Wikipedia:Featured article candidates/Parity of zero/archive1


 * The following is an archived discussion of a featured article nomination. Please do not modify it. Subsequent comments should be made on the article's talk page or in Wikipedia talk:Featured article candidates. No further edits should be made to this page.

The article was not promoted by SandyGeorgia 02:41, 8 April 2010.

Parity of zero

 * Nominator(s): Melchoir (talk) 10:56, 4 April 2010 (UTC)

I started this article in September 2007. Since the peer review in August 2009, I've moved it from "Evenness of zero" to "Parity of zero" and made improvements to the prose. Very recently, I've also rearranged some of the material in the "History" introduction (per the PR) and in "Group discussions".

I haven't done a FAC in years! Hopefully this article is like 0.999... — except, you know, better. ;-) Melchoir (talk) 10:56, 4 April 2010 (UTC)
 * Coments. NO dab links or dead external links. Ucucha 11:26, 4 April 2010 (UTC)


 * Oppose—sorry. I know it is expected to include the title of the article in the first sentence but it is not working here at all. The introductory sentence from Parity is much better. There are other expressions that are difficult to understand. The second sentence, for example is tantamount to gobbledegook: "Such proofs follow immediately from the definition of the term "even number", whose applicability to zero is not arbitrary in the least; it can be further motivated by the familiar rules for sums and products of even numbers." What on earth does "further motivated" and "not arbitary (sic) in the least" mean? And, what are these "familiar rules"? What is meant by "On the human level"? Does this mean it is better understood by chimps? And who are we writing for? I get the impression that the article is written for teachers of mathematics, "Discussing the parity of zero in class can spark vigorous debates as students encounter basic principles of mathematical reasoning". The term "students" is used relentlessly throughout this article. I feel the article is not about the parity of zero at all—it is about how to teach it.Graham Colm (talk) 19:48, 4 April 2010 (UTC)
 * I often omit the title of an article from the first sentence myself, when it feels unnatural or artificial. Back when this article was named "Evenness of zero", that phrase certainly wasn't in the first sentence. Since it's been moved to "Parity of zero", which works better, I thought I'd include it. Why do you think it's not working / worse than Parity (mathematics)? Melchoir (talk) 21:33, 4 April 2010 (UTC)
 * Second sentence: Does this edit help? I've replaced those phrases. Melchoir (talk) 21:33, 4 April 2010 (UTC)
 * "On the human level" is a transition phrase between paragraphs. The preceding paragraph is all about how zero is definitely even; the following paragraph is all about how it's not so simple in people's minds. I'll admit that these four words have a low information content, but if they make the prose easier to read, they're worth it. Melchoir (talk) 21:33, 4 April 2010 (UTC)
 * The word "student" or "students" appears around 25 times in the first top-level section: "In education". It appears just once in the other four sections, which make up the bulk of the article: "Numerical cognition", "History", "Mathematical contexts", and "Everyday contexts". Isn't that what you'd expect? Melchoir (talk) 21:33, 4 April 2010 (UTC)
 * I have toned down my comments, they were a little over the top, sorry. Let's see what other reviewers have to say. Graham Colm (talk) 13:20, 5 April 2010 (UTC)
 * No prob! Please feel free to follow up on individual points as well. I'm willing to make big changes, but I'll want to have a conversation about them first. Melchoir (talk) 16:21, 5 April 2010 (UTC)


 * Oppose. The structure of the article, and the length of the text under "in education", make this read like a classroom guide or education essay. The education section should not appear so early in the article - history at the very least should precede it; possibly so should the mathematical contexts. There appears to be too much detail on educational / developmental studies. The lead is not a summary of the whole article, but emphasises education and cognition at the expense of history and mathematical context (all should be there). BTW i didn't really understand the use of the expression "on the human level", so i would re-think that transition. hamiltonstone (talk) 23:18, 4 April 2010 (UTC)
 * I have the "In education" section first because it has the "Explanations" subsection. This subsection is the most accessible part of the article, and it explains why zero is even. Wouldn't you agree that it's a high priority to get that in as early as possible? If "In education" were split up into two top-level sections, I could see "History" going in between them -- not "Mathematical contexts" though (it's too long). Melchoir (talk) 00:02, 5 April 2010 (UTC)
 * "History" and "Mathematical contexts" are represented in the first paragraph of the lead. Is there some additional sub-topic from those sections that you would like to include? Melchoir (talk) 00:02, 5 April 2010 (UTC)
 * For "on the human level": are you commenting on the transition itself, or the wording used to execute it? Melchoir (talk) 00:02, 5 April 2010 (UTC)

