of the function as the vector v changes. I don't think that's what the directional derivative does; often v is a constant vector. It doesn't make sense to take the derivative with respect to a constant.

You could argue that the gradient of f at x is equal to df/dx

$\nabla {f}(\mathbf {x} )={\frac {df(\mathbf {x} )}{d\mathbf {x} }}$

but I haven't given it enough thought to decide if that idea is problematic.

I actually agree with you on the d/dt notation, but several places on Wikipedia people have gone through and changed my italic d's to upright, so I assumed that was some sort of style guide convention. MarcusMaximus (talk) 16:24, 6 October 2008 (UTC)

When I wrote d/dv, I was thinking in terms of a connection, specifically in its manifestation as a covariant derivative. From that perspective, d/dt is differentiation with respect to the a vector which points in the direction of the positive t axis and has length 1.

I think it's reasonable to write the gradient as df/dx. But this sort of notation is never used, nor is d/dv, and I don't know why. I'd guess that in practice, it's messier than the usual notation.

Currently the WP MoS specifies that the d in d/dx can be either italic or upright. It also says not to change it from one to the other except for consistency within the article (or if you're rewriting from scratch). So if someone changes your italic d's to upright, I think you ought to revert! Ozob (talk) 21:57, 6 October 2008 (UTC)

As an engineer I'm not well educated in the more abstract principles of connection and contravariance. It sounds like you can call a scalar variable a vector in its own right? That seems trivial to me, but I'm not here to judge the value of mathematical concepts.

After thinking about it more, it seems to me the reason the gradient is not generally written df/dx is because the function f(x₁,x₂,x₃) of which we are taking the gradient is not truly a function of the vector x in general. It is a scalar function of an arbitrary number of scalars. If you wrote it out, you generally wouldn't have any occurrences of the vector x made up of components in the standard basis. However, each scalar has its own axis and can be thought of as a scalar component of a vector x = x₁i + x₂j + x₃k, but the vector x does not actually appear in the function f itself, unless you wanted to recast the function so that every instance of (x₁,x₂,x₃) was a dot product of x with i,j,k. MarcusMaximus (talk) 05:01, 7 October 2008 (UTC)

Yes, I am calling a scalar a vector. I agree that it's trivial: A one-dimensional vector space is just the space of scalars. But if you think in those terms then you can see an analogy between the notation d/dt and the notation d/dv.

I disagree that f is not a function of x. To every x, you get a unique output f(x); this is the definition of a function. The way it's written is unimportant. As you say, you could write dot products every time you want to take a component. Doing so demonstrates that f is a function of x. But you could also add and subtract the same number, for example, f(x) = (x·i + 1) - 1. This formula specifies an algorithm to compute f(x) which goes like: Take the dot product of x and i, add one, then subtract one. As a function, this is the same as f(x) = x·i, even though the latter specifies a different algorithm, namely, take the dot product of x and i. In the same way, the distinction between f(x) = x·i and f(x) = x₁ is only a matter of the algorithm specified by the formula, not the function.

I suppose that if one wanted to be very pedantic, then one could argue that even though x is an element of a three dimensional vector space with a fixed basis, the underlying set of that vector space might not be the set of all triples (x₁, x₂, x₃); instead it might be something like "all polynomials of degree less than or equal to two with basis 1, x, x²". But vector spaces with chosen basis are naturally isomorphic to arrays of numbers, so I don't think it's an important distinction. Ozob (talk) 22:39, 7 October 2008 (UTC)

I do see your analogy now. Here's my theory on d/dv question.

Usually people expect to the arguments to appear explicitly in the formula for the function. With that in mind, f can be cast as a function of x; however, in general, it is not cast that way.

To use your example f(x) = x₁, there is no connection between f and x unless you use a separate equation to define the relationship between x and x₁, such as x = x₁i + x₂j + x₃k. In that case, most people would infer that x is a function of x₁ rather than the inverse (even though both are true). In that case it's counterintuitive to say that f is a function of the vector x; most people would say that both f and x are functions of x₁.

The alternative is to define x₁ = x•i, which does create the necessary intuitive order. But even in this instance you don't get the explicitness most people expect and desire. If you write

f(x) = x₁ where x₁ = x•i,

even though it is strictly true, it makes about as much intuitive sense as writing g(z) = y. People wonder what the heck you're talking about, until you tell them, oh, by the way, y = h(z). Then they wonder why the heck you wrote g(z) on the left side instead of g(y) but wrote the right side in terms of y rather than explicitly in terms of z.

So back to the main point, I think it is clear that we should really be talking about the gradient, not the directional derivative. In my opinion the main reason the gradient is not commonly written as d/dv is that it often requires counterintuition. I'm not arguing that you can't write the gradient as d/dv, but it only makes sense sometimes and it's more general to just use $\nabla$.

It's also not obvious to me (without knowing a priori how to take the gradient) what exactly you're supposed to do when you see df(x)/dx. You're actually taking the derivative of a scalar function f with respect to the sum of three vectors x₁i, x₂j, x₃k, which doesn't make a lot of sense to me. It appears that you have to take the formula on the right hand side of f(x), which is a scalar algebraic expression containing x₁,x₂,x₃, and implicitly differentiate it with respect to x using the chain rule. Then you have an algebraic expression in terms of x₁, x₂, x₃, dx₁/dx, dx₂/dx, and dx₃/dx. Next you have to find expressions for dx₁/dx, dx₂/dx, and dx₃/dx. I'm not sure what those would be, since there is no such thing as vector division that I know of. Maybe they are i,j,k, respectively? MarcusMaximus (talk) 08:54, 8 October 2008 (UTC)

That's a good point that while f(x) = x₁ is counterintuitive. I was only paying attention to the formal logic, but you're right.

If we continue to think of d/dx as the gradient, then dx₁/dx would be the gradient of x₁, hence i, and similarly you'd get j and k for x₂ and x₃. And no, there is no such thing as vector division in general; division is a very, very restrictive condition.

I agree that the "right thing" to think about in a lot of cases is the gradient, not the directional derivative. A better thing to think about, it turns out, is differential forms and exterior derivatives. But in order to make sense of them and their relationship to the gradient, you need to distinguish between the tangent space and cotangent space, and this is more effort than most people are willing to make. Ozob (talk) 17:42, 8 October 2008 (UTC)

Forgive my ignorance, but could you be more explicit? You said, "If we continue to think of d/dx as the gradient, then dx₁/dx would be the gradient of x₁, hence i, and similarly you'd get j and k for x₂ and x₃."

This becomes circular, because I'm trying to find an expression for dx₁/dx in order to prove that d/dx is the gradient. I just need to show that dx₁/dx is i, but how do I get there? MarcusMaximus (talk) 23:26, 10 October 2008 (UTC)

Well, after a little thought,

$x_{1}=\mathbf {x} \cdot \mathbf {i} ,$

therefore

${\frac {dx_{1}}{d\mathbf {x} }}={\frac {d\mathbf {x} }{d\mathbf {x} }}\cdot \mathbf {i} +\mathbf {x} \cdot {\frac {d\mathbf {i} }{d\mathbf {x} }}.$

Since di/dx is the zero vector, we are left with

${\frac {dx_{1}}{d\mathbf {x} }}={\frac {d\mathbf {x} }{d\mathbf {x} }}\cdot \mathbf {i}$

If you substitute the derivative of x the equation becomes a triviality, collapsing to dx₁/dx = dx₁/dx. It seems that the value of dx/dx must be an entity that dot multiplies with the vector i and leaves it unchanged. The only thing I know of that does that is the unit dyadic (ii + jj + kk), but I have no idea how that would come into play. I'm still stumped. MarcusMaximus (talk) 04:04, 11 October 2008 (UTC)

Hmm. If I understand you correctly, you're looking for a way to manipulate the symbol d/dx (using the usual rules) that makes the expression for the gradient pop out. I'm not sure whether or not one can do this. At some point one has to define what d/dx means; I was intended to define it to be the gradient because that seemed to be the only way to make it consistent. You seem to be looking to define it by certain properties that it should satisfy (the product rule, chain rule, etc.), but I don't think that's enough to get a unique expression out. (My reasoning comes from Riemannian metrics; the gradient is what one gets by taking the exterior derivative of f and contracting with the metric, so if one changes the metric one gets a different gradient. If you normalize d/dx by choosing the values of dx₁/dx and similar expressions in the other variables, you should have enough information to determine the gradient. But without that there are too many possible metrics.)

I also think that if f is a vector-valued function, then d/dx should mean (by definition again) the total derivative. This is consistent with the use of d/dx to mean "derivative with respect to the variable x"; if x happens to be a one-dimensional vector (so that it's okay to write x = x), then d/dx is equal to d/dx just like it should be.

Does this work? I think I've dodged circularity this time by making a definition. Ozob (talk) 23:07, 11 October 2008 (UTC)

That is rather unsatisfying. It just seems to me (with no particular reason) that we should be able to prove that d/dx is the gradient. We already know how to take derivatives according to the definition based on the limit of the slope of the secant, and we know what a vector is. What we don't know, I guess, is what it means to take the derivative with respect to a vector, but I was hoping to be able to derive it. MarcusMaximus (talk) 09:14, 12 October 2008 (UTC)

Hey, I just got an idea! Let's go back to the definition. I'm going to take this as the definition of the derivative in one variable:

$\lim _{h\to 0}{\frac {|f(x+h)-f(x)-f'(x)h|}{|h|}}=0.$

(That is to say, f'(x) is the unique number which makes the above equation hold.) OK, now I make everything a vector:

$\lim _{\mathbf {h} \to 0}{\frac {\lVert f(\mathbf {x} +\mathbf {h} )-f(\mathbf {x} )-f'(\mathbf {x} )\mathbf {h} \rVert }{\lVert \mathbf {h} \rVert }}=0.$

Now, would you agree that df/dx ought to satisfy this equation? But this is exactly the definition of the total derivative.

When f is a real-valued function, this is not exactly the same as the gradient; instead it's a linear transformation R³ → R. If one fixes a basis of R³ (which is the same as fixing a Riemannian metric at the point we're differentiating at) then one can identify R³ with its dual space and convert the linear transformation into a vector in R³. That vector will be the gradient. Ozob (talk) 20:19, 12 October 2008 (UTC)

Excellent. So ƒ’(x) (ƒ prime) is dƒ/dx, the gradient of ƒ(x). Then ƒ’(x)h is the juxtaposition of two vectors...a dyadic? Or does there need to be a dot product in there, ƒ’(x)•h, because the other two terms in the numerator are scalars? Even if ƒ(x) is a vector function you have the sum of two vectors with a dyadic. MarcusMaximus (talk) 07:07, 13 October 2008 (UTC)

No, $f(\mathbf {x} )$ is a linear transformation. If f is a real-valued function, then $f(\mathbf {x} )$ is a linear functional: It takes a vector, in this case h, and returns a scalar. When f is a vector valued function, then $f(\mathbf {x} )$ can be written as a matrix. (Sorry for the TeX, but I'm having strange formatting issues.)

I think it's worth pointing out that a dyadic tensor is the same thing as a linear transformation (see the last paragraph of the dyadic tensor article as well as dyadic product). In that interpretation, f'(x)h is the application of h to the dyadic tensor f'(x); in the case when f is real-valued, however, it's a dyadic tensor in the basis vectors ii, ij, ik (and no others). Ozob (talk) 15:00, 13 October 2008 (UTC)

So is this definition operational? Can I plug in real expressions and do some algebra and calculus to get a real answer? Starting with ƒ(x) = x•i = x₁,

${\begin{aligned}0&=\lim _{\mathbf {h} \to 0}{\frac {\lVert f(\mathbf {x} +\mathbf {h} )-f(\mathbf {x} )-f'(\mathbf {x} )\mathbf {h} \rVert }{\lVert \mathbf {h} \rVert }}\\&=\lim _{\mathbf {h} \to 0}{\frac {\lVert (x_{1}+h_{1})-(x_{1})-f'(\mathbf {x} )(h_{1}\mathbf {i} +h_{2}\mathbf {j} +h_{3}\mathbf {k} )\rVert }{\sqrt {h_{1}^{2}+h_{2}^{2}+h_{3}^{2}}}}\\&=\lim _{\mathbf {h} \to 0}{\frac {\lVert h_{1}-f'(\mathbf {x} )(h_{1}\mathbf {i} +h_{2}\mathbf {j} +h_{3}\mathbf {k} )\rVert }{\sqrt {h_{1}^{2}+h_{2}^{2}+h_{3}^{2}}}}\\&=?\end{aligned}}$

MarcusMaximus (talk) 03:21, 17 October 2008 (UTC)

I don't think so. Usually one proves that for a continuously differentiable function, the total derivative equals the matrix of partial derivatives; then one computes the total derivative using partial derivatives. But I don't know how else to do it. Ozob (talk) 18:35, 17 October 2008 (UTC)

I suppose it is useful in mathematics to prove something is true after you have the correct answer. However, for an engineer using applied mathematics, it is important that definitions be operational. I'll keep looking. MarcusMaximus (talk) 23:32, 18 October 2008 (UTC)

The point of such a theorem is that d/dx can (under mild hypotheses) be computed easily. Taking partial derivatives is easy, and putting them in a matrix is even easier. So this theorem tells you that the total derivative, while a priori hard to compute, is actually easy to compute. I agree that the computation can't be done easily from the definition itself, but that's no different from computing any complicated derivative. Think about differentiating a function where you need to use the product and chain rules in combination several times; directly from the definition, it's a huge and nearly impossible mess, but with the product and chain rules it becomes easy. Computing the total derivative is analogous: An hard definition (the one above) which one proves to be the same as an easy rule (take partial derivatives and put in a matrix). Ozob (talk) 01:00, 19 October 2008 (UTC)

Vector spaces

Hi Ozob,

I have asked for a GA review at the round table, but people are busy/dizzy with LateX formatting and icon questions ;) I thought you might be interested in having a look at vector spaces and giving it a GA review? This is the page. Thanks a lot. Jakob.scholbach (talk) 14:13, 1 December 2008 (UTC)

AfD nomination of Bishop–Keisler controversy

An article that you have been involved in editing, Bishop–Keisler controversy, has been listed for deletion. If you are interested in the deletion discussion, please participate by adding your comments at Wikipedia:Articles for deletion/Bishop–Keisler controversy. Thank you. Mathsci (talk) 05:42, 14 December 2008 (UTC)

Radius of convergence

Hi, your tweak does help, thanks. Do you happen to know what the coefficients of x^n would be in standard form?Regards, Rich (talk) 02:08, 16 December 2008 (UTC)

It'd be something to do with the round down of the base 2 logarithm of n. Looks like it'd be

$a_{n}={\frac {(-1)^{\lfloor \lg n\rfloor }}{2^{\lfloor \lg n\rfloor +1}\cdot (\lfloor \lg n\rfloor +1)}}$

Ozob (talk) 02:53, 16 December 2008 (UTC)

Table on trig identities

[3] I disagree. Provide reasoning as to why it's clearer. It looks to me as though there are more functions than there are. The parenthesis makes it clear what are the abbreviations. —Anonymous Dissident^Talk 05:12, 20 December 2008 (UTC)

Flagged Revisions Trial

Thanks for all your work on this difficult proposal. I am enjoying that a great deal of the effort into ensuring that any trial would be well-run and give us the right information is coming from editors on the oppose side of things. :) Lot 49a^talk 22:31, 6 January 2009 (UTC)

Flagged Revs

Hi,

I noticed you voted oppose in the flag revs straw pole and would like to ask if you would mind adding User:Promethean/No to your user or talk page to make your position clear to people who visit your page :) - Thanks to Neurolysis for the template   «l| Ψrometheăn ™|l»  (talk) 07:22, 8 January 2009 (UTC)

About math formulae

Thanks for addressing 800x600 window size of a math formula. See explanation at User_talk:Wikid77#Confusion over math formulas. -Wikid77 (talk) 12:35, 24 February 2009 (UTC)

Calculus lead

Hi Ozob, I really don't think that "a course of study" is a good descriptor there, both on the substance and in terms of compatibility with the rest of the lead. For one thing, it's too narrow: calculus, as a mathematical discipline, consists of a collection of techniques and some proofs that go along with them. Now, there are some courses that purport to teach these techniques … (Techniques: fundamental; how/whether they are taught: secondary). Do you see what I mean? Further down, the lead talks about how calculus is widely applicable. Obviously, it's the principles and techniques of calculus that are applied, not "the course of study". I don't insist on the word "discipline", but calculus is a fairly well defined part of mathematics, and it's a lot more than the name of a course or a popular textbook title. I've made a few other changes (might as well …), but this is what triggered my involvement. Good job, otherwise! Cheers, Arcfrk (talk) 04:16, 23 April 2009 (UTC)

Having read your argument, I agree with you: "course of study" isn't as good as I thought it was. I'm going to put "discipline" back in. Thanks for the feedback! Ozob (talk) 19:19, 23 April 2009 (UTC)

Calculus

Hi Ozob, I removed places that for my view have confusing grammar. however if you find some more places with poor grammar i will appreciate your help. Aleks kleyn (talk) 02:27, 26 April 2009 (UTC)

List still up to date?

