Wikipedia:Articles for deletion/Classical Hamiltonian quaternions


 * 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   keep.  MBisanz  talk 00:14, 10 March 2009 (UTC)

Classical Hamiltonian quaternions

 * ( [ delete] ) – (View AfD) (View log)

Procedural nomination after addition of AfD by anon. Septentrionalis PMAnderson 02:28, 5 March 2009 (UTC)
 * Comment: This page has severe problems, but its core is an account of William Rowan Hamilton's own notation for quaternions. I'm not sure this warrants an article. An anon put on the afd tag during the discussion of the matter, and may be right. Septentrionalis PMAnderson 02:28, 5 March 2009 (UTC)
 * I removed the section on context (which expresses Hobojak's own POV, which he repeats below) after this comment, but before any of the !votes. That in itself was an improvement. Septentrionalis PMAnderson 20:12, 6 March 2009 (UTC)

*Delete Believe it or not, I think  Classical Hamiltonian Quaternions are quaternions. The sad fact is that just about all of the vocabulary of Hamilton's calculus has been poached by other writers. According to this logic, a quaternion is a mathematical entity as defined by Hamilton. A large number of really good old books have been written on this mathematical entity. Hamilton's ideas are still relevant. On the other hand, some mathematician can name his pet donkey a quaternion, claim that Hamilton's ideas are old, and steal the name space created by Hamilton for an article about donkeys. The sad fact is that in a lot of ways, this is essentially what the main article on quaternions had degenerated into. So this article essentially serves to keep Hamilton's ideas from getting in the way, of new and different mathematical entities which have stolen the name quaternion but are not the mathematical entity defined by Hamilton. But there is another problem. I am feeling discouraged. I was reading about where it talks about this in the guidelines. When the first article an editor ever writes gets deleted, it tends to convince the editor, that contributing to wikipedia is a waist of time. While I might think about contributing a little more on the subject of entropy and H-theorem, right now I feel that contributing to the subject of quaternions, especially given the current level of mass hysteria on the subject is a waist of time. Wikipedia is created by people who are unpaid. Sometimes I have found that when you do volunteer work, no matter how much you do it is never enough, they always want more. So for example careful research into Gibbs 1901 writings on vector analysis are not enough. Apparently it does not matter that you hot link to the very page on google books were Gibbs wrote the very argument of interest, because in the idiocracy of wikipedia, giving the exact page number where Gibbs said something is not good enough. You have to find some secondary source that says Gibbs said what he said, and then some other source to say that was relevant. Some day very possibly all the information in the universe will get sucked up into black holes and vanish for ever. The sad fact is that it appears that some law of entropy dictates that any useful information created by my efforts will vanish from wikipedia log before that.Hobojaks (talk) 02:29, 6 March 2009 (UTC) Note: the above "Delete" note was entered by the discouraged single most productive contributor to named article; sorry, User:Hobojaks, but your contribution might be valued by some after all :) ... thanks for your hard work!
 * Keep We have a fair number of articles on historical mathematics.  In modern terms quaternions are interesting as an important algebraic structure and computational technique; but the history is also quite interesting as a major development in algebra, and for introducing terms like "vector" and "scalar" (and using them in a slightly different way) long before the later development of vector analysis which re-interpreted them.  An article on this material is admittedly specialist, but it is encyclopedic.  It is useful to have this as a separate reference, rather than getting in the way at Quaternion and History of quaternions (however the latter article ends up).  Jheald (talk) 10:41, 5 March 2009 (UTC)
 * Note: This debate has been included in the list of Science-related deletion discussions.  -- the wub  "?!"  13:55, 5 March 2009 (UTC)
 * For example, John Baez's paper (to which there are several links, in multiple formats here, is a reliable secondary source. Reading it first would have simplified and speeded the writing of this article, and much more so the history of quaternions. But writing here will be edited mercilessly; as it says below this edit screen.
 * Keep Still needs work, especially by anyone who has read through the infinite blizzards of Hamilton's prose. Septentrionalis PMAnderson 23:47, 5 March 2009 (UTC)
 * Strong keep - the article is primarily historical, and points out many details that were "hot" at the time. Its length or detail shouldn't be a problem, and since it's historical I see no need for hurry in getting the material polished. Seriously, I have never before seen an encyclopedic article on historical quaternions, of that detail. I read a copy-edited version of Hamilton's original 1944 paper (ed. Wilkins, 2000), and that's it. The article here in Wikipedia has the tags up top that make it clear that this article is being worked on, and if it's in good shape in five years, then it's a wonderful addition to knowledge. Give a man a break - in this case, User:Hobojaks. Jens Koeplinger (talk) 02:13, 6 March 2009 (UTC)
 * PS: Actually, the article has already come long ways from when I saw it last. It's really becoming a good article; again, I see no need for hurry at all. Thanks, Jens Koeplinger (talk) 02:26, 6 March 2009 (UTC)
