Wikipedia:Articles for deletion/Transreal number

The following discussion is an archived debate of the proposed deletion of the article below. Please do not modify it. Subsequent comments should be made on the appropriate discussion page (such as the article's talk page or in a deletion review). No further edits should be made to this page.

The result was redirect to NaN. —Mets501 (talk) 22:35, 14 December 2006 (UTC)

[edit] Transreal number

Original research: this "transreal math" appears to be self-published original research, with no peer review. For something that claims to revolutionize arithmetic, peer-reviewed publication is essential. --Carnildo 19:30, 7 December 2006 (UTC)

• Speedy delete This is a re-creation of the previously deleted Wikipedia:Articles for deletion/Transreal number line. linas 19:41, 7 December 2006 (UTC)
  • Comment No it isn't. I created it, and I never saw that article before. Eliot 19:47, 7 December 2006 (UTC)
  • Comment OK, sorry. I wasn't happy about the earlier incarnation, and had made the following comments: The concept is not new, but the name seems to be a neologism. Computer science guys have versions of this, with lots of different NaN's. I am certain I heard of the thing in grade school, but don't know what name it was given then. I take Φ to be a nimber, namely Conway's star. (Just in case its not obvious why Φ is star, refer to Conway's book, wherein division is defined through an axiomatic system for numbers and games, and zero divided by zero is indeterminate, its star. Among other things, you'll find a proof that star is greater than -1 but less than +1 and is incomparable to everything in between. I would prefer that such concepts be treated in terms of the sound, well-developed, commonly accepted axiomatic footing, rather than invented from scratch, on a whim). I'm not convinced there is a need for the current article, it seems awfully simplisitic. linas 15:59, 24 November 2006 (UTC) To which I add: Conway is a world-class mathematician, nimbers and the entire panalopy have been researched in detail for many decades (or centuries? dating back to Dedekind cuts and Cantor??). Anderson seems happy to promote a neologism on BBC, and that strikes me as the worst sort of mathematical illiteracy. linas 19:58, 7 December 2006 (UTC)
    • Comment. Φ is clearly not Conway's star. I'd assign it a value of , but I don't remember whether that's in On Numbers and Games or Winning Ways for your Mathematical Plays. It's still not quite right, as 0 × Φ = Φ, but it's closer. — Arthur Rubin | (talk) 01:28, 8 December 2006 (UTC)
      • The axioms for arithmetic, incl. division, are in "On Numbers an Games", at the very begining. The axioms are straightforward, and generate the smallest possible games. So would be born on day ω, and clearly, that's wrong, whereas * would be born on day one, which sounds about right to me. Will have to take a look, though. We should put the axioms in a WP article somewhere. linas 01:06, 9 December 2006 (UTC)
        • Never mind, I misunderstood. Yes, I guess Φ might not map cleanly to anything in particular. Hmm. linas 01:09, 9 December 2006 (UTC)
• Delete but not speedily, this is not really worth having an article about, but because of the widely linked BBC news story on the subject, there are hordes of people looking up nullity. Would we rather speedy this article a dozen times today, or just delete it once next week? Eliot 19:47, 7 December 2006 (UTC)
  • Can someone please explain what is wrong with "nullity"? If this is major front page news, maybe it is notable, and maybe it should have an article? I'll admit, I came here because I read the BBC article, which didn't do a good job of explaining nullity, so I came to Wikipedia to find out more, and just found this. --Cyde Weys 19:56, 7 December 2006 (UTC)
    • Comment: what’s wrong with nullity is exactly what’s wrong with mainstream news sources dealing with science: they usually hardly know anything about what’s at stake. Until a panel of specialists have peer reviewed the new theory/tool/proof/etc., Wikipedia should not talk about it (we can however talk about the buzz going around it). I understand it’s nice to come to Wikipedia and find an analysis of that “new” tool, but as of now it’s original research. Sam Hocevar 20:03, 7 December 2006 (UTC)
      • So in other words nullity is just this thing made up by an elementary school math teacher, and doesn't have any real publications in the mathematical literature that proves it to be more than just a made-up name? --Cyde Weys 20:04, 7 December 2006 (UTC)
        • This discussion would be worth having on the talk page for the article instead. Eliot 20:07, 7 December 2006 (UTC)
    • Unless there are other unlinked sources, this doesn't seem likely to be "major front page news". Although the BBC can carry a lot of weight, the linked article in this case is a minor local news story (in fact it's not even branded as "news", but "people"), and is more about the reactions of the kids at a local school than the shattering importance of the theory. --McGeddon 20:48, 7 December 2006 (UTC)
  • The problem, as I see it, is that its a shallow reinvention of well-known concepts in mathematics (see above), a neologism, that fails to advance the state of human knowledge, and demonstrates ignorance of mathematics on the part of the inventor. If this was the re-invention of some mind-boggling difficult concept, I would have no complaint. However, this idea appears to lame and shallow, something that eager teenagers dream up by the dozen in grade-school algebra. linas 20:07, 7 December 2006 (UTC)
• Delete as per my above comment. Sam Hocevar 20:14, 7 December 2006 (UTC)
• Delete. I've read through the paper twice now, and I'm still not convinced as to how this is really a notable article. The claims made in the paper are dubious at best. --King Bee 20:27, 7 December 2006 (UTC)

• Comment. I just decided to watch the video on the BBC article; pure nonsense. I change my stance above to strong delete. --King Bee 22:15, 7 December 2006 (UTC)

