Talk:Classical Hamiltonian quaternions

See also:Articles_for_deletion/Tensor_of_a_quaternion

See also:Talk:The_vector_of_a_quaternion

Tone
Statements such as Here is where it gets interesting. need to be removed, per WP:STYLE and WP:NPOV (not to mention the whole article needs sourcing per WP:V) Marasmusine (talk) 17:18, 26 January 2008 (UTC)

I agree it has been removed. Thank you so much for looking at this new page and commenting so quickly. —Preceding unsigned comment added by Hobojaks (talk • contribs) 17:33, 26 January 2008 (UTC)

Original when I created this page
Hello and welcome to Classical Hamiltonian Quaternions.

This page began because the historical section was growing faster than the modern section, and I feared that soon a single section, 10.1 of that page, would contain more chapter headings than the rest of the entire page combined.

Thats not fair to modern quaternions. They are a living breathing growing mathmatical entity, which is constantly finding new uses for itself.

This page is not about that, it is about the quaternions of the 19th century. I suggest that sources cited would be more interesting if they were actually from that era.

The story of 19th century quaternions ends in 1901, which interestingly was the date of the publishing of Gibb's book vector analysis.

A 21st century reader reading vector analysis,  would find much of the notation very familar. But go back any farther and things are very different. The words mean something different than the do today.

Of particular importance, the words vector and tensor meant something different in the quaternion system.

"quaternion products" is also a 20th and 21st century idea.

So well lets get started. I am very much suprised that this material is not on  wikipedia already in this format.

Hobojaks (talk) 17:30, 26 January 2008 (UTC) 17:30, 26 January 2008 (UTC)Hobojaks (talk)

Scalar or scaler
The common modern spelling is scalar, but scaler is used quite often in the article. I will bulk correct this on my next pass, but I wanted to make sure there was no subtle distinction between the two.

While I suggest not worrying too much about technical aspects (spelling, detailed grammar, wiki tags), the article appears dangerously WP:OR, at least partially due to writing style. I suggest concentrating on fixing tone issues which have produced WP:V unverifiable claims, and the secondly fixing the potentially verifiable statements for which you have provided no WP:RS reliable source.

I'll work on correcting the technical aspects so the article appears better at first glance. I've already taken care of the technical problem that was preventing headers from working correctly, now there are just the spelling errors and wiki links, I think. JackSchmidt (talk) 18:04, 26 January 2008 (UTC)

Your right it is a typo.

Have a look at section VIII

I believe it to be the first occurence of the word scalar. http://historical.library.cornell.edu/cgi-bin/cul.math/docviewer?did=05230001&seq=78&frames=0&view=100

Hamilton had been lecturing and exchanging letters with fellow thinkers of his day on the subject of quaternions since his discovery of them in 1843.

Lectures on Quaternions however is his first published work.

Am I misinformed, my conception of the past is that Hamilton is at the very least the leader in a joint effort in the 19th century to develope quaternions.

You get the feeling from reading his lectures that his students, all of them very high level  university math students, have never even been exposed to the word vector used with the precise mathmatical definition that he gives it.

Hamilton called a radius vector a Vectum, or I don't  speak latin, like his students obviously did. —Preceding unsigned comment added by Hobojaks (talk • contribs) 18:34, 26 January 2008 (UTC)

Quadrential versor or quadrantal versor
Two similar spellings, apparently used interchangeably. Which single one should be used, and should the other be mentioned as an alternate spelling or is it just a typo? JackSchmidt (talk) 18:11, 26 January 2008 (UTC)


 * quadrantal
 * http://historical.library.cornell.edu/cgi-bin/cul.math/docviewer?did=05230001&seq=79&frames=0&view=100
 * Hobojaks (talk) 18:40, 26 January 2008 (UTC)


 * I fixed both scaler and quadrential.
 * I would suggest just working on the OR problems paragraph by paragraph. Even ones that are "pure speculation and have no business on wikipedia" might be just a few word changes away from a "well sourced interesting statement demonstrating the utility and reliability of wikipedia".  Most of the ones I have marked are likely to be in this form.  Instead of claiming to know the inner thoughts, motivations, and emotions of Hamilton, just describe his observable actions.  If you do want to get more heavily into the inner workings of Hamilton the man, then use not only his lectures but his letters.  Remember too that wikipedia is not for original WP:SYNTH synthesis of material, which is almost unavoidable when *only* referring to primary sources (like Hamilton's own 19th century writings).  Instead, also use secondary sources written by historians who already make the claims that you want to make yourself.  This article has a lot of potential, and its problems are almost entirely due to being new to wikipedia procedures -- that is, they are all easily fixed, but it may take a little time. JackSchmidt (talk) 19:03, 26 January 2008 (UTC)

I took the liberty of copying and paisting the two last sections of this article into the new history of quaternions article. To be honest I am more interested in working on an article about classical quaternian notation than cronicaling the history.

I think that it should be left to the historical article to demonstrate the enormous influence Hamilton had over classical quaternion notation. So in my most recent edit I have removed the names of persons, and left only their ideas. If people want to who and when, ideas came about, they should read it in a history article. If they want to know about a historical notation, then this is the place they should come.

Thanks for the encouragement. I plan to work hard to document this article to show that I am not making up some new notation here, but rather cataloging some rather interesting 19th century information.

Hobojaks (talk) 01:55, 28 January 2008 (UTC)

Does this belong some place else
I moved a lot of text into history of quaternions article. I don't think that it most of it fits in to an article about history rather than an article about a historical notation.

I first suggested that this be done in this talk page, and then did it some time  later  when there were no objections.

Hobojaks (talk) 01:59, 28 January 2008 (UTC)

Removed reference to radius vector.
Before Hamilton representing a point in Cartesian Space as a radius vector did not exist yet.

This sentence was poorly written and did not contribute much to the article which is supposed to be about the vector idea of classical quaternions.

I hope that no one objects to this little edit. I would be happy to put into the article someplace if some could verify it. But maybe not in this spot especially now that some new text with direct verifiable quotes have been added.

Historical division from quaternion page arguement

At one time much of the material on classical quaternion notation appeared in the history section of the main article on quaternions. Below is an old argument which was agreed to by everyone at the time that new sections on the in depth history of quaternions as well as this current article on classical quaternion notation before 1900

Original argument for creation of classical notation article
There are two different issues.

The first is what were classical quaternions.

It would explain classical notation, classic structure.

The second issue is who and when and why.

Who and when  would be about names of people and events and dates in the history of quaternions.

Inside of who and when should go an in depth history longer than the one offered as the brief history on the main quaternion page for those interested in more information in this long and facinating subject.

How classical quaternion calculus differed from the early modern forms of vector analysis that replaced them as far as main stream use around the turn of the century, would also belong in an in depth history section.

Also unlike classical quaternion notation, now of interest to those attempting to read and understand old text books, the history of quaternions has gone on into the 20th and 21st centuries where ideas about quaternions are expressed by game developers in the latest programing languages.

So are there any objections to me doing a little more work on dividing this article (main article on quaternions including overly long history section) into two parts?

Right now it is about two different things?

Hobojaks (talk) 05:37, 27 January 2008 (UTC)

Classical hamilton quaternions now has more than a dozen citations
I feel that it is now very possible that there exist sections within this article that can no longer be considered original research but have plenty of references.