 * Keep. It is clear that quaternions have a long and varied history, and quaternions as they are used today appear to differ in many ways from quaternions as they were used in Hamilton's era. While they are essentially the same mathematical concept, they were originally the precursor to linear algebra and vector calculus. While the classical use of quaternions was largely replaced by linear algebra and vector calculus, quaternions have found new applications in computer graphics and some newer theories of physics. There are a number of independent sources that go into details on the classical quaternions, for example: A History of Geometrical Methods has a section on "The quaternion calculus of Hamilton", and Oliver Heaviside: The Life, Work, and Times of an Electrical Genius of the Victorian Age has a secton on "William Hamilton and Quaternions"; in addition any of the numerous sources about quaternions written in the 19th and early 20th centuries would be appropriate to use for this article. This should be structured as a summary style spinout from the main quaternion article, but that is an editing issue. DHowell (talk) 06:09, 6 March 2009 (UTC)
 * Note Hamilton should be considered the single most important authority on the subject of quaternions who has ever lived. I feel that Hamilton's books on quaternions have more authority than all the other books on quaternions ever written.  There are a large number of perfectly good books written on the subject of quaternions which address the subject of quaternions with out redefining them.  Sadly I don't think I have found any that were written after the year 1905.  About the last good one was written by Jasper Jolly, and I plan on ordering the 2006 edition, which is exactly the same word for word as the 1905 addition.  May I remind you folks that we are now living in the 21st century.  After about 1905 just about everything written about quaternions now caries the vile stench of the mass insanity of that century.  But I have to get to school now, I can type a little more on this subject soon.  The whole idea of classical hamiltonian quaternions is an original research idea, that I created by accident.  Sorry about that. I will concede this point in the interest of a obtaining concensus.  I would like to keep a copy of some of the work I have done on my personal talk page were it can have unlimited revisions.  If you want to keep the content of this article, it which I agree with, it should be put in the main article on the subjec t of quaternions.  Also alot of the unverififiable stuff in the current article by 20th century crack pots probably at some point needs to go.  Why should Hamilton's ideas be ghettoized into some obscure original research (argument retracted)Hobojaks (talk) 03:59, 9 March 2009 (UTC) article that no one really works on?  Having this article which should not exist seems to provide an unreasonable justification for this. — Preceding unsigned comment added by Hobojaks (talk • contribs)
 * We are not here to express anybody's very strong feelings. That's what WP:NPOV means. Hire a blog. Septentrionalis PMAnderson 18:17, 6 March 2009 (UTC)
 * Please don't count this little trolls vote, he has basically wasted a lot of peoples time and effort with his doomed plot to delete this article and wasted a lot of peoples time and effort in a discussion that was forced upon us by the desire to cause trouble in his black little heart. These snide little remarks don't really contribute to an intelligent discussion.  My new tactic in dealing with the your continued unreasonable and disruptive annoyance is to simply ignore you.Hobojaks (talk) 03:59, 9 March 2009 (UTC)
 * Hobojaks - you name "classical hamiltonian quaternions" an original research idea of yours, which would be a problem to have in Wikipedia unless it receives attention. But as for terminology, the current page title serves its purpose well: It shows a classical concept (not the modern one), information on quaternions is distilled in the way Hamilton would have written it. I see value in an article of this sort; if the lead-in is clear, then readers will know what to take from it. Tracing modern ideas (modern tensors, Clifford algebra) to its roots (Hamilton tensors, vectors, scalars, versors, and so forth) is valuable and notable information. With original research, the first sources appear often cluttered when looking back, and this article attempts to arrange it (sourced). I also opt for keeping the page separate from the main quaternion article, and have the main article focus on current attention, terminology, use, and similar. Thanks, Jens Koeplinger (talk) 19:26, 6 March 2009 (UTC)
 * Seems to me like the trouble with that is that we would be creating an artificial fictional mathematical entity. Are you willing to admit that the mathematical entity created by Hamilton and his cohorts and called a quaternion, is a different mathematical entity from the this so-called modern quaternion that now controls that name space?  This diabolical plan to exclude more reputable sources from the discussion of quaternions has some major flaws.  The next book I was planning to buy and read, and possibly use to source some material on the subject of quaternions was Jasper Jolly's book, from 1905.  What we are proposing is that this new mathematical entity that I basically invented and then forced to be ever frozen in time since no sources for it are allowed after 1901 can't possibly be related to what Jolly is talking about since he wrote after 1901.  So Jolly's book being written after 1901, mysteriously becomes a book about a another new artificial entity called a modern quaternion.