Hallo Ozob, is this list Talk:Problem_of_Apollonius#Old_sources still up to date? Is the help still needed? Have you found some of the sources? --DrJunge (talk) 17:59, 1 May 2009 (UTC)

Derivative of a Vector Function

Hi Ozob.

I like your improvement of the intro to this section, except that I disagree with this statement:

A different choice of reference frame will produce the same derivative function, but it will usually have a different formula because of the different choice of reference frame.

In general, the derivative of a vector function is different in every reference frame. Your statement seems to confuse a reference frame with set of basis vectors. If we were only talking about multiple different bases fixed in the same reference frame, the statement would be true.

The concept of relative velocity is a good counterexample, I think. If you consider that the velocity (as the derivative of displacement or position) of a pilot sitting in an airplane, it should be apparent that you don't get the same function by differentiating in different reference frames. The velocity of the pilot relative to the Earth may be very large and time-varying, but his velocity relative to the airplane is identically zero. It is not merely switching bases, but it is an entirely different function.

Do I misunderstand you? MarcusMaximus (talk) 00:50, 1 August 2009 (UTC)

No, I think you do understand me, but we have a difference in viewpoint. I think I am still right; what's confusing is that in a certain sense I think you are also right. I am considering the reference frame as a coordinate chart on a manifold, i.e., we have functions x,y,z : M → R, where M is the space under consideration (which just so happens to be Euclidean space) and the map (x,y,z) : M → R³ is a diffeomorphism. The velocity function is a function on M, so it and its derivative are absolute in some sense. I.e, assuming a choice of connection, there is only one derivative of a function, namely the one given by the connection. But the derivative can be coordinatized in many different ways, and a choice of x,y,z leads to a choice of a derivative in your sense. Your sense, as far as I understand it, is that there is no space M, but only what I would call coordinate charts and their automorphisms. From this viewpoint, one always defines things in coordinates and then checks that it behaves under coordinate chart changes; that is, that it transforms tensorially. And since there is no analog of M, there is no sense in which there is one function with many possible formulas. Instead you get a different function in every reference frame.

There is another complication, which is that you seem to always use the standard Euclidean connection in each reference frame. This explains your airplane example: "Velocity relative to Earth" is one connection, and in the reference frame in which Earth is fixed, it is the standard Euclidean connection; "Velocity relative to the plane" is a different connection, given in the reference frame of the plane by the standard Euclidean connection. Of course, when you transform one reference frame into another, you don't transform the two connections into each other!

Does that make sense? I'm not sure what to do about the article, but am I at least understanding your viewpoint? Ozob (talk) 19:02, 1 August 2009 (UTC)

No, I actually have no idea what that means. I apologize, but I'm not trained in the mathematical theory you are talking about. I'm only trying to say that for a Euclidean vector, as they are called in the article, the right hand sides of the derivatives taken in two different reference frames are not merely the same function expressed in different bases, in which case you could perform a series of substitutions and get the same formula. They are literally different functions, related by the second formula shown here defining the derivative of a vector function is one reference frame as a function of the derivative taken in another reference frame.

Perhaps you could explain how what I see as two different functions, i.e. identically zero velocity vs. a time-varying velocity, are the same function? (that is a serious question, not rhetorical) MarcusMaximus (talk) 23:48, 1 August 2009 (UTC)

OK, I'll try again. In more elementary language, what I'm saying is that your notion of derivative changes when you change reference frames. Not only is the identically zero function not the same as a non-identically zero function; they are not the same kind of derivative! Abstractly, this is described by a connection. A connection is just an abstraction of the differentiation operator. When you take velocity relative to the Earth, you're measuring a rate of change with respect to the Earth, and this is a totally different rate of change than rate of change with respect to the plane. But once you have chosen something to measure against, the rate of change is independent of the reference frame.

Let me put some formulas to things. Suppose that x(t) = t is the position of the plane relative to the Earth. If we want to find the velocity of the plane with respect to the Earth, we take the derivative and get 1 unit per unit time. Suppose now we measure the position of the plane in its own reference frame and we get y(t) = 0. To measure the velocity of the plane with respect to itself, we take the derivative and get zero. OK so far. But what if we are in the reference frame of the Earth and we want to know the velocity of the plane with respect to itself? We can't take the derivative because we are in the wrong reference frame to do that. What we would like to do is convert to the reference frame of the plane, take the derivative there, then convert back to the reference frame of the Earth. That three-step operation satisfies all the formal properties of the derivative, e.g., it has a Leibniz rule. Therefore it's a connection. But it's not the usual connection (because that's the derivative, and the derivative in the reference frame of the Earth is velocity with respect to the Earth). Instead it lets you measure things relative to the plane while you're in the reference frame of the Earth; e.g., the Earth itself is found to be moving at velocity -1 relative to the plane. And that velocity is independent of the reference frame: The Earth is always moving at velocity -1 with respect to the plane, no matter what reference frame you're in!

Does that make more sense? Connections turn up in general relativity and in the Yang-Mills equations, so you might be able to find a better physically-motivated description of them in stuff on those. Ozob (talk) 20:00, 2 August 2009 (UTC)

Yes, I think we are in agreement on the basic phenomenon,

When you take velocity relative to the Earth, you're measuring a rate of change with respect to the Earth, and this is a totally different rate of change than rate of change with respect to the plane.

which I believe is the end of the discussion. However, this part really baffles me:

But what if we are in the reference frame of the Earth and we want to know the velocity of the plane with respect to itself? We can't take the derivative because we are in the wrong reference frame to do that. What we would like to do is convert to the reference frame of the plane, take the derivative there, then convert back to the reference frame of the Earth.

With respect to the bold text, why does it matter what reference frame "we" are "in" when we take this derivative? "We" don't appear anywhere in the equations that define the position of the pilot, the airplane, or the Earth. The equation for the derivative only takes account of the reference frame in which the derivative is being taken. There appears to be no other dependency; we are only talking about the relative motion of points with respect to each other. What I mean is, the velocity of the pilot relative to his plane is merely the velocity of the pilot relative to his plane—the velocity of a pilot-fixed point moving through a field of infinitely many airplane-fixed points. It matters not how any other objects or persons in the universe are moving. Am I mistaken? MarcusMaximus (talk) 06:47, 3 August 2009 (UTC)

I think we've just about worked it out, but that part you quoted I phrased badly. Let me try yet again. This time I'll start by asking, physically, what is the derivative? It is the rate of change in a reference frame; in the reference frame of the Earth, it's the rate of change with respect to the Earth, and in the reference frame of the plane, it's the rate of change with respect to the plane. Suppose that we want to measure the velocity of a bird relative to the plane. We observe that in the reference frame of the Earth, the plane has position x(t) = t and the bird has position b(t) = 0.1t. How do we measure the velocity of the bird relative to the plane? We can't do this by taking the derivative of the position function of the bird. This is what I meant when I said that we were in the wrong reference frame to do that: "Take the derivative" means "Find the velocity with respect to the present reference frame, i.e., with respect to the Earth"--which of course is not what we want. That's where the three-step procedure (and the connection it determines) come in. In the reference frame of the plane, the bird moves like -0.9t. The derivative in this reference frame is -0.9. Finally, that -0.9 was measured in the reference frame of the plane, so to be scrupulous and pedantic we must convert back to the reference frame of the Earth, because that's where we got our measurements from. The velocity doesn't change when do this, though; this last step isn't actually necessary. (But I'm including it anyway, because if you were trying to determine a position in the reference frame of the Earth by converting to the reference frame of the plane, then this step would be important.)

Are we agreed? As I said before, I dont't know what to do about the article; what I wrote has inspired so much discussion above that there must be a better way of saying it. Ozob (talk) 03:52, 4 August 2009 (UTC)

I still don't think I agree. While the velocities of the bird and the airplane relative to Earth are interesting, they are not necessary. The velocity of the bird in the reference frame of the airplane is the derivative of the position vector connecting a point in the bird to any point fixed in the airplane (since in the airplane frame, by definition, all points fixed in the airplane have zero velocity). There is no need to worry about the Earth or any measurements taken from it--it's a problem involving only two points and one reference frame.

If, as you are suggesting, we are constrained to take measurements from a different reference frame, that is a subjective limitation, not one inherent to kinematics. MarcusMaximus (talk) 04:22, 4 August 2009 (UTC)

Such limitations can be real. What if instead of a plane and a bird we have two elementary particles or two stars? We currently have no way of taking measurements in those frames directly.

Besides your comment about necessities of measurement, I couldn't see any specific objections in what you wrote. Ozob (talk) 04:30, 4 August 2009 (UTC)

Now I am interested to know what this statement means:

There are infinitely many possible reference frames because there are many nonequivalent bases for a vector space, even after rescaling.

I think different reference frames are more than just different bases in a vector space, aren't they? MarcusMaximus (talk) 07:34, 4 August 2009 (UTC)

And by the way, let me say that I really appreciate the discussions we have had on this page. Thank you for your patience and insight. MarcusMaximus (talk) 07:48, 4 August 2009 (UTC)

The discussions have been good for me, too. It's clarified my own understanding.

Or at least, it has to the point of realizing that I'm clueless. I've decided that I don't know what a frame of reference is. What I thought at the beginning was that it was the same as choice of an orthonormal basis, what I would call a frame. That would be nice, right? Frame and frame of reference? That's what I was thinking when I made that edit. But of course you can't represent curvilinear coordinates by taking linear combinations of basis vectors. So then I decided that it was a choice of coordinates, as I said above. In that case, the statement you quoted above is obviously wrong. But a mere choice of coordinates isn't enough to distinguish an inertial frame of reference from a non-inertial one. You can't tell whether there are any fictitious forces solely on the basis of your coordinates; you can use cartesian or polar coordinates for both inertial and non-inertial reference frames.

What I think a reference frame might be now is a choice of a connection. This might sound kind of goofy, because a connection is something that lets you take derivatives. It makes some sort of sense to me because an acceleration is a second derivative, so if you get fictitious forces, then your second derivatives are bad. If I'm right, an inertial reference frame is a flat connection, and a non-inertial reference frame is a non-flat connection. This is speculation, though; someone at WP:WPPhys might actually know. Ozob (talk) 00:32, 5 August 2009 (UTC)

Ok, well, I can't comment on connections. But I can say that to confuse vector bases, coordinate systems, and reference frames is one of the most common errors in kinematics, and there is no shame in it. In my experience even most college professors don't seem to understand it clearly. Many people blend the concepts together by talking about a hybrid entity called a "coordinate frame", which I and my colleagues regard as just asking for trouble. There is actually a hierarchy among them. First you need a reference frame. Then you can fix in that reference frame a set of mutually orthogonal basis unit vectors, which are free vectors that have a direction only. Tnen you pick any point in the reference frame as the origin and establish a coordinate system by defining coordinate axes parallel to the basis vectors. Reference frames are still quite useful even without coordinate systems. MarcusMaximus (talk) 01:09, 5 August 2009 (UTC)

When you pick a reference frame, what does that mean mathematically? How does the choice of reference frame affect a calculation? Ozob (talk) 14:00, 5 August 2009 (UTC)

I'm afraid I can't give you a rigorous mathematical definition of a reference frame in terms of manifolds or connections all that stuff. But a reference frame is fundamentally a set of points whose relative positions are constant with time. Therefore, if you have a door on a hinge with a vector embedded in the door (imagine an arrow painted on the door representing the vector), there are two reference frames that are immediately relevant: a reference frame consisting of the door and all points fixed in the door, and all "imaginary" points in the universe extending in all directions that move with the door as it swings; and a reference frame fixed relative to the doorframe/house/Earth. Now imagine swinging the door open and closed--the vector you painted on the door obviously remains unchanged in the reference frame of the door, always pointing exactly parallel to the door. But relative to the Earth, that vector is swinging back and forth, pointing in a different direction relative to the house at every instant.

The calculation of the derivative is different in each reference frame, for example, because when you express the vector using a formula in terms of a basis fixed in the door and take the derivative in the reference frame of the door, the derivatives of all the door-fixed basis vectors are zero, so the second term in the product rule goes to zero and you have a derivative like this one.

However, using exactly the same formula for the vector (using basis vectors fixed in the door) and taking the derivative in the Earth-fixed frame, the basis vectors fixed in the door have nonzero derivatives as the door swings. This is shown here.

If you compare the formula at the first link to the first formula at the second link, you'll see that the only difference is the second part of the product rule for differentiation is zero in the first case.

You can also use a linear transformation (like a direction-cosine matrix) to express the vector in terms of vectors fixed in the Earth frame at any step along the way and get a different formula. However, a linear transformation cannot get you from one reference frame to the other, because they are fundamentally different functions.

This concept took me a while to wrap my mind around. MarcusMaximus (talk) 16:43, 5 August 2009 (UTC)

By the way, I just took a look at the article on frames of reference. It is terrible. It is self-contradictory. In the opening sentence it says a reference frame is a coordinate system. Then it quotes 5 or 6 guys who say the concepts of reference frame and coordinate system are distinct. No wonder nobody knows what they are talking about! MarcusMaximus (talk) 04:00, 6 August 2009 (UTC)

Well, I tried looking in the two books on mathematical physics that I happened to have handy, namely Frankel's Geometry of Physics and Dubrovin–Fomenko–Novikov's Modern Geometry, Part 1 (which isn't really on physics, but it talks about physics a bit). The first wasn't helpful at all; I didn't see any mention of moving reference frames. The second was only slightly helpful; at one point they talk about reference frames moving with respect to each other in terms of Lagrangians. I've never studied enough physics to really figure out Lagrangians, so this left me unenlightened. All I got out of it was that it may be possible to describe the rotation (or lack of rotation) of a reference frame by putting certain terms in the Lagrangian.

