Wikipedia:Featured article candidates/Parity of zero/archive2


 * 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 promoted by User:Ucucha on 01:43, 21 August 2013.

Parity of zero

 * Nominator(s): Melchoir (talk) 21:13, 26 June 2013 (UTC)

I ran the article through a peer review and a failed FAC a few years ago, and I've implemented a lot of feedback since then. (See the talk page and especially the links in the "Article milestones" template.) I recently held another peer review, which had (a small amount of) good feedback. Now it's time for FAC round 2! Melchoir (talk) 21:13, 26 June 2013 (UTC)


 * What is the image in the Numerical cognition section supposed to convey? Nergaal (talk) 05:49, 1 July 2013 (UTC)
 * It's a statistical analysis showing that zero is special. Melchoir (talk) 06:29, 1 July 2013 (UTC)
 * I meant that to a casual reader that is completely not clear. what are the axes? the colors? Nergaal (talk) 01:27, 2 July 2013 (UTC)
 * Okay, I expanded the caption on the image description page and added a link from the caption, which is hopefully a little clearer. The description page now says that the axes aren't meaningful, and it expands on the description of the colors, which have to do with whether an odd or even number was responded to with the left or right hand. For the present article, the colors aren't really relevant, so I think we can leave them out of the caption.
 * Is that better? Melchoir (talk) 02:42, 2 July 2013 (UTC)
 * Not really, but at least now I know where it is coming from. As a side note, the 1 is missing in the image. To me 1 seems as isolated in that graph as 0. Although I am a scientist, I have no idea what SSA means, therefore I feel like I am looking at Pollock painting. Going back to axes: what does the 2D space of the graph represent? Nergaal (talk) 06:04, 2 July 2013 (UTC)
 * Good catch, I accidentally cut off the 1 on the right side when I cut down NuerkFigure4.svg to make Nuerk figure 4 bare.svg! I just re-added it: vs.
 * The 2D space of the graph doesn't represent anything. It's just a way to arrange the data in such a way as to bring correlated series closer together. To quote the cited source:
 * "In this study, nMDS is used to map the number stimuli (different numbers for different response hands) in a space of low dimensionality such that stimuli with high (positive) correlations are mapped close to each other while stimuli with low (negative) correlations are placed far apart. In nonmetric MDS only the pattern of ordinal relations among correlations (larger vs. smaller) is mapped into the corresponding pattern of ordinal relations among distances between stimulus points (Borg & Lingoes, 1987). … In contrast to metric MDS or other metric multivariate dimension-reducing procedures, the dimensions of the solution space themselves are not interpreted. It is the configuration of stimulus points in space that matters (Borg & Lingoes, 1987)."
 * The authors later discuss why nMDS is appropriate for this kind of experiment. Briefly, they're looking for categorical effects, not linear effects, and their data include responses by many individuals, who may have different response patterns. It's all very interesting. Melchoir (talk) 07:20, 2 July 2013 (UTC)
 * Don't get me wrong, I do think that the image is trying to convey something useful and interesting. However, I am not sure exactly how is the information understandable if the axes are meaningless. Nergaal (talk) 15:31, 2 July 2013 (UTC)
 * Hmm, do you think it would help to say more about the interpretation of the diagram in the caption? I don't want it to get too long, but something like this maybe?
 * Statistical analysis from a reaction time experiment, showing separation of 0. In this diagram, only the clustering of data is meaningful; the axes are arbitrary. See image description for details.
 * Melchoir (talk) 22:12, 2 July 2013 (UTC)
 * Referring the reader to the image description page in order to understand the figure is a very bad solution, and a self-reference at that. It would be of no use if someone printed the page, for example. There really needs to be an explanation in the article, without having to go to another page to see it. Short would be good, but if necessary a paragraph in a subsection with the figure could be used. Modest Genius talk 23:34, 29 July 2013 (UTC)
 * Okay, how about this? Melchoir (talk) 23:57, 29 July 2013 (UTC)


 * Image copyright review by Stifle: All images are free and properly licensed and tagged. Stifle (talk) 14:25, 24 July 2013 (UTC)