I agree that there are sections within the article that still have this problem and suggest that these be marked individually instead of the entire article.

I have marked two of them which continue to be particulary problematic.

The plauge of modern notation
Friends the plauge of modern vector notation has snuck into this article.

Where I had written A "cross" B someone put A X B to mean the modern cross product.

We need some way to distinguish between the modern cross product and the classical quaternion product.

May I suggest that when ever i, j, and k are modern and not classical that in this article they be shown in a different color, perhaps read. —Preceding unsigned comment added by Hobojaks (talk • contribs) 06:06, 28 January 2008 (UTC)

Links to page scans of classical texts all broken?
I was just looking at the references and the links to the page scans of the classical texts seem to all be broken, and only lead to the text and not the indivevidual pages.

A sadly lot of work will be needed to reconstruct these references. —Preceding unsigned comment added by Hobojaks (talk • contribs) 07:10, 18 July 2008 (UTC)

New section on right vectors.
I have added a new section about right vectors.

I feel that this new section makes the section that I wrote earlier contrasting quaternion notation with the modern notation of vector analysis redundant and was contemplating either moving it or deleting it altogether.

What I like about my new method, is that it takes care of the problem that I was having in early versions of this article with mixing old and new notation. Hopefully most of the readers of this article will be understand that the scaler product and dot product mean the same thing in modern use. The same can be said for the vector product, or cross product.

At least wikipedia thinks so, because when I link vector and scaler product which were terms more popular at the turn of the century they seem to link right up with the correct mathmatical concepts.

Yet before I go and delete a large section of text I thought it might be good to get other ideas. The other option is to move that text to the history section. —Preceding unsigned comment added by Hobojaks (talk • contribs) 21:07, 18 July 2008 (UTC)
 * Don't you mean "right versor" instead of "right vector" ? The versor concept was important in the classical quaternion theory, and it was the 90 degree arc versors that were used to produce the spatial vector subspace.Rgdboer (talk) 23:48, 18 July 2008 (UTC)

I agree that I was mistaken about the use of the term right vector.

What I was looking for was right quaternion. Or vector of a quaternion, but I searched and hamilton never used right quaternion

Hobojaks (talk) 06:31, 20 July 2008 (UTC)

Recent blanking of large section of text?
Hi and thanks for contributing to classical Hamiltonian quaternions.

I notice that someone recently blanked a fairly large section of text.

I was wondering if that person found this article as a possible side effect of the current mass hysteria going on over in the article on the history of quaternions article.

Actually if you noticed that section 6 of the article really does not belong in the article I really have to agree with you, however there is a small problem with this. As I see it we really don't have a good comprehensive history article. If we had one, and it included comprehensive coverage of how terminology has changed with time, and even why, then an article on classical quaternion notation would not have the burden for example of explaining that when we say tensor, we mean something different from what this term means in the 20th century.

The small section of historical notes currently in the article I feel are essential for the understanding of any reader seriously considering picking up a book on quaternions from the 19th century quaternions. I agree that the current text is somewhat problematic because it does not cite any secondary sources.

Never the less I am convinced that the basic breakdown of points of view in the 19th century on the subject is verifiable and correct. Pick up any book from that period, and see what I mean if this fact is in question. The language used is often amusing and most colorful, those guys thought it was either quaternions or Gibb's system of vector analysis but not both.

I think the mass hysteria going on in the history article right now, is a dispute about events that started to take place after 1901, and so, since the scope of this article ends in 1901, the relationship between 19th century quaternions and 20th century developments in special and general relativity, as well as quantum mechanics are not relevant. Sorry, this article is about 19th century quaternions, and none of those ideas existed in their current form yet.

I would suggest that we wait to do to much changing of section 6 of this article until the dust settles. And then work on moving some of the essential ideas, into the history article. After all an article devoted exclusively to 19 century ideas, shouldn't really need to explain 20th century vocabulary, and how it is different from 19th century notation. But it does need to be explained, so if we can agree that this section exists for now, as a result of defects in other articles. Hobojaks (talk) 00:40, 4 March 2009 (UTC)
 * The possessive of Josiah Willard Gibbs is Gibbs's.
 * Similarly, Hobojaks should find one spelling for Ferdinand Georg Frobenius, preferably the correct one, and stick to it.

The removed material is, in its entirety:


 * ''A quaternion positive algebra positive point of view sees both algebra and quaternions as useful. Few if any took this view in the 19 century.


 * ''An important variant on this last point of view is the quaternion positive algebra positive but impossible view. This view did not exist in the 19th century, but it goes like this:


 * ''Just because a space is physically impossible and does not exist, does not imply that it is not useful. In order to solve a system of linear equations in five unknowns the notion of an impossible space consisting of five time dimensions is very useful indeed.  Just because Newtonian mechanics is physically impossible because it does not work if you go to fast does not mean that it is not very useful.


 * ''Nobody in the 19th century had ever seen anything solid go fast. When in the 19th century Frobenius proved that Euclidean space was impossible, and when in the 19th century Maxwell used the math that Hamilton invented and figured out that light always traveled at the speed of light, which also proved that Euclidean space was impossible, the meaning of these things was incomprehensible.


 * ''To the 19 century mind, Euclidean space and the Newtonian physics based on it were both useful and possible. More than possible 19 century thinkers thought Euclidean space was something real. They even called it real space.  Real space is an idea so useful that the idea it was also impossible was inconceivable to the 19th century mind.

This is entirely unsourced; it is also a polemical expression of opinion. It is unacceptable on either ground. Septentrionalis PMAnderson 01:09, 5 March 2009 (UTC)

More unsourced
Similarly, ''Quaternion negative nomenclatures often expropriate terms from classical quaternion nomenclature and redefine them to a point that it makes very difficult to understand classical texts. '' is both jargon and POV. Quaternion negative is a nonce-term; expropriate is a Marxist polemical term, which we should use only in summarizing texts which actually use it.

It may be removed on either ground, and will be removed on both. WP is not the place for essays on the oppressed virtue of anything, let alone quaternions. Septentrionalis PMAnderson 01:16, 5 March 2009 (UTC)

Sum of tensors

 * The product of two tensors is another tensor, the sum of two tensors is another tensor, and the quotient of two other tensors is another tensor.

Does Hamilton actually ever add tensors for quaternions which are not multiples of each other? The sum of tensors for arbitrary quaternions is not the tensor of the sum, although it obeys the triangle inequality.