But now I've gotten pretty confident that a reference frame is really a connection like I was thinking before. I'm going to write this all down here, mostly for my own benefit, but maybe you'll get something out of it too.

Here's the setup I want to use: Let the manifold M be the real numbers R. Choose a coordinate t on M. Let E be the trivial vector bundle on M of rank three (for simplicity). In other words, E is just one copy of R³ for each point of M; since M is just R, E is really R¹ × R³ together with the information that the first copy of R is special and corresponds to M. A (smooth) section of E is by definition a (smooth) function s from M to E of the form t → (t, s¹(t), s²(t), s³(t)); that is, for each time t, s chooses a vector in R³, i.e., s is really a parameterized curve in R³ written in a funny way.

A connection (mathematics) can be defined in many ways—I like connection (vector bundle)—but for the present purposes it's good to think of it as a covariant derivative. A covariant derivative ∇ with coefficients in E is a function that takes two things, a vector field and a section of the vector bundle E, and determines another section of E called the derivative of the original section with respect to the vector field. It satisfies a bunch of good properties which I won't list here. The important thing for the present purposes is that a covariant derivative can always be expressed as follows: Suppose that the section is written (using the Einstein convention) as sⁱe_i, where e₁, e₂, e₃ are the standard basis sections of E (i.e., for each time t, e_i(t) is the ith standard basis vector of R³ at time t). Suppose also that d/dt represents the tangent vector field on M which points to the right with length one at all times. Then we always have the following formula:

$\nabla _{d/dt}(s^{i}\mathbf {e} _{i})={\frac {ds^{i}}{dt}}\mathbf {e} _{i}+s^{i}\nabla _{d/dt}(\mathbf {e} _{i}).$

This is the Leibniz rule for connections. $\nabla _{d/dt}(\mathbf {e} _{i})$ is a section of E by definition, so it must have an expression in terms of the basis sections, too. We set:

$\nabla _{d/dt}(\mathbf {e} _{i})=\omega _{i}^{k}\mathbf {e} _{k}.$

The ω^k_i are called the coefficients of the connection; it's fair to interpret them as the curvilinear partial derivative of e_i in the kth coordinate direction. Note that they have only two indices instead of the usual three because M has only one coordinate and hence there's no point in indexing over that one coordinate. In terms of these coefficients, we get, after reindexing:

$\nabla _{d/dt}(s^{i}\mathbf {e} _{i})={\frac {ds^{i}}{dt}}\mathbf {e} _{i}+s^{j}\omega _{j}^{i}\mathbf {e} _{i}=\left({\frac {ds^{i}}{dt}}+s^{j}\omega _{j}^{i}\right)\mathbf {e} _{i}.$

This should be looking familiar. If the connection coefficients are zero, then we're in the case of a non-moving reference frame. If not, then we should be able to use the connection coefficients to describe how the reference frame's movement affects the derivative of s. That is, we need to replicate the formula:

${\frac {{}^{\mathrm {N} }d\mathbf {a} }{dt}}=\sum _{i=1}^{3}{\frac {da_{i}}{dt}}\mathbf {e} _{i}+\sum _{i=1}^{3}a_{i}{\frac {{}^{\mathrm {N} }d\mathbf {e} _{i}}{dt}}$

somehow. This is easy. We let ωⁱ_j equal the ith component of ${}^{\mathrm {N} }d\mathbf {e} _{j}/dt$. Tada! There we go. Ozob (talk) 22:49, 6 August 2009 (UTC)

Just out of curiosity, does this definition of angular velocity agree with your analysis?

${}^{\mathrm {N} }\omega ^{\mathrm {E} }=\mathbf {e} _{1}({\frac {{}^{\mathrm {N} }d\mathbf {e} _{2}}{dt}}\cdot \mathbf {e} _{3})+\mathbf {e} _{2}({\frac {{}^{\mathrm {N} }d\mathbf {e} _{3}}{dt}}\cdot \mathbf {e} _{1})+\mathbf {e} _{3}({\frac {{}^{\mathrm {N} }d\mathbf {e} _{1}}{dt}}\cdot \mathbf {e} _{2})$

Or in simpler notation, where the overdot replaces ${}^{\mathrm {N} }d/dt$,

${}^{\mathrm {N} }\omega ^{\mathrm {E} }=\mathbf {e} _{1}{\dot {\mathbf {e} }}_{2}\cdot \mathbf {e} _{3}+\mathbf {e} _{2}{\dot {\mathbf {e} }}_{3}\cdot \mathbf {e} _{1}+\mathbf {e} _{3}{\dot {\mathbf {e} }}_{1}\cdot \mathbf {e} _{2}$

MarcusMaximus (talk) 03:50, 7 August 2009 (UTC)

Well, let's find out if I can fit it in somehow. I don't know how one would define "angular velocity" in an intrinsic way except by trying to use the curvature of the connection, so I'm going to try that first.

I'm going to describe connections in the way that connection (vector bundle) does. That is, now ∇ is a vector bundle homomorphism E → E ⊗ Ω that satisfies the Leibniz rule; here Ω is the cotangent bundle of M. In coordinates, this means that ∇ looks like this:

$\nabla (\mathbf {e} _{i})=\omega _{i}^{k}\mathbf {e} _{k}\otimes dt.$

The curvature is ∇² : E → E ⊗ Λ²Ω. But Λ²Ω is the zero bundle; in local coordinates, the unique coordinate dt on Ω determines the coordinate dt ∧ dt, which is zero.

OK, that didn't work. But one thing that's been bothering me since yesterday is that the approach I'm taking really doesn't unify space and time; it treats them as separate (time is the manifold, space is the vector bundle). So I'm going to try something else.

Let M be R⁴. Give M the standard Lorentzian metric, that is, we define the dot product of two vectors (x₀ = t, x₁, x₂, x₃) and (y₀ = u, y₁, y₂, y₃) to be tu − x₁y₁ − x₂y₂ − x₃y₃. (Note c = 1.)

The tangent bundle of M is TM = M × R⁴. A connection on the tangent bundle of M is a vector bundle homomorphism ∇ : TM → TM ⊗ Ω satisfying the Leibniz rule; in coordinates, it sends

$\nabla (\partial _{i})=\Gamma _{ji}^{k}\partial _{k}\otimes dx^{j}.$

(This is really the same as the definition of a connection I gave above, but rephrased.) The Γs are the ωs from before, but now a lot more of them are zero. If we have a tangent vector field $s^{i}\partial _{i}$, then using the Leibniz rule we get:

$\nabla (s^{i}\partial _{i})=\partial _{i}\otimes ds^{i}+s^{i}\nabla (\partial _{i})=\partial _{i}\otimes ds^{i}+s^{i}\Gamma _{ji}^{k}\partial _{k}\otimes dx^{j}.$

To replicate the results of my last post, we just let all the coefficients $\Gamma _{ji}^{k}$, where j is not zero, equal zero. Sort of; to handle a curve a(t), what we ought to do is pullback the tangent bundle of M along a and use the pullback connection. Unfortunately then we're in the same situation as above, where the curvature is zero for dimension reasons. I'm going to press on with the computations in the hope that this reveals something to me.

Anyway, there's a standard formula for the curvature of a connection which can be found at Riemann curvature tensor:

$R_{jkl}^{i}=\partial _{k}\Gamma _{lj}^{i}-\partial _{l}\Gamma _{kj}^{i}+\Gamma _{km}^{i}\Gamma _{lj}^{m}-\Gamma _{lm}^{i}\Gamma _{kj}^{m}.$

Look at the last two terms, the ones with only Γs and no partial derivatives. Recall that $\Gamma _{ji}^{k}$ is zero when j is not zero; so unless both l and k are zero, those last two terms vanish; and if they're both zero, then upon substituting zero we see again that the last two terms also vanish. So we get:

$R_{jkl}^{i}=\partial _{k}\Gamma _{lj}^{i}-\partial _{l}\Gamma _{kj}^{i}.$

By similar reasoning, we get:

$R_{jkl}^{i}=0,$ when k and l are both not zero,

$R_{jk0}^{i}=\partial _{k}\Gamma _{0j}^{i},$ when k is not zero,

$R_{j0l}^{i}=-\partial _{l}\Gamma _{0j}^{i},$ when l is not zero,

$R_{j00}^{i}=\partial _{0}\Gamma _{0j}^{i}-\partial _{0}\Gamma _{0j}^{i}=0.$

This looks like it can't replicate the angular velocity that you have above. There are no partials in the time direction, i.e., nowhere do you get a $\partial _{0}$. I guess this is consistent with the observation that it didn't work before.

For the moment, I'm out of ideas as to what the angular velocity represents in a strictly mathematical sense. Maybe this is obvious, but could you tell me where that formula comes from? It's pretty opaque to me. Ozob (talk) 00:36, 8 August 2009 (UTC)

It came from a very good dynamics textbook, Dynamics: Theory and Applications by Kane and Levinson. I work with Levinson on a daily basis and he taught me most of what I know about kinematics and dynamics. You can download the book for free here. The definition of angular velocity is presented at the top of page 16 of the text, which is page 36 of the PDF. I'm not sure if the definition of angular velocity is derived from anything, but it's a very intuitive definition--at least it makes sense physically in my head. I'll try to think of a way to explain it in text.

I was hoping this equation

$\nabla _{d/dt}(s^{i}\mathbf {e} _{i})={\frac {ds^{i}}{dt}}\mathbf {e} _{i}+s^{j}\omega _{j}^{i}\mathbf {e} _{i}=\left({\frac {ds^{i}}{dt}}+s^{j}\omega _{j}^{i}\right)\mathbf {e} _{i}.$

would lead logically to this one

${\frac {{}^{\mathrm {N} }d\mathbf {a} }{dt}}=\sum _{i=1}^{3}{\frac {da_{i}}{dt}}\mathbf {e} _{i}+\sum _{i=1}^{3}a_{i}{\frac {{}^{\mathrm {N} }d\mathbf {e} _{i}}{dt}}={\frac {{}^{\mathrm {E} }d\mathbf {a} }{dt}}+{}^{\mathrm {N} }\mathbf {\omega } ^{\mathrm {E} }\times \mathbf {a}$

because somehow the indices on the $s^{j}\omega _{j}^{i}\mathbf {e} _{i}$ would work cyclically to form ${}^{\mathrm {N} }\omega ^{\mathrm {E} }\times \mathbf {a} .$

If you start with the statement you made, can you make any progress from there?

We let ωⁱ_j equal the ith component of ${}^{\mathrm {N} }d\mathbf {e} _{j}/dt$.

I don't really know what ranges those indices are supposed to cover, or I'd do it myself.

MarcusMaximus (talk) 06:41, 8 August 2009 (UTC)

The indices are supposed to go from 1 to 3; x₁, x₂, and x₃ are the x, y, and z coordinates, respectively. (The reason for using this notation rather than using x, y, and z is just that it's convenient for making computations.)

The first part of the first equation that you quoted leads to the first part of the second equation that you quoted. We have:

$\nabla _{d/dt}(s^{i}\mathbf {e} _{i})={\frac {{}^{\mathrm {N} }d\mathbf {a} }{dt}},$

${\frac {ds^{i}}{dt}}\mathbf {e} _{i}+s^{j}\omega _{j}^{i}\mathbf {e} _{i}=\sum _{i=1}^{3}{\frac {da_{i}}{dt}}\mathbf {e} _{i}+\sum _{i=1}^{3}a_{i}{\frac {{}^{\mathrm {N} }d\mathbf {e} _{i}}{dt}}.$

I should reindex the left-hand side of the first equation by swapping the is and js in the second term. If I also stop using the Einstein summation convention on the left-hand side, then I get:

$\sum _{i=1}^{3}{\frac {ds^{i}}{dt}}\mathbf {e} _{i}+\sum _{i=1}^{3}\sum _{j=1}^{3}s^{i}\omega _{i}^{j}\mathbf {e} _{j}=\sum _{i=1}^{3}{\frac {da_{i}}{dt}}\mathbf {e} _{i}+\sum _{i=1}^{3}a_{i}{\frac {{}^{\mathrm {N} }d\mathbf {e} _{i}}{dt}},$

which I think makes the equality a little more transparent: a_i equals sⁱ, and ω^j_i is the component of ^Nde_i/dt in the direction of the jth basis vector.

The one thing which I haven't yet worked out is where the cross product comes in. So I looked at the book you referenced. It looks very good! Unfortunately, as you say, it doesn't justify the definition of angular velocity, it simply states it. It's still helpful, though: It's convincing me that angular velocity behaves in a good way, and that the definition above isn't arbitrary but really comes from something.

I'm going to try to reason my way backwards this time, by equating the two terms that I don't understand. For each i, we can suppose that a(t) = s(t) = e_i, and then we ought to have:

$\omega _{i}^{j}\mathbf {e} _{j}={}^{\mathrm {N} }\omega ^{\mathrm {E} }\times \mathbf {e} _{i}.$

Equations (9) and (10) on page 17 of the textbook tell me that the right-hand side should equal ${\dot {\mathbf {e} }}_{i}.$ But that's just the statement that we can write things in terms of ^Nde_i/dt as above, so that's not really helpful. What I think I'd like to do is to see what components ^Nω^E should have. Let's write its kth component as ^Nω^E_k. If we write out all the terms of that equation above, we get:

$\omega _{1}^{1}\mathbf {e} _{1}+\omega _{1}^{2}\mathbf {e} _{2}+\omega _{1}^{3}\mathbf {e} _{3}=\omega _{1}^{i}\mathbf {e} _{i}={}^{\mathrm {N} }\omega ^{\mathrm {E} }\times \mathbf {e} _{1}={}^{\mathrm {N} }\omega _{3}^{\mathrm {E} }\mathbf {e} _{2}-{}^{\mathrm {N} }\omega _{2}^{\mathrm {E} }\mathbf {e} _{3},$

$\omega _{2}^{1}\mathbf {e} _{1}+\omega _{2}^{2}\mathbf {e} _{2}+\omega _{2}^{3}\mathbf {e} _{3}=\omega _{2}^{i}\mathbf {e} _{i}={}^{\mathrm {N} }\omega ^{\mathrm {E} }\times \mathbf {e} _{2}={}^{\mathrm {N} }\omega _{1}^{\mathrm {E} }\mathbf {e} _{3}-{}^{\mathrm {N} }\omega _{3}^{\mathrm {E} }\mathbf {e} _{1},$

$\omega _{3}^{1}\mathbf {e} _{1}+\omega _{3}^{2}\mathbf {e} _{2}+\omega _{3}^{3}\mathbf {e} _{3}=\omega _{3}^{i}\mathbf {e} _{i}={}^{\mathrm {N} }\omega ^{\mathrm {E} }\times \mathbf {e} _{3}={}^{\mathrm {N} }\omega _{2}^{\mathrm {E} }\mathbf {e} _{1}-{}^{\mathrm {N} }\omega _{1}^{\mathrm {E} }\mathbf {e} _{2}.$

So we deduce that:

${\begin{array}{lll}\omega _{1}^{1}=0,&\omega _{1}^{2}={}^{\mathrm {N} }\omega _{3}^{\mathrm {E} },&\omega _{1}^{3}=-{}^{\mathrm {N} }\omega _{2}^{\mathrm {E} },\\\omega _{2}^{1}=-{}^{\mathrm {N} }\omega _{3}^{\mathrm {E} },&\omega _{2}^{2}=0,&\omega _{2}^{3}={}^{\mathrm {N} }\omega _{1}^{\mathrm {E} },\\\omega _{3}^{1}={}^{\mathrm {N} }\omega _{2}^{\mathrm {E} },&\omega _{3}^{2}=-{}^{\mathrm {N} }\omega _{1}^{\mathrm {E} }&\omega _{3}^{3}=0.\end{array}}$

OK, this is looking promising! Apparently there really is some sort of good relation between the connection coefficients and the angular velocity. But I'm not really sure how to express it abstractly: All I see at the moment is "plug in the numbers in a nice-looking way". This is some sort of low-dimensional phenomenon relating three-dimensional vector spaces and three-dimensional matrices; you can't do this in two or four and higher dimensions because you don't have the right number of matrix entries. And at the moment I can't see what the relation is; I'm sure I can look it up somewhere, though. Ozob (talk) 16:09, 8 August 2009 (UTC)

Oh, wait, this is obvious. There is a linear transformation of vector spaces R³ → R³ determined by "send v to its cross product with ^Nω^E". ω^j_i is just the matrix of that linear transformation. The skew-symmetry of the matrix corresponds to the symmetry you see in the formula for a cross product (which ultimately comes from the skew-symmetry of the wedge product).