Comments from Ceranthor

 * Lead
 * Zero fits the definition of "even number" - I think there should be an "an" before even.
 * Solved by removing the word "number". Melchoir (talk) 02:35, 26 July 2013 (UTC)
 * In the binary numeral system used by computers, it is especially relevant that 0 is divisible by every power of 2; in this sense, 0 is the "most even" number of all. - I hope this is explained later in the article! Otherwise it sounds like OR.
 * Yes, it's explained in the "2-adic order" section. Melchoir (talk) 02:35, 26 July 2013 (UTC)
 * Why zero is even
 * In the second paragraph of the basic explanations bit, it's a bit confusing when you switch between numerals and the spellings of the numerals. Just checking because I want to confirm that I'm reading it correctly; are you using the numerals for the actual diagram?
 * When a number is used as a quantity, like "six apples", I always spell it out. In that case, I'm referring to a property of the numbers themselves, as in "6 is even". It also helps to connect to the diagram, yes. Melchoir (talk) 02:35, 26 July 2013 (UTC)
 * Before the 20th century, definitions of primality were inconsistent, and significant mathematicians such as Goldbach, Lambert, Legendre, Cayley, and Kronecker wrote that 1 was prime.[9]  - This is an example of this inconsistency. Here one should be spelled out. In fact, this is quite an inconsistent mess throughout the article I realize.
 * I don't agree that it's a mess. The spelled-out version "one" is used throughout to quantify a noun or as a pronoun, and "1" is used to refer to the number. Does that make sense? Melchoir (talk) 02:35, 26 July 2013 (UTC)

I love mathematics articles because they are fascinating, and this one does not disappoint. I just wish more people cared about math around here! That's it for now.  ceran  thor 22:51, 25 July 2013 (UTC)
 * Thanks! I wrote some replies above. Melchoir (talk) 02:35, 26 July 2013 (UTC)


 * Mathematical contexts
 * example, the fact that positive numbers have unique factorizations - link factorizations
 * Fixed Melchoir (talk) 18:47, 28 July 2013 (UTC)
 * Not being odd
 * Rather than prove that there exists a completely labeled subsimplex by a direct construction, - jargon
 * Fixed  Melchoir (talk) 18:27, 28 July 2013 (UTC)
 * Even odd
 * such, it is useful for computer logic systems such as LF and the Isabelle theorem prover - LF is linked but the article doesn't exist. Not helpful at all
 * Fixed with a redirect Melchoir (talk) 19:11, 28 July 2013 (UTC)
 * If a (connected) graph - why is connected in parens?
 * Fixed Melchoir (talk) 18:50, 28 July 2013 (UTC)
 * What is an "explicit bipartition"?
 * Fixed Melchoir (talk) 18:50, 28 July 2013 (UTC)
 *  There are only two cosets of this subgroup—the even and odd numbers—and it can be used as a template for subgroups with index 2 in other groups as well. A - jargon and just plain confusing
 * Fixed Melchoir (talk) 19:27, 28 July 2013 (UTC)
 * 2-adic
 * number, but it is tricky to quantify exactly how many times that is. For - tricky is slang
 * Fixed Melchoir (talk) 19:02, 28 July 2013 (UTC)
 * is the number of times n is divisible by 2, or the exponent of the largest power of 2 that divides n, or the multiplicity of 2 in the prime factorization of n - no need to repeat or twice, once will suffice
 * Fixed Melchoir (talk) 20:51, 28 July 2013 (UTC)

More later!  ceran  thor 01:53, 28 July 2013 (UTC)


 * Student knowledge
 * couple fourth-years realized that zero can be split into equal parts: "no one gets owt if it's shared out - this quote is hardly encyclopedic!
 * Fixed Melchoir (talk) 15:44, 29 July 2013 (UTC)
 * Isn't et all usually italicized?
 * I seem to remember researching this and concluding that "et al." shouldn't be italicized. A quick Google search seems to confirm that. It's also listed in Manual of Style/Abbreviations without italics. The MoS also says it should normally only be used in references, but I'm not sure that writing out "Levenson, Tsamir, and Tirosh" would be any easier to read. Melchoir (talk) 01:17, 29 July 2013 (UTC)
 * Why is one study linked but not the others?
 * Fixed Melchoir (talk) 01:23, 29 July 2013 (UTC)
 * Referring to a person as a major is slang.
 * I'm not sure about that. The cited source, Dickerson & Pitman (2012), uses the phrase "mathematics majors" four times, including once in the abstract. Melchoir (talk) 01:32, 29 July 2013 (UTC)
 * Teacher knowledge
 * a more in-depth 2008 study - should be an NBSP between 2008 and study
 * Fixed Melchoir (talk) 01:19, 29 July 2013 (UTC)
 * This misconception was held even by a teacher who is exemplary by all measures; it was "one of the few incorrect answers she gave" on their test.[47] - This sentence is awkward.
 * Fixed  Melchoir (talk) 16:08, 29 July 2013 (UTC)
 * The literature contains a couple of data points concerning teachers' attitudes - The literature?
 * Fixed? Melchoir (talk) 01:34, 29 July 2013 (UTC)
 * Group discussions
 * 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.[52] - why are these italicized?
 * Fixed Melchoir (talk) 05:15, 29 July 2013 (UTC)
 * students have learned something valuable about their own learning process.[56] - switching tenses within the sentence
 * Fixed Melchoir (talk) 01:36, 29 July 2013 (UTC)
 * Everyday
 * That is, the numbers read ...6420135... from port to starboard.[78 - the diction here is not encyclopedic
 * Fixed Melchoir (talk) 01:49, 29 July 2013 (UTC)
 * The game of "odds and evens" is also affected: if both players cast zero fingers, who wins?  - I really don't think this should be phrased as a question
 * Fixed Melchoir (talk) 02:39, 29 July 2013 (UTC)