• redirect NaN. Also see Wikipedia:Articles for deletion/Perspex machine which is a possibly more sound concept by the same person. --Salix alba (talk) 20:31, 7 December 2006 (UTC)
• Keep, not that you care anyway. Where was I when you made up all these policies? Rōnin 20:42, 7 December 2006 (UTC)
• Redirect to NaN, which then needs a note at the bottom about the perpetual attempts to define NaN that keep getting people excited but never actually make any mathematical headway. Xkcd 20:46, 7 December 2006 (UTC)Xkcd
• Keep but make sure that anything that comes close to acknowledging it as anything more than fringe, mathematic speculation without concensus be removed as NPOV. Unfortunately, the BBC article seems to make it notable. While it is not "front-page" stuff, it is the BBC. Redirect The new addition to NaN is sufficient.-Seidenstud 20:55, 7 December 2006 (UTC)
  • Comment: in this article on the perspex machine the concept of nullality has a bit more relavance. In it Anderson considers spaces of homogeneous coordinates, (x,y,z,w) which have the equivilence relation (x,y,z,w) ~ (x/w,y/w,z/w,1) to complete the set of posible coordinates there is a need to represent the number (0,0,0,0) (typically not included in homogeneous coords, but might have a use in his specific application). Taken as specific element in this set it actually has a subitily different meaning to just dividing 0/0 in the reals. So its technically different to NaN or nimber. Basically BBC got it well wrong. --Salix alba (talk) 20:59, 7 December 2006 (UTC)
    • Hmm. A four-dimensional projective variety with the disjoint union of a particular point? Is the resulting space still a variety? linas 21:43, 7 December 2006 (UTC)
      • Reading further he seems to be taking the set of oriented lines, rather than unoriented lines. I can see why this would be useful for computer vision. Indeed there does see to be quite a lot on Oriented Projective Geometry. Still don't quite understande where the nullity fits in. --Salix alba (talk) 23:01, 7 December 2006 (UTC)
• Comment: boldly redirected to NaN. Sam Hocevar 21:13, 7 December 2006 (UTC)
  • Good boldness, but I reverted it since you're not supposed to be bold about removing pages that are being discussed for deletion. Eliot 21:24, 7 December 2006 (UTC)
    • Oh, I was under the impression that if the consensus was to delete or redirect one did not have to wait until the end of the process. Are we going to leave an unsourced article that’s only a few hours old for 5 whole days? The fact that starting an AfD blocks everything doesn’t look like a good way to improve things. Anyway, I’ll stick to editing the current article. Sam Hocevar 21:31, 7 December 2006 (UTC)
• Redirect to NaN, as it seems to only be a symbolic stand-in for the inability to solve. Smeggysmeg 21:28, 7 December 2006 (UTC)
• Redirect to NaN. Agree with Salix Alba, Xkcd, etc. In the event that mention of this media event remains in WP, it should be balanced by discussion of its mathematical limitations such as can be found here. —David Eppstein 21:29, 7 December 2006 (UTC)
• Delete or redirect, whatever it takes to achieve consensus; don't keep. I think everything has been said above. Melchoir 21:34, 7 December 2006 (UTC)
• Strong Keep - no reason to delete; just made the BBC news, incidentally.139.48.81.98 21:36, 7 December 2006 (UTC)
• Redirect to NaN. That's all it really is, anyway. --Powerlord 21:41, 7 December 2006 (UTC)
• Delete; BBC Berkshire doesn't meet notability standards, especially for self-published drivel like this. EdC 21:58, 7 December 2006 (UTC)
• Redirect To our fav article -- NaN. Also the BBC doesn't seem to know what the hell they are talking about, why is this teacher telling this to his students before going before peers? Complete idiot. MrMacMan 22:32, 7 December 2006 (UTC)
• Redirect to NaN, possibly with some kind of explanation or mention on this or the NaN page, or people will just recreate the entry. MMad 22:33, 7 December 2006 (UTC)
• Comment: To me, this appears to be as much a revised mathematical notation, as the introduction of any actual new concepts. New notations can, of course, be important, but in this case, I would leave to the math editors the question of whether there is anything useful here or whether this is pure, not "original research," but an original notation format for otherwise commonplace concepts. Newyorkbrad 22:45, 7 December 2006 (UTC)
• Comment: According to the PDF discussing this topic on Anderson's website, "this paper will be published in Vision Geometry XV, Longin Jan Lateki, David M. Mount, Angela Y. Wu, Editors, Proceedings of SPIE Vol. 6499 (2007)". Does this not count as a peer reviewed journal? --Tjohns ✎ 23:03, 7 December 2006 (UTC)
• Delete or Redirect. Whatever. Just get rid of it.

And to address the above comment, no, proceedings are not reviewed. Lunch 23:17, 7 December 2006 (UTC)

• Delete Get rid of it as fast. Its nonsense. Or redirect to self-publicised pseudo-science Lee-Jon 23:20, 7 December 2006 (UTC)
  • Delete Agreed, this is nothing more than a relabelling. Sekky 00:27, 8 December 2006 (UTC)
• Delete, based off what Lunch said above and per WP:NOR. --Tjohns ✎ 23:30, 7 December 2006 (UTC)
• Delete but do NOT redirect to NaN. NaN is a comp sci construct, not a mathmatical one. It seems like OR to me, and it's not really notable either. I came up with this idea (although I used a different symbol) back in high school, and "Wikipedia is not for things made up in school one day". Even I quickly gave it up, realizing that it was just plain silly. NaN does all that we need it to do. All of the "problems" with it are actually features. --W0lfie 23:36, 7 December 2006 (UTC)
• Delete. It's just a rehash of a common extension to the real numbers, with a "definition" for division by zero in the space. It might be a scientific paper but I don't believe it is notable. I could create a space where I defined 1/0=3, but it would be unencyclopedic. It must go. Readro 23:47, 7 December 2006 (UTC)
• Keep. Total baloney but baloney that wp should explain given its notability atm. --Ævar Arnfjörð Bjarmason 00:08, 8 December 2006 (UTC)
• KEEP per the comment directly above mine - Stoph 00:21, 8 December 2006 (UTC)
• Delete I question the integrity of the journals/books the two articles are to be published in. Are they peer reviewed? Are they notable? Doubtful. This article sounds masturbatory. Carboneyes 00:35, 8 December 2006 (UTC)
• KEEP it wouldn't be notable if it hadn't been on BBC and slashdot, but given that it's been sensationalized there, it'll be useful to keep this article alive. TenthServant 00:44, 8 December 2006 (UTC)
  • BBC is NOT a scientific journal! Inner Earth 15:27, 8 December 2006 (UTC)
• Redirect to NaN, (and be careful with incoming links). Not exactly a re-creation of transreal number line, but not notable. (The perspex machine seems to be a "mathematical" interpretation of a comp-sci contruct, so it fits better than one would think.) As for SPIE, I thought it was a peer-reviewed journal, but Vision Geometry VIII wouldn't have been accepted by a peer-reviewed science journal. Could be philosophy, I suppose. — Arthur Rubin | (talk) 00:46, 8 December 2006 (UTC)