In a sense, this answers the question of the relationship between ^Nω^E and ω^j_i. But in another sense it doesn't: For a linear transformation to have the form "cross product with a vector" is very, very special. In three dimensions (which we're in), this happens exactly when the matrix is skew-symmetric. As it turns out, skew-symmetry of the matrix of connection coefficients happens exactly when the connection is "compatible with the metric", i.e., that it satisfy a certain condition relating the connection and inner products. So that explains why angular velocity is a vector and why the interesting part of the connection can be represented as a cross product: It's because the connection is compatible with the metric and we're in three dimensions.

So here is the overall picture as I see it at the moment:

• Spacetime, in classical physics, is R¹ × R³.
• A reference frame is a connection on the tangent bundle of spacetime which is:
  1. Compatible with the metric, and
  2. Zero in all the spacelike directions.
• The derivative in a certain reference frame is just an application of the connection.
• The angular velocity of a reference frame with respect to an inertial frame of reference is the connection form.
• Because the connection is zero in all the spacelike directions, the interesting part of the connection form is a 3 × 3 matrix.
• Because the connection is compatible with the metric, the 3 × 3 matrix is skew-symmetric.
• Skew-symmetric 3 × 3 matrices are determined by vectors. The vector corresponding to the connection form is the angular velocity.
• A connection determines an inertial frame of reference if and only if its torsion tensor vanishes.
• All reference frames correspond to a flat spacetime, meaning that the Riemann curvature tensor vanishes.

OK, that's a lot more complicated than I thought it would be way back when we started this discussion. But I think I've got it; do you have any comments? I hope I haven't lost you! Ozob (talk) 20:51, 8 August 2009 (UTC)

I just moved, so I've been without internet access for a while. Unfortunately a lot of what you just said is over my head, but I do know about the relationship between skew-symmetric matrices and the cross product.

The only comment I have is that you don't have to specify that one of the two reference frames is an inertial reference frame; this relationship of derivatives works for any two reference frames. This is a purely kinematical (which roughly means "geometric and mathematical") relationship, while inertia and "inertiality" only is important when you're dealing with dynamics and kinetics (the interaction of bodies and forces).

Thanks for the fantastic discussion. I'm glad to see that all of this makes sense at a fundamental level, even though my knowledge only starts somewhere in the middle of the hierarchy. MarcusMaximus (talk) 18:42, 20 August 2009 (UTC)

Hmm. Well, even if neither of the reference frames is assumed inertial, we should still be able to figure out the angular velocity somehow. I'm going to guess that all one does is compute the angular velocities of the two reference frames with respect to an inertial frame, then takes their difference.

Come to think of it, I bet there's a direct way of doing this. There was a step above where I said:

$\omega _{i}^{j}\mathbf {e} _{j}={}^{\mathrm {N} }\omega ^{\mathrm {E} }\times \mathbf {e} _{i}.$

Now, while it doesn't look like it, there's an inertial frame of reference hidden here on the right hand side. The cross product is usually defined as a goofy looking differential operator with some weird stuff happening in the indices; in fact, it's not, it's very natural and comes right out of the wedge product and the Hodge dual. The Hodge dual is something to do with the ordinary differential d on Euclidean space, that is, it's related to the Euclidean derivative. I wouldn't be surprised if there's some way to define a curved Hodge dual with respect to a connection; and that using this you could define a curved cross product. If you stuck in the curved cross product on the right hand side, then you'd eliminate the implicit use of an inertial reference frame. That may not be particularly useful; after all, it should just work out to be what you'd get by finding the angular velocities of N and E with respect to an inertial frame and taking their difference. But it would be satisfying if it were true, because then all of this stuff would be kinematic like it ought to be.

Discussing these things with you is always enlightening. If you have any more questions, just ask. I'm sure I'll learn something. Ozob (talk) 22:04, 20 August 2009 (UTC)

Did your talk page stuff get deleted some how?

First, I don't think I deleted any of your comments on quaternion talk. If I did I am terribly sorry, and am wondering if it might have somehow been an edit conflict, where we were both typing at the same time.

Second yes, this question that I am wondering about right now, I have been editing a bit, because the way I first typed it did not really sound as clear as I could make it after I went back and read it some more. Plus I wanted to add links to it.

Right now I am reading Jasper Jolly's 1905 Manual of Quaternions. Jolly if you don't know him well, was a royal astronomer of Ireland, a post that Hamilton had once held, and edited the 1898 version of Elements of Quaternions that Hamilton died before completing, based on the earlier 1865 version.

I will try and be more diligent in avoiding deleting comments, not sure if I actually did that, but if I did I am sorry and will not do it again.

Thanks for all your interesting comments and contributions. I always find it very interesting reading about what you have ask for. TeamQuaternion (talk) 01:34, 8 August 2009 (UTC)

Jacobson radical

Although this is relatively minor, I happened to notice the addition of, "If R is unital and is not the trivial ring {0}, the Jacobson radical is always distinct from R.", to the article. Are there any interesting non-trivial consequences of this property? In many interesting cases of the theory, it is desirable to study rings with J(R) = R; for instance "If R is nil, is the polynomial ring over R Jacobson radical?", is an equivalent form of the (open) Köthe conjecture. Apart from the fact that the quotient R/J(R) will be non-trivial for a unital ring, I do not know of any properties which can be deduced from this. Could you please tell me what you had in mind? Thanks, --PST 00:46, 20 August 2009 (UTC)

Oh, all I had in mind there was to not lose the fact that you'd removed (because it had been incorrectly stated). I noticed that the fact, properly stated, was a trivial consequence of Zorn's lemma, and while I really don't know anything about these sorts of rings, it seemed to me that J(R) equaling R or not would be pretty important. You seem to know more about these things; if it's actually not an interesting fact, then feel free to remove it. Ozob (talk) 21:44, 20 August 2009 (UTC)

Thanks, I have kept the fact but added a sentence which covers more general cases that I mentioned above. --PST 04:22, 25 August 2009 (UTC)

Mathematic typing style

Dear Ozob, thanks for your advise on User talk:129.97.227.25. The edit was mine. I do not understand, why dx should be written as dx as this is to my view clearly against any common sense: variables are generally written in italics and are composed out of one (1) letter, every other use would start confusion (this notations is according to AMS style). This "d" here is not to be taken as a variable multiblied by x.

Otherwise, what is the value of $\int _{0}^{\pi }\sin(t)d\rho dt$

I wonder, whether it is $\pi \sin(t)dt\,$ or $2d\rho \,$

Well, as it seems, you define this with spaces and so on, ok. but I disagree. However it will be like it says.

Cheers, Saippuakauppias ⇄ 01:13, 5 December 2009 (UTC)

I agree that variables are often written in italics and are only one letter long. However, dx can be considered as an infinitesimal variable, in which case it does not make sense to separate the d from the x. One can also consider d to be a function, the exterior derivative, and functions are also often written in italics. There are many ways of interpreting dx, and it often makes sense to italicize the d. I think that I have always seen the d italicized in AMS publications.

I would like to know where you learned to write an upright d. I have only ever seen it done on Wikipedia, but you seem to have learned it somewhere else. Where? Ozob (talk) 13:44, 5 December 2009 (UTC)

Thank you

I very much appreciate your work here. :) --Moonriddengirl ^(talk) 14:52, 20 December 2009 (UTC)

Speedy?

The lead section of arithmetic variety didn't seem to be copied from the source, although the section on Kazhdan's theorem was. I removed the speedy tag and stubbed the article. If you disagree, then please restore the tag. Also, I have been tagging the articles with {{copyvio}} rather than {{db-copyvio}}. Is the latter preferred in some more obvious cases? Sławomir Biały (talk) 13:09, 21 December 2009 (UTC)

Yes, I think I may have been a bit too hasty with the speedy tag on that article. I've been using {{db-copyvio}} when I felt that nothing substantial would be left. In the case of arithmetic variety, we would be left with two not obviously equivalent definitions and no context; I suppose that's something, so {{copyvio}} looks more appropriate. But the {{db-copyvio}} template I just added to noncommutative resolution is okay, for example, because the article had a single sentence, and that sentence was a copyvio. Ozob (talk) 17:38, 21 December 2009 (UTC)

Another potential approach

Hi. A contributor to the clean-up at the CCI asks whether material can be presumptively deleted. It can, in accordance with policy. There's more about this at Wikipedia talk:WikiProject Mathematics#Copyright concerns related to your project, including a template that may prove helpful should you wish to take this approach. --Moonriddengirl ^(talk) 18:16, 21 December 2009 (UTC)

Speedy deletion declined: Albert–Brauer–Hasse–Noether theorem

Hello Ozob, and thanks for your work patrolling new changes. I am just informing you that I declined the speedy deletion of Albert–Brauer–Hasse–Noether theorem - a page you tagged - because: Not an unambiguous copyright infringement, or there is other content to save. Please review the criteria for speedy deletion before tagging further pages. If you have any questions or problems, please let me know. JohnCD (talk) 18:50, 21 December 2009 (UTC)

Apologies - I meant to come back sooner and add to the rather curt notice that the CSDHelper script produces. My reasoning was that the copyvio passage could be removed leaving a valid stub article. I didn't realise what a swamp I was stepping into, see conversation with Moonridengirl here. Regards, JohnCD (talk) 20:39, 21 December 2009 (UTC)

That's okay. But the first sentence may also be a copyvio: See the first sentence of the source he cites for it. Given that and this user's history (and that the template lets you fill in only one url as far as I'm aware) I thought it was better to just nuke the page. Failing that I think it should be blanked and rewritten; I'm sure I could use the sources he cites to come up with appropriate content. Ozob (talk) 04:22, 22 December 2009 (UTC)

Email

Hi Ozob, I've sent you email. Paul August ☎ 18:21, 29 December 2009 (UTC)

Thank you

		The Copyright Cleanup Barnstar
		Your work on this contributor copyright investigation is very much appreciated. Moonriddengirl (talk) 17:14, 12 January 2010 (UTC)

Thanks. :) --Moonriddengirl ^(talk) 17:14, 12 January 2010 (UTC)

MoS markup messup

What process was used to create this edit to the Manual of Style? Was it some external editor? It generated some real howlers in the resulting page. Eubulides (talk) 17:08, 8 February 2010 (UTC)

:-O I had no idea that happened. No, all I did was use the usual edit link—but the old edit box has been replaced by a new weird and broken one. (You can see a notice about its brokenness on your watchlist.) It looks from this like it mangles ampersands, too. I'm going to submit a bug report. Ozob (talk) 18:01, 8 February 2010 (UTC)

It's now bug 22435. Ozob (talk) 18:22, 8 February 2010 (UTC)

I'm afraid it happened again, later, with this edit. I suggest disabling this new edit box, and sticking with the old edit box, until the bugs are fixed. Also, have you recently edited any other pages that might be affected by the bug? Eubulides (talk) 00:14, 9 February 2010 (UTC)

Blast. Of the articles I've edited, it seems that only the MoS is affected by this; it's weird. The bug has been fixed in the current Mediawiki source, but I don't think that fix has been pushed out to Wikipedia's servers yet. Thanks for cleaning up again. I hope this bug died a painful death. Ozob (talk) 04:47, 9 February 2010 (UTC)

DYK nomination of Lefschetz theorem on (1,1)-classes

Hello! Your submission of Lefschetz theorem on (1,1)-classes at the Did You Know nominations page has been reviewed, and there still are some issues that may need to be clarified. Please review the comment(s) underneath your nomination's entry and respond there as soon as possible. Thank you for contributing to Did You Know! Marylanderz (talk) 01:42, 18 February 2010 (UTC)

DYK for Lefschetz theorem on (1,1)-classes

On February 21, 2010, Did you know? was updated with a fact from the article Lefschetz theorem on (1,1)-classes, which you created or substantially expanded. You are welcome to check how many hits your article got while on the front page (here's how, quick check ) and add it to DYKSTATS if it got over 5,000. If you know of another interesting fact from a recently created article, then please suggest it on the Did you know? talk page.

Ucucha 18:10, 21 February 2010 (UTC)

List of algebraic geometry topics

I've added dévissage and generic flatness to the list of algebraic geometry topics. If you know of other articles that should be listed there and are not, could you add those too? Michael Hardy (talk) 04:42, 2 March 2010 (UTC)

Four Egyptian geometry formulas may qualify. In the Rhind Mathematical Papyrus problems 41, 42, and 43 report the area of a circle as A = [(8/9](D)]^2 cubit^2 (formula 1.0), where pi =256/81 and radius R = semi-diameter D/2. MMP 10 also used formula 1.0 to compute the area of a semi-circle/. Gillings suggested C = (pi)D was involved in formula 1.0. Skipping over the area debate, scribal algebra added height (H) in two cases V = (H)[8/9)(D)]^2 cubit^3 (formula 2.0) and V = (3/2)(H)[(8/9)(D)]^2 khar (formula 3.0). An interesting algebraic geometry devives from V = (2/3)(H)[(4/3)(D)]^2 khar (formula 4.0), reported in RMP 43 and the Kahun Mathematical Papyrus. Did two scribes modify formula 3.0 by applying these algebraic steps:

1. considering V = (3/2)(H)(8/9)(8/9)(D)D)

multiplying both sides by 3/2 such that

2. (3/2)V =(3/2)(3/2)(H)(8/9)(8/9)(D)(D) khar = (4/3)(4/3)(D)(D) khar

and multiplying both sides by 2/3, such that

3. V = (2/3)(H)[(4/3)(D)]^2 khar (formula 4)?

as cited on the math forum: http://mathforum.org/kb/thread.jspa?threadID=2109309&tstart=0

Anneka Bart may wish to comment on this topic for an added reason. Ahmes in RMP 41, 42 and 43 divided the khar unit by 20, and found a 100-hekat unit (*reported by Peet and Clagett). A single hekat total was reported by multiplying the 100-hekat value by 100, a step that Ahmes did not clearly report. The scaled scribal hekat context shows that Ahmes scaled a khar to 5 hekat, a conclusion that Dr. Bart disagrees. She suggests without writing out mathematical statements associated with scholar references that a khar properly contained 20 hehat. Scribal algebraic geometry discussions may offer conflicting points of view. Let the raw data and the scholars openly debate the history of math geometry formulas and the unit values contained therein. Wikipedia entries that contain controversial topics should be noted, thereby avoiding needless Wiki-debates and Wiki-wars.