Here is an example http://books.google.com/books?id=TCwPAAAAIAAJ&dq=lectures+on+quaternions&printsec=frontcover&source=bl&ots=bOy1BhGbhA&sig=frI4KxlT4PociUTljrUl3iT_0Xw&hl=en&ei=kRCySbnDCZ3gsAPC5qCPAQ&sa=X&oi=book_result&resnum=2&ct=result#PRA1-PA675,M1

Scroll down to the middle of the page, technically here tensors are being subtracted, but examples of them being added exist as well. In Lectures on quaternions Hamilton says tensors can be better thought of as unsigned numbers, but then in other places it is less clear when he means just a positive number. Later on, when he gets into bi-quaternions, they have bi-scalar coefficients. Hence the tensor of a bi-quaternion can actually can actually be a 'negative tensor'. Or even stranger a bi-quaternion can have a tensor of zero even when not all the individual coefficients are zero. In this case its inverse is infinite, or at least I think I remember reading something along those lines. Also one can find sentences where Hamilton uses the words metric and tensor in the same sentence.Hobojaks (talk) 07:01, 7 March 2009 (UTC)

If he does, it should be explained in more detail; if he doesn't, the clause should be removed. Septentrionalis PMAnderson 15:39, 5 March 2009 (UTC)
 * But the result of the subtraction is not a tensor of any quaternion; instead, it's zero, and the algebra here is simply a condition on the tensors being equal. That's not the same thing; it simply asserts that the tensor of a quaternion is a non-negative number, which is a property of square roots. Septentrionalis PMAnderson 18:49, 7 March 2009 (UTC)


 * I meant to reply to this earlier. Hamilton introduced the term "tensor", as I learned through the current article (yet another key concept he coined). He used it in a somewhat different manner, though. I'm not competent on exactly Hamilton's use of the term, so I might not be of much value here; all I want to ask for is caution. Maybe a direct quotation (e.g. book so-and-so page so-and-so) would help? Just a suggestion. Thanks, Jens Koeplinger (talk) 02:45, 6 March 2009 (UTC)
 * Try absolutely different; the citations of Tait make clear that Hamilton's "tensor" is the "square root of the norm" of a quaternion, and so a one-dimensional quantity. (The "square root of the norm" above is, I think, an exact quotation of Tait; would putting it in quotes help?) Septentrionalis PMAnderson 19:20, 6 March 2009 (UTC)
 * I see ... it appears almost as if Hamilton (or Tait) would attempt to construct an algebra of magnitudes (which would be why the "minus" operation is problematic). The "citation needed" tag is there, that should help getting it clarified. Thanks, Jens Koeplinger (talk) 19:37, 6 March 2009 (UTC)


 * Not that I really care one way or the other, but perhaps your readers would greatly benefit from a clever rewording that would stress the basic concept rather than getting completely lost in Hamilton's annoying over analysis of this subject particularly in his first book Lectures on Quaternions. Perhaps a first step would be to look at the category of the article, it is in the subject of geometry, not algebra.  Now start thinking geometrically not in terms of algebra.  Go find some sand, and draw an arrow in it that starts at the start point, and ends at the end point, congratulations you have just created a geometrically real vector!  Here is the critical concept, an act of tension makes the arrow longer or shorter, but critically the arrow while longer or shorter is still going in the same direction.  So the central concept, that you would want to get across to some poor confused reader, stumbling across the article is stretching, but not changing direction.  I would suggest that part of the difficulty your are having, is one that I encountered, when I first addressed the subject, completely unaided by the then current content of wikipedia, is that in order to learn about Hamilton's ideas about quaternions, you have to first unlearn what you already know.


 * Lets say you take a rubber band, and stretch it till it is twice as long, but keep the rubber band still having the same physical alignment. Congratulations, you have just multiplied the rubber band by a tensor with a value of two.  Lets say you discovered another tensor, and it has the value of five. You can add two and five, and you get another tensor equal to 7.  This is pretty much common knowledge to any child in kindergarten who can count to 10.  With the operation of subtraction all bets are off.  Five minus two is three, which is still a tensor.  However three minus five, is not a tensor, but a completely different kind of number, called a scalar.  A scalar can be either positive or negative but a tensor can't.  A negative scalar reverses the direction of a vector. I don't mean to suggest that anybody reading this is ignorant of these basic mathematical ideas.  Hamilton assumes a level of mathematical sophistication just a little above grade school, he is giving a lecture to university students.  I would suggest that there is some clever way to word this concept so as to skirt around any potential OR objections.


 * On the other hand, your definition of a scalar is in error. Start thinking of a vector in the terms that Hamilton thought of it in, as vection.  Like starting at your house, and going to the store.  Vectors are real, just a different kind of real called geometrically real.  "There is nothing imaginary about them."  That is a direct quote from Hamilton I believe.  By the way, I think you create an OR problem by saying that the word tensor in the context of quaternion theory is different from a tensor in some other theory.  Better to just say, this section is about tensors in the context of classical Hamiltonain Quaternion nomenclature, for other meanings of the word tensor....  and then send a link, because there are a couple other meanings of the word tensor.


 * Also at one point this article used to contain some content, regarding Tait's use of tensors, to represent stresses and strain's. Hence, Tait can use quaternion notation, to construct what we now call a stress tensor, which can have torque and strain in more than one direction.  So I would say, instead of leaving yourselves open for the next round of massive deletions, by including anything that could possible be considered, OR, just reclaim Hamilton's original context.  Believe it or not, probably a lot of people reading this article will be high school kids that have never heard of a tensor calculus anyway.


 * I don't agree that you need a source to show that 2 + 3 = 5. I would argue that this is pretty much common knowledge. Anybody, who does not have a doctorate in math, can pretty much figure that out on their own.  You are doing a great job, but at the same time, making things just a little more complicated than they really need to be.
 * The claim, however, that the sum of tensors is a tensor is either vacuous or suggests that 2i and 3j sum to something with a tensor of 5 - which is manifestly false. I have seen no evidence that Hamilton or Tait said anthing so silly, and suggest that we not encourage this misunderstanding. Septentrionalis PMAnderson 23:22, 8 March 2009 (UTC)


 * Please read a little more of one of the basic texts on quaternions, and please stop introducing gross factual errors into the text. I do like your edit of the chapter headings.  —Preceding unsigned comment added by 130.86.71.127 (talk) 22:52, 9 March 2009 (UTC)

Proposed AfD
Per the decision here that the "History of quaternions" article should be replaced with a redirect, this article should clearly also redirect to the main quaternion article. 72.95.229.48 (talk) 01:30, 5 March 2009 (UTC)


 * (1) That was not the decision there. The decision was keep.
 * (2) This is a different article, which has not been considered at AfD. An article specifically discussing the language used to describe quaternions in the 19th century has some significant value, IMO. Jheald (talk) 02:26, 5 March 2009 (UTC)
 * I tend to agree. Confined to Hamilton's notation, this would be a useful article; I hope it's accurate. Septentrionalis PMAnderson 02:58, 5 March 2009 (UTC)
 * Agreed, too - editing for style and sourcing is ongoing, as I see. This is the right place for the material. Thanks, Jens Koeplinger (talk) 03:09, 5 March 2009 (UTC)

Use English

 * ''At a basic level it is alright to think a tensor as just a positive number.<:ref>Hardy 1881 pg. 5 Mathematically it functions exactly like a positive number.  If you add two tensors you get another tensor, just like when you add two positive numbers.  The same is generally true with multiplication and division.  On a more technical level Hamilton's classical definition of a tensor is of a signless number.  In other words a number with out a plus or minus sign in front of it.  5 is an example of a tensor and so is 2.  A plus sign is an operator, and you can put an operator inbetween two tensors and perform the operation of addition producing a new tensor.  Zero is the problem child of the tensors, if you divide by zero the answer is infinite.  On the other hand if you add zero to another tenser you get the same number you had before.  For example 0 + 2 = 2.  According to Hamilton's notation it is OK to just leave off the zero, write in shorthand +2 = 2.  When two tensors are subtracted the answer may not be a positive number, and hence not a tensor, but a new and different kind of number called a scalar. For example 2 - 5 = -3.  Minus two is not a tensor.  Actually -3 like any negative number can be written as 0 - 3.  Hamilton asks you to agree that there is really no need to write a zero in front of the three, with the understanding that -3 is really just short hand for 0 - 3. In the classical treatment of the subject it is skipping ahead to say that

This is flatly unacceptable,. First of all, it isn't coherent English; it's a mass of sentence fragments, filled with misspellings; Hamilton's word is the Latin tensor, not tenser.