Almost there! :)  ceran  thor 00:26, 29 July 2013 (UTC)


 * Update
 * I still have some issues with the education and everyday sections. I'm going to wait for hamiltonstone to provide you with more comments before I !vote.  ceran  thor 02:56, 29 July 2013 (UTC)
 * Okay, thanks for the feedback so far! I'm done for the moment. Did you have more specifics on the Everyday section? Melchoir (talk) 17:44, 29 July 2013 (UTC)
 * Final Everyday stuff
 *  In a 2012 news article on gas rationing in New York, care is given to explain that zero is considered an even number.[73 - I really don't think this adds anything useful to the article.
 * Removed. (That reference was added by another editor, and I was reluctant to remove it unilaterally at the time.) Melchoir (talk) 04:17, 31 July 2013 (UTC)
 * There are also situations where calling zero even or odd has consequences. - I don't think this is phrased like an encyclopedia. I mean technically it always has consequences, petty or not. Needs to be rephrased.
 * In other situations, it can make sense to separate 0 from the other even numbers - Same as above.
 * Eh, I've simply removed both sentences. The idea was to delineate the grouping of examples, but maybe that isn't necessary. Melchoir (talk) 04:26, 31 July 2013 (UTC)

Otherwise, I'll support on the basis of the prose, which has improved a lot.  ceran  thor 03:42, 30 July 2013 (UTC)