Best Regards, Milogardner (talk) 14:53, 14 September 2010 (UTC)

I would say that the material from the Rhind Mathematical Papyrus is not algebraic geometry at all. The rest of the comments about disagreements is completely besides the point and not relevant to the discussion here. --AnnekeBart (talk) 19:08, 15 September 2010 (UTC)

Thanks

Thank you very much for brokering the WQA and ANI reports on my behalf. Things seem to be moving in a more productive direction at Gravitational potential now, although they are no less frustrating. Even though no action came out of the incident, RHB at least seems to be a little less confrontational now. Best wishes, Sławomir Biały (talk) 01:37, 18 March 2010 (UTC)

Which vs that

In the US, it is incorrect to use 'which' in a restrictive clause, according to the Chicago Manual of Style and every other reference I know. It is not incorrect in the UK, but 'that' in a restrictive clause is also not wrong...so following the US rule creates something that is correct in both countries. Thanks. —Preceding unsigned comment added by 75.0.176.7 (talk) 04:37, 2 April 2010 (UTC)

Reference

I have a question about your edit. I wanna know that ... is there any policy about referencing/citation in Wikipedia? (It's just a question, not quarrel) -- Modamoda (talk) 16:14, 19 April 2010 (UTC)

Yes, there's WP:CITE. For footnotes, see WP:FOOT. Neither of these specify whether we should group adjacent footnotes together or not. I prefer not to; that's what I'm used to, and that's what I usually see others do. (You can observe WP:FOOT not group them under "Ref tags and punctuation".) I agree that the cluster of footnotes at the start of integral domain looks odd, but it's there because of a quarrel on the talk page. Ozob (talk) 23:45, 20 April 2010 (UTC)

I see, thanks anyway -- Modamoda (talk) 10:01, 21 April 2010 (UTC)

Good faith

You wrote in Wikipedia talk:Words to watch#Question for Philip as a parting shot "I believe therefore that it is fair to characterize your views as primarily a content objection. Your process objections are red herrings intended to slow us down."

If I did not assume good faith which you do not seem to be extending to me I could argue that "Your process objections are red herrings intended to speed up the process to sneak in changes and then game the system by arguing that it needs consensus to change them back". But as you are clearly a honest person I am sure that you would not sink to such depths and I would appreciate it if you would extend good faith to my motive. If so you will strike out the comment as it does not help us reach a consensus. -- PBS (talk) 02:05, 26 April 2010 (UTC)

I will not strike out my comment. Please answer the question I posed you. Ozob (talk) 02:17, 26 April 2010 (UTC)

Spectral sequences

Hi Ozob,

I was the anonymous user that changed the discussion of the differentials in spectral sequences.... I'm a noob here, so I hope this is the right place to discuss.....

I think it's actually "up or down" at the zero level, and "left or right" at the one level - according to J. McCleary's User's Guide, the bidegree is (-r,r-1) for homological type and (r,1-r) for cohomological type.

Cheers, Mathjd

Whoops. You're right; I completely botched that one. Thanks. Ozob (talk) 19:49, 2 May 2010 (UTC)

Substing Welcome Templates

Just a quick note, can you make sure you subst welcome templates when you add them to a users talk page? Thanks =] ·Add§hore· ^{Talk To Me!} 18:59, 18 May 2010 (UTC)

Whoops. Thanks for catching that. Ozob (talk) 02:34, 19 May 2010 (UTC)

I have marked you as a reviewer

I have added the "reviewers" property to your user account. This property is related to the Pending changes system that is currently being tried. This system loosens page protection by allowing anonymous users to make "pending" changes which don't become "live" until they're "reviewed". However, logged-in users always see the very latest version of each page with no delay. A good explanation of the system is given in this image. The system is only being used for pages that would otherwise be protected from editing.

If there are "pending" (unreviewed) edits for a page, they will be apparent in a page's history screen; you do not have to go looking for them. There is, however, a list of all articles with changes awaiting review at Special:OldReviewedPages. Because there are so few pages in the trial so far, the latter list is almost always empty. The list of all pages in the pending review system is at Special:StablePages.

To use the system, you can simply edit the page as you normally would, but you should also mark the latest revision as "reviewed" if you have looked at it to ensure it isn't problematic. Edits should generally be accepted if you wouldn't undo them in normal editing: they don't have obvious vandalism, personal attacks, etc. If an edit is problematic, you can fix it by editing or undoing it, just like normal. You are permitted to mark your own changes as reviewed.

The "reviewers" property does not obligate you to do any additional work, and if you like you can simply ignore it. The expectation is that many users will have this property, so that they can review pending revisions in the course of normal editing. However, if you explicitly want to decline the "reviewer" property, you may ask any administrator to remove it for you at any time. — Carl (CBM · talk) 12:33, 18 June 2010 (UTC) — Carl (CBM · talk) 13:34, 18 June 2010 (UTC)

Thanks! Ozob (talk) 02:29, 21 June 2010 (UTC)

Talkback

Hello, Ozob. You have new messages at Wikipedia talk:Manual of Style (words to watch).
You can remove this notice at any time by removing the {{Talkback}} or {{Tb}} template.

Weaponbb7 (talk) 02:43, 26 June 2010 (UTC)

Andre - Quillen vs.Harrison (co)homology ?

Dear colleague, I do not have Andre's and Quillen's papers. From what You have written it seems to me that Andre-Quillen is the same as Harrison's ones. I guess the relation is very well-known, would You be so kind to comment on it. —Preceding unsigned comment added by Alexander Chervov (talk • contribs) 17:48, 22 July 2010 (UTC)

Quillen discusses this in his paper. Try [4]. Ozob (talk) 00:13, 27 July 2010 (UTC)

Thank You very much. So it seems Harrison was the first to define this cohomology, while Quillen generalizes to the "relative case" A->B, while Harrison treats just "B" meaning k->A , "k" is basic field. I think in some future it would be better to create a page "Homology of commutative rings" with redirect from Andre-Quillen and Harrison cohomology to such page. Harrison's approach is downtoearth while Quillen's is most not downtoearch... 17:14, 28 July 2010 (UTC) —Preceding unsigned comment added by Alexander Chervov (talk • contribs)

Your revert on Template:Group-like structures

https://secure.wikimedia.org/wikipedia/en/w/index.php?title=Template%3AGroup-like_structures&action=historysubmit&diff=385478429&oldid=385423672

Actually, Magmas are called groupoids sometimes. This is actually on the first line of the article. It is also in several books that I've been reading.

I think your change is not a good idea. The additional information makes it less confusing for readers, like me, who don't know much about the subjects. Tony (talk) 03:11, 19 September 2010 (UTC)

Hmm. As I said, I've never seen "groupoid" used this way, only in the way it's used in the groupoid article. I suspect that "groupoid" for "magma" is obsolete. But you say that it's in books you're reading, so maybe I'm just out of touch. I think the right thing to do is for you to bring this up on the article's talk page. Maybe we can get some additional opinions as to the right way forward here. Ozob (talk) 12:57, 19 September 2010 (UTC)

Barnstar!

		The Barnstar of Diligence
		Hi Ozob – just noticed your lil’ edit to Riemann integral, and recognized you (from Problem of Apollonius). Thanks for your specific edit (yeah, jargon should really be avoided on elementary pages – oops), and for your consistent pattern of making Wikipedia (Math) just that much better and more polished – thanks! —Nils von Barth (nbarth) (talk) 06:09, 20 September 2010 (UTC)

RfC closing

Letting you know that there is opposition to your closing and interpretation of the results about italic titles at Wikipedia talk:Article titles#Again. _Xeworlebi ^(talk) 21:31, 27 September 2010 (UTC)

RFC of Italics closing

I read the RFCs on this. Simple, plain response is that i wholeheartedly dispute both you closing it for being involved and for your assessment. Your own tally does not support what you put forward as consensus. I waited for a response as Xeworlebi advised you of this 10 days ago. Today i reverted the policy to what it was before you changed it. Surely someone will not like that but hopefully someone notices why i changed it. The problem is that italic titles have now been implemented site wide in all relevant infobox template, which are all protected. It will be a pain to undo all of it. I read all of it and i see you having added the "limited use support" into the "full support" to claim that sufficient people support it to implement it. Thing is those same people who support limited use would also oppose full use (or else they would have voted for full use). Hence the consensus was to not implement italics beyond the limited use and you misrepresented things. I call upon you to revise your close or to re-open the RFC, and to have italics removed from all infoboxes where it has been added subsequent to your close of the RFC on 19 September, and to then have someone who truly is not involved close the RFC. Other than this i am not too sure what to do short of an RFC on your closing of the RFC and even i know that sounds somewhat silly just to write. But i am serious. delirious & lost ☯ ^~hugs~ 17:29, 7 October 2010 (UTC)

Go for it on the RFC on my RFC. If there is someone who actually wants to read all the arguments, tally the votes, and come up with a coherent policy statement, then I'd prefer that they do it. I did it only because nobody else was going to (look at the timestamps). I tried to be as objective as I could, but as I think was clear from what I wrote, I'm not a fully objective party. Ozob (talk) 21:03, 7 October 2010 (UTC)

Since you've posted essentially the same objection at WT:AT, I have made essentially the same reply more publicly there. Let's continue the discussion there instead. Ozob (talk) 21:23, 7 October 2010 (UTC)

Just for a record, i posted there some time ago now and you didn't respond. So today i added a 2nd notice of my contesting the closing by reverted the policy change. That i think is what got someone's attention. However the consensus is that it is too late to contest since it is now in full widespread use and would require a new consensus to undo what you claimed. :S
I would prefer the formal RFC on the RFC but someone beat me to it with another subsection simply contesting the close based on my stated concerns and their own. That you just simply leave it closed and invite someone else to re-open it... really, who is going to do that? Noöne.
As my issue is first and foremost with you closing it despite being about as involved as anyone there is, and as my secondary issue is with being completely baffled by your conclusion that results in changing the policy, and as my attempt at addressing this on the policy talk page went pretty much unnoticed i would rather discuss this here.
At the most basic level i do not see where you find the support. To simplify it, there is a Yes, No, & Kinda. Yes and No are about even. Kinda is conveniently about the same and thus the majority could swing a few ways depending on what you want.
Those who like the close you did surely will not be objecting to it.
Those not liking the close you did are either not in the mood to bother or believe it to be futile to object, or they don't know it was closed.
Then there is the flaw in the entire set-up. I hate consensus ruling (not a secret) but i do know that it will surely fail if there are more than 2 options. That part of consensus on WP is to allow as many options as people care to put forward is why things get stalemated, such as the removal of admin rights. This RFC had 3 major options with a couple of subsections depending on your choice of major. By design that will result in indecision and massive vote splitting. That is what happened and yet you found a 'clear winner'.
If someone had simply told me of this or if i had stumbled upon it before its implementation flooded my watchlist then yes i would have closed it. I read it and my conclusions do not agree with yours. Now i too am too involved to close it and if i were to well it would not go as smooth as your closing did, and i never actually voted :P I had no idea the template existed let alone the long ongoing discussion about forcing its use. delirious & lost ☯ ^~hugs~ 22:11, 7 October 2010 (UTC)

Since you say, "I would prefer the formal RFC on the RFC", please do that. If you don't want to do that, I suggest raising the issue at WP:VPP. I would prefer either of those to another meandering debate on WT:AT. Ozob (talk) 22:28, 7 October 2010 (UTC)

Shell (mathematics)

How do you know its a hoax? Do you mean a hoax, that there is no such thing, or just erroneous? I have removed the speedy, and suggest you take it to AfD, not prod, for a community decision. It would be well to notify the mathematics wikiproject to get some informed comment. DGG ( talk ) 23:28, 25 October 2010 (UTC)

Composite Number Factoring Theorem

I see you tagged this article for speedy deletion. That was rejected. I've posted a proper AfD. The article's AfD page can be found here. Thanks. — Fly by Night (talk) 17:51, 30 November 2010 (UTC)

Email

Hello, Ozob. Please check your email; you've got mail!
It may take a few minutes from the time the email is sent for it to show up in your inbox. You can at any time by removing the {{You've got mail}} or {{ygm}} template.

Access

I hope you're enjoying this discussion about access. It is something our project needed to address. --Anthonyhcole (talk) 12:29, 21 January 2011 (UTC)

Dashes and music-album lists

Hi, I think this is what it's referring to. Tony (talk) 12:25, 31 January 2011 (UTC)

WP:WPM interview

Update: Thanks for participating in the interview. Just a heads up that section editor Mabeenot, has move the publication date to this coming Monday, 21 February. The final draft has now been posted. Please go through it to check for any inaccuracies, etc. Thanks again. – SMasters (talk) 23:48, 16 February 2011 (UTC)

The Signpost

Hi, could you review how I've presented the successful nomination of the two animations in "Featured pictures"? If there's a way of presenting what they're about to the intelligent non-mathematician, that would be good. link. Tony (talk) 10:29, 20 February 2011 (UTC)

Sorry, I was away all weekend, so this is too late to help you. But the description is fine. Ozob (talk) 12:21, 23 February 2011 (UTC)

Derivative

Hi Ozob, I see that you've reverted my modification in the article Derivative, section Derivatives of elementary functions, from $f'(x)=0.25x^{-0.75}\,\!$ back to $f'(x)=(1/2)x^{-1/2}\,$. I wonder why the latter seems superior to you? I do see a couple of reasons myself why mine might be somewhat clearer. Iamthedeus (talk) 22:15, 25 February 2011 (UTC)

Well, my reasoning is mainly that 1/2 is a simpler number to think about than 0.25. I also prefer to use fractions rather than decimals because too many students identify numbers with their decimal expansions, and I think that using fractions fights that. So it's nothing deep. It sounds like you have a reason for preferring 0.25, so please say why. Ozob (talk) 02:05, 26 February 2011 (UTC)

Well in the case of using 1/2 or 0.5 as the value of r in $f(x)=x^{r},\,$ one finds created in the resulting derivative a visual symmetry that is meaningless and thus potentially misleading: the number one-half appears both as the coefficient and, in negative form, as the exponent. Of course this is an anomaly that occurs for only one of the infinite possible values for r, and thus is meaningless, and yet it is a rather salient feature of the example, all the more so for readers with less of a grasp on math. This seemed to me reason enough to change the value of r in the example to some other number, such as one-quarter, in order to avoid any unnecessary confusion as to the true rationale for the values of the coefficient and exponent in the derivative function, while preserving the other important features of the example (such as the derivative being undefined for negative values of x).

This, too, is nothing deep, and surely most readers would not be thus confused upon encountering the one-half version, but I see no harm in opting to avoid that possibility entirely.

As for my choice of decimal over fraction, it was merely that the "0.25" strikes in me a slightly sharper conception of the number than does "1/4"—I suppose I myself am one of those who at heart identify numbers with their decimal expansions—but I certainly see the value of discouraging that, so I do not dispute your preference for using fractions.

Also, I noticed that you reverted a number of modifications I had made to various formulas on the page; specifically, I inserted "\,\!", forcing them to be rendered as TeX PNGs. I did this because they had been rendered in HTML (for me, at least—even if they contained just "\,") and as such happened to have some readability issues that were fully avoided by rendering them as images. Is there any reason I should know of for which "\,\!" would be undesirable in these cases?