 * There is another problem I am worried about. The article on this other fictional mathematical entity we are essentially creating, this so called modern quaternion to Hamilton's way of thinking has glaring factual errors in it.  The worst one being the number of square roots of minus one.  Hamilton in his treatment of quaternions proves very early on, that in addition to the infinite number of square roots of minus one listed in the current article on so called modern quaternions, which could be thought of as the geometrically real kind there has to be at least one more. The square roots listed in the current modern article are what he calls the vector kind. But Hamilton proves that there was at least one more imaginary of a scalar nature.  In other words an imaginary number having magnitude but no direction.  The imaginary of plain old ordinary algebra. As he continues he proposes in his later writings to call this new number h.  Then interestingly in each one of his proofs he says states over and over "assuming that h follows the rules of a scalar, that is that it is associative and commutative" as if he is planing to eventually talk about another case.  We know from his private letters that he knew about the idea of a non-associative non-commutative imaginary scalar roots of equations as well.  I don't pretend to understand octonians all that well, but with the proper rules 1,h,i,j,k,hi,hj,hk it would seem would be the basis for an octonian, and with the other set of rules as the basis for the bi-quaternion.  But this was not thought of as 8 dimensions, but rather as the one real scalar, the three geometrically real vectors, then h, the indicator of geometric impossibility.  I don't see how this can be left out of any credible article on the subject of quaternions, unless of course, you invent this artificial entity called a modern quaternion and force it to be based on the misguided drivel of misinformed writers, who you elevate based on some very questionable time based criteria.  If you want to have a quick look an important demonstration is in 

So this might be a little to technical for an administrator reading this, but by creating these two artificial new entities, we essentially block, or at least create an method for blocking out Hamilton's and most of the other more credible authors on the subject from the very entity that they created.

I was frankly shocked, by the book I read written in 1995 on quaternions quantum mechanics. I only got to look at a little bit of it, before they started wanting me to pay $200 dollars for it. The guy might have been smart and had interesting things to say, but it sounded to me that he just started out with the boughham bridge law, and invented his own new mathematical entity, and completely ignored a lot of things that Hamilton had proved years before. It sounded to me like the poor guy had never really read a worthwhile book on the subject. It sounded like a lot of what he was writing about was based on his misconceptions from what he had learned about bi-scalars, (complex numbers).

Modern Quaternions don't really have very much consistency at all that I can see. More like different authors are just making things up as they go along. Another example of this is the sight ranked just below the wiki site on quaternions on google, written by this guy who is attempting to write all the laws of physics in terms of quaternions. But his quaternions are not like anybody elses, just a bunch of symbols and names that he basically made up. I am not really sure that this so called modern notation and terminology being proposed is enough to really discuss the subject with intelligence. It is getting better, some classical ideas are starting to slip into the article, like now at least we explain that a quaternion has a scalar part and a real part, which was not explained very well when we started. When I first came here, there were 10 different quaternion products, now we at least have a Hamilton product.

Another thing, a Quaternion is defined as the ration of two vectors. If you don't believe me, ask Hamilton, and Tate, and Jolly, and Hardy. If division isn't defined as is the contention of the laughable article on modern quaternions contends, how can you define a quaternion??????????