Review by Charles Edward
 * General
 * The opening sentence in the lead is somewhat confusing, and as a single sentence, it should be integrated into the following paragraph. Maybe something like "Zero is an even number. The evenness and oddness of a number is its parity." You need to define and link parity somehow in the lead. Many readers won't know what it is.
 * How about this? Melchoir (talk) 03:14, 8 April 2010 (UTC)
 * That is much better! You could still omitt " In other words", the rest of that sentence stands well on its own. &mdash;Charles Edward (Talk 12:39, 8 April 2010 (UTC)
 * I suppose so, but without some kind of connector, the relationship between the first two sentences would be unclear. We don't want to give the reader the impression that they say different things. Melchoir (talk) 01:39, 9 April 2010 (UTC)
 * Maybe I misunderstand this subject, but it seems like the primary topic of the article should be the fact that zero is an even number. But throughout all the explanations, the article keeps coming back and explains how the concept effects education. It would be much better, in my opinion, if you made a couple straight up sections only talking about the parity of zero, and leave out all mention of students, teachers, etc. Focus on defining the topic. Then put all the education related stuff into separate sections.
 * You say that "the article keeps coming back" to education. I'm not sure what you mean by that, since most of the article has nothing to do with education and doesn't mention the issue. Could you please clarify? Melchoir (talk) 03:06, 8 April 2010 (UTC)
 * See my comment on the next item &mdash;Charles Edward (Talk 12:39, 8 April 2010 (UTC)
 * The section concerning education should come later in the article, while the section laying out what the parity of zero is should come first. Right now the article jumps into the education aspect at first without fully defining the topic. Correct me if I am wrong, but the primary application of partiy of zero would be in mathematical contexts, so those sections should come first.
 * The "In education" section is the section that explains the parity of zero. It begins with a simple proof that zero is even, and its first subsection is all about elementary explanations of that fact. I agree that this material should come first. In fact, "In education" is the first section precisely because I wanted to present that material as early as possible. Did you have another section in mind? Melchoir (talk) 03:06, 8 April 2010 (UTC)
 * The above comment and this one go together. The mathematical sections also make a good explanation of what the parity of zero is, and how it is mathematically determined. It also gives a bit of history of it all. However in the education section, the article defines the parity of zero in a basic way in the first sentence, but throughout the section it ties it back to education, students and teachers. You could take that opening sentence out of the education section, move it to the head of the mathematical section, and use the mathematics sections as your opening section. That would give a very thorough overview of the parity of zero and its mathematical application before delving into its educational usefulness. &mdash;Charles Edward (Talk 12:39, 8 April 2010 (UTC)
 * Hmm. I'll give it a try. My practical concerns are: (1) Presenting the explanations without commentary means that an Education section later on will have to refer to those explanations when it says "explanation X is suitable for audience Y". This seems like duplication of material, and the reader might be forced to scroll between the distant sections to understand what the latter is saying. (2) Much of the material currently in "Mathematical contexts" is very advanced. Most readers won't appreciate it, and in the worst case it will cause them to stop reading, so they'll miss the more accessible discussion of education and cognition. I also have a theoretical concern, namely, all the material about explanations is taken from books and journal articles written by educators, for educators. The cited sources are discussing explanations with the assumption that the reader doesn't need them. If we just state the explanations, implying that the reader does need them... it's not exactly sticking to the sources, and it's a little condescending. Of course you could argue that my version is patronizing in its own way. We'll see how the execution works. Melchoir (talk) 01:59, 9 April 2010 (UTC)
 * I agree with the above comments that the article reads much like and essay. It is very editorial-like in places, especially the education sections. Check out WP:TONE. Here are a few examples.
 * "There are several ways to determine whether an integer is even or odd, all of which indicate that 0 is even:" How about "Each method used to determine whether an number is even or odd proves zero is even:"
 * There's actually a subtle problem with both options: they suggest that it's necessary to consider all methods to determine the parity of zero, when any one suffices. I've tried another option. Melchoir (talk) 03:38, 8 April 2010 (UTC)
 * "First of all, the concise definition of "even" is often not intuitive to children.", who says this is the first most important thing? Drop the "first of all"