It is unsourced, and attributes to Hamilton intensions he never had: Hamilton asks you to agree that there is really no need to write a zero in front of the three is personification more suitable to a child's book of knowledge than an encyclopedia.

5 is an example of a tensor is misleading to the point of vacuity; 5 is the tensor of 5i, but that's not the same thing. Septentrionalis PMAnderson 14:51, 10 March 2009 (UTC)
 * I quote from Elements of Quaternions, p. 169: And although, if we attended merely to lengths, we might be led to say that the tensor of a quaternion was a signless number* expressive of a geometrical ratio of magnitudes, yet when the recent construction (fig. 48) is adopted, we see, by either of the two resulting expressions (188) for Tq, that there is a propriety in treating this tensor as a positive scalar, as we have lately done, and propose systematically to do.
 * A tensor is a function from the quaternions to the reals (or scalars), not a type of magnitude of its own. Septentrionalis PMAnderson 15:58, 10 March 2009 (UTC)


 * It will be hard for you to convince many people to do a lot of work on content that gets deleted the next day. Have you read the first few chapters of lectures on quaternions?  That would help to resolve this issue.  That the methodology of presentation is the exact approach Hamilton took.  Read more, source more delete less.  —Preceding unsigned comment added by 130.86.71.98 (talk) 19:02, 10 March 2009 (UTC)
 * This edit has two problems, besides the uncivil edit summary: it doesn't support the text, doubtless because A. S. Hardy regarded the assertion that square roots of positive quantitities are positive as obvious; the text requires no support, because it isn't controversial among the numerate. Septentrionalis PMAnderson 22:36, 10 March 2009 (UTC)

Failed verification
Hamilton did not, as now claimed, define a tensor to be "a signless number"; what he actually says is: This is clear enough; a tensor is a property (or function) of a quaternion; 5 is not a "tensor" by inself, unrelated to any quaternion. What Hamilton does here is to extend the meaning of "tensor" so that one may speak of the tensor of a quaternion with norm less than 1 (and greater than zero), which diminish the length of the vector. Here Hamilton does speak of "signless number" as the strictly proper range of the operation of taking the tensor; elsewhere, as quoted above, he intends, and declares his positive practice, to have the range be the "positive scalars". Septentrionalis PMAnderson 16:44, 11 March 2009 (UTC)
 * it seems convenient to enlarge by definition the signification of the new word tensor, so as to render it capable of including also those other cases in which we operate on a line by diminishing instead of increasing its length ; and generally by altering that length in any definite ratio. We shall thus (as was hinted at the end of the article in question) have fractional and even incommensurable tensors, which will simply be numerical multipliers, and will all be positive or (to speak more properly) SignLess Numbers, that is, unclothed with the algebraical signs of positive and negative ; because, in the operation here considered, we abstract from the directions (as well as from the situations) of the lines which are compared or operated on.


 * Thank you for your contribution. You have found something really important here that I missed.  I read Cayley's article before, but never noticed that he changed, or shall I say mangled, the definition of a quaternion around pretty drastically. I am moving this discussion over to the talk page of the main article for a while, and maybe that will help to resolve some of the issues.


 * This is an important discovery that belongs in the main article. I know it is frustrating when you get to a portion of an article that is so technical that changing a few words around can destroy some very important ideas of Hamilton's that really need to be on Wikipedia.


 * Another thing that you might have discovered, or caused me to discover, is that I have made a mistake in not putting Hamilton's definitions in the correct order. Vector must be defined before tensor.  So you are contributing, but please be careful because there are some pretty complicated ideas in this article, and you have to read a long time before you edit.


 * If you would like to arrange the three citations in the first sentence of the section on tensors more to your liking, or reword the first sentence with out changing its meaning, that is helpful. You have been doing some really great clean up work in the article.  But please don't go rummaging around in  an article looking for sentences that don't have a citation and deleting them like you did a couple of times.


 * You have deleted a lot of content from the article that I thought had some potential for improvement and could have become part of a good article. I let that go because I always try to make people feel welcome, but maybe that gave you the idea that if you could not delete the entire article as you recently proposed to do, that you could delete it a section or two at a time, and then a sentence or two at a time.  That is what they basically did with the history article when they lost that vote, and remember you voted no on that one as well.


 * So yes, to be blunt, I am watching some of your activities closely, and I am sorry that you feel that the documentation of my edits may somehow be uncivil, however these comments are not directed at you, I am not a snitch and not the type of guy that is going to run crying to an administrator, to try to manipulate content with brute force, when discussion is the best way to resolve things. But the reason for me edits does need to be documented, and if things continue the way they are eventually an administrator is going to get involved.


 * I notice that someone has now proposed the deletion of another article in this content area, and I think I know who. That means that administrators will be following the links to this article and looking at its edit history to understand the potential motives for suggesting yet another article for in this case speedy deletion.


 * So essentially you are proposing to delete entire articles, and then helpfully editing them, when your proposal fails. This type of behavior makes me suspicious of your motives here.Hobojaks (talk) 05:01, 12 March 2009 (UTC)

Hmm - a page on "classical Hamiltonian quaternions" should be written closely to the source, IMHO, e.g.: "In (ref) Hamilton says '(this-and-that)'. His notation is (this-and-that, more-stuff) In comparison, modern understanding (brief summary and link to primary quaternion article)." I don't see that wording in the current page, so there are definitely problems. If we make important discoveries here, then I suggest to write a paper about it and advertise for interest once published. If there is no interest received, then it shouldn't be here. On the main "quaternion" page, the amount of interest should somewhat reflect its general importance (i.e. a good amount of notability). On a historical or highly specialized page, a few peer-reviewed papers might do (just as an example). All of this is has nothing to do with administrators or any forms of "power" here in Wikipedia; it's simply trying to keep it what it should be: An encyclopedia. -- I like the material that is on the page today, and all the references; and I also agree on the tags that are currently placed on top (as rude as they may sound). I might try a rewrite sometime later this year, but it'll be July or August at the earliest. Until then, have a beer or two, maybe even begin writing an paper on your own? Use LyX as editor if you want print-quality LaTeX output; just a suggestion. Cheers, Jens Koeplinger (talk) 14:45, 15 March 2009 (UTC)

Section on tensors greatly reduced
I give up, so the section on tensors is greatly reduced, to the disadvantage of readers of the subject, due to the apparent need to source every sentence in a starter article with several citations. I am moving back to the four operators, which might be less controversial.

Maybe this will allow discussion in this article to at least become more civil and we can move the more controversial parts to other areas. Nobody very much really seems to care about quaternion notation, unless it comes with analysis, which is why I have now undertaken to understand the cryptic words on Hamilton on the subject of the relationship between addition and subtraction and multiplication and division and analysis and synthesis. Thus enlightened, as the the relation between various types of vection, to claim that an act of revection or following a revector back to the starting point is technically analysis and not synthesis, with build in hyperlinks, to the proper terms, that will prove my case.

