Best way to incorporate orthogonality/orthonormality proofs

[Howard C. Berkowitz]

But this is the physics workgroup.

It's the physics forum. I meant in mainspace/CZ space. Things can be awfully hard to find in the forums.

[Dan Nessett]

But this is the physics workgroup.

It's the physics forum. I meant in mainspace/CZ space. Things can be awfully hard to find in the forums.

Since I am new, I guess I need some education on what is done where. Are you saying that the fora are not appropriate venues for discussing issues pertinent to Citizendium workgroups? If so, what is the correct venue? Also, if we move to another venue, we should at least copy what has so far been discussed on this forum to that place. How is that accomplished?

[Howard C. Berkowitz]

But this is the physics workgroup.

It's the physics forum. I meant in mainspace/CZ space. Things can be awfully hard to find in the forums.

Since I am new, I guess I need some education on what is done where. Are you saying that the fora are not appropriate venues for discussing issues pertinent to Citizendium workgroups? If so, what is the correct venue? Also, if we move to another venue, we should at least copy what has so far been discussed on this forum to that place. How is that accomplished?

It's fair to say there are differences of opinion of the utility of the Forums; Larry Sanger does believe this is the right place. Personally, given we have the search tools, related articles, etc., in the main (or CZ) space, I think it's easier to preserve the decisions -- not necessarily the detailed discussion -- on a workgroup page.

What workgroup?  Good question. Indeed, we've recently introduced the concept of subworkgroup, not for approval but for interdisciplinary subjects (e.g., chemical engineering).  This not being my field, I don't know if a subgroup might be appropriate for formal notation, proofs, or some other title meaningful to experts.

[Dan Nessett]

Since I am new, I guess I need some education on what is done where. Are you saying that the fora are not appropriate venues for discussing issues pertinent to Citizendium workgroups? If so, what is the correct venue? Also, if we move to another venue, we should at least copy what has so far been discussed on this forum to that place. How is that accomplished?

It's fair to say there are differences of opinion of the utility of the Forums; Larry Sanger does believe this is the right place. Personally, given we have the search tools, related articles, etc., in the main (or CZ) space, I think it's easier to preserve the decisions -- not necessarily the detailed discussion -- on a workgroup page.

What workgroup?  Good question. Indeed, we've recently introduced the concept of subworkgroup, not for approval but for interdisciplinary subjects (e.g., chemical engineering).  This not being my field, I don't know if a subgroup might be appropriate for formal notation, proofs, or some other title meaningful to experts.

Well, probably a case can be made that this question is relevant to Mathematics, Physics and Engineering. The first is concerned with producing the results and the latter two use them. However, I am new here and so someone else needs to determine where this discussion belongs. Also, if we move the discussion, we need someway of copying the history. If only the decision needs to be documented, then we can continue discussing the issue here and when a decision is made, note that in the appropriate place.

[Hayford Peirce]

Personally, I think that the Forum is a *terrible* place to discuss anything beyond generalities. Why? Because it's so freakin' #@$%^&* impossible to find earlier discussions!  What's the point of the Search box up at the upper-right of the screen?  What does it search for? Type in, for instance, Oldest Confession, a phrase that I have use numerous times in the last couple of months in several different Forum threads. What is the result of this Search?

Nothing. Nada. Rien. Zero.

Suppose, three weeks from now, I wanted to find this particular discussion right here, one that, has, let us say, not had anything added to it during the past three weeks.  How do I find it?

Trial and error....

Grrrrrrrr!

My feeling, therefore, is that almost any discussion is better off on the Talk page of some particular article. Not all, but many of them....

[Dan Nessett]

Personally, I think that the Forum is a *terrible* place to discuss anything beyond generalities. Why? Because it's so freakin' #@$%^&* impossible to find earlier discussions!  What's the point of the Search box up at the upper-right of the screen?  What does it search for? Type in, for instance, Oldest Confession, a phrase that I have use numerous times in the last couple of months in several different Forum threads. What is the result of this Search?