I believe Vision Geometry is a conference, not a journal. I didn't find anything about whether it has a high or low acceptance rate in a cursory search but its review process appears to be on the basis of 2-4 page abstracts rather than full papers. —David Eppstein 01:18, 8 December 2006 (UTC)

• Delete, don't redirect. The guy has re-discovered NaN's. Now "transreal number" is nothing but a neologism at present, and we can always include a redirect once the term has caught on Dr Zak 00:50, 8 December 2006 (UTC)
• Keep, The topic is receiving some news coverage, but that coverage does not (in many cases) actually explain what is being discussed. Having a article in Wikipedia allows people who see the coverage to gain some understanding of what is being talked about and therefore has value (even if you think the concept is complete bunk). That said, it would be appropriate for the article to be edited to be more neutral and offer arguements against the theory. (UTC) —Preceding unsigned comment added by 68.23.177.140 (talk • contribs) 01:08, 8 December 2006

  Comment. The coverage doesn't explain what is being discussed. That's because, if it did, the readers could see there was nothing there. — Arthur Rubin | (talk) 01:28, 8 December 2006 (UTC)

• Delete - Any crackpot professor who makes up a term to describe something that already has a term does not deserve to have their new term on WP. This is a neologism. --Wooty Woot? contribs 01:22, 8 December 2006 (UTC)
• Weak delete. The basic problem in my opinion is that it's impossible to write an article about this that is both neutral and no original research. The concept is not discussed in the mathematical literature and I doubt it ever will, which means that we can't offer arguments against the theory, or say that it's basically the same as NaN's (if it is). However, if we have an article we must make it clear that the concept is rejected by mathematicians.
  The SPIE Proceedings have minimal review: the Call for Papers states "To ensure a high-quality conference, all abstracts and Proceedings manuscripts will be reviewed by the Conference Chair/Editor for technical merit and suitability of content.", which I take to mean that the Chair/Editor may refuse submissions that are obviously unsuitable, but that no rigorous peer review takes places. Furthermore, SPIE is the International Society for Optical Engineering, which is perhaps not the most proper body to review novel mathematical theories.
  There is a case for notability following the media coverage (BBC Berkshire and Slashdot), and that's why I only say "weak delete", but I expect that everybody will have forgotten about it by the time that this AfD closes. -- Jitse Niesen (talk) 01:26, 8 December 2006 (UTC)
• Delete. Jitse Niesen and linas said it very well. shotwell 01:34, 8 December 2006 (UTC)

• Redirect to NaN. I don't believe this should be deleted while the BBC covergage is still fresh in our minds. However, it's premature to give this its own article. If there is long-term usefulness it would be as an alternative to IEEE NaN's, so redirect there and add a short note in that article. Philtech-oh 01:46, 8 December 2006 (UTC)

• Redirect to NaN I agree w/ ^^. This theory is a joke. There is a reason no respectable mathematics or CS journal would accept it. It has not been peer reviewed, nor is it likely to receive (or deserve) any such review. We should let people realize that the concept of "nullity" is nothing more than a dedicated NaN for 0/0. Glaucus 02:23, 8 December 2006 (UTC)

• Merge & Redirect to NaN: you guys waste too much time debating and suppressing psuedoscience rather than addressing it. Cwolfsheep 02:28, 8 December 2006 (UTC)

• Delete, appears to be original research. Please do not redirect to NaN: that's a completely different thing from what is being discussed here. -- The Anome 02:52, 8 December 2006 (UTC)
  • Comment: you might want to zot the redirects Nullity (transreal) and Nullity (Transreal) at the same time, if this AFD goes through. -- The Anome 03:00, 8 December 2006 (UTC)
• Delete per above. MER-C 04:11, 8 December 2006 (UTC)
• Keep, Intelligent design is a bunch of bullcrap too, but there's an article on it, because it's something that's receiving a fair amount of attention, and nullity/transreal math should be kept for the same reason. --Bewebste 04:52, 8 December 2006 (UTC)

• Keep. Our opinions on the validity of the concept do not change the fact that per its media mention and inclusion in education (however isolated) it is now a part of the public discourse. If the concept is hooey (and personally, I do side with believing it probably is), then that puts it in the same category as the Flat Earth Society: reason to have the article reflect the strength of these objections, but not reason to not have it. Fractalchez 05:24, 8 December 2006 (UTC)
  • I am changing my vote to Merge and Redirect to James Anderson (computer scientist). If he really is the only significant proponent of the concept then, yes, it has not earned its own page. However, if it is being taught to students, however few (and remember that if one person does, others might start doing the same out of the media spotlight), then his students and/or their parents might come here looking for more information on what they are learning. Any information Wikipedia provides, including, if deemed appropriate, a hard uncomprimising debunking page, does them more a service than providing nothing at all. Fractalchez 18:38, 13 December 2006 (UTC)