Iamthedeus (talk) 01:31, 3 March 2011 (UTC)

I agree with your reasoning, so I've changed the article to use 1/4 instead of 1/2. To me, 0.25 seems much less precise than 1/4: The former literally means "25 parts out of one hundred", and I have a hard time visualizing one hundred parts; whereas the latter means "one part out of four", which I can easily visualize.

\, should always force a formula to be rendered as HTML, unless perhaps you've changed your math rendering preferences. Wikipedia:Manual of Style (mathematics) explicitly suggests \, as a way to force PNG rendering. I figured that your use of \,\! was an attempt to prevent the formulas from having extra space at their ends. This can't happen in practice because of how they're rendered, so I thought the extra characters amounted only to clutter. But if they have a real effect then you should start a thread about this at the math MoS, as a lot of articles may have to be changed. Ozob (talk) 01:57, 3 March 2011 (UTC)

I'm not sure what the default math rendering preference is, but mine is set to "HTML if possible or else PNG", which would explain why \, was insufficient. In any case I was guided by Help:Displaying_a_formula#Forced_PNG_rendering which seemed to indicate that the practice of using \,\! is acceptable. I suppose, though, that the rendering option "Recommended for modern browsers" would be more ideal for someone like me with a modern browser, so I'll switch to that. Iamthedeus (talk) 04:59, 3 March 2011 (UTC)

The italics issue

Hi. Just a note to say that I have raised the italics issue here (with a mention here). I am broadly in favour of re-opening the discussion — as a proper centralized discussion — though obviously without wanting to take on a huge workload personally. Regards. --Kleinzach 04:23, 28 March 2011 (UTC)

Salebot

Hi Ozob; "Boubaker polynomials" are pretty infamous on frwiki, and Salebot is trained to automatically revert edits containing the term (in French), ignoring 1RR for this specific case. You're on Salebot's whitelist now. --gribeco (talk) 00:32, 4 May 2011 (UTC)

Hi. Just for your information, Rirunmot was blocked (global account) in May 2009 on it: as sockpuppet of Softer, main account of the "boubaker team" on it:. Rhadamante (talk) 04:33, 4 May 2011 (UTC)

Wikipedia talk:WikiProject Mathematics/Straw poll regarding lists of mathematics articles

In light of your participation in the discussion(s) regarding the treatment of disambiguation pages on the "Lists of mathematics articles" pages, please indicate your preference in the straw poll at Wikipedia talk:WikiProject Mathematics/Straw poll regarding lists of mathematics articles. Cheers! bd2412 T 18:58, 23 May 2011 (UTC)

Good advice at WT:WPM

I shouldn't have gotten heated. I'll try to count to ten in the future. In hind sight I can see that if I don't understand the words it is a bit silly to take offense to them. Thenub314 (talk) 21:29, 25 May 2011 (UTC)

Spacing of en dashes

I just wanted you to know that I've since loosened up my thinking about the rules on the spacing of certain en dashes (the "von Keipert" thing) – and I think I took a rather too hard line against your proposals at MoS, last year, was it? Tony (talk) 04:08, 18 June 2011 (UTC)

(Sorry for the delay, I've been on vacation.) Yes, you did take a rather hard line. I did too. I've also softened on this issue, and I don't object to spaces as much as I used to anymore. I'm sure that we can come to some consensus! Ozob (talk) 12:41, 20 June 2011 (UTC)

pentagram map questions

Hi Ozob, I tried to answer your questions on the pentagram map discussion page. I didn't do a perfect job, but I hope it helps. RichardEvanSchwartz (talk) 05:46, 30 June 2011 (UTC)

Riemann Integral

Thank you for your edits...I made a lot of stupid typos despite my efforts with the "Show Preview" button.

Fraqtive42 (talk) 18:54, 22 July 2011 (UTC)

Infinite Numbers

Thank you for your mathematical insights. I could follow almost all of them. Indeed Infinite reals can be straightforwardly added and subtracted in a convergent manner, but they CANNOT be multiplied convergently. You may not even multiply a real by an infinite real by your argument. Then again, who says that numbers have to be multiplyable, maybe we can be SATISFIED with mere addition and subtraction. Anyway I had fun concocting this and fun reading your eloquent treatise. Thank you Sir! — Preceding unsigned comment added by BenHeideveld (talk • contribs) 21:04, 14 August 2011 (UTC)

Hey ozob

Thanks for showing me what was wrong, I'm just writing here to let you know I read your response. I won't make those mistakes again, but I definitely need to do something about that derivatives page. It is way too hard for learners to understand.

Anyway, thanks for your message! — Preceding unsigned comment added by Evan2718281828 (talk • contribs) 02:49, 15 August 2011 (UTC)

If you have any suggestions or ideas, please be bold and add them to the article. Or if you're not sure how, you can write a note on the article's talk page asking for help. Myself, I am pretty much out of ideas on how to make the article more accessible. Ozob (talk) 12:00, 15 August 2011 (UTC)

Yes, I probably put my edit in the wrong place.

I spend very little time voting and engaging in the behind the scenes stuff that helps keeping wikipedia rolling along. This is a good reason as to why. Thanks for paying attention even tho I apparently was not. EInar aka Carptrash (talk) 15:08, 15 September 2011 (UTC)

"Outline of" articles

TT's thoughts

I think you may have overlooked a context of the word "outline". One major use of the term is short for "hierarchical outline", which is synonymous with "hierarchically structured list". The context is used mostly in academia, writing, and in the realm of professionally published encyclopedias (most notably the Encyclopædia Britannica and the World Book Encyclopedia).

The Wikipedia article tree structure presents the hierarchical outline as one of the forms of tree structure.

It is obvious that "Hierarchical outline" is just too cumbersome for titles. Therefore, we use its shortened form "Outline" in titles, which is the same way that teachers, writers, and publishers of other encyclopedias refer to hierarchical outlines.

Hierarchical outlines have several major uses, from the document planning skeletons (for books/papers/reports) taught in primary school as a writing tool, to reverse outlining for revising existing documents, to the topic outline synopses provided by college professors to their students, to the subject outlines presented in professionally published encyclopedias — World Book uses them as article summaries, while the Encyclopædia Britannica developed one colossal outline, of all knowledge, as a plan for the encyclopedia's 15th edition, and published it as a topic outline to show how everything is related to everything else.

Here's a little glossary of outline-related jargon:

• Outline - Short form of "hierarchical outline". The conventional form of hierarchical outline is an indented list where each item on the list is preceded by an alphanumeric prefix (e.g., I.A.1.a... or 1.1.1.1..., etc,). The prefix establishes a path for each item. Though there are many other formats, including non-prefixed. The important thing is that all (hierarchical) outlines represent their items in a hierarchy, that is, they present them in levels. Wikipedia outlines do this through subheadings, followed by indented lists (bulleted or not).
• Sentence outline - hierarchical outline composed of sentences. Used by students to plan papers, and by authors to plan books. Also, it is the format of Britannica's Outline of Knowledge, which is a topic outline in which most of the topics are presented as sentences (due to lack of simple terms to describe them).
• Topic outline - hierarchical outline composed of topics, as opposed to sentences. For most topic outlines, the topics are single words, or terms, though some topics require an entire sentence to name them. Used in secondary education to present course
• Reverse outline - hierarchical outline built from an existing non-outline document (book, paper, etc.). Often used as a revision tool or to build a table of contents. On Wikipedia, most "Outline of" articles start out as reverse outlines of the subject material present subject's myriad of articles across all of Wikipedia.
• Subject outline - outline of a subject, rather than of a specific document.

"List of ... topics"

By suggesting that outlines be "eliminated", you inadvertently targeted outlines titled "List of ... topics". Most of the opponents of "Outline of" articles are equally opposed to "List of ... topics" which differ from "Outline of" articles only very slightly (mostly in name) - the contents (below the lead section) are almost identical in structure.

Please be more careful in the future. I don't want to see topic lists deleted any more than you do.

Based on their content, structured topic lists are hierarchical outlines. As soon as you've added topical subheadings to a topic list, you've given it a hierarchy. It then falls under the definition of "hierarchical outline". It doesn't matter how far down the levels go. Because in a summary format (which is one application for outlines), you can be as detailed or as little detailed as desired.

Keep in mind that merging outlines into indexes is the same thing as deleting outlines. "Outline" refers to the format. Remove the format, and you've deleted the outline.

If "Outline of" articles get deleted by community consensus, whether by AfD or via merge-proposal, the "List of ... topics" articles won't be far behind. Most opponents of outlines don't differentiate between "Outline of" and "List of ... topics". And some are opposed to all topics lists (including the "Index of" articles).

Mathematics

I've been leaving the mathematics topics lists alone, even though they are hierarchically structured topics lists (topic outlines).

Concerning the new guy (Gamewizard)... He isn't a member of WikiProject Outlines, and has been acting entirely on his own. He apparently likes lists, and has been revamping them all over the place (topic lists, timelines, help menus, outlines, etc.). He's been damaging outlines as much as the other list types, though he tends to add valuable links to outlines, so I haven't been too critical. He's unfamiliar with our guidelines and conventions, and he's a bit talk-page shy, but his energy-level and enthusiasm are awesome. I hope he doesn't get discouraged from editing Wikipedia by you guys coming down on him too hard. (Please don't scare him away). I believe he'll make a fine editor once he has learned the ropes.

Come to think of it, I should probably invite him to join the Outlines WikiProject.

Outlines WikiProject

Keep in mind that even if the outlines get renamed, the WikiProject will most likely get renamed along with them. The focus of the outlines wikiproject is on hierarchical outlines (hierarchically-structured topics lists, as opposed to alphabetical topics lists), regardless of the outlines' titles. See also Wikipedia:WikiProject Indexes.

What's next?

I look forward to your thoughts and ideas. The Transhumanist 22:18, 16 September 2011 (UTC)

Well, that's not TLDR for me, but I don't mind reading. (If I did I wouldn't be on Wikipedia. :-)

My objection

As I see it, right now, the only important difference between a "list of ... topics" article and an "outline of ..." article is that the former is sometimes a hierarchically structured list of articles, and usually the articles have no annotations; and the latter is always a hierarchically structured list of articles, and most of the articles have annotations. In addition, the latter sometimes has prose which is not well integrated into the list structure: While the prose may be under a topic heading, it could stand alone.

I don't mind having hierarchically structured annotated lists of articles grouped by topic. I think that would be wonderful. (And in fact I'm rather dismayed that most of the support so far for my RfC has been from the "throw out all navigational aids" crowd. I don't agree with them.) But I do object to standalone paragraphs and to annotations which might as well be standalone paragraphs. They are redundant content forks, and I have a strong aversion to content forks. They are impossible for editors to maintain and annoying as all heck for readers.

I don't think that annotations alone make a list a redundant content fork. (Everyone agrees that summary style is desirable and effective, and it's not a redundant content fork.) It's the scale of the annotations that bother me. They seem to grow without end; like how some medieval authors annotated the works of the ancients so heavily that they ended up writing their own books. If the annotation needs footnotes then I think it's gotten too big.

I can't tell what your eventual goal and what the Outlines Project's eventual goal is for these articles. But judging from what people say are the good outlines, it looks like that goal includes what I would call content forking. I don't support content forking, hence my proposal to eliminate outlines. (There's some hair-splitting going on here, since the hierarchically structured annotated lists grouped by topic that I approved of above are, as you pointed out, outlines in the dictionary sense of the word.)

Naming

My objection is mostly not to the name "outline". I think that sometimes that name sounds silly (Here is an outline of a circle: ∘), but it seems to be appropriate for what you are trying to accomplish.

I would prefer if outlines were all named "List of ... topics". And I think alphabetical lists of articles would be better off at "Index of ... articles". "List of ... articles" would be OK, but I think it might be confusing since the names would be so similar. Of course, achieving that kind of consistency on Wikipedia is probably hopeless.

The new guy

I don't want him to be discouraged, either, even though I didn't like what he did. He seems kind of young to me, but I think he has lots of potential. (He's bold and I like that.) I think he'd make a good member of the Outlines project.

Outlines WikiProject

As long as the Outlines WikiProject doesn't advocate content forks, I don't want them to go away. Right now I don't think (or I am at least not convinced) that's the case; this is why I said in my RfC that the project would be marked historical. But if I'm wrong about that, then that part of the proposal is unnecessary.

I think the Outlines project would do itself a huge favor if it (1) came up with some careful guidelines about what is and is not appropriate in an outline, and (2) raised at least three outlines to FA status. The two are complementary: If you have careful guidelines, that helps everyone (including FA reviewers) know what a good outline is; and if you can raise three outlines to FA status, then you will have received a lot of feedback from a lot of people on what a good outline is (which helps you to write good guidelines).

FA might not be the right forum. FL might be more appropriate. I'm not sure.

One of the reasons why I think this is necessary is because right now nobody knows what an outline is or what it's good for. I have been disappointed at the quality of the oppose votes on my RfC, because they are mostly just WP:ILIKEIT. (Granted, that's also true of a lot of the supports, and most votes on most things are that way...) Having guidelines for an outline would clarify the purpose of an outline. Knowing what an outline is would help people explain why they think outlines are useful; and you would probably not get any more RfCs like mine.

It seems pretty clear to me that the eventual result of the RfC will be "no consensus". If, after it's over, everybody goes their own way and pretends like the RfC didn't happen, then I will be very disappointed. If an Outlines guideline comes out of this somehow, I will be satisfied. Ozob (talk) 00:20, 17 September 2011 (UTC)

Oh, and I should add that while I have expressed disgust at the Outlines WikiProject, it was directed at what I see as inappropriate behavior, specifically, non-consensus page moves. The project stopped that behavior stopped a long time ago. I wrongly assumed that the new guy was a member of the Outlines project and so laid some of the blame for his moves at your feet. But I was wrong, and I would like to own up to being wrong. Ozob (talk) 01:47, 17 September 2011 (UTC)

Reply to Ozob

I'm glad we can talk about this casually, rather than in the combative argumentative mode that has been all too common concerning these pages.

The new guy

Gamewizard71 appears to have disappeared. His last edit was September 7th. I hope we haven't scared him away. Hopefully, he's just busy with the new school year.

Content forking

I believe the redundant content forking guideline is intended specifically to prevent Wikipedia from having 10 articles on the same precise subject under various synonyms. For example: "United States", "The United States", "United States of America", "USA", "The USA", etc. If there was an article by each of these names, that would be rather confusing. It would also detract from the quality of Wikipedia, which would be chock full of incomplete duplicates. Finding the most complete article on each subject would be a pain.

I do not believe the guideline was intended to prevent different types of pages on the same subject from existing. The purpose of a list (including indexes and outlines) is different than the purpose of a prose article.

The guideline generally does not pertain to the subsection level, as that falls under the summary format guideline.

Leads and annotations

You stated: "I don't mind having hierarchically structured annotated lists of articles grouped by topic." You also mentioned that you didn't like stand-alone paragraphs or annotations as extensive as paragraphs. You also suggested that we develop outlines to Featured status.

The above stance is currently contradictory, in that section leads are generally required for a list to reach Featured List status, and hierarchical outlines are lists.

I understand your objection to section leads - they defeat the purpose of an outline. They are a non-hierarchical format. Paragraphical format is the exact opposite of an outline. So then, why have a lead paragraph at all? Let me explain...

