Some questions about policy

[Paul Wormer]

Me engineer. Me not theoretician. Me get very frightened when textbook says "it will be obvious that" and goes on for five pages of proof. Don't let that stop you, though.,   

Howard, when a mathematician says "it will be obvious that" (s)he means: "I'm too lazy to give the proof" and  (s)he won't give it.  When (s)he gives a proof, it usually goes:
  Proof "Bla bla bla . It is easy to see that the result to be proved follows." (small square).

[Peter Schmitt]

Howard, when a mathematician says "it will be obvious that" (s)he means: "I'm too lazy to give the proof" and  (s)he won't give it.  When (s)he gives a proof, it usually goes:
  Proof "Bla bla bla . It is easy to see that the result to be proved follows." (small square).

Well, I think I should join the argument and defend my profession ;-)
While it is true that mathematicians (out of laziness) tend to use "obvious" and "trivial" too often (and there are popular jokes about this),
they usually are quite willing to expand the proof if asked (though this does not always make things better :-)
But is this so much different from physics, ... ? In every science there are only some who are good in exposition.
(Ask as baseball fan to explain the game to an uninitiated European, for instance.)

[Howard C. Berkowitz]

Howard, when a mathematician says "it will be obvious that" (s)he means: "I'm too lazy to give the proof" and  (s)he won't give it.  When (s)he gives a proof, it usually goes:
  Proof "Bla bla bla . It is easy to see that the result to be proved follows." (small square).

Well, I think I should join the argument and defend my profession ;-)
While it is true that mathematicians (out of laziness) tend to use "obvious" and "trivial" too often (and there are popular jokes about this),
they usually are quite willing to expand the proof if asked (though this does not always make things better :-)
But is this so much different from physics, ... ? In every science there are only some who are good in exposition.
(Ask as baseball fan to explain the game to an uninitiated European, for instance.)

I must digress to one of my favorite cartoons:
*First pane: professor writing on board mumbling "it is obvious"
*Second: Voice from class: "Is it obvious, sir?"
*Third: Stares at board. Dismisses class.
*Fourth: Class returns 48 hours later. Professor, unshaven, unkempt, with demented look of lack of sleep in eyes, shouts" It is obvious"

I am proud to say that in the midst of writing one of my texts on Internet routing, I caught myself explaining one tricky protocol mechanism with "it is obvious." Finding moral courage, I went to the nearest mirror, slapped myself across the face several times, and went back to my keyboard to explain the nuances of how a technique was decidedly not obvious.

This still doesn't rule out proofs on a subpage, probably with an explanation, if there is one, of how knowledge of the proof is interesting to the practitioner, or even to the researcher, rather than simply documenting the derivation.

[Paul Wormer]

Dan,  you must have gathered from the discussion so far that we are very free here. You won't be bothered  by people complaining about  proofs being too long or the absence of proofs. When somebody complains  (which rarely happens) it will be done in a very polite way on a discussion page, either your page or the one of the pertinent article. So, I say, join!  And write in the manner that gives YOU the most satisfaction.

[Dan Nessett]

Dan,  you must have gathered from the discussion so far that we are very free here. You won't be bothered  by people complaining about  proofs being too long or the absence of proofs. When somebody complains  (which rarely happens) it will be done in a very polite way on a discussion page, either your page or the one of the pertinent article. So, I say, join!  And write in the manner that gives YOU the most satisfaction.

Thanks for the encouragement Paul. I applied for membership this morning.

[Dan Nessett]

I am now a Citizendium member, but since this thread was started in the non-member discussion forum, I think it prudent to continue discussion of this issue here. It appears not to be controversial whether mathematical proofs are allowed on CZ (it seems there is no general policy against them). However, individual cases vary and so I imagine not every proof will find a place here. So, I thought it useful to provide some motivation why proofs of non-trivial mathematical assertions is a good thing. I will use personal experience for this purpose.

I am a retired computer scientist who decided to study physics. I have a friend and former colleague (a physicist) who is tutoring me via email. At the present time, I am studying quantum mechanics and have made it to the part of the textbook (Shankar) that covers rotationally invariant systems. This section presents arguments for using spherical harmonics as eigenfunctions for solutions of the Schroedinger equation in such systems. The spherical harmonics themselves are built from other functions, known as the associated Legendre functions and the orthonormality of the spherical harmonics rests on the orthonormality of the associated Legendre functions.