• Keep When I saw the story online about some guy discovering how to divide by zero, I suspected it was a bunch of hogwash. Wikipedia was where I turned to find out! dyknowsore 08:25, 8 December 2006 (UTC)
• Delete. Some person invents a new type of mathematical idea (which has already been handled by computers in the terms of inf(=a/0), -inf (=-a/0) or NaN (=0/0), and claims that he has now solved an ancient problem, of course shattering some other mathematical axioms to pieces along the way and thereby solving nothing. Some journalist believes in it and writes an article about it. No big deal. This is a fickle and will go away. Sjakkalle (Check!) 09:20, 8 December 2006 (UTC)
• Keep as a debunking page - merging or redirecting to NaN gives this far too much credibility. Perhaps add a link to NaN so after people read this, they can read something better. Quack 688 12:01, 8 December 2006 (UTC)
• Delete - non encyclopedic, nothing new, so I doesn't classify it as "Original Research". - Cate | _Talk 12:17, 8 December 2006 (UTC)
• Weak delete, nothing special, obvious extension of arithmetic. The only slightly odd thing is that he defines 1/0 as positive instead of having indeterminate sign, which I find aesthetically displeasing. Only weakly because of silly media mentions. In one year, nobody will care about this anymore and this will be as forgotten as Elin Oxenhielm. Kusma (討論) 12:36, 8 December 2006 (UTC)
• Keep - It's been on the BBC, slashdot, etc, so it's notable. Also, 1/0 makes sense depending on your point of view picture this: 1 pie and 1 person = 1/1 or 0, so the pie is gone. However, think 1 pie and 0 people = 1/0 = 1, the pie is still there. Just because it's new doesn't mean it's wrong. fintler 13:05, 8 December 2006 (UTC)
  • 1/1 is not equal to 0. You are thinking about subtraction. Sjakkalle (Check!) 13:31, 8 December 2006 (UTC)
  • BBC is NOT a scientific journal! Inner Earth 15:27, 8 December 2006 (UTC)
    • Um, it's still notable. I don't think that only scientific journals are notable. 155.247.181.52
      • Comment Well the BBC is a notable broadcasting institution. They produce reliable news reports on current events and are widely cited here for such things. But they are not a notable scientific, peer reviewed publisher of mathematics. And their Berkshire local news section certainly isn't. Sources which would confer verifiability here are sorely lacking.Inner Earth 17:54, 8 December 2006 (UTC)
• Comment - This doesn't necessarily pertain to the debate, but I have an issue with one of the axioms. Mr Anderson claims that Φ ^{− 1} = Φ. But doesn't that mean that by multiplying on the left by nullity, we get 1 = Φ²? Shouldn't there have to be a null identity of sorts to make this whole thing consistent? I also don't see the inverse operator defined in this set. The more I read this thing, the less convinced of it I become. Readro 15:17, 8 December 2006 (UTC)
• Delete. The claims this guy makes that computers can't handle division by zero is absolutely bogus. Also the math employed looks a bit shady. Lord Yaar 15:23, 8 December 2006 (UTC)
• Delete Recent papers published don't seem to be peer reviewed, and one bbc news arcicle does not a notable theory make. Missed WP:OR and WP:RS. After publication in a respectable journal, the story may well change. But BBC is NOT a scientific journal! Inner Earth 15:24, 8 December 2006 (UTC)
• Comment - Just been thinking about this, and the set is not consistent as it does not obey the axioms of a field. Mr Anderson conveniently excludes certain members of the set when "showing" that the axioms are obeyed, whereas the definition of a field clearly states that all the members of the set must satisfy the axioms. Also, BBC local news is hardly a reputable source. They've frequently made mistakes. Readro 15:25, 8 December 2006 (UTC)

• Comment. That's what I noticed as well. The transreal numbers aren't a field. I really think that working over a field is preferable, but every field has the same "problem"; you can't find the multiplicative inverse of 0. It just doesn't have one. --King Bee 17:06, 8 December 2006 (UTC)