Please keep in mind that outlines are evolving, and the whole endeavor has been a trial and error learning process. Many subjects are not self-explanatory - you can't tell what they are by their subject titles. So to aid in subject identification, we started adding short lead sections. But when we took on the geography branch of knowledge and endeavored to build an outline for each country, writing a lead from scratch for each was too much for the small team to handle. So we copied the lead section of each country with the intention of condensing them down to the bare essentials for each country, to perhaps the one or two things each country was most renowned for. To help readers recognize what country they were reading about.

The team disbanded after about a year, and it was too much for me to handle it all by myself, due to subsequent events. A particular individual began to wage war on the outlines and upon me, and I became engaged in defending the outlines against him with little time to develop them. The war lasted a whole year. When it began, I found that any outline I worked on became his focus, and so I took the opportunity to work on a volunteer project in my locality. Meanwhile, I switched to cleaning up the damage the opposer inflicted rather than develop the outlines (he had turned it into an uphill battle). My switching to repair turned it into an uphill battle for him. He was like an ant attacking an elephant. After a year, he had damaged about 10% of the 500+ outlines. Since then, most of his damage has been repaired.

So we were left with bloated lead sections in the country outlines. Eventually, according to plan, they will be condensed, but there is a lot of other issues that need to be cleaned up first.

What we were aiming for was similar to the Featured List criteria: "It has an engaging lead that introduces the subject and defines the scope and inclusion criteria." Though instead of "engaging", our aim was on assisting with subject identification and minimizing confusion, and minimizing the need to click all over the place to other pages trying to figure out what subject the outline was about. In accordance with FLC, I agree that the subject should be introduced in the lead section.

As far as I'm concerned, the lead isn't part of the outline itself. It's just a description of the subject that precedes the outline, which is the content of the page (this is expressed in the final sentence of each lead section: "The following outline is provided as an overview of and topical guide to"...).

An example of a nice short lead that assists in subject identification can be found in Outline of basketball.

I don't agree with FLC that each section needs a lead paragraph. That can usually be accomplished with a list item with a short annotation. I don't believe section lead paragraphs violate the content fork guideline, it's just that they're not hierarchical content.

Concerning annotations, the need arose out of the necessity to click on each link to see if you wanted to read about it. To see what it was. So we started adding annotations to aid in topic selection. Even though the main purposes of outlines are structural and summarizing, as navigational aids outlines function much like menus or tables of contents, and brief descriptions have proven very useful for browsing.

To get the general gist of what a list of 50 topics are, it is much faster to read 50 annotations than it is to click on each of the 50 links to read their descriptions and return to the list to read the next one. This is the main reason we started adding them.

History of the endeavor, and naming

It started with the discovery of a page in the Wikipedia namespace called "Wikipedia:Basic topics". It was a list of pages called "Basic x topics", where x was the subject of each list. The list included about 50 subjects.

The set of pages was created by Larry Sanger at the dawn of Wikipedia to identify missing topics for major subjects via redlinks.

Eventually, all the links turned blue, and so what you had were rudimentary topics lists on each subject gathering dust. Some of the lists had been renamed and moved to article space. So I cleaned up the rest and turned them into "List of basic x topics" articles and moved them into the encyclopedia proper. I had done work on navigation menus for Wikipedia, so naturally I added the list of basic topics lists to it.

I noticed big gaps in the set and started filling them in with new list pages. Under their various names from that time and since, I've created hundreds of these pages (under my current nym and previous nyms).

But something unexpected happened. The lists expanded beyond basic. Editors just kept adding more links and the lists grew more and more comprehensive. And due to the visibility of the project, with its own navigation page and WikiProject support, most of the lists became more comprehensive than the corresponding topics lists. (Non-basic topics didn't have a WikiProject devoted to them back then, but now they have two: the Outlines WikiProject and the Indexes WikiProject). Another factor was that the "basic" lists were all hierarchical. The whole thing was growing into an outline of all of human knowledge. It was obvious a rename was needed.

Initially, we were going to rename them to List of x topics, but we discovered there were two sets of lists competing for that same name: hierarchical topics lists and alphabetical topics lists.

To solve that problem, I started renaming them to outlines and indexes.

The important thing is that there are two sets of names, to accommodate the two sets of lists.

Interestingly, there were never any complaints about the index renames. The name is very intuitive, almost natural. Unfortunately, relatively few people know what a hierarchical outline is. But since that was the most accurate name for the structured topics lists, we used it. And, since the indexes were also topics lists, it seemed ludicrous to use "topics" for outlines while there was clearly another type of topics list that wouldn't be included (indexes). I figured that using the two separate names for the two types of topics list was less awkward semantically.

But before I could finish renaming outlines, I got into a heated argument with someone, he took it personally, and the war mentioned above started. I should have just let him blow off steam in the initial encounter, rather than blowing steam back at him. Oh well. Live and learn.

A resulting problem

One problem that has emerged from this progression of events is that there are two names for outlines on Wikipedia: "Outline of..." and "List of ... topics". As you touched upon above, they differ little in their content scope and formatting.

There are about 500 "Outline of" pages and around 200 "List of ... topics" pages.

Except for the math lists, the selection of "List of ... topics" are almost random compared to the list of outline-ofs.

Outside of math, there is virtually no development support nor WikiProject support for "List of ... topics". Most of them sit for years almost untouched. Meanwhile, there's at least one outline developer (me) who continuously monitors outlines to maintain them and in addition tries to cycle through them all at least once per year to update and further develop them (including placing links leading to them).

When I pull a "List of ... topics" page into the outline project, I do so with the intention of cleaning it up and of bringing more visibility and support to it. "Outline of" pages generally receive more edits due to their inclusion as a subsystem of Wikipedia's contents system, and their growing recognition by readers as a standard article type and navigation aid.

As an example of the work I put into such a conversion, compare the Outline of poker with the way it was before the conversion. If the conversion work I do gets renamed back to "List of", I have less incentive to upgrade such pages. It would be more productive for me to start new outlines from scratch on each subject, or simply create outlines for subjects with no topic list coverage yet.

I'd like to further develop the poker outline to be comparable with Outline of chess. They're natural siblings.

Featured status

We tried to get one of the outlines to featured status, but the participants at Featured Lists insisted that every item in the list have a citation, just to prove that it belonged to the subject (i.e., met the inclusion criteria). I thought that was ludicrous, since the overarching subject is usually self-evident once you click on the link. See Wikipedia:Featured list candidates/List of basic geography topics.

It is mind-numbingly tedious to gather citations that state something belongs to a particular subject, for instance to verify that "mountain" is a geography topic. The semantics of the rules come into play, and there's a whole debate as to what the source needs to say. Is a statement needed? Or is inclusion in a geography textbook good enough? Some would claim that providing the latter is original research, that it's inclusion is being interpreted. It's a quagmire.

Since then, we've been adding annotations to outlines, so it might be enough to provide citations for the claims made in the annotations rather than to support the inclusion of the listed items themselves.

But my guess is that an effort to build a featured outline will not be undertaken again until outlines have attained critical mass. Prior to that, a nomination would probably revert into a naming war. Not worth the trouble.

The eventual goal

The Outline of chess is the model I'm working toward. Short lead paragraph that identifies what chess is without itself becoming the article. No lead paragraphs in sections. Short annotations just long enough to explain what each topic is.

Outline guidelines

There is an essay concerning the formatting and development of outlines. See Wikipedia:Outlines. I expect that eventually it will evolve to guideline status.

The essay is informative, as it covers how to develop an outline. Those interested in establishing a guideline should probably discuss and edit the essay.

I hope this all makes more sense

I've done my best to provide some background on how outlines evolved into outlines and the rationale behind it.

I look forward to your comments (especially on the eventual goal mentioned above) and will be happy to answer any questions you may have. The Transhumanist 00:35, 20 September 2011 (UTC)

Reply to The Transhumanist

Content forking

For the most part, WP:CFORK doesn't address content forking in the present context. It's focused on forking entire articles (as in the examples you gave). But there are a few parts which seems relevant. Under WP:CFORK#Redundant content forks, there's the sentence, "flesh out a derivative article rather than the main article on a topic". It's not clear to me what the sense of "derivative" is, but it seems to mean "related". Also, there's the section WP:CFORK#Related articles, which talks about articles whose content has a lot of overlap. It's not clear from this just what proper summary style is, and just how much duplication is acceptable.

You brought up the example of leads and prose in featured lists. Perhaps you will not be surprised to find that I am also critical of the current interpretation of WP:FL?. I don't see anything wrong with the featured list criteria as they are written, but in practice the result is often a minor content fork. While it may not be possible in practice to write a list that would be promoted to featured status and would also meet my standards (and I admit that I'm quite stringent on this topic), I don't believe that it's impossible in principle.

You express the hope that we're almost in agreement over what outlines should and shouldn't be. I am not so hopeful. I see this as a major point of contention.

Featured status

You comment that, "It is mind-numbingly tedious to gather citations that state something belongs to a particular subject". I agree. My impatience for citation gathering is why I don't do FAs. But that is not why the FL nomination for List of basic geography topics failed. It failed because there were no citations for the structure of the list. So, for example, you break down geography into human geography and physical geography, and you provide citations for that. Good. But then you go on to say that there are some further branches: Integrated geography, geomatics, and regional geography. It's you who's saying that, not a reliable source. That's a problem.

Let me give another example, this time from my own field of mathematics. Suppose that you are trying to determine the right structure for the List of mathematics topics. You want to know: What should the top level headings be, what should their subheadings be, and so on? Well, it turns out that there is a standard for such things. The American Mathematical Society created the Mathematics Subject Classification so that it would be easier for research mathematicians to look up papers they're interested in. So you could use that to organize the list of mathematics topics.

But that's not your only option. The Library of Congress assigns call numbers using their own classification (sketched at Library of Congress Classification:Class Q -- Science#QA Mathematics, though it's actually finer than that). And the Arxiv created and uses their own classification system. And you're not done there, because the International Mathematical Union uses yet another. Which suggests the question: Who's right? The answer is that none of them are right. The systems are meant for different purposes: The MSC is for indexing all research papers ever published, the LOC system is for monographs and books, the Arxiv system is for tracking recent preprints, and the IMU system is for deciding which talks you want to go to at the International Congress of Mathematicians.

If you're going to make a list of mathematics topics then you can only use one system. If you used one of the above-mentioned systems, then you'd be able to cite a source for your list's structure. If you make up your own system, then you're introducing your own point of view as to what the important divisions of mathematics are and are not. That's a POV issue.

I think this is an almost insurmountable problem with outlines. I think it's very, very hard to find a reliable source that gives a comprehensive list of all topics in a subject area. But if you're going to keep outlines in article space, then they need reliable sources. If that's not possible, then they should be in a different namespace with different featured criteria. And if it's not possible to raise an outline to featured status, then I am not sure what outlines are doing on Wikipedia on the first place. Any content that we want to have should have the possibility of featured status.

(By the way, I have said before that I think that when the annotations in an outline have footnotes, then they are too long. I'd like to say that I see that as a different context from the present one. There is nothing wrong with the structure of the outline being properly cited and footnoted.)

Naming

Wikipedia:Outlines points out that outlines are a type of list article (under WP:OUTLINE#Wikipedia outlines are list articles, and share list article features). I said above that I think it would be good for all alphabetical lists of articles to be named indexes and for all outlines to be named list of ... topics. I still believe that would be a good idea. It would be easier on our readers. At the least, I think it would be a good idea to rename all the alphabetical lists to indexes. I said before that I didn't know whether that was a realistic goal. Do you think it might be? If so, then that would be a good step for Wikipedia. Ozob (talk) 00:52, 21 September 2011 (UTC)

Reply to Ozob

Content forking

You mentioned that leads are a major point of contention.

I'm sorry, I forgot to lay out a possible easy fix for this. First, let me cover section leads:

Rather than section leads, the section's main list item could be included, with an annotation like the other items, like this (from the roasting section of the Outline of food preparation):

Roasting – cooking method that uses dry heat, whether an open flame, oven, or other heat source. Roasting usually causes caramelization or Maillard browning of the surface of the food, which is considered by some as a flavor enhancement.

• Barbecuing – method of cooking meat, poultry and occasionally fish with the heat and hot smoke of a fire, smoking wood, or hot coals of charcoal.
• Grilling – applying dry heat to the surface of food, by cooking it on a grill, a grill pan, or griddle.
• Rotisserie – meat is skewered on a spit - a long solid rod used to hold food while it is being cooked over a fire in a fireplace or over a campfire, or while being roasted in an oven.
• Searing – technique used in grilling, baking, braising, roasting, sautéing, etc., in which the surface of the food (usually meat, poultry or fish) is cooked at high temperature so a caramelized crust forms.

As for article leads, I've been working on a possible solution to this, called the "Nature of" section. I've been using it to describe the classes the subject of the outline belongs to, but it could be expanded or modified to include the main attributes of the subject.

The main thing I'm concerned about is that the reader be able to ascertain what the outline is about without having to click somewhere else to find out.

But, fixing outlines to your specifications would prevent and thus preclude them from becoming featured lists. You and Featured Lists are working at cross-purposes. I would go so far as to say that the Featured List Criteria of the inclusion of leads has community consensus, while your objection does not. However, I don't care about featured lists, and I think spending the time to reach their arbitrary standards is a waste of time.

Integrating everything into the hierarchical structure of each outline would be fine with me.

So, in your opinion, how can we best convey the definition of the outline's subject?

Citations

With respect to citing the structure of an outline, that's ludicrous. That would be the same as requiring citations for the headings and subheadings of articles, and for their order of presentation. There is no requirement on Wikipedia for that. One standard subtopic is "History of". It would be insane to require a citation to establish that such a subtopic belongs. Verification is required only where challenged or likely to be challenged. I'm dead set against holding outlines to providing citations when the corresponding article lacks them. Whatever citations the outlines need, articles on Wikipedia should already have.

But, showing that branches of a field are branches is easy, and the citations for this can be included in the annotation. Proving that every item in an outline belongs to the subject isn't even a standard we apply to articles.

Remember, outline articles are not about outlines, they are outlines. In articles, the structure of paragraphs (the order of sentences) and of headings, is not subject to citation — and similarly such citations aren't required of outlines either. Factual statements are what need citations.

Naming

Yes, I think renaming alphabetical topic lists to "Index of" is practical and realistic, because the name is so intuitive that virtually nobody objects. Almost all of the alphabetical topic lists are already named this (go on, take a look around). And guess who renamed them?

But, alphabetical topic lists are still topic lists. Which makes giving another class of topics list the class name somewhat awkward, semantically speaking, since it implies that alphabetical topic lists are not topic lists. The Transhumanist 02:47, 21 September 2011 (UTC)

Reply to The Transhumanist

Content forking

I think your idea for replacing section leads is excellent, as I think it matches the philosophy of outlining much better. However, it doesn't change my stance on whether or not such an item is a content fork. Being a content fork or not is independent of format.

Having no lead at all would, I think, be somewhat jarring for the reader. The reader needs at least a single sentence, maybe more. There's a little space available before it becomes a content fork. Also, I am not convinced "Nature of" will work for every outline. For some it will (outline of chess, for example). But it doesn't seem to fit outline of Japan very well.

I agree that FL and I are working against each other. I don't mind being a minority or disagreeing with consensus. I am still strongly opposed to what I see as content forks, but if you think that I don't represent the community consensus on this matter, then you can choose to ignore me. (I won't be offended.)