Shankar does not demonstrate the orthonormality of either set of functions and being a somewhat skeptical person when it comes to unsupported mathematical claims, I decided to prove it. This task turned out to be beyond my powers, so I poked around on the web looking for a proof. To my surprise I couldn't find one. So, I worked with my tutor to develop one. This was not an original proof, but rather reworked some material in the book by Riley, Hobson, and Bence, (Mathematical methods for physics and engineering). After we tightened up the proof, I thought it would be a service to other QM students to make the proof available on the web. I made a proposal on Wikipedia, which was rejected on the basis that Wikipedia doesn't do proofs. I won't go into the details of the discussion that led to this conclusion, but it wasn't a pleasant experience.

Now I am sure most reading this post couldn't care less about the details of my experience (spherical-schmearical; the associated what?). But, I think it provides evidence that making proofs available on the web meets a need. In fact, there was a post on a physics forum (not associated with any wiki) a few years ago that basically asked the same question I did. Good students do not trust their professors when they say that some mathematical assertion is true, but the proof is too tedious to relate. Good students want to know. (I am here not slandering students who may have no interest in proofs, such as those focused on engineering. They simply are interested in other things and tend to spend their time "proving" that the theory actually works).

Of course, advanced topics such as the orthonormality of certain function families is of interest to a limited audience. It is probably not prudent to poke the general reader in the eye with them. Putting them on an "advanced" or "proof" sub-page is a perfectly acceptable strategy. That way they are available to those who find them interesting and yet do not clutter up the general flow of words in the relevant article.

[Matt Innis]

Hi Dan, first let me say welcome!  Then let me say that I think others would be interested in your proof(s) and whether you put them in subpages or elsewhere (wherever you mathmeticians and physicists decide).  However, please make yourself aware of the Neutrality and Original Research prerequisites.  In other words, everything that we present does need to be presented neutrally, so if this proof is actually 'original research', it needs to make sure that it is explained exactly that way - giving notice that it is 'not tested' if that is appropriate, or any other way that makes it clear that Citizendium is not endorsing this proof as anything other than what it is, especially if it is not something that the physics and math communities do not yet support.

I think if you present the original work that you were explaining and then use your proof on a subpage or even a 'signed article' page, we might find that it fits in.  Having said that, though, I am sure that you understand that we reserve the right to move the article out of mainspace until you get some corraboration.  It would only serve to protect your reputation as well as Citizendium's.

So I am interested in your presentation and look forward to how it is received by our community.

[Dan Nessett]

Hi Dan, first let me say welcome!  Then let me say that I think others would be interested in your proof(s) and whether you put them in subpages or elsewhere (wherever you mathmeticians and physicists decide).  However, please make yourself aware of the Neutrality and Original Research prerequisites.  In other words, everything that we present does need to be presented neutrally, so if this proof is actually 'original research', it needs to make sure that it is explained exactly that way - giving notice that it is 'not tested' if that is appropriate, or any other way that makes it clear that Citizendium is not endorsing this proof as anything other than what it is, especially if it is not something that the physics and math communities do not yet support.

I think if you present the original work that you were explaining and then use your proof on a subpage or even a 'signed article' page, we might find that it fits in.  Having said that, though, I am sure that you understand that we reserve the right to move the article out of mainspace until you get some corraboration.  It would only serve to protect your reputation as well as Citizendium's.

So I am interested in your presentation and look forward to how it is received by our community.

Understood. The proofs are actually reworked versions available in well-known texts. They are not original. The reworking didn't change the logic, only the presentation. That said, I have no problem that they exist out of the main namespace until they are corroborated. If necessary, I would be happy to put them on a signed page. If Citizendium editors wish to label them as not endorsed by the community that is also fine. What ever works.

Note: I have opened up a topic about these proofs on the Workgroup Boards->Physics forum. It is titled "Best way to incorporate orthogonality/orthonormality proofs" for anyone who wants to look at the proofs themselves (there are pointers to them in my latest message).

[Paul Wormer]

Suddenly I remembered a fierce discussion (about publishing proofs)  that occurred before my joining CZ, see http://en.citizendium.org/wiki/Talk:An_elementary_proof_that_22_over_7_exceeds_%CF%80. It is not unlikely that this discussion chased away one or two math editors (which I regret).   I noticed this discussion last March when David Volk said that  the  actual proof was lacking in this article. Because of David's comment  I  put more details of the proof on a student subpage.