What the article should probably say is that some crack pot, who never really read a real book on quaternions, put a chapter in the back of his book, that used the word quaternions, but didn't really contain any real theory of quaternions, and didn't even bother to define division, because that would force them to admit that the rest of the book could be proven to be absurdity by a full exposition of Hamilton's ideas, of course that is just a guess because the whole article is with out inline sources.

It doesn't really matter if you keep the article or not, I am not going to work on it any more, and chances are that no one else is willing to actually expend any effort on actually reading what these now ghettoized authors have to say, people are now deleting whole large blocks of text out of the article with out discussion rendering the article logically incoherent. Most of the links to the external sources are now broken, very possible because people found the subject interesting enough and followed the links enough that cornell us down. I can't really be sure of that.

Looks to me like the same mentality that is seeking to delete the article, is just going to delete it one line at a time, if we keep it, or turn it into gibberish, unless someone puts in the effort to baby sit it which I am no longer willing to do.

Look what happened to the history article, I thought that it was improper to delete properly referenced material? And also a nice move delinking it from the main article so no body can find it.

So I am tired of typing right now, I don't really think anybody is going to change their minds based on this discussion.

Do I at least get my three reverts a day on this article?

I thought consensus meant we talk it over and come to a solution every one can agree to, democracy doesn't really work all that well when there are three or four wolves and one sheep voting on what we are going to have for dinner.

Whats next, are we going to have modern 5 and classical 5 and claim that the number five somehow changes based on what century it is in as quaternions apparently do?
 * No, you do not get three reverts a day. The three-revert rule limits edit warring. It does not entitle users to revert a page three times each day, nor does it endorse reverting as an editing technique.
 * Whether Hamilton's quaternions are "the same" as the modern objects of the same name is a metaphysical question; we cannot discuss it in article space unless a secondary source has used quaternions as an example in the long wars between Hilbertians and constructivists - which may well have happened. There is little profit and no likelihood of settlement outside article space.
 * Certainly, however, they follow the same laws of addition and multiplication; there is therefore a series of isomorphisms between the two. (I say series, because Hamilton's extra root of -1 should, if followed out, yield the tensor product (in the modern sense) of the quaternions and the complexes - a consistent algebra, but not a deeply interesting one: it has zero divisors, like 1+hi; it is not the octonions, because the squares of hi, hj, and hk are +1.)
 * If the expression (hi)(hi) is considered, as long as you allow h to jump over i to get to the other h, like an ordinary scalar you are correct, you get positive one, a case that Hamilton states in proof sheet after proof sheet, but remember him and Graves were talking about these stranger rules were things were both anti-commute and anti-associate. The key part of Hamilton's work, if you include private letters, is the number 8, where I think it must constantly be born in mind that the imaginary scalar is not some mysterious new dimension but rather an indicator of geometric impossibility.  But while I think this is a good thing to think about the question remains which I will ad at the end of the page.Hobojaks (talk) 05:16, 7 March 2009 (UTC)
 * My opinion of the philosphical question, for what it is worth, is that objects identical up to isomorphism are the same for practical purposes, but that it doesn't really matter. I therefore hold that Hamilton used a different notation in describing the same object. Septentrionalis PMAnderson 01:31, 7 March 2009 (UTC)
 * Hence, a quaternion should be by definition the quotient of two vectors????
 * As a Hilbertian, I define a quaternion as an element of a four-dimensional vector space over the reals which has a product yielding a division algebra. Hamilton's construction (without h) will yield one of these, and it will not be difficult to show that all of them are isomorphic.
 * The "crackpots" you are decrying include G.H. Hardy, John H. Conway and Lord Kelvin. I would be the last to deny that they are all a touch eccentric, but they all know more mathematics than most Wikipedians, including myself. Septentrionalis PMAnderson 01:20, 7 March 2009 (UTC)
 * No wrong century I am talking about more recent books on the subject, some of them use the word quaternion in ways that I don't think Hamilton would even recognize as being remotely related to the entity he defined. Many of them starting with the absence of a distinction between a vector and an imaginary scalar, and ending with the absence of the concept of dividing vectors.Hobojaks (talk) 05:16, 7 March 2009 (UTC)