Citations

Citing certain aspects of an outline's structure seems reasonable to me. Difficult, yes. But unreasonable, no. If an outline is an article—if it is more than just a navigational aid—then all of its content must be properly sourced.

In an ordinary article, that means that the facts contained in the prose or in lists must be sourced. Because its structure doesn't say anything vital about the nature of the subject, there's no reason for its structure to be sourced. But for an outline, the meaning of the content depends vitally on the structure. For example, the outline of finance lists short-rate model and spectral risk measure as "Fundamental financial concepts". Are they? I wouldn't call them fundamental; I don't think they're as fundamental as interest or money. If I did call them fundamental, it would only be my opinion. If you choose to call them fundamental, then that's your opinion. But we're not supposed to provide our opinions.

Maybe that's not a particularly good example, because most of the bullets under "Fundamental financial concepts" stand alone; they don't have anything beneath them. That's why I think the fields of mathematics are a good example. Each of them is a broad topic, and there's space for large outlines underneath all of them. And you can't justify any one organization better than any other; it's just an opinion. You're not allowed to express your own opinion on how mathematics should be organized here. You need to cite someone else.

I agree that it's not necessary to establish that "History of" is a subtopic of a given topic. It's also not necessary to establish that a topic can have fundamental subtopics. I am even willing to say that it is probably not necessary to provide citations for the major sections of most outlines. (By which I mean: They are not likely to be challenged.) But it is necessary to provide citations for some of the subtopics, like which financial concepts are fundamental or what the subfields of mathematics are. These are things that would need citations in an article, so they need citations in an outline, too. That doesn't mean that every item in an outline needs a citation justifying its existence. You might be able to find a reference that gives a list of fundamental financial topics; then you would only need to cite that list, and only once. If it's not possible to provide a citation, then the choice of which topics are "fundamental" is clearly an opinion, and it shouldn't be in Wikipedia.

Featured content

Is there any kind of plan (or even just vague hope) to ever make any outline into featured content? Would you hope to make outlines into featured lists, or into something new ("featured outlines")? Ozob (talk) 01:19, 22 September 2011 (UTC)

Reply to Ozob

Content forking

I'm glad you like the idea for replacing section leads with list items including annotations.

Granted, content forking is still a concern, but not if annotations are made only as long as is needed to convey the meaning of each term. Elaboration may still fall within Wikipedia:Summary style, but threatens to weaken an outline's structure with linear paragraph pose.

Concerning the main lead section, a similar approach may work, with a short statement as to the contents of the page followed by the outline's first list item, the subject itself including an annotated description. For an example see this version of the Outline of chess. I look forward to your comments on this approach.

Another option would be to put the subject's list item in the "Nature of" section, but I believe it would be more intuitive to Wikipedia's readers if it were presented in the outline's lead section.

Citations

You mentioned that all content must be sourced, including structure. I agree that all outline content (including structure) must be subject to Wikipedia's content policies, including WP:VER. I don't believe that means that the entire structure of a subject must already exist out there (in the form of a classification system), because presenting such a structure would itself be a copyright violation (we used to have the entire structure of the Propaedia in proect pages, for instance, but they had to be deleted for copyright concerns). The relationships between headings and subheadings are the important thing: that's where the structure comes from, in answering the question "what is a subtopic of what?". In cases that are not obvious (i.e., likely to be challenged), citations can be called for.

Note that the relation to a subheading of subtopics presented within paragraph prose under that subheading in an article are equally subject to WP:VER. For example, not all subfields are obvious, and not all subfield descriptions include the statement that they are a subfield of the subject; when the relationship isn't stated, a citation is still needed to verify it is a subfield.

I agree with your assessment of "fundamental" sections. Each branch of an outline is itself a list, and each item in that list must meet the inclusion criteria for that section. That is, they must legitimately fall under the subheading, or be what the subheading says they are.

Featured content

Where does featured content lie in the future of outlines? Well, once outlines achieve critical mass, with a worthy number of developers, then it will be feasible to propose a Featured outlines department. It could be a sub-department of Featured lists, and as such its featured-status outlines would be presented in the Featured list section of the Main Page (not in addition to).

Critical mass

Critical mass will occur when outline traffic reaches sufficient levels to attract frequent contributors to each outline. Search engines aren't currently recognizing the subjects of outlines - they seem to be treating the word "outline" in the title as part of the subject of each article. But these articles aren't about outlines, that just happens to be their format. It's frustrating.

A solution needs to be found to match the relevance of outlines to search queries specifying the base subject. After all, who ever searches for "Outline of" anything?

Search engine optimization is one possible approach. But I think the problem resides primarily in the search engine algorythms themselves. They simply don't recognize the relationship of the content to the title of the page. Relevance is lost to their equations.

As always, I look forward to your insightful comments.

Sincerely, The Transhumanist 02:34, 27 September 2011 (UTC)

A humble request

The village pump discussion on outlines has devolved into a deletion debate, and neither of us wish deletion.

I believe there are more diplomatically productive means through which we can improve structured topic lists on Wikipedia.

Based upon the above thread, we're almost in agreement over what outlines should and should not be. The name is the only big sticking point between us, and the proposal's discussion pretty much blew past that issue.

Please consider withdrawing your proposal.

Sincerely, The Transhumanist 01:25, 20 September 2011 (UTC)

The discussion has mostly petered out, and it's pretty clearly no consensus. I don't see an open RfC as a threat to outlines; so after a week or so with no discussion, I'll close it if nobody else has done so first. Ozob (talk) 00:54, 21 September 2011 (UTC)

Richard D'Oyly Carte

Hi. Your close header is too high. It should be below the discussion about whether to add an infobox to the Richard D'Oyly Carte article. That discussion is ongoing (although I agree that some of the comments there are general, the discussion is supposed to be about whether or not to add an infobox to that article - you could move the general comments out of it and into your closed section if you think that is necessary). Would you please move it down to where the general discussion about infoboxes for the project begins, please? -- Ssilvers (talk) 00:44, 3 October 2011 (UTC)

Mystery

Please solve this mystery if you can...

On September 23rd, traffic to Portal:James Bond doubled, and has stayed at the new level since then. I can't figure out what happened.

See http://stats.grok.se/en/201109/Portal%3AJames_Bond

Traffic to Outline of James Bond stayed the same (though it was at the higher-level already), which leads me to suspect changes made somewhere in Wikipedia.

See http://stats.grok.se/en/201109/Outline%20of%20James_Bond

I'd like to find out what happened, in case it reveals helpful link placement tips that can double the traffic to outlines too!

I look forward to your reply. The Transhumanist 22:33, 5 October 2011 (UTC)

Shapley–Folkman lemma at Featured Article nomination

Hi Ozob!

Editor Jakob.scholbach recommended your experience with Featured Articles on mathematics. The article Shapley–Folkman lemma has received 3 (non-mathematical) FA assessments; the "usual suspects" have already contributed thorough GA and A-class assessments, so fresh eyes and experience would be especially valuable.

Best regards,  Kiefer.Wolfowitz 11:43, 7 October 2011 (UTC)

Your close of RfC: Elimination of outline articles

I think you should reconsider your close of the RfC: Elimination of outline articles. Normally the difference between no-consensus and oppose is symbolic, but here, my alternative proposal of establishing a clear guideline on outline content seems to have had a consensus. Your close seems to derail that notion, and I don't think it is a fair reading of consensus. Monty₈₄₅ 03:12, 12 October 2011 (UTC)

I'm sorry, that was a mistake on my part. I was thinking only of my own proposal. Your proposal did clearly gain consensus, so I've updated my closing statement. Ozob (talk) 11:48, 12 October 2011 (UTC)

Thanks for fixing it. I don't think the version there is ready to be an enforceable guideline yet, so I have moved it to Wikipedia:Proposed Outline Guideline and expanded it a bit. While I understand you don't like the idea of outline articles generally, I would welcome your input with the draft. I don't wish to make it a mere tool to be used to defend anything that can be called an outline, and I'm serious about creating an guideline that can also be used to fix problematic outlines, whether that means improving them to be good outlines, or getting rid of them in some form. As you seem very interested in policing bad outlines, your input would be valuable. Monty₈₄₅ 16:19, 12 October 2011 (UTC)

A beer for you

Thankyou for participating in my request for adminship. Now I've got lots of extra buttons to try and avoid pressing by mistake... Redrose64 (talk) 14:51, 14 October 2011 (UTC)

Edit war notice

You currently appear to be engaged in an edit war according to the reverts you have made on Square pyramidal number. Users are expected to collaborate with others, to avoid editing disruptively, and to try to reach a consensus rather than repeatedly undoing other users' edits once it is known that there is a disagreement.

Please be particularly aware, Wikipedia's policy on edit warring states:

1. Edit warring is disruptive regardless of how many reverts you have made; that is to say, editors are not automatically "entitled" to three reverts.
2. Do not edit war even if you believe you are right.

If you find yourself in an editing dispute, use the article's talk page to discuss controversial changes; work towards a version that represents consensus among editors. You can post a request for help at an appropriate noticeboard or seek dispute resolution. In some cases it may be appropriate to request temporary page protection. If you engage in an edit war, you may be blocked from editing. 86.24.46.135 (talk) 8:22, 20 November 2011 (UTC)

smooth completion

Hi ozob, I would appreciate if you could check smooth completion for correctness. Tkuvho (talk) 13:44, 6 February 2012 (UTC)

There's nothing wrong that I can see. I touched up the lead a little, but it's just a change in presentation, not in content. If you need a reference, I think all of this is in Hartshorne, chapter 4. Ozob (talk) 23:35, 6 February 2012 (UTC)

Thanks. Comment at the AfD if you get a chance. Tkuvho (talk) 08:17, 7 February 2012 (UTC)

Group of rational points on the unit circle

Hi, I put some more work into the above recently. I'd like someone else to read it and see if it still makes sense. If you have a chance and feel like it, I'd appreciate you doing that. Thanks, Richard Peterson198.189.194.129 (talk) 21:52, 21 February 2012 (UTC)

Hi Richard,

I have some concerns about the article. First, let me get out of the way a minor concern: Italics for variables. Normally, single-letter Roman type variables like x, y, and G are italicized. So are single-letter functions such as f. (But Greek-letter variables such as α and multi-letter functions such as exp are usually left upright.) The article doesn't consistently italicize x, y, t, u, G, H, and so on.

On to more interesting things. Under the heading "Group structure", one of the sentences is garbled. Currently it says:

If C₄ denotes the cyclic subgroup with four elements generated by the point (0, 1) and Z is any infinite cyclic subgroup generated by a point of form elements generated by the point 0+i, and Z is any infinite cyclic subgroup generated by a point of form (a^2-b^2)/p + i2ab/p where $p=a^{2}+b^{2}$ and p is a prime of form 4k + 1, (and a, b are positive) then G is isomorphic to H = {C₄} ⊕ Z ⊕ Z ⊕ ..., going on forever.

I think it ought to say:

If C₄ denotes the cyclic subgroup with four elements generated by the point (0, 1), and Z is any infinite cyclic subgroup generated by a point of form (a^2-b^2)/p + i2ab/p where $p=a^{2}+b^{2}$ and p is a prime of form 4k + 1, (and a, b are positive) then G is isomorphic to H = {C₄} ⊕ Z ⊕ Z ⊕ ..., going on forever.

That is, one phrase got repeated. But even without this phrase I don't think the sentence is clear. While G is abstractly isomorphic to C₄ plus an infinite number of copies of Z, it's confusing to identify all the infinite cycle subgroups of G by Z. I would suggest giving these subgroups different names. Maybe this sentence could become:

Let G₂ denote the subgroup of G generated by the point (0, 1). G₂ is a cyclic subgroup of order 4. For an odd prime p, let G_p denote the subgroup of elements with denominator p or 1. G_p is either empty or an infinite cyclic group. If p ≡ 1 (mod 4), then Fermat's theorem on sums of two squares says that p can be written as p = a² + b² for two positive integers a and b. The point (a² - b²)/p + (2ab/p)i is a generator of G_p. If p ≡ 3 (mod 4), then G_p is empty. Furthermore, by factoring the denominators of an element of G, it can be shown that G is a direct sum of G₂ and the G_p. That is:

$G\cong G_{2}\oplus \bigoplus _{p\equiv 3{\bmod {4}}}G_{p}.$

This might be too long (I tend to be too verbose) but I think it is much clearer: Each sentence expects less from the reader.

I have the feeling that there should be a relation between the groups G_p and heights. I don't really understand heights, so this is sort of a guess; but I think it's something like, "The subgroup generated by the points of (multiplicative) height less than or equal to M is the subgroup generated by G_p for p ≤ M." That sounds innocuous enough; maybe it's true?

Finally, here is an omission: The group of rational points on the circle is SO₂(Q), the (definite) rank 2 special orthogonal group of the rational numbers. The group of rational points on the hyperbola is SO_1,1(Q), the indefinite rank 2 special orthogonal group of the rational numbers.

Ozob (talk) 01:56, 22 February 2012 (UTC)

Thanks i've put in your sentence already. I think some things after it will need to be adjusted to the symbols in your sentence.The SO2(Q) is indeed an omission, i think SO2(R) is also, or was also, omitted from circle group. Whichever of the articles gets it in can have it mostly copied and pasted to the other.Thanks again, Rich198.189.194.129 (talk) 19:48, 22 February 2012 (UTC)

I know that by SO_1,1(Q), you mean a group that preserves a quadratic form with 1,-1 sighnature, but that's about all i know about it.-Rich198.189.194.129 (talk) 20:42, 28 February 2012 (UTC)

Points on the unit circle have the form (cos θ, sin θ). Points on the unit hyperbola have the form (±cosh θ, sinh θ). If we want to hyperbolically rotate such a point through an angle φ, then we use the hyperbolic addition formulas cosh(θ + φ) = cosh(θ)cosh(φ) + sinh(θ)sinh(φ) and sinh(θ + φ) = cosh(θ)sinh(φ) + sinh(θ)cosh(φ). We can write this as a matrix:

${\begin{pmatrix}\cosh(\theta +\phi )\\\sinh(\theta +\phi )\end{pmatrix}}={\begin{pmatrix}\cosh(\phi )&\sinh(\phi )\\\sinh(\phi )&\cosh(\phi )\end{pmatrix}}{\begin{pmatrix}\cosh(\theta )\\\sinh(\theta )\end{pmatrix}}.$

SO_1,1(R) consists of real 2×2 matrices with determinant 1 that preserve a signature (1,1)-form. That would be exactly the above matrices together with the matrices you get by replacing cosh(φ) by −cosh(φ). These matrices have determinant one by the analog of the Pythagorean theorem, i.e., the relation cosh(φ)² − sinh(φ)² = 1. SO_1,1(Q) is of course the subgroup of such matrices having rational coefficients. Ozob (talk) 02:34, 29 February 2012 (UTC)

On the (co-)homology of commutative rings

Hi Ozob. I was reading the wikipedia page Andre Quillen cohomology and I want to look at Quillen's paper On the (co-)homology of commutative rings. I checked on AMS but they don't seem to have it. Since you were the only one who edited that page, I thought you might know where to find it. Can you give me a link? Thanks in advance. Money is tight (talk) 12:10, 25 August 2012 (UTC)

If you do a Google Books search for "on the co-homology of commutative rings", it's the first hit (the title is the name of the conference, "Applications of categorical algebra"). Ozob (talk) 12:36, 25 August 2012 (UTC)

Thanks! Money is tight (talk) 03:37, 28 August 2012 (UTC)

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)