[Peter Schmitt]

Suddenly I remembered a fierce discussion (about publishing proofs)  that occurred before my joining CZ, see http://en.citizendium.org/wiki/Talk:An_elementary_proof_that_22_over_7_exceeds_%CF%80. It is not unlikely that this discussion chased away one or two math editors (which I regret).   I noticed this discussion last March when David Volk said that  the  actual proof was lacking in this article. Because of David's comment  I  put more details of the proof on a student subpage.

I have not yet read all of the discussion. However, seeing it I wonder that still there is no /Proofs subpage.
Moreover, for consistent use of subpages there should be some consensus about the purpose and level of the different possibilities:
/Student Level, /Tutorial, /Advanced, and hopefully some of /Proofs /Examples, /Formulas (more?)
in connection with mathematics related articles.
(There is a /Function, that is not mentioned on CZ:Subpages, but according to CZ:Function is intended for use in Biology,
and probably should have a name preventing interpreting as a mathematical page?)

[Dan Nessett]

Suddenly I remembered a fierce discussion (about publishing proofs)  that occurred before my joining CZ, see http://en.citizendium.org/wiki/Talk:An_elementary_proof_that_22_over_7_exceeds_%CF%80. It is not unlikely that this discussion chased away one or two math editors (which I regret).   I noticed this discussion last March when David Volk said that  the  actual proof was lacking in this article. Because of David's comment  I  put more details of the proof on a student subpage.

I just read the series of posts cited above. It was both fascinating and sad. Fascinating since it delved deep into an issue I find almost practically irrelevant (what are allowable words in the title of Citizendium articles). Sad, since everyone seemed to get very upset by people who held an opinion the opposite of theirs. It is really tragic if competent editors left Citizendium because of this discussion, because the importance of it is premised on an outdated idea, viz., people pay a lot of attention to article titles. That this is unlikely is supported by two points, which I shall illustrate anecdotally.

I remember when I was active in research and participating in the tedious, but necessary work of reading papers submitted to conferences, most were titled with precise but generally incomprehensible language. Before reading the paper I normally payed little attention to the title (except perhaps to screw up my face and mutter something like, "what the heck is this thing about?"). After digesting the content, I had a better understanding of the title, but at that point it became only a convenient handle for referring to the paper's content. For this purpose the title could have been "The fractious distemination of fribbles satisfying the Hoboken criterion". It didn't matter. When referring to the paper in verbal discourse I would normally say something  like, "Basil Fawlty's paper on distributed synchronization." When referencing it formally in written material, I would copy the proper citation information to the references section and then immediately forget the title. So, I think the importance of title verbiage is overrated as long as it is accurate.

The second principle rests on the well documented change in the way people find information these days. I almost never go to a site to find information on some topic. Invariably I Google an appropriate set of query words and follow the links in the list. So, I never go to Wikipedia and search for information. Instead, I follow links to Wikipedia articles given in a search result list. I rarely look at the title of an article or web page when I follow a link returned by Google.

This last point suggests an issue that should be important to Citizens of Citizendium - specifically, Google search results almost always return pointers to Wikipedia articles at the top of the list, but rarely return pointers to Citizendium articles in this position. Someone asked me in another forum whether I was aware of a particular Citizendium article. I had to reply that prior to a couple of weeks ago, I had no knowledge that Citizendium even existed. I learn of information sources through Google searches (and I think I am probably pretty typical in this behavior). I generally don't go around looking for sites that warehouse information and then search within them.

Perhaps this is already the topic of a discussion on some Citizendium forum, but if not it should be. We should be spending some time figuring out how to get Citizendium's articles listed at least on a par with those of Wikipedia.

[Shamira Gelbman]

Suddenly I remembered a fierce discussion (about publishing proofs)  that occurred before my joining CZ, see http://en.citizendium.org/wiki/Talk:An_elementary_proof_that_22_over_7_exceeds_%CF%80. It is not unlikely that this discussion chased away one or two math editors (which I regret).   I noticed this discussion last March when David Volk said that  the  actual proof was lacking in this article. Because of David's comment  I  put more details of the proof on a student subpage.

I just read the series of posts cited above. It was both fascinating and sad. Fascinating since it delved deep into an issue I find almost practically irrelevant (what are allowable words in the title of Citizendium articles). Sad, since everyone seemed to get very upset by people who held an opinion the opposite of theirs. It is really tragic if competent editors left Citizendium because of this discussion, because the importance of it is premised on an outdated idea, viz., people pay a lot of attention to article titles. That this is unlikely is supported by two points, which I shall illustrate anecdotally.