Comments from Hamiltonstone
Interesting stuff. The article has improved, though it still shades into being a pedagogical manual for teachers. I have a few specifics that focus in the section on education:
 * I don't think the following is of great interest and could be omitted. It is of some amusement or concern in a teacher training context but not in an encyclopedia article (which in my view is already a bit on the long side in its 'education' section):
 * I've shortened those two sentences, which should help. If that still feels like too much emphasis, we could also remove the mention of the exemplary teacher. I would like to retain the mention of the math coach, though, as coaches aren't mentioned elsewhere in the article. It's interesting to note that they can play a role. Melchoir (talk) 16:08, 29 July 2013 (UTC)
 * Lichtenberg's study was published over forty years ago. i think it is seriously misleading to write about it in the present tense. Given the age of a the study and the fact that education and training has likely changed significantly since then, and that it is only a single study, i would in fact consider deleting it.
 * Okay, I put it in the past tense. I would be very reluctant to lose this study, since it's the best we have. I did qualify the generality of the result ("It is uncertain...", "One report comes from..."), and it should help that the date is mentioned. Melchoir (talk) 16:29, 29 July 2013 (UTC)
 * I trimmed it a bit further. hamiltonstone (talk) 11:30, 30 July 2013 (UTC)
 * This para has some issues, and I also question its value in an encyclopedia article: First of all, "a couple of data points" is both colloquial ("couple") and oddly formal ("data points"); then in fact there seems to be only one data point; then it turns out not to be about teachers, but about college students; it is a study of just 10 people; then it tells us the result but without fully explaining why it matters. Again, I'm not sure why this is being included.
 * Removed Melchoir (talk) 16:34, 29 July 2013 (UTC)
 * The subsection "group discussions" probably is not needed. The amount of weight given to the Ball research is way out of proportion to its significance, and i don't think the subsection adds anything substantive to what i learned through reading the "students knowledge" section. hamiltonstone (talk) 01:40, 29 July 2013 (UTC)
 * I think the subsection is useful, but I agree that Ball was overweighted. I cut the second paragraph on that research. Melchoir (talk) 17:00, 29 July 2013 (UTC)
 * Maybe we can see what others think. I literally cannot understand what Ball is telling me: I can extract absolutely no information from this para. Maybe the nature or significance of her research results needs to be explained differently. The table of claims seems a slightly more complex version of info in the "students' knowledge" section and, if I could work out what Ball is talking about, my guess is that it belongs as an additional general sentence at the end of the third para under that earlier heading. I'm not trying to be difficult - can you try and explain to me what Ball's point is? hamiltonstone (talk) 11:30, 30 July 2013 (UTC)
 * I think the general point for Ball is that the children are doing mathematics. They're not just solving exercises correctly or incorrectly, depending on how smart they are. They're engaging in questions of definition and of the relative importance of patterns, and they're backing up their claims with examples. Also, it's surprising that the spectrum of claims is so rich. You might expect the claims to come in only two forms: "zero is even" and "zero is odd". After reading about Frobisher's studies, you might think there are four possible claims: even, odd, both and neither. What Ball observed was still more complicated: the children seem to be making modal claims about what "must" be true and what "will" be true. I know that's not what I expected! So, hopefully you agree that this information is interesting in principle. I might need a few days to re-read the sources and see if there's a better way to explain it, though. I wouldn't want to copy what I just wrote into the article; there might be some Original Research in there. Melchoir (talk) 05:12, 31 July 2013 (UTC)
 * I might try and have a go at revising it if I get a moment in the next few days. Thanks for the explanation, I hadn't understood that that was her point. hamiltonstone (talk) 00:02, 1 August 2013 (UTC)
 * Well, I should probably wrap up this issue. For the public record: I'll make some kind of edit to that paragraph in the next 24 hours. There, I said it; now it has to happen. :) Melchoir (talk) 06:56, 7 August 2013 (UTC)
 * ...a little late, but here's what I've got: Melchoir (talk) 08:02, 10 August 2013 (UTC)
 * OK, I conducted some significant surgery on the section. It now reflects how I thought it should look and has trimmed material from what I always thought was an overly long section of the article. I'm happy to support the article in this form, but I recognise that the nominator or others may not be happy with my edits, and I will monitor for discussion or different views. hamiltonstone (talk) 01:07, 12 August 2013 (UTC)
 * That works, thanks! Melchoir (talk) 07:56, 14 August 2013 (UTC)
 * Thanks! I think I've addressed all the specifics. What are your thoughts on what remains? Melchoir (talk) 17:41, 29 July 2013 (UTC)
 * On other material: "Often students will independently ask if zero is even; Israel's national mathematics curriculum reminds first grade teachers that zero is even but advises that it is unnecessary to mention this unless the class brings it up". I think this can be deleted. I don't think what Israel's curriculum says is that important; it seems to me unremarkable information that students will sometimes ask the question; and also this doesn't seem to be relevant to "group discussions", the heading under which it occurs. hamiltonstone (talk) 11:30, 30 July 2013 (UTC)
 * Hmm, now that you mention it, yeah, that's a weak sentence. Removed. Melchoir (talk) 04:53, 31 July 2013 (UTC)
 * One other thing: I have never seen such a long "other reading" list in an article with an already enormous bibligraphy, and none of them seem directly to pertain to the subject. See also WP:FURTHER: "This section is not intended as a repository for general references that were used to create the article content." Happy to hear other views, but my inclination would be to delete it.hamiltonstone (talk) 11:34, 30 July 2013 (UTC)
 * Okay, I've moved it to the talk page.  Melchoir (talk) 04:49, 31 July 2013 (UTC)
 * Good idea. hamiltonstone (talk) 00:02, 1 August 2013 (UTC)
 * Suggest you get rid of the graph "The 2-adic integers". It is not comprehensible to a lay person, nor is it referenced in the article text. hamiltonstone (talk) 00:33, 12 August 2013 (UTC)
 * Actually, I just went ahead and did this as part of my reorganisation of the next section. hamiltonstone (talk) 01:07, 12 August 2013 (UTC)

Comments from Casliber

 * Reading through now - a bit scared to copyedit - will post queries below. Cas Liber (talk · contribs) 03:08, 8 August 2013 (UTC)


 * we have "Zero is an even number." and "Zero fits the definition of "even" " two sentences apart - be good if we could combine or streamline these. Makes the prose a bit laboured as is.
 * I think it's good to have both a plain statement of fact, which should be as short as possible, and an explicit argument from the definition a little later. The relationship between the sentences wasn't clear, I agree. This change should help: Melchoir (talk) 08:13, 10 August 2013 (UTC)
 * Yes reads better now. Cas Liber (talk · contribs) 08:29, 10 August 2013 (UTC)