Nothing. Nada. Rien. Zero.

Suppose, three weeks from now, I wanted to find this particular discussion right here, one that, has, let us say, not had anything added to it during the past three weeks.  How do I find it?

Trial and error....

Grrrrrrrr!

My feeling, therefore, is that almost any discussion is better off on the Talk page of some particular article. Not all, but many of them....

Well, we could move the discussion to the page on Associated Legendre Functions (which is where the proof would fit) or Spherical Harmonics (which seems to be the topic under discussion). However, the discussion is really about a larger issue. What are the criteria that determines whether a proof is redundant and not suitable for hosting on Citizendium? Personally, I think alternate proofs are a good idea. In this case there are two pedagogical approaches supporting the idea that two ways of proving a similar result is a worthy goal.

There is another issue. We have been discussing the question in the context of physics. However, the result is as important to electrical engineering as it is to physics. So, while the physics workgroup editors may decide that they only want one way of proving the result, the engineering workgroup may want the alternate proof, since it better fits the way they normally attack the problem. In addition the mathematics workgroup may have an opinion that should be taken into account. These are organizational issues that merit attention from organizational people.

I could just put the proof on a subpage of the Associated Legendre Functions page. That would be bold. But given I am new here and don't want to start things off by irritating a physics editor, I have decided not to do that.

Anyway, I need some guidance on culture. Wikipedia is a jungle partly because people do things without regard to the views of others. On the other hand, we can spend so much time debating whether this or that proof belongs on Citizendium that all of our effort is drained by debate (sounds a bit like an ISO standards meeting) :-D

[Howard C. Berkowitz]

...that all of our effort is drained by debate (sounds a bit like an ISO standards meeting) :-D

Do not even think that. I was at some of the OSI meetings.

[Paul Wormer]

I could just put the proof on a subpage of the Associated Legendre Functions page.

To me that sounds like a very good idea. As discussed, the orthogonality is not the major problem, but the normalization is far from trivial. It seems to me that the Addendum page is very suitable for that (a link to the proof  must be added in the main article, once you're done). You know that you have to go to the talk page and click the button on the "Unused Pages" line, don't you?

Is your proof similar to the one of Whittaker and Watson, Modern Analysis, p. 324?  (This proof deals with associated Legendres directly). Another possible proof is the construction of normalized spherical harmonics through step operators and then the use of the connection between the two kinds of functions. The latter proof would not fit the spherical harmonics as they are introduced now --- by normalized associated  Legendres.

[David E. Volk]

Do we have Proofs subpage?  We have discography, filmography, etc, so clearly the math group should be able to have a
Proof subpage.

[Dan Nessett]

I could just put the proof on a subpage of the Associated Legendre Functions page.

To me that sounds like a very good idea. As discussed, the orthogonality is not the major problem, but the normalization is far from trivial. It seems to me that the Addendum page is very suitable for that (a link to the proof  must be added in the main article, once you're done). You know that you have to go to the talk page and click the button on the "Unused Pages" line, don't you?

Is your proof similar to the one of Whittaker and Watson, Modern Analysis, p. 324?  (This proof deals with associated Legendres directly). Another possible proof is the construction of normalized spherical harmonics through step operators and then the use of the connection between the two kinds of functions. The latter proof would not fit the spherical harmonics as they are introduced now --- by normalized associated  Legendres.

OK. I will put the proof on the Addendum page of the Associated Legendre Functions page. I will post a note here when I am done. Since I am new, if I didn't put it in the right place, feel free to move it.

The proof is based on one in Riley, Hobson, and Bence: "Mathematical methods for physics and engineering". The reference (including page number) is at the bottom of the proof.

[Dan Nessett]

I could just put the proof on a subpage of the Associated Legendre Functions page.