Till then, I think it might be best to remove to other articles the more advanced topics on the subject of the tensor of a quaternion, to the main article which no one will care about, the history article where it will probably be ignored, and the main article, where many experts will be needed to puzzle over the fact that Cayley believed that the tensor was the square root of the norm, while that article which cites no sources claims that the tensor is the norm.

Those seeking to destroy content on the subject of Hamilton's thinking have sown the wind, and must now reap the whirl wind. Hobojaks (talk) 02:25, 13 March 2009 (UTC)

I give up now, like I said I would. No more troll food.
(1) Don't feed trolls.

(2) Hey what happened to the tag about this page being nominated for deletion? I think that that tag is very important, and people need to read that discussion, please put that back or I am complaining to an administrator.

(3) I still agree with everybody typing on this discussion that this whole page should be blanked and we should start over.

(4) Thanks for vandalizing my user page, I now have multiple accounts, and keep stuff I am working on that I think should be part of wikipedia on a user page that only watches and does not type so you will never be able to pull that one again.

(5) This content I feel is more useful on a user's personal page as tool for creating content for other pages. That way the user will have all those links that he can explore, all those definitions of esoteric terms, hyperlinked together, that he can use as a tool, for researching good content that can go on other pages. That was part of the keep agreement that we all agreed to that I would get to have a user page that I could use, remember.

(6) A state of war exists within the article space in Wikipedia, I didn't start it, but we all need to agree that it exists. There are people that want to keep Hamilton's ideas off Wikipedia, and want to distort the history of human thought so that it excludes his thinking in favor of their own so called modern perspective. If reading books written by Hamilton somehow automatically constitutes original research then letting people with a hostile agenda have access to that research is a sign of weakness, and giving aid and comfort to the enemy. If they want to dispute facts, they can start by reading and making their own list of difficult terms from scratch like I did.

(7) Remember I wanted to delete this page, and move the content into the main article, no one else works on it, and it is to much work for me to defend it against vandalism. Enough of its content has already been deleted to make it unintelligible to any reader that happens across it. We also agreed that in order achieve a agreement that Hamilton's work can't be completely excluded from a main page on quaternions. Any content I add from now on is going on the main page, and we can fight about it there. Its going on one carefully spell checked sentence at a time, with five or six citations.

(8) I agree, with what ever the trolls say, I am going to start blanking this page three times a day, and at least one troll will be blanking it three more. If someone else wants to develop some content, I can agree to leave it up what they develop, if it is factual. I will have some pretty good tools on my user page to dispute that if it is not. But I think that no one really cares but me.

(9) If someone wants to start over again this summer that is great, maybe I can help, but I am tired now, the trolls have one I give up.


 * Comment: The AFD tag was removed since the article was kept at Articles for deletion/Classical Hamiltonian quaternions. What trolls are harming the page?  I can't see any recent issues?  MBisanz  talk 19:53, 16 March 2009 (UTC)


 * Please put that tag back, along with a tag indicating that this page has been vandalized  The problem child is Septentrionalis PMAnderson who is currently deleting the tensor of a quaternion sub article.  He is trying to chip away at Hamilton's ideas one sentence, or small section at at time. This breaks the truce agreement.Hamiltons wrath (talk) 01:34, 17 March 2009 (UTC)


 * Hi - I've got very little time now, sorry if I sound short. Couldn't leave a note this morning because some admins blocked the outgoing IP address from one of our work proxies. "Anonymous proxy" it says, though I don't know what's anonymous about me editing, with user name and password ... anyway - please don't do drastic changes to the page. When I expressed my interest in a "rewrite" then I meant a purely editorial change (wording, quotations, etc) and no change to the actual material. I think you would care less if I change a sentence from "A versor is a ..." into "Hamilton introduces a 'Versor' (ref) as ...". Unless I'm mistaken, you would see such an update as un-essential wording change, and that's what I meant. No change to actual material, just writing it in the style of an encyclopedia. Gotta go. Thanks, Jens Koeplinger (talk) 22:54, 16 March 2009 (UTC)


 * Your contributions are always productive and welcome Koeplinger. You are part of the solution, not the problem.  However your work belongs in a copy of this article on the main page.Hamiltons wrath (talk) 01:41, 17 March 2009 (UTC)

Please. Thanks. Peace. Koeplinger (talk) 01:52, 17 March 2009 (UTC)

What is presently being factually disputed?
Is there still a factual dispute going on? —Preceding unsigned comment added by Homebum (talk • contribs) 16:48, 2 April 2009 (UTC)

Trying to rebuild after desasterious deletion episode.
I have noticed some recent edits to the section about tensors used in the Hamiltonian context.

The particular section is now problematic due to the deletion of massive amounts of text from this article.

(1)There used to be an entire section dedicated to the idea that terms used in a Hamiltonian context are different from those of a modern context. This section came under attack as being OR, but if there is now going to be a move to restore these concepts to the article, we would need to bring back this section.

(2)An entire article on Tensors in the sense of Hamilton's usage was deleted, after much bitter discussion.

The present section being edited, is intended to be about a kind of number called a tensor. There is also an operation called take the tensor of which bears the same name. The three citations to the work of Hamilton, and the secondary sources of his contemporaries support the statement that a tensor is by definition a positive or signless number, please don't move the citations to support the contention that a tensor is the square root of the common norm. That the tensor of a quaterion has the property that it is equal to the square root of the common norm is a property that Hamilton proves, it is neither the definition of the operation of taking the tensor of a quaternion, nor is it the definition of what a tensor is as a numerical quantity.

Also the evolution of terms and notation is an emotional topic better suited to another article, such as the history of quaterions. That the common norm as defined by Hamilton, is different from the norm defined by other writers is a minor point for those serious about learning Hamilton's ideas about quaterions. —Preceding unsigned comment added by Homebum (talk • contribs) 17:26, 11 April 2009 (UTC)


 * I was trying to clarify one small part of the article. Describing the tensor of a quaternion as "positive numerical quantity, or more properly signless, number" without saying how this quantity is related to or can be derived from the quaternion itself is vague and useless. Similarly, describing the versor as "another special type of quaternion with useful properties" is of no help at all to the reader. However, the whole article is now so muddled, bloated and confused that I give up. Gandalf61 (talk) 23:00, 11 April 2009 (UTC)

Contexts of Quaternion Geometry and Linear Algebra - OR ?
The new section (from Contexts of Quaternion Geometry and Linear Algebra down to See also) is unsourced and reads like an OR and POV essay. It overstates the difference between Hamilton's terminology and modern terminology. Hamilton uses the terms "scalar", "vector", "conjugate" and "quaternion" with essentially the same meanings as modern mathematicians. He also introduces some terminology that has not survived in current usage, such as "versor" for what we call a unit vector or unit quaternion. As far as I can see, the only term introduced by Hamilton that has a fundamentally different meaning in modern usage is "tensor", which Hamilton uses to mean what we would today call "norm" or "magnitude". Unless its opinions can be sourced, this section should be removed. Gandalf61 (talk) 17:26, 13 April 2009 (UTC)


 * I don't want you to feel frustrated, I know that there is a lot of work to do here. I agree that this section needs to be totally rewritten, and I think that this might be a great job for you Gandalf61.  It seems to be something that interests you.  This is not a new section but rather an old section of the article.