 * The "first of all ... moreover" construction helps to demarcate the two related problems, the first straightforward and the second more subtle. Anyway, I can see how it could be read as indicating importance. Changed. Melchoir (talk) 03:59, 8 April 2010 (UTC)
 * "Often curious students will directly ask if zero is even"
 * I assume your beef is with the word curious; removed. Melchoir (talk) 04:01, 8 April 2010 (UTC)
 * Yes :) &mdash;Charles Edward (Talk 12:39, 8 April 2010 (UTC)
 * "It is important for teachers of mathematics to understand such basic facts as the even parity of zero." - says who? Needs attribution and citation
 * Removed. The journal article distinguishes between "specialized context knowledge" and "common content knowledge", giving the parity of zero as an example of the latter, which justifies the "basic facts" label. But it's not worth it to try to introduce that distinction; it would just distract. Melchoir (talk) 04:33, 8 April 2010 (UTC)
 * "Unfortunately, many teachers harbor misconceptions about zero, although it is hard to quantify how many." - Unfortunate? Needs attribution and citation.
 * Removed. Melchoir (talk) 04:35, 8 April 2010 (UTC)
 * "There is some subtlety here: subjects are known to compute and name the result of multiplication by zero faster than multiplication of nonzero numbers, but they are slower to verify proposed results like 2 × 0 = 0." - I am not sure just what "subtly" is referring to here, perhaps it could be spelled out more clearly
 * Removed. Naively you'd think that the speed of computing a result and the speed of certifying a result would be well-correlated, so it's a surprise that one is faster and the other is slower when 0 gets involved, and it's not completely obvious which result is more important to mentally deciding if 0 is even. But it's perhaps not necessary to warn the reader that something tricky is going on. Melchoir (talk) 04:41, 8 April 2010 (UTC)
 * "This strong dependence on familiarity again undermines the mental calculation hypothesis." - Attribution and citation needed.
 * Added. Melchoir (talk) 04:50, 8 April 2010 (UTC)
 * "It is difficult to say when in the history of mathematics the first person examined the parity of zero;" - but the article goes on to explain the first known clearly known instances of the discussion of the topic in the 7th century. I would put more emphasis on the first known instance, rather than the unknown.
 * They discussed zero in the 7th century, but not necessarily its parity. I can find no evidence of any discussion of the parity of zero earlier than a primary-source example from 1849. That leaves a gulf of over a thousand years when the first discussion might conceivably have happened -- we really don't know! Melchoir (talk) 04:57, 8 April 2010 (UTC)
 * I still find the wording of that section to be little too wordy. I am striking this though. &mdash;Charles Edward (Talk 12:39, 8 April 2010 (UTC)
 * "Some other mathematical contexts, where the presence of 0 in the even numbers can be felt, follow.", you could drop that whole sentence
 * It establishes the relationship between that section and the following section. Melchoir (talk) 05:08, 8 April 2010 (UTC)
 * There is quite a few other examples, but hope this helps to identify them
 * Um... not really? Perhaps if you provide feedback on the edits I've made above? Melchoir (talk) 05:18, 8 April 2010 (UTC)
 * I have now. :) &mdash;Charles Edward (Talk 12:39, 8 April 2010 (UTC)
 * Citations needed
 * paragraph beginning "Age-appropriate explanations that zero is even...."
 * paragraph beginning "Early in elementary school, numbers..."
 * I'll see if I need to come back to these after trying different section orders. Melchoir (talk) 02:02, 9 April 2010 (UTC)
 * paragraph beginning "The chart on the right depicts"
 * Fixed. Melchoir (talk) 01:50, 8 April 2010 (UTC)
 * "This time the number of children in the same age range identifying zero as even dropped to 32%. "
 * Fixed. Melchoir (talk) 01:57, 8 April 2010 (UTC)
 * "Success in deciding that zero is even initially shoots up and then levels off at around 50% in Years 3 to 6. "
 * Fixed. Melchoir (talk) 01:57, 8 April 2010 (UTC)
 * "A couple fourth-years realized that zero can be split into equal parts: "no one gets owt if it's shared out."" - uncited quote, see WP:CITE
 * Fixed. Melchoir (talk) 02:03, 8 April 2010 (UTC)
 * "A second-year was "quite convinced" that zero was odd, on the basis that "it is the first number you count"." uncited quote
 * Fixed. Melchoir (talk) 02:03, 8 April 2010 (UTC)
 * paragraph beginning "More in-depth investigations were conducted"
 * Fixed. Melchoir (talk) 02:06, 8 April 2010 (UTC)
 * "The claims about zero alone take many forms: Zero is not even or odd; Zero could be even; Zero is not odd; Zero has to be an even; Zero is not an even number; Zero is always going to be an even number; Zero is not always going to be an even number; Zero is even; Zero is special."
 * Fixed. Melchoir (talk) 02:16, 8 April 2010 (UTC)
 * "Ball later asked her students to reflect on this "particularly long and confusing discussion on even and odd numbers"." - uncited quote
 * Fixed. Melchoir (talk) 02:16, 8 April 2010 (UTC)
 * "Data is also scarce for teachers' attitudes on students' attitudes."