To me that sounds like a very good idea. As discussed, the orthogonality is not the major problem, but the normalization is far from trivial. It seems to me that the Addendum page is very suitable for that (a link to the proof  must be added in the main article, once you're done). You know that you have to go to the talk page and click the button on the "Unused Pages" line, don't you?

Is your proof similar to the one of Whittaker and Watson, Modern Analysis, p. 324?  (This proof deals with associated Legendres directly). Another possible proof is the construction of normalized spherical harmonics through step operators and then the use of the connection between the two kinds of functions. The latter proof would not fit the spherical harmonics as they are introduced now --- by normalized associated  Legendres.

I have added an Addendum subpage to the Associated Legendre Function page and put the proof on it. I have also linked the page to the subpage proof with a short link next to the appropriate integral in the Orthogonality relations section. If at some later time it is decided that a proof class of subpages is desirable, we can move it there. To keep the proof as tight as possible, it references a standard table of integrals at one point. There is a page on Wikipedia that provides these, but I could not find a corresponding page on Citizendium. So, I have left the reference to the Wikipedia page in the proof. This probably should be fixed by creating a Citizendium page of standard integrals. I left the subscripts for the function as l and k. I can change these to l and l' if that is what people want. Also, the proof uses the more common m superscript (rather than (m)), which we can change if desired.

I should mention one other thing. I had a hard time finding the Associated Legendre Functions page. I began by navigating to the Natural Science page from its link on the main page and drilled down to the Mathematics workgroup articles "top." I had no luck finding anything on that page that led to the Associated Legendre Functions page. Finally, I had to search all of Citizendium to find the page. This suggests that the top level navigation in the mathematics section needs some work.

[Peter Schmitt]

I should mention one other thing. I had a hard time finding the Associated Legendre Functions page. I began by navigating to the Natural Science page from its link on the main page and drilled down to the Mathematics workgroup articles "top." I had no luck finding anything on that page that led to the Associated Legendre Functions page. Finally, I had to search all of Citizendium to find the page. This suggests that the top level navigation in the mathematics section needs some work.

Just look for "Legendre" in the search box.

[Peter Schmitt]

Do we have Proofs subpage?  We have discography, filmography, etc, so clearly the math group should be able to have a
Proof subpage.

No. And no /Examples and /Formulas, either, which also might be considered.

[Dan Nessett]

I should mention one other thing. I had a hard time finding the Associated Legendre Functions page. I began by navigating to the Natural Science page from its link on the main page and drilled down to the Mathematics workgroup articles "top." I had no luck finding anything on that page that led to the Associated Legendre Functions page. Finally, I had to search all of Citizendium to find the page. This suggests that the top level navigation in the mathematics section needs some work.

Just look for "Legendre" in the search box.

This is what I did. But, there appears to be islands (perhaps continents) of material that cannot be reached (or easily reached) from the Citizendium main page. While I have argued (and continue to argue) that most access to Citizendium will come through sites like Google, there will still be a reasonable percentage that starts with the main page and drills down to topics of interest. So, obvious connectivity from the main page to mathematical topics is desirable.

[Howard C. Berkowitz]

This is what I did. But, there appears to be islands (perhaps continents) of material that cannot be reached (or easily reached) from the Citizendium main page. While I have argued (and continue to argue) that most access to Citizendium will come through sites like Google, there will still be a reasonable percentage that starts with the main page and drills down to topics of interest. So, obvious connectivity from the main page to mathematical topics is desirable.

This is an example of what I'll compress and call the "orphaned article" versus "strong article" problem.  Not everyone agrees that strong articles are desired, but their characteristics are:
*Linked to from at least three other nontrivial pages (i.e., not subpages, not redirects unless the redirects have definitions or related articles). These pages may be Related Articles.
*Can trace to a top-level article in a discipline, if not the workgroup or home page
*Have Related Articles subpage

There's a rambling discussion of issues at CZ Talk: Usability.