I remember when I was active in research and participating in the tedious, but necessary work of reading papers submitted to conferences, most were titled with precise but generally incomprehensible language. Before reading the paper I normally payed little attention to the title (except perhaps to screw up my face and mutter something like, "what the heck is this thing about?"). After digesting the content, I had a better understanding of the title, but at that point it became only a convenient handle for referring to the paper's content. For this purpose the title could have been "The fractious distemination of fribbles satisfying the Hoboken criterion". It didn't matter. When referring to the paper in verbal discourse I would normally say something  like, "Basil Fawlty's paper on distributed synchronization." When referencing it formally in written material, I would copy the proper citation information to the references section and then immediately forget the title. So, I think the importance of title verbiage is overrated as long as it is accurate.

The second principle rests on the well documented change in the way people find information these days. I almost never go to a site to find information on some topic. Invariably I Google an appropriate set of query words and follow the links in the list. So, I never go to Wikipedia and search for information. Instead, I follow links to Wikipedia articles given in a search result list. I rarely look at the title of an article or web page when I follow a link returned by Google.

I think your second point is more compelling than the first. Titles matter very little in academic research communities, where, as you point out, we talk about each other's work by author (maybe adding a key phrase or perhaps the year or publication outlet to clarify which of that author's works is being referred to), but encyclopedia articles are usually intended for lay readers who don't share that norm. At least when it comes to traditional print encyclopedias, article titles matter a lot, since they are readers' first stop for figuring out where the information they're looking for is.

[Howard C. Berkowitz]

The second principle rests on the well documented change in the way people find information these days. I almost never go to a site to find information on some topic. Invariably I Google an appropriate set of query words and follow the links in the list. So, I never go to Wikipedia and search for information. Instead, I follow links to Wikipedia articles given in a search result list. I rarely look at the title of an article or web page when I follow a link returned by Google.

This last point suggests an issue that should be important to Citizens of Citizendium - specifically, Google search results almost always return pointers to Wikipedia articles at the top of the list, but rarely return pointers to Citizendium articles in this position. Someone asked me in another forum whether I was aware of a particular Citizendium article. I had to reply that prior to a couple of weeks ago, I had no knowledge that Citizendium even existed. I learn of information sources through Google searches (and I think I am probably pretty typical in this behavior). I generally don't go around looking for sites that warehouse information and then search within them.

Perhaps this is already the topic of a discussion on some Citizendium forum, but if not it should be. We should be spending some time figuring out how to get Citizendium's articles listed at least on a par with those of Wikipedia.

I don't disagree that search engines are the primary point of entry; I've had some very frustrating arguments here over a fairly arbitrary article name, especially when it's a transliteration or translation of a non-English name. To me, the point is that there be adequate redirects and embedded text for the search engine to get to the basic article.

I will disagree, however, that, assuming some of our designs go the way we hope, that once a person arrives at a site, the Related Articles system, especially (ducking as Hayford throws things) the top-level and "non-orphaned" rules are in place. In other words, once someone gets here through one means or another, if they see our additional knowledge navigation structure, they may use tools here rather than starting completely new searches.

[Dan Nessett]

I will disagree, however, that, assuming some of our designs go the way we hope, that once a person arrives at a site, the Related Articles system, especially (ducking as Hayford throws things) the top-level and "non-orphaned" rules are in place. In other words, once someone gets here through one means or another, if they see our additional knowledge navigation structure, they may use tools here rather than starting completely new searches.

That is a reasonable point. Once I arrive at an article I generally navigate to others that it links to. However, the text I use to decide whether I want to view the article is not the article title. It is the text piped in the link reference.

[Howard C. Berkowitz]

I will disagree, however, that, assuming some of our designs go the way we hope, that once a person arrives at a site, the Related Articles system, especially (ducking as Hayford throws things) the top-level and "non-orphaned" rules are in place. In other words, once someone gets here through one means or another, if they see our additional knowledge navigation structure, they may use tools here rather than starting completely new searches.

That is a reasonable point. Once I arrive at an article I generally navigate to others that it links to. However, the text I use to decide whether I want to view the article is not the article title. It is the text piped in the link reference.

By piped text, do you mean what appears on the Wikilink in the main article, or the entry in Related Articles, which also has a definition and context? How do we encourage use of the contextualized Related Articles, which I honestly believe is one of our differentiators?