• Speedy keep. True, there are a few problems with the sources, but I'm sure that this will appear in a scientific journal before long. --Jrothwell ^(talk) 17:26, 8 December 2006 (UTC)
• Comment Anybody who wants to help in the debunking of this theory can assist me by providing some additions to the report I'm writing at http://www.stylebucket.co.uk/Nullity.pdf any quotes, useful information or even if you'd like to write a little something to add, they would all be welcome. Sekky 17:42, 8 December 2006 (UTC)
• Keep - It serves to shed light on the debate far better than deleting it would. If I had found nothing when looking this up, I'd have no grounds to go on as to whether this was a crackpot idea or not. And do keep in mind people like Georg Cantor before dismissing this idea out of hand. Dante-kun 18:39, 8 December 2006 (UTC)
• Keep just like any other notable pseudoscience. Just because it is stupid doesn't mean it shouldn't be on Wikipedia. Instead it should be explained why it is stupid. Grouse 19:26, 8 December 2006 (UTC)
• Psudo-Redirect to NaN: The article in question does have some noteablility due to the BBC article, but isn't really deserving of a full article, and even if it was, no sources are available to work from, making it either OR or posesing of NPOV problems, or both. Stub it, and link to NaN, until such a time as there are peer-reviewed papers or such to allow a well-written full article. Kinkoblast 19:39, 8 December 2006 (UTC)
• Comment I think it's a standard conclusion on AfD that a single, local, human-interest newspaper article on some topic does not make it notable, on the grounds that newspapers will report on anything and that Wikipedia is not a news aggregator. Generally, encyclopedic notability demands multiple, nontrivial reviews. If this reasoning applies to elements of popular culture, how much more must it apply to science? If the article hadn't been unearthed by Digg and Slashdot, would anyone even be here defending it? Melchoir 19:50, 8 December 2006 (UTC)
• KeepPureLegend 20:03, 8 December 2006 (UTC)
• Rewrite and rename I've come across a bunch of much more mathematically sound papers.
  1. Jesper Carlstrom, Wheels on Division by Zero, Mathematical Structures in Computer Science 14(1):143–184, 2004.[1]
  2. A. Edalat and P. J. Potts. A new representation for exact real numbers. In S. Brookes and M. Mislove, editors, Electronic Notes in Theoretical Computer Science, volume 6. Elsevier Science Publishers, 2000. (suggested that two extra `numbers', and , be adjoined to the set of real numbers, thus obtaining what in domain theory is called the `lifting' of the real projective line, in order to make division always possible.)
  3. A. Setzer. Wheels 1997. (draft) [2], First defines a wheel as a field plus an aditional element.
• It seems like there is enough here to write a better article, which misses the spin and has some peer review references. --Salix alba (talk) 22:24, 8 December 2006 (UTC)
  • We already have a separate article on wheel theory. (Please add those citations there.) Transreal numbers are not wheel theory. Uncle G 12:51, 9 December 2006 (UTC)
• Comment. There seem to be a lot of 'keep' comments based on "we should cover this debate", "this will make it into a peer-reviewed journal", etc... As it stands now, there is no peer-reviewed debate about this subject. In fact, it is highly unlikely that any mathematician will respond to this in a serious manner. At the very most, Notices will write about "Nullity" as an example of mathematical reporting gone horribly wrong. Nullity is not mathematically profound, innovative, interesting, or noteworthy. Some of the claims about "nullity" border on mathematical nonsense. He's simply added a disconnected point to the extended real line, claimed that being able to divide by zero is more important than the topological properties this breaks, made a bizarre argument about why it's a field, and then made some grandiose claims about the importance of this "discovery". As for any serious "division by zero" research, we already have Division by zero. I would note, however, that division by zero is a non-issue. shotwell 22:58, 8 December 2006 (UTC)

Correction. I'm being kind about "adding a point to the extended real line". He also added some nonsensical arithmetic. shotwell 23:04, 8 December 2006 (UTC)

• Delete There is nothing significant about this topic whatsoever, and the only reason anybody is talking about it is because people got upset about some local fluff piece that made it's way onto Slashdot. Rljacobson 00:23, 9 December 2006 (UTC)
• Keep The concept has been used in a publication in a well-known, peer-reviewed journal: Phil. Trans. R. Soc. London B in 1997 (see Section 4 of that paper defending its utility in projective geometry problems dealing with the intersection of non-distinct lines in computer vision). Per my similar vote/comment on the perspex machine AfD page, I suggest keeping: the author and press may have gone overboard with the whole division by zero idea, but it appears that the use of the basic concept in computer vision may support its presence on wikipedia. digfarenough (talk) 00:38, 9 December 2006 (UTC)
  • Comment. ISI Web of Knowledge reports this paper has been cited zero times. Google scholar reports three citations -- two are from the author. "Perspex machine" doesn't seem to give results on any relevant database (aside from Anderson's stuff). Even the arXiv fails to give results. I also wonder why this paper was published in the biological division of Philosophical Transactions. Seeing as how the paper was published in 1997, there has been ample time to drum up attention. Please correct me if I'm wrong about the above claims. shotwell 01:42, 9 December 2006 (UTC)

To add a little bit, the Philosophical Transactions publishes three kinds of articles: review articles, articles in a "themed" issue, and conference proceedings. The article cited above comes from conference proceedings and was not peer-reviewed. For those without access to the abstracts, here it is:

This paper introduces perspex algebra which is being developed as a common representation of geometrical knowledge. A perspex can currently be interpreted in one of four ways. First, the algebraic perspex is a generalization of matrices, it provides the most general representation for all of the interpretations of a perspex. The algebraic perspex can be used to describe arbitrary sets of coordinates. The remaining three interpretations of the perspex are all related to square matrices and operate in a Euclidean model of projective space-time, called perspex space. Perspex space differs from the usual Euclidean model of projective space in that it contains the point at nullity. It is argued that the point at nullity is necessary for a consistent account of perspective in top-down vision. Second, the geometric perspex is a simplex in perspex space. It can be used as a primitive building block for shapes, or as a way of recording landmarks on shapes. Third, the transformational perspex describes linear transformations in perspex space that provide the affine and perspective transformations in space-time. It can be used to match a prototype shape to an image, even in so called 'accidental' views where the depth of an object disappears from view, or an object stays in the same place across time. Fourth, the parametric perspex describes the geometric and transformational perspexes in terms of parameters that are related to everyday English descriptions. The parametric perspex can be used to obtain both continuous and categorical perception of objects. The paper ends with a discussion of issues related to using a perspex to describe logic.