I can't see any other prose or comprehensiveness issues that I can tell, so I am tentatively support ing (pending what other folks say). Cas Liber (talk · contribs) 08:29, 10 August 2013 (UTC)

Comments from 99of9

 * Ball, Deborah Loewenberg (2003) is not linked from anywhere. --99of9 (talk) 05:37, 8 August 2013 (UTC)
 * Good catch, that must have been cut in an earlier edit. Fixed: Melchoir (talk) 08:05, 10 August 2013 (UTC)

Delegate comments
This review has been open six weeks without achieving clear support for promotion. If Hamilton and Cas are still in the process of commenting and might wish to declare one way or another, I'm prepared to leave it open a little longer, otherwise it will have to be archived as no consensus. Cheers, Ian Rose (talk) 01:47, 10 August 2013 (UTC)
 * This is tricky - I read a comment about the prose being a bit to "how-to-ey" but I think that it does help for mathematical articles as I think they pose an interesting challeng to make accessible. I read through and only found one real improvement that needed making (noted above). Given that it is a mathematical article (which are underrepresented) I'd be thinking of cutting some slack timewise to try and reach consensus. I will read through again but am inclined to think it is at or near-FA-worthy. Cas Liber (talk · contribs) 02:50, 10 August 2013 (UTC)
 * Thanks Cas! I know this FAC has been open for a while, but it took some time to pick up steam. Once it was listed at User:Deckiller/FAC urgents, it started progressing pretty well, I think. Of course, a delegate-nudge helps. :)
 * About the "how-to-ey"-ness, that is indeed an interesting challenge. In previous incarnations of the article, a lot of the content in the "Why zero is even" section was posed as an overview of explanations recommended in the education research literature. The general feedback was that the article shouldn't address the content as if to teachers, but rather present the explanations directly to the reader. Melchoir (talk) 08:30, 10 August 2013 (UTC)
 * It seems fine to me.  ceran  thor 04:17, 12 August 2013 (UTC)
 * Hi Ian et al. Per my post above, I went in and edited the education section, and if other editors are ok with my version, I am supporting it, as i was already happy with the other aspects. hamiltonstone (talk) 06:01, 12 August 2013 (UTC)
 * Okay, where are we at now? I plan to close this long-running nom in the next day or so, one way or the other... Cheers, Ian Rose (talk) 01:46, 17 August 2013 (UTC)
 * I take it you are hoping Casliber will come back and take a further look? It appears Melchoir and I are happy as it stands, as was ceranthor. I'm pinging cas now... hamiltonstone (talk) 10:05, 17 August 2013 (UTC)
 * I am happy with it. I can't think of anything else I'd add or change, but I concede I am no expert in the area (I tentatively supported above). Cas Liber (talk · contribs) 14:45, 17 August 2013 (UTC)

Comments by the Dr.

 * Can you format the dates of the C. Arnold source in words rather than digits? ♦ Dr. Blofeld  20:25, 20 August 2013 (UTC)
 * Fixed Melchoir (talk) 00:56, 21 August 2013 (UTC)
 * "Understanding zero is one goal, but there is also a wider lesson" seems a bit "text bookish" for an encyclopedia article.♦ Dr. Blofeld  20:27, 20 August 2013 (UTC)
 * Removed Melchoir (talk) 00:56, 21 August 2013 (UTC)
 * "More in-depth investigations were conducted by Esther Levenson, Pessia Tsamir, and Dina Tirosh," -do you have a time period for this?
 * Well, the article date is 2007. The article doesn't specify when exactly the interviews were conducted. Does it matter though? The rest of the references in that section don't mention dates. Melchoir (talk) 00:56, 21 August 2013 (UTC)
 * "Adults who do believe that zero is even can nevertheless feel unfamiliar or uncomfortable with the fact, enough so to measurably slow them down in a reaction time experiment. " Can you cite this directly, seems a bit OR, quite a generalized statement.
 * Fixed? The former phrasing with "uncomfortable" is hard to cite, but "familiar" is well-cited elsewhere in the section. Melchoir (talk) 00:56, 21 August 2013 (UTC)

Support -Absolutely, seems an authoritative article on the subject. Excellent work.♦ Dr. Blofeld  20:50, 20 August 2013 (UTC)
 * Thanks! Melchoir (talk) 00:56, 21 August 2013 (UTC)


 * Closing note: This candidate has been promoted, but there may be a delay in bot processing of the close.  Please see WP:FAC/ar, and leave the  template in place on the talk page until the bot goes through. Ucucha (talk) 05:39, 21 August 2013 (UTC)