 * I took the liberty of placing some text you thought important into this section. You might want to start with the section on tensors. Note that according to Hamilton's definition, the operation of taking the tensor of a quaternion, involves by definition taking the tensor of each of the vectors of which the quaternion is a quotient, and then dividing them to obtain the tensor of the quaternion.Homebum (talk) 18:00, 13 April 2009 (UTC)


 * I don't think you read what I wrote. I did not suggest that this section needs to be rewritten; I said it should be removed unless you can provide sources for opinions such as "quaternion geometry and multi linear algebra are two completely different contexts"; "modern quaternion negative nomenclatures tend to use words with negative connotations for classical quaternion concepts"; "some modern thinking uses the word quaternion to refer to some extension of modern algebra that has little in common with the classical quaternion"; and "a quaternion always consists of one time dimension and three space dimensions" (!!).
 * Wonderful the content creation team will get right on it! I don't understand your position, are you saying that you are not willing to help with finding sources?  This would make improvement of this section go much more quickly.


 * Yes, Hamilton initially defines the tensor of a quaternion q as the quotient of the tensors of any two vectors a and b such that qa=b (Lectures on Quaternions para. 90).


 * By jove you have got it! This is an important definition, and the properties of the tensor of a quaternion are also important, yet distinct from the definition.  Sorry if I seem tedious about this, but the more you study Hamilton the more you learn how important it is to pay attention to these seamingly small details.Homebum (talk) 03:18, 14 April 2009 (UTC)

But he later shows that it is equal to sqrt(r2 - s2) where r and s are the scalar and vector parts of q (para. 111) and also equal to sqrt(q*q) (para. 163). This shows that Hamilton's tensor is identical to the modern concept of norm or magnitude, for scalars, vectors and quaternions.


 * Yes which is dutifully included in the proper location, as an important property of tensors, notice however that Hamilton defines the common norm as the square of the tensor, not as the tensor. However these comparisons of notation are really stuff for other articles?Homebum (talk) 03:18, 14 April 2009 (UTC)


 * The whole article is rambing, incoherent and repetitive (for example, you have now repeated the definition of "tensor" in at least four different places). It needs to be much shorter and can be made much clearer. Please stop adding new sections at random. Start out with a top-level logical structure for the article - if you don't have one then I can make some suggestions - and work from that. See Writing better articles.

Gandalf61 (talk) 19:46, 13 April 2009 (UTC)


 * OK I will have a look at the section you suggest, thanks for being so patient and helpful, part of the problem is the somewhat convoluted nature of Hamilton's work, but give it time and we will work it all out.Homebum (talk) 03:18, 14 April 2009 (UTC)


 * Hold on, right now I am working on getting the material from the article vector of a quaternion moved into the single article, as you suggested. Let me get that chore done and we can discuss the other stuff.  Lot of work involved in that already.Homebum (talk) 20:18, 13 April 2009 (UTC)


 * Keep holding on, the questionable work of rolling yet another sub article into the main article is completed but this effort necessitated placing a lot of draft level material into the main article that now needs to be cleaned up, after that is complete I could help with finding the sources you requested.Homebum (talk) 03:07, 14 April 2009 (UTC)

Reverse of normal process
Writing_better_articles

I have been reading this section with amazement. Apparently some articles actually evolve in the exact opposite of the way this article is evolving, by spawning new sub articles. Contrary to this approved trend this article seems to be having its substructure forced back into an increasingly long single article.

I have now completed much of the work of rolling two subsections back into the main article.

This process has been over my objection, and as the article now continues to grow in content I was wondering at what point any of the people proposing to delete substructure might change their minds?

There is a minority element within the wiki-community that has historically had the aim of keeping content on the subject of Hamilton's treatment of quaternions off wikipedia, using just about any pretext to delete content. Hopefully the futility of this tactic will soon occur to them. Homebum (talk) 06:49, 14 April 2009 (UTC)


 * Oh dear. It is always a bad sign when someone has to invoke a conspiracy theory to explain similar concerns raised by multiple editors. Please consider for a moment a simpler explanation, which is that maybe you are wrong . Our aim in Wikipedia is to write encyclopedic articles on notable subjects that are accessible, neutral and reliably sourced. An article that summarises Hamilton's original approach and explains some of his terminology is fine. But there is no need to restrict ourselves to using only his notation, neither do we need to replicate every step of his journey - Hamilton's style was famously prolix and opaque. And unsourced opinion about "negative nomenclatures" and a supposed bias against a geometric treatment is definitely out of place here. Gandalf61 (talk) 09:55, 14 April 2009 (UTC)

I notice that some gross factual errors have been introduced into the article?
Have to get back to this, however if any facts on the subject of quaternions have been eliminated the solution will require reverting all the changes. Robotics lab (talk) 20:36, 14 April 2009 (UTC)

For one thing, the concept of cardinal operators and ordinal operators with some important cited material has been removed, can you please but that back. Addition Subtraction Multiplication and Division are operators of a different sort that the S, T, U, V and K operators.

More than 10k of material has been deleted.

Just spent an Hour fixing recent deletions of critical material
Addition, multiplication, subtraction, and division are all key operations that need to be explained in detail. This the content in this article is of a rough draft starter article, and these sections will be greatly expanded as time permits.

Please stop deleting them, and please stop changing the first paragraph of the article explaining what it is about. The same element that proposed deleting the article is not trying to change what it is about apparently.Homebum (talk) 22:59, 14 April 2009 (UTC)


 * Homebum has reverted my attempts to start improving this article, and has accused me of vandalism. For the record, some of my issues with this article are:


 * 1) The lead - arbitrary editorial comments such as "This article is written exclusively in Hamilton's original notation, using his original definitions of terms" and "It uses only Hamilton as its primary source and reliable secondary sources written on or before 1905" have no place in a Wikipedia article. We are creating an encyclopedia here, not a historical re-enactment. Both the notation and the sources should be those that best explain the subject of the article. Parts of Hamilton's notation will be unfamiliar to the modern reader, and so need to be explained in terms that a modern reader can understand.
 * 2) The length - much too long, partly because there is no coherent structure, partly because of pointless repetition (e.g. Hamilton's usage of the term "tensor" is described in four separate sections, which could be replaced by one much shorter section), and partly due to an inability to focus on the important aspects of the topic.
 * 3) The style - parts of the article have a poorly written essay-like style - which is also a factor in the length of the article. Hamilton had a penchant for inventing strange and complex terminology, and much of his writing is prolix and obscure but there is no need to repeat that style this article. An example - "The vector of a versor is then once again an element of pure distance not associated with time" - huh ??
 * 4) The inappropriate POV - the article seeks to promote Homebum's opinion that modern mathematics takes a "quaternion negative" stance. To do this, it exaggerates the differences between Hamilton's approach to quaternions and the modern approach. There is a legitimate (and much shorter) article to be written summarising Hamilton's geometric approach to quaternions and making it accessible to the modern reader - but this bloated and rambling POV vehicle is not it.