Like Slotwell said above, that this is in a biology journal smells funny, too. Lunch 01:48, 9 December 2006 (UTC)

• Keep The notability of a concept may arise in ways that are not determined by its contemporary validity. Lumos3 00:55, 9 December 2006 (UTC)
• Keep as it's raised attention and as it is a place to explain why it's not all that special. —Ben FrantzDale 02:20, 9 December 2006 (UTC)

I've been swayed. I now say redirect to James Anderson (computer scientist). (See discussion below.) —Ben FrantzDale 03:30, 13 December 2006 (UTC)

• Keep or Non-speedy delete as the BBC and Slashdot stories have popularized it, at least for the time being. The article can always be deleted later if it turns out to be unimportant in the long run. --Cybercobra 06:39, 9 December 2006 (UTC)
• Keep the amount of controversy and attention this is gathering outside of Wikipedia makes it notable by itself. Ashanthalas 07:04, 9 December 2006 (UTC)
  • Comment: there seems to more controversy and attention here than outside of Wikipedia. I really don't think the blogs (even the blog on the BBC page) count as indications of "notability". — Arthur Rubin | (talk) 07:46, 9 December 2006 (UTC)
• Delete or Redirect to NaN - WikiXan 15:09, 9 December 2006 (UTC)
• Keep for the moment. It's generated a fair amount of buzz. It doesn't hurt to have it now, and we can always re-evaluate at a later date. All the discussion about whether or not it is useful or factual completely miss the point. Deleuze 18:01, 9 December 2006 (UTC)
• Weak Delete or provide more sources that would explain this concept's notability. There are thousands of ideas living their lives in published papers, just check Google Scholar "division by zero". Nothing in this article has proven to me that this quite simple idea (although the theory itself might be complicated, I don't know) has any usefulness and/or notability (this article has been created because of a single BBC television segment which featured Anderson teaching schoolchildren?). The idea, the way it's presented now, brings nothing new and even looks "fishy" to any person who once computed limit of a function. All I can see now is that some mathematician has published and is developing the theory. What is more, the idea is very young (2006) and it is very possible that it will have no followers in future. In short: this article is unencyclopedic; it brings no insights, nor it describes something important. SalvNaut 21:48, 9 December 2006 (UTC)

Weak Keep for the moment. It's a good way to introduce readers to other concepts, other articles connected with this topic.SalvNaut 23:38, 9 December 2006 (UTC)

• Keep or redirect... I came here after reading the BBC, so it IS notable in some way!! http://www.bbc.co.uk/berkshire/content/articles/2006/12/06/divide_zero_feature.shtml --Sonjaaa 23:13, 9 December 2006 (UTC)
• Delete, or rewrite to reflect reality The concept of 'nullity' is notable only for its remarkable lack of utility; it solves a non-problem, and does so poorly. Do we want *every* amatuer mathematician creating a page about his or her lame-brained ideas? How about other fields of study? Should I be able to create a page about a computer language used only by its creator? —The preceding unsigned comment was added by 70.133.194.192 (talk)
• Delete. Just not notable enough. For mathematics, we require reliable sources in books, journals, etc. All I see here is a couple of articles by the same authors with no subsequent work by others. If we created Wikipedia entries for anything written by someone a few times in some conference proceedings, we would be drowning in crap, and I don't think Wikipedia is that bad yet. --C S (Talk) 09:20, 10 December 2006 (UTC)
• Strong Speedy Delete. Easy to prove as wrong, not peer reviewed, not even notable. The key flaw is he assigns 0 a positive value, when it is neither positive or negative on the real number line, so when he divides 1 by it, the answer should have an undefined sign, not just "positive infinity".220.253.57.87 13:31, 10 December 2006 (UTC)
• Delete. This is mostly a joke, has never been -for example- submitted for peer-review at a journal. --NavarroJ 13:48, 10 December 2006 (UTC)
• Keep due to the media exposure and hype on the "new number discovered"; but criticize its obliviousness to existing fields of research that attempt to deal with this situation in ways that are much more rigorous (e.g. Mark Burgin's hypernumbers [3] , [4] ), or more generally scoped ( e.g. Charles Musès' [5] ), or simply more neutral (like e.g. Hyperreal number ). The notability of the program in my opinion, at this point, is not its mathematical content, but it's publicity. Peer-review and connections to existing fields of research is urgently needed. Jens Koeplinger 14:50, 10 December 2006 (UTC) PS: add surreal number to the list of notables. Jens Koeplinger 15:31, 10 December 2006 (UTC)
• Delete. I was debating with myself to vote for deletion or redirect to NaN with a brief mention. I decided on deletion for the following reason: there is nothing original or interesting in this concept, and any WP mention of it should clearly state the following

(A): that the idea of extending a number system in a way which extends otherwise undefined operations is trivial.

However, as a result of some interpretations of the sensible WP policy on no original reseacrh, until such time as we can refer to some published source which states (A) we can't say this in a WP article.---CSTAR 20:06, 10 December 2006 (UTC)

• Keep: Anyone can invent anything they want, and anyone who is curious about that invention should be able to find out more about it. It may not be accepted by anyone, but that doesn't mean it shouldn't exist. —The preceding unsigned comment was added by 71.141.103.60 (talk)
  • Actually, per our Wikipedia:No original research policy, the fact that an idea hasn't been accepted by anyone is exactly why there should be no encyclopaedia article on that idea. Uncle G 01:08, 11 December 2006 (UTC)
• Keep: There needs to be at least something about this number/concept, because it has been mentioned, and it does not seem right to just delete it, just because it may not be completely sound --Warlorddagaz 23:21, 10 December 2006 (UTC)
• Merge & Redirect to NaN: as Cwolfsheep have already said, you guys waste too much time debating and suppressing psuedoscience rather than addressing it. cow_2001 23:33, 10 December 2006 (UTC)
• Comment: The papers concerning transreal numbers are PDF's linked to here; I trust this will be helpful. Septentrionalis PMAnderson 23:56, 10 December 2006 (UTC) (no relation ;->)

Yeah, nice. But the papers are not relevant. Selfpublished, not peer reviewed. Thus not good enough science to include. --Soyweiser 04:07, 11 December 2006 (UTC)