 * I have no citation for that assertion; it was just a way to introduce the topic of the paragraph. This edit should feel less like it needs a citation. Melchoir (talk) 02:21, 8 April 2010 (UTC)
 * "Adults who do believe that zero is even can nevertheless feel unfamiliar or uncomfortable with the fact, enough to measurably slow them down in a reaction time experiment."
 * "Repeated experiments have shown a delay at zero for subjects from a variety of national and linguistic backgrounds, representing both left to right and right to left writing systems; almost all right-handed; from 17–53 years of age; confronted with number names in numeral form, spelled out, and spelled in a mirror image."
 * paragraph beginning "The precise definition of any mathematical term..."
 * Fixed. Melchoir (talk) 02:33, 9 April 2010 (UTC)
 * paragraph beginning "The above rules would therefore..."
 * Fixed. Melchoir (talk) 02:46, 9 April 2010 (UTC)
 * The first section in "Mathematical contexts" has no cites
 * Yes, the text "Most of the intuitive reasons ... Some of these follow." is meant to briefly summarize the section. Do you think it's a policy issue? Melchoir (talk) 02:26, 9 April 2010 (UTC)
 * paragraph beginning "The observation that zero is not odd..."
 * paragraph beginning "Zero is the starting point of the even natural numbers..."
 * paragraph beginning "One way of interpreting the evenness..."
 * Skimming through the existing citations doesn't reveal a source for this paragraph, and I can't find one on Google either. I'll have to read through all the sources to see what support I can find; I know Frobisher has some quotes that are related but not ideal. For reference, this paragraph was discussed at Talk:Parity of zero. Unfortunately the other editor has left Wikipedia... so no help on citations there. Melchoir (talk) 02:13, 9 April 2010 (UTC)
 * paragraph beginning "Some multiples of 2 are more even..."
 * Fixed. Melchoir (talk) 05:50, 8 April 2010 (UTC)
 * paragraph beginning "It is clear that 0 is divisible by 2..."
 * Fixed. This is a good catch -- it wasn't covered by the neighboring citations, so I had to find new ones! Melchoir (talk) 05:50, 8 April 2010 (UTC)
 * MOS
 * The notes section should precede the reference section. See WP:CITEX
 * The references each contain a short paragraph following them explaining them. Those descriptions should be removed and put into the body of the article if they matter, otherwise removed completely.
 * The article mixes shortened refs with full refs. That is a little confusing, although not required by the MOS, I'd suggesting fully using the shortened citation method.
 * I'll give it a try. The reason for the current references style is that there are really two distinct kinds of references being used. First, there's a handful of authors who provide "significant coverage" of the parity of zero in the sense of Notability. These are the backbone of the article. Then, there's the rest: sources that mention the parity of zero only in passing. Calling out the significant sources in References, while leaving the rest to Notes, helps make this distinction for the reader who wants to do further research. One drawback of the current scheme is that Ball has many entries, but only one is called out. Mostly for that reason, I'm willing to move to a more standard-looking format. But I would still want some text at the top of References that points to the most valuable sources. Melchoir (talk) 02:22, 9 April 2010 (UTC)
 * Why is the TOC moved to the right? It should probably be left to default.
 * Agreed, and removed. Another editor introduced the template with the edit summary "whitespace". I didn't care enough to challenge it at the time, but now that someone else has complained, I'll use the opportunity. :-) Melchoir (talk) 01:26, 8 April 2010 (UTC)
 * Images
 * File:Balance_scale.jpg, has no source, author, date, etc. It is not obviously public domain either.
 * Fixed. You're right, on closer inspection, it seems the national lab retains copyright. I've removed the PD tag and marked it for deletion. The replacement is commons:File:Scale_of_justice_2.svg, which is on firmer ground: the original comes from a URL starting with "fbi.gov/publications", which seems unambiguous enough. Melchoir (talk) 00:50, 8 April 2010 (UTC)
 * File:0143Pairs.svg has no source
 * Fixed. Melchoir (talk) 01:19, 8 April 2010 (UTC)
 * File:FrobisherZeroParity.svg source listed is Frobisher 1999, but there is no other information regarding Frobisher on the page. A full citation, with page numbers, is needed.
 * Fixed. Melchoir (talk) 00:58, 8 April 2010 (UTC)
 * File:RecursiveEvenPolygon.svg, no source given. However is borderline common knowledge. Still a cite would be useful
 * Citation given. Like the case of 0143Pairs.svg, there is some originality in my presentation. Melchoir (talk) 01:03, 8 April 2010 (UTC)
 * File:RecursiveEvenBipartite.svg no source
 * Explained with citation, although this is another case where I've found no good analogous image. Melchoir (talk) 01:15, 8 April 2010 (UTC)
 * File:EvenIntegersSubgroup.svg no source
 * For that image, there is no source but me. Clarified in this edit. Melchoir (talk) 01:19, 8 April 2010 (UTC)
 * Other images check out
 * Prose looks great
 * References are acceptable