 * Homebum, you clearly seek to own this article, and you do not want to collaborate with other editors. This is contrary to Wikipedia's guiding principles. As the essay Collaboration first says: "In a collaborative environment such as a wiki, contributors who are unable or unwilling to collaborate with others should be politely but firmly excluded from the portions where conflict occurs, or even excluded from the community." I am not interested in arguing endlessly with you. Eventually you will get bored or be banned, and then the article can be usefully re-written. Gandalf61 (talk) 09:44, 15 April 2009 (UTC)


 * Key word is agreed upon editorial distinction used to organize the material. Please go back and read the deletion discussion. There was a minority opinion that the content of this article should be merged merged into the main article.  This is the agreed upon topic of this article.Robotics lab (talk) 01:22, 16 April 2009 (UTC)
 * And getting longer! There is a lot of material to organize here.  I am thinking about a summary style.Robotics lab (talk) 01:22, 16 April 2009 (UTC)
 * Some what of a cheap shot. Remember that you proposed to roll some very raw draft material into an article that was still in a very raw but somewhat more polished state.  Work is proceeding as fast as possible on improvementsRobotics lab (talk) 01:22, 16 April 2009 (UTC) Also an objection to text that no longer exists.
 * This one is already fixed by the way. So you have your way on one out of four topicsRobotics lab (talk) 01:02, 16 April 2009 (UTC)
 * Wow, you seem to have mind reading powers here. You got your way on section six, how about a compromise on the section explaining what the article is about?Robotics lab (talk) 01:22, 16 April 2009 (UTC)
 * Nothing could be farther from the truth. Perhaps you should work to achieve consensus for rolling the contents of this article into the main article, but I really doubt it.  One problem you seem to be having is consistently introducing horrific factual errors into the article with each edit you make.  On the other hand you are improving.  Perhaps if you would like to discuss changes you would like to make before making them instead of the slash and burn and Coercion.Robotics lab (talk)
 * For example you recently deleted the sections on cardinal and ordinal operations. There are a large number of confusing terms regarding these operations that need exposition, including factor, faciend and factum, which are not really hard to understand once they are hyperlinked to but really need to be included in an article on Hamilton's terminology and approach to quaternions.Robotics lab (talk)


 * Not interested in arguing with you or your sockpuppets. But please note that it is very poor Wikiquette to intersperse your responses inside the original message, as it makes it impossible for a third party reader to determine who said what in a thread. This is the second time you have scrambled one of my posts by interspersing responses - please do not do that again. I have collected your responses above into one block with numbered paragraphs, as they should have been in the first place. Gandalf61 (talk) 12:46, 16 April 2009 (UTC)

Reference links for material (for completeness and relevance)
Looks like for now we've got a lot of material loaded into the article. The "cohesion" tag is up top and needs to remain there for a while. For the sake of record keeping, and for my personal sanity, I'd like to point out the following reference versions of material that was merged together. Versions are of the date/time prior to the recent move of material:


 * Classical Hamiltonian quaternions ID=272052451 (20 Feb 2009)
 * Classical Hamiltonian quaternions ID=283900894 (14 April 2009)
 * Tensor of a quaternion ID=280406103 (29 March 2009)
 * The vector of a quaternion ID=277104326 (13 March 2009)

Have a look! nutfarm(talk)
 * Here is another favorite

Those four links capture the entirety of the material for me. Once editing has calmed, this could be used as references to gauge relevance and completeness of the material.

Thanks, Jens Koeplinger (talk) 01:11, 15 April 2009 (UTC)


 * Thanks for the help with these links to early articles! Your work and help is always appreciated.  I am thinking about creating a template, which might help to organize the vast amount of material that Hamilton's work entails.  —Preceding unsigned comment added by Homebum (talk • contribs) 01:40, 15 April 2009 (UTC)

A very cool fact about Hamilton.
Hamilton writes in an early version of hypertext, which makes it really nice, because he provides article numbers in his text to spots where the hyper links should go. Once these links are in place every time you come to a confusing term in a quote you can just click on it to find out what it means, and after you do that, his writing becomes much more understandable.

Right now, to finish up the quote on the definition of a versor, I have discovered that one more spot needs to by hyperlinked to defining what the plane of a quaternion is, but that will have to be work for another day.

Article is really starting to take shape! Good hyper linking of Hamilton's thinking just might help us to preserve what little is left of our collective sanity. —Preceding unsigned comment added by Quaternionist (talk • contribs) 16:43, 15 April 2009 (UTC)

Page now 63k long
I took the liberty of deleting the last section of this article. It was written mostly by a less sophisticated user, and while there are some good ideas in this section, if it is possible that we could re-agree that this article should be devoted exclusively to Hamilton's point of view, which was the consensus when it was agree as a result of the deletion discussion.

According to this plan, we leave comparison with other notation systems, to other articles. We keep the article about the views of Hamilton, using other classical quaternionists as good secondary sources, but leave contrasting this view with other views to articles which take a more general approach to the subject.

Recall in the deletion discussion it was agreed to remove all original research from the article. Contrasting Hamilton's thinking with other thinking, is the source of that problem, and needs to be in other articles. —Preceding unsigned comment added by Robotics lab (talk • contribs) 19:31, 15 April 2009 (UTC)


 * What're those other articles? Can't something more constructive be done than simply deleting all of that? Banaticus (talk) 20:16, 15 April 2009 (UTC)


 * Thanks for your concern Banaticus, currently that text has been moved to history of quaternions, but then I went and checked and the people over there deleted it again. Perhaps you should sick cluebot on them, but I don't really want to get in an edit war with them.


 * Unfortunately there is a lot of opposition to this text from a certain quarter. Your concern is inspirational, and perhaps you can take it up with the folks maintaining the history article.  I can assure you that the sources of content creation in this article will not object, mostly because fans of Hamilton's ideas have been pretty well ground down and demoralized, and will not object any further to this change.


 * But please don't take my word for it, I assume you are watching large deletions of text as suspected vandalism, and it is your job to make sure that what I am saying is true. I am staying out of the history article, but if you wanted to go over there and do battle with those folks, I would salute you!Robotics lab (talk) 23:27, 15 April 2009 (UTC)

Point by point rebuttal

 * Homebum has reverted my attempts to start improving this article, and has accused me of vandalism. For the record, some of my issues with this article are:


 * 1) The lead - arbitrary editorial comments such as "This article is written exclusively in Hamilton's original notation, using his original definitions of terms" and "It uses only Hamilton as its primary source and reliable secondary sources written on or before 1905" have no place in a Wikipedia article. We are creating an encyclopedia here, not a historical re-enactment. Both the notation and the sources should be those that best explain the subject of the article. Parts of Hamilton's notation will be unfamiliar to the modern reader, and so need to be explained in terms that a modern reader can understand.


 * Key word is agreed upon editorial distinction used to organize the material. Please go back and read the deletion discussion. There was a minority opinion that the content of this article should be merged merged into the main article.  This is the agreed upon topic of this article.Robotics lab (talk) 01:22, 16 April 2009 (UTC)


 * 1) The length - much too long, partly because there is no coherent structure, partly because of pointless repetition (e.g. Hamilton's usage of the term "tensor" is described in four separate sections, which could be replaced by one much shorter section), and partly due to an inability to focus on the important aspects of the topic.