• keepI am not willing to second-guess the PRS editors, even the conference editors. math articles typically get relatively few citations, and they are a long time coming.DGG 01:58, 11 December 2006 (UTC)
• Delete We need less wierd untested pseudo math. Not more. --Soyweiser 04:05, 11 December 2006 (UTC)
• Redirect To James Anderson (computer sceintist) which should explain that he is a crackpot. Authors are normaly taken as more notable than their contributions. Alternaticely, create an article on mathematics crackpots which talks about several notable ones and redirect all these articles there. Perspex & Anderson are not notable for scientific merits but they are notable as well know parts of the cultural phenomenon of mathematics crackpotery. JeffBurdges 12:05, 11 December 2006 (UTC)
  • ps, To everyone talking about not second guessing mathematical content. All professional mathematician commenting on this say Anderson's "mathematical" work is garbage. He is a computer scientist who imagines that his incorrect version of NaN has mathematical consequences; it does not. JeffBurdges 12:05, 11 December 2006 (UTC)
• Delete The article is close to useless as-is, and the concept has not been peer-reviewed, isn't cited anywhere and has serious problems. As a random formal systsem it's fine, but it doesn't deserve a page here unless it is taken up by other mathematicians. Jgrahamc 16:38, 11 December 2006 (UTC)
• Delete, per Jgrahamc. WMMartin 19:04, 11 December 2006 (UTC)
• Funny coincidence The article Blaow, which refers to the same concept but with a different name, was proded for being considered something made up in school one day. 193.217.242.140 22:21, 11 December 2006 (UTC)
• Strong keep. This is not "easy to prove wrong". From everything I've read (e.g., the talk page) this is a consistant algebra. It's just a bit nuts. As for notability. This page is the best discredidation of the topic I've seen. If nobody remembers the idea in a year, then maybe delete it, but for now it's serving a valuable purpose, even if the page is a bit ugly. —Ben FrantzDale 04:46, 12 December 2006 (UTC) [struck, already voted —Ben FrantzDale]
  • Are you changing your vote above from "keep" to "strong keep"? And are your comments directed to a particular argument above? I might also ask do you think the topic is worth discrediting (if that's the purpose the Wikipedia page serves)? That is, how much discussion of this has there been outside of Wikipedia? (That is, what other news outlets other than Slashdot and the Berkshire local BBC have covered this topic?) Thanks, Lunch 05:47, 12 December 2006 (UTC)
    • Wikinews. Uncle G 11:52, 12 December 2006 (UTC)
    • Oops. I forgot I already voted.Thanks for catching that. I was responding to an anonymous vote above that begins saying the concept is "easy to prove wrong". If it were easy to prove wrong, I'd be more for deleting the article, but the pattern I see from discussions and from my own thinking about it is this: (1) Hua, it's like NaN. (2) Look, I proved it inconsistent. (3) No, actually it is consistent after all. This article has the potential to explain not just to the general public that the idea is crazy, but to mathematically sophistocated readers that the system isn't "wrong", but rather that it isn't really a solution to a problem. —Ben FrantzDale 15:24, 12 December 2006 (UTC)
• Comment - On BBC Radio, he admitted that the theory hasn't been peer reviewed by any mathematical journal. RealPlayer stream of the BBC Radio discussion Readro 17:00, 12 December 2006 (UTC). P.S. He adds "It remains to be seen whether this is correct or not." Oh dear. Readro 17:08, 12 December 2006 (UTC)
• Delete. Wikipedia:No original research policy is clear. Since the idea hasn't been accepted by anyone, there should be no encyclopaedia article on that idea. Plain and simple. 199.212.18.131 17:10, 12 December 2006 (UTC)
• Strong keep - The subject is infuriatingly wrong-headed, but it has garnered sufficient publicity and attention to be encyclopedically notable. In particular, given its history, it should make an ideal example for the pseudomathematics article. --Piet Delport 17:20, 12 December 2006 (UTC)
• Comment - it seems clear to me now that Mr Anderson's main motive is profit, not advancing knowledge. On this page is a link to a business presentation he conducted at Reading University - [6] - and here are some good quotes from it.
  • "What's wrong with arithmetic? Can't explain how computers work."
  • "How much would you pay to know that the engine in your ship, car, aeroplane, or heart pacemaker won’t just stop dead."
  • "How much would you pay to know that your Government’s computer controlled military hardware won’t just stop or misfire."
  • "Standard arithmetic is invalid."
  • "I will help you unify QED and gravitation if you want me to."

Readro 17:59, 12 December 2006 (UTC)

• Delete or redirect to NaN per discussion waaay at the beginning of this page. Where did all of these recruits come from, anyway? I understand voters being recruited for bands or people and such ... but mathematical theories? Is there some math blog out there that's doing this? --Cyde Weys 18:29, 12 December 2006 (UTC)
• Delete. Unless someone can come up with a reliable source other than Dr. Anderson, this is OR. If James Anderson (mathematician) survives AFD, perhaps we can merge and redirect this article there. Lunch 19:08, 12 December 2006 (UTC)

  I s'pose also that this should not redirect to NaN. It's not another name for NaN and is only somewhat related. In the same vein, I don't think it should redirect to wheel theory, nimber, hyperreals, or the like. Lunch 22:45, 12 December 2006 (UTC)