Oppose, this article still needs a fair bit of work. The referencing issues are my biggest concern, followed by the tone of the education section. I have not listed all the issues with the references or tone, but this should be enough to demonstrate where the issues are. Good job on the article so far, its really is a very interesting read and I can see alot of research has went into it. Keep up the good work and you will soon have it up to FA standards. :) &mdash;Charles Edward (Talk 12:56, 7 April 2010 (UTC)
 * Thanks for the detailed comments! I'll get to work on the individual items, and I'll also want to follow up on the larger points. I'll make all notes inline above, and I'll add another comment down here when I'm done (for now). Melchoir (talk) 00:39, 8 April 2010 (UTC)


 * I struck what you've resolved and replied to a few. After this review closes, I'd suggest taking the article to WP:PR where you could get some more useful feedback on improving it. It is an interesting topic and would make a worthy featured article. &mdash;Charles Edward (Talk 12:39, 8 April 2010 (UTC)
 * Confused by the statement above; this review is already closed (see below). Sandy Georgia  (Talk) 12:40, 8 April 2010 (UTC)
 * Right, but the bot hasn't came by and archived the discussion and fixed the talk page. The editor would want to wait until after that to do the peer review, otherwise the PR template will give him errors because it will think the FAC review is still open. Sorry, I should have been clear. :) &mdash;Charles Edward (Talk 12:53, 8 April 2010 (UTC)
 * The previous PR was disappointing in that it didn't attract significant feedback. I can certainly try another, but I don't have high hopes that it'll be useful... Melchoir (talk) 01:37, 9 April 2010 (UTC)
 * Okay, I think I'm done for today. Some of the line items remain unaddressed; I might work on them and/or do some of the heavy lifting (layout) over the weekend. If this page gets locked down by a bot, so be it -- there are always talk pages! Melchoir (talk) 02:54, 9 April 2010 (UTC)


 * The above discussion is preserved as an archive. Please do not modify it. No further edits should be made to this page.