 * And getting longer! There is a lot of material to organize here.  I am thinking about a summary style.Robotics lab (talk) 01:22, 16 April 2009 (UTC)


 * 1) The style - parts of the article have a poorly written essay-like style - which is also a factor in the length of the article. Hamilton had a penchant for inventing strange and complex terminology, and much of his writing is prolix and obscure but there is no need to repeat that style this article. An example - "The vector of a versor is then once again an element of pure distance not associated with time" - huh ??


 * Some what of a cheap shot. Remember that you proposed to roll some very raw draft material into an article that was still in a very raw but somewhat more polished state.  Work is proceeding as fast as possible on improvementsRobotics lab (talk) 01:22, 16 April 2009 (UTC)


 * Also an objection to text that no longer exists.


 * 1) The inappropriate POV - the article seeks to promote Homebum's opinion that modern mathematics takes a "quaternion negative" stance. To do this, it exaggerates the differences between Hamilton's approach to quaternions and the modern approach. There is a legitimate (and much shorter) article to be written summarising Hamilton's geometric approach to quaternions and making it accessible to the modern reader - but this bloated and rambling POV vehicle is not it.


 * This one is already fixed by the way. So you have your way on one out of four topicsRobotics lab (talk) 01:02, 16 April 2009 (UTC)


 * Homebum, you clearly seek to own this article, and you do not want to collaborate with other editors. This is contrary to Wikipedia's guiding principles. As the essay Collaboration first says: "In a collaborative environment such as a wiki, contributors who are unable or unwilling to collaborate with others should be politely but firmly excluded from the portions where conflict occurs, or even excluded from the community." I am not interested in arguing endlessly with you. Eventually you will get bored or be banned, and then the article can be usefully re-written. Gandalf61 (talk) 09:44, 15 April 2009 (UTC)


 * Wow, you seem to have mind reading powers here. You got your way on section six, how about a compromise on the section explaining what the article is about?Robotics lab (talk) 01:22, 16 April 2009 (UTC)


 * Nothing could be farther from the truth. Perhaps you should work to achieve consensus for rolling the contents of this article into the main article, but I really doubt it.  One problem you seem to be having is consistently introducing horrific factual errors into the article with each edit you make.  On the other hand you are improving.  Perhaps if you would like to discuss changes you would like to make before making them instead of the slash and burn and Coercion.

For example you recently deleted the sections on cardinal and ordinal operations. There are a large number of confusing terms regarding these operations that need exposition, including factor, faciend and factum, which are not really hard to understand once they are hyperlinked to but really need to be included in an article on Hamilton's terminology and approach to quaternions.

I reposted my point by point address of your issues. If you insist on making multiple points in a single article and object to me rebutting them point by point in your original text that is fine, but I maintain the right to make a copy and rebut point by point. Hope you are OK with that.Robotics lab (talk) 20:08, 16 April 2009 (UTC)

This arguement has been moved to a new section for responce.
Original argument:

Homebum, you clearly seek to own this article, and you do not want to collaborate with other editors. This is contrary to Wikipedia's guiding principles. As the essay Collaboration first says: "In a collaborative environment such as a wiki, contributors who are unable or unwilling to collaborate with others should be politely but firmly excluded from the portions where conflict occurs, or even excluded from the community." I am not interested in arguing endlessly with you. Eventually you will get bored or be banned, and then the article can be usefully re-written. Gandalf61 (talk) 09:44, 15 April 2009 (UTC) —Preceding unsigned comment added by Robotics lab (talk • contribs)

Original Additional closing comment:

Not interested in arguing with you or your sockpuppets. Gandalf61 (talk) 12:46, 16 April 2009 (UTC)

reply, sorry you are not interested in these discussions any more. But if you don't want to discuss things, if might be difficult for you to edit constructively. Doing things like randomly removing large blocks of text with a comment unnecessary section are hard to clean up when other people make good edits after you.

Also changing the topic of the article over and over is not very constructive, and to be honest I view it as a prelude to more disruptive behavior. You appear to be part of a small click of users, who hang out in the math discussion groups and plot on ever more clever ways to wiki-hound less experienced users.

In the interest of achieving concensus, can you please stop your endless changing of the start of the article which explains what the article is about.

As far as anybody thinking that they own this content, you might be interested to know, that an early very prolific editor on this topic, who's work we are now consolidating was very much opposed to keeping this article and believed that all of the content should be merged into the main article.

In fact everybody, except that user at first voted to keep the article, he was the only one who wanted to delete it and merge the content into the main article.

It was agreed that the way the text would be arranged was to have a fork of content dedicated to Hamilton's views on quaternions. But sadly some people, including some of your henchmen who you correspond with regularly, had no intention of honoring this agreement. Their intent was to delete all the content first paragraph by paragraph, and then even sentence by sentence.

One of the most horrific of these was Septentrionalis PMAnderson claim for example that tensors can not be subtracted. No matter how much it was attempted to politely explain to him that tensors were just positive numbers like 3 and 5 and that 3 - 5 = -2 he would not listen to reason.

Strange how you seemed to show up at the exact same moment he left?

So I am sorry you are not interested in these discussions. Maybe if you got a good book basic book on quaternions, like one by Jasper Jolly or Tait, or even read Hamilton's lectures and elements cover to cover, you might be able to contribute something.

But just random clueless deleting of text, based on your apparent view that as little of Hamilton's thinking on the subject as you can get away with in an article is the best article, and in particular endlessly changing the topic of the article, is going to increasingly be viewed as a deliberate disruption.

Go back and look again at the point by point rebuttal, and see that three out of four of your demands have been agreed to.

Anyway, if you don't want to read long and musty books on 19th century math, and carefully discuss them, it does not mean that you are a bad person, I am sure you have a lot of other good qualities, but just might not be well suited to contributing to this sort of rather complex article. I noticed you made some rather unkind changes to the small Hamilton's work link from the main article to this one.

Look on the bright side, come back in six months, and we can vote again to delete and merge this article into the main article. Or you could start merging content now, into the main article if it is your true heats desire the expound upon Hamilton's views in a more general context?

Good luck and happy editingRobotics lab (talk) 20:42, 16 April 2009 (UTC)

Hi Everybody!
I remember at one time, that was hard, but now I noticed it is back to nobody really caring enough about Hamilton's ideas to do any editing with sources.

Everybody is welcome!

I make a new resolution to make people feel welcome. There is plenty of work to be done!

Mostly I want to work on adding references. —Preceding unsigned comment added by 76.191.171.210 (talk • contribs) 00:31, 25 June 2009

Other double quaternions

 * Hamilton died before he worked on these strange entities. His son claimed it to be a "bow for another Ulysses".

"Claimed" is an odd choice of word, implying that the remark – meaning that some other genius would have to take up the work – was controversial. (Penelope challenged her unwelcome suitors to shoot with a bow that only her husband could draw.) This is more of a disclaimer, if anything. —Tamfang (talk) 22:34, 20 June 2010 (UTC)

Link to main Tensor page is confusing.
The link "Main Article: Tensor" is misleading, because the main article is about an entirely different concept. This link should be retained, but in a sentence that explicitly mentions that the tensor in this article is not the tensor in the main article. I'd hate for someone interested in the modern meaning of this well-known word to be misled.

HendrikBoom3 (talk) 16:53, 16 February 2011 (UTC)