• Redirect to James Anderson (computer scientist), and expose him for the fraud he is in that article. Misinformed math students will come looking for "nullity" on Wikipedia, and they should find it. When they do, it shouldn't be described as a legitimate mathematical concept (that would be both a travesty against education and original research), but as a word used by a pseudomathematician. The theory is original research, but the phenomenon of a pseudomathematician deluding his students for his own benefit is well covered in the news. rspeer / ɹəədsɹ 22:47, 12 December 2006 (UTC)
• Weak keep If indeed James Anderson's concepts are pseudomath and/or an unoriginal rehash of ideas that have been used before, why not keep the article but specify the holes in the theory or the equivalencies that are claimed? That might provide useful information to anyone else trying to develop a similar idea. The subjects pass notability by merit of the ongoing public discussion. The subjects pass OR by merit of being verifiably published by third-parties. Treat it like Intelligent Design or Flying Spaghetti Monster. Pseudoscience, pseudoreligion, pseudomath. Oneismany 00:35, 13 December 2006 (UTC)
  • I like this solution. It sounds increasingly like he's a vocal guy who may come up with other crazy stuff in the future that might also get press coverage. Moving coverage of nullity to his page would make it clear that the idea isn't a mainstream idea and would direct deserved scrutiny on the man himself rather than raising "transreal number" to the level of a Wikipedia article. —Ben FrantzDale 03:30, 13 December 2006 (UTC)
• Keep (possible redirect to clarification on another page, such as NaN or James Anderson (computer scientist) Since when did Wikipedia only include true or uncontested theories? I came to this page b/c I read the BBC article and knew it was unreliable. I wanted to see something on WP that addressed the issue in a fair, unbiased way. I was glad that there was an article here, but if WP consensus is that Anderson's concept shouldn't be dignified by a full article, that's fine. Just have something here (i.e., a redirect) so people who've heard about the concept in the media can get the full story. Evan Donovan 00:44, 13 December 2006 (UTC)
  • You've misunderstood our Wikipedia:No original research policy. A theory that has been proposed by one person or group, and that has gained no traction in the world at large, having not been acknowledged by anyone else (either supporting or contesting it) outside of its creator(s)/proponent(s), does not belong in Wikipedia. Everything in Wikipedia must have gone through a process of fact checking, peer review, and acceptance into the corpus of human knowledge.

    This is certainly true of Anderson's "perspex machine". You argue that Wikipedia should have a fair and unbiased article on the subject. Please think that argument through. Wikipedia is not magic. There is no way to have a fair and unbiased article on a subject when the only person to have ever properly written and published works about it is its creator and proponent.

    Similarly, there is no way for Wikipedia to magically have a reliable article on something where the source is, in your very own word, "unreliable".

    "transreal numbers" and "nullity" have been contested and discussed by people other than Anderson. But only very weakly and badly. Most of the sources are unreliable, being pseudonymous web log postings of unknown provenance. Only Daniel Firth did the right thing. Uncle G 10:55, 13 December 2006 (UTC)

• Unlike the case of the Perspex machine (AfD discussion), there are people other than James Anderson that have discussed "nullity" and "transreal numbers". However, they have not discussed them standalone. They have only ever discussed them in conjunction with Anderson xyrself. James Anderson (computer scientist) and this article share the majority of their sources, notice. Wikipedia should reflect how the sources address subjects, and only discuss these ideas in the context of discussing their creator. Merge with James Anderson (computer scientist). Uncle G 10:55, 13 December 2006 (UTC)
• Keep per Dante-kun: the concept is nonsense, but there should be an article to discuss the fact that it is nonsense, especially since plenty of non-mathematical people will want to learn about this and what it is (a hoax or a mistake). CRGreathouse (t | c) 01:08, 14 December 2006 (UTC)
  • The problem is that there are no reliable sources that assert that it is nonsense. Only Daniel Firth has actually tried to address this properly, and xe hasn't finished yet. Most of the discussion is by pseudonymous people, who cannot be traced, writing on web logs, and a lot of that discussion is, moreover, wrong. (One pseudonymous web log posting that I read this morning tried to prove the system faulty by asserting that in the transreals it could be proven that 1 = Φ. The proof was flawed, since it involved cancelling 0 with 0 ^{− 1} to yield 1, something which the transreal axioms don't allow.) The fact that pseudonymous postings on web logs clearly haven't been fact checked or peer reviewed is why they are unacceptable sources.

    The only proper way to discuss this system of numbers is in the same way that the only reliable sources that we have discuss it: in the context of discussing James Anderson (computer scientist). Uncle G 12:30, 14 December 2006 (UTC)

• Keep I have a Ph.D. in Computer Science and Engineering. I have read the article and it has merits in Computer Science and Math .This is different than NaN. Computers stop calculating when a calculation results NaN. But in some cases the calculation can continue and can result in zero. I think the axioms are incomplete and by correcting or adding some more axioms (which will be rules for computers dealing with these situations), it can be a complete system useful in the future computer systems. This should definitely be linked to James Anderson (computer scientist), the original author. —The preceding unsigned comment was added by 69.212.40.35 (talk) 05:53, 14 December 2006 (UTC).
  • Computers do not "stop calculating when a calculation results NaN". To augment your Ph.D., please read our article on NaN, which explains this. Whether the article has merits is immaterial. We don't keep things because editors come along saying "I like it. I think that it has merit.". Please read our Wikipedia:Verifiability and Wikipedia:No original research policies, which are two of a several content policies that govern what we include and what we do not, and our Wikipedia:Notability guideline, which shows how we should include things that we don't have enough material on, from independent sources, for a standalone article (as is the case for this subject). Uncle G 12:30, 14 December 2006 (UTC)
• Keep per CRGreathouse. --Stlemur 07:31, 14 December 2006 (UTC)
• Comment: We have a cleaned up version of James Anderson (computer scientist), please consider redirecting this article there if you voted keep. Nothing wrong with deleting this article either. We have the only article we need on the subject now. JeffBurdges 13:43, 14 December 2006 (UTC)

Comment:I still feel that the two articles should remain seperate. One is a person, the other is a concept. Also, the James Anderson (computer scientist) article references this one to explain the concepts he has been developing. I'm still voting on keep.fintler 14:20, 14 December 2006 (UTC)

• Keep. Regretably. Thanks to the Internet, this nonsensical concept has attracted enough attention to merit its own article. Phils 21:21, 14 December 2006 (UTC)

The above discussion is preserved as an archive of the debate. Please do not modify it. Subsequent comments should be made on the appropriate discussion page (such as the article's talk page or in a deletion review). No further edits should be made to this page.