- Why should a main article on quaternions exclude Hamilton's thinking? I thought that this was supposed to be based on so called reputable sources. Why shouldn't Hamilton be the most reputable of these? When other authors make statements that Hamilton proved false, can we really say that the time limit on Hamilton's relentless logic has expired? If you scroll back up the link I made, you will find that the existence of some imaginary non-vector quantity according to Hamilton is a logical consequence of the fact that quaternions obey the distributive property. Maybe algebra lets you make up these strange groups that exclude imaginary scalars, but according to Hamilton geometry does not. -
 * The key point here isThis is an interesting discussion, but why create an article for no purpose other than to Ghettoize Hamilton's thinking outside of a its rightful central place in the main article on quaternions. The way the main article should read if this resolution passes is, This article is about just about any mathematical entity that anybody wants to make up, as long as they lived after 1901, and specifically excludes Hamilton's definitions of another mathematical entity of the same nameHobojaks (talk) 05:16, 7 March 2009 (UTC)

Hobojaks - thank you for explaining in detail your thoughts about the article. You've made it clear that your concern is about what the material means, as compared to what Hamilton, Tait, et al wrote about it. Wikipedia is at is most powerful as an encyclopedia, i.e., a tertiary source, capturing and referencing the "who-said-what-when" and organizing it. This is not always possible, for example in the current article, where we're mostly forced to draw from the original material. Wikipedia here becomes more like a secondary source. That is no problem to me, either, as long as we keep that in mind. As far as separating what quaternions "really mean", whatever that might mean in itself, I believe the material is organized well: The main "quaternion" article is written as a tertiary source, it aggregates and organizes material from other secondary and tertiary sources. It is the topic-entry page for most readers of Wikipedia, who are looking for quaternions. Conversely, the "classical Hamiltonian quaternion" article is placed alongside, but one click removed from, the topic entry page. Only if the reader of the "main" article is interested in how it all started, or has some doubts, or wants to drill to the bottom of it, or doubts the mainstream, or ... you name it: Whenever the reader choses to be interested in it, he or she can drill down to the historical entity. If you personally believe that the modern conception of quaternions is skewed, not because of differences in its definition (which are nil, as you point out), but in differences of its interpretation, then this might become your personal field of research. For Wikipedia, however, this is out of scope for the main "quaternion" article. This is not "mainstreamism", pushing through a majority opinion; to the contrary: Wikipedia allows to separate other agendas main articles, and to place them alongside for the interested reader. To me, that's one of the many things that make Wikipedia so powerful.

In general, I believe the AfD here it mute, as the above discussion clarified that the dispute is about the meaning of the content, not about the content in itself. Thanks, Jens Koeplinger (talk) 15:26, 7 March 2009 (UTC)

In the interest of achieving a consensus can we stipulate that agreeing to the need for a detailed article on the ideas of some particularly important thinkers on the subject of quaternions, does not imply agreeing that their ideas should be entirely excluded from a main article? Also I now believe that those who argue against my contention that the article as presently constituted contains any original research, have argued more eloquently that I have and to achieve a consensus I change my opinion to agree with theirs if we can agree to make this view unanimous. With this concession, I suppose I could make the vote to keep the article unanimous?Hobojaks (talk) 22:36, 7 March 2009 (UTC)


 * Keep What is left of it after being mostly gutted. Assuming every one agrees to the stipulation aboveHobojaks (talk) 06:43, 8 March 2009 (UTC)
 * Keep per above.Biophys (talk) 23:06, 8 March 2009 (UTC)
 * Keep on procedural grounds: anonymous editors are not capable of nominating an article for AfD, see Guide to deletion, since they cannot create new pages. While the same guide says: "You must perform all three stages of the process" (so also create this discussion page) and "If this is the case, consider creating a user account before listing an article on AfD." My conclusion is that the nomination by the anon is not valid. If interpreted as an AfD by the nominator here: PMAnderson voted keep, so that would mean a withdrawal of the AfD. -- Crowsnest (talk) 13:38, 9 March 2009 (UTC)
 * I think anons should be able to nominate, but agree that there is, now, consensus against deletion. Septentrionalis PMAnderson 18:24, 9 March 2009 (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.