Talk:History of quaternions

message: Hi, I have taken  the liberty of copying and pasting some material from Classical_Hamiltonian_Quaternions into this empty space for an article.  I don't pretend that this material constitutes any where near what is needed for an in depth article about the history of quaternions, however I do think there is some valuable material here.
I have a suggesting for a description of the article.
It should be a history of the who and when of quaternions.  Issues of historical notation and methodology should go into either classical_hamiltonian_quaternions for things written in the notation of 19th century authors, up until 1901, when Hamilton's second and final volume of elements of quaternions was written.
Math and modern quaternions already contains a short history of quaternions.
The material in this article originally started out in that article but it was suggested that the material be split off from the main article.
It still needs a lot of work.  —Preceding unsigned comment added by Hobojaks (talk • contribs) 22:28, 27 January 2008 (UTC)
thread_title:  Article creation 

message: Wikipedia just doesn't do multi-coloured text.  It's not it's style.
So I've removed the  tags.   Where we really need to underline that something is modern notation, we can say so as and when.  Jheald (talk) 09:58, 13 September 2008 (UTC)
replies: text: I have now copy-edited the text a bit, and I think it should now always be clear from the context, without highlighting, when old notation is being used and when new notation is being used.  Jheald (talk) 11:43, 13 September 2008 (UTC)
thread_title:  Red text 

message: Please be aware of WP's policies WP:No original research and its subsection WP:No original syntheses.
I have serious concerns about the latest additions to this article, particularly the line of thinking that Special Relativity and General Relativity in some way "vindicate" Quaternions.   
This is a pretty out-there claim to make, and to stay in the article it needs to be line-by-line sourced -- and in particular, sourced to articles which actually explicitly make that claim, not just articles from which the wiki-editor thinks it can be inferred.  Jheald (talk) 21:11, 14 September 2008 (UTC)
thread_title:  Original research 

message: I have a copy of Minkowski's paper front of me right now.  Interestingly it does not have any matrix algebra in it at all.  He died just one year later.
I suppose that there must have been some other articles he wrote, but his metric in terms of a matrix is absent from this particular paper.
The first metric tensor I can find in my collection of articles titled "principle of relativity"  is Einstein's article 
The foundation of the General Theory of Relativity in 1916.
In this article Einstein gives a metric tensor with a trace of (-,-,-,+), which is essentially the scalar part of Hamilton's product.  It seems to me that at this point a critical line of thinking had changed among the German Physics community, in that the Scalar part of a quaternion had been ripped away from the complete whole and viewed as an entity in its own right.
:* It didn't have anything to do with quaternions.  Quaternions don't represent 4-vectors, because there's no appropriate way to make them transform like 4-vectors.  Jheald (talk) 12:37, 15 September 2008 (UTC)
replies: text: * You're horribly confused here.  Hamilton's scalar was just that - a scalar.  Not a time co-ordinate.  Hamilton may have flirted with the idea of calling it a time co-ordinate, but it is simply not used as a time co-ordinate.  Jheald (talk) 13:09, 15 September 2008 (UTC)

text: *Smolin doesn't even mention Hamilton or quaternions.  To put the words "some things that Hamilton and his cohorts had proven through cold logic had become lost." into Smolin's mouth is simply and utterly without foundation.  Jheald (talk) 12:41, 15 September 2008 (UTC)

text: * No, it is Maxwell's equations that require that light always travel at the speed of light.  The fact that the equations could be written using quaternions is neither here not there.  Quaternions were simply a way of writing them down; just as Heaviside and Gibbs could write them using vectors.  The important point is that the Quaternion formulation could not even simply represent Galilean transformations, never mind Lorentz transformations.  It is not quaternions that require that light always travel at the speed of light. If anything, Quaternions serve to obfusticate the fact that Maxwell's equations do not transform appropriately under Galilean transformations, not point the way to something new.  Jheald (talk) 13:00, 15 September 2008 (UTC)

text: * Saying "the intrinsic four dimensional nature of space" or "the Lorentz invariant" can be deduced from Hamilton's quaternions is drivel.  The quaternions are simply one mathematical structure among many, many others.  Saying that there are features of the quaternion structure which must be reflected in the physical world automatically provokes the question "Why?"  And with good reason.  The places where division breaks down in some other algebras turn out to be just what you need to describe the geometry of higher dimensional projective spaces, and the geometry of space-time.  Jheald (talk) 13:00, 15 September 2008 (UTC)

text: * In case you hadn't noticed, if you mean "based on flat space", then Quaternions in the way Hamilton used them are wholly and entirely Euclidean too.  Jheald (talk) 13:00, 15 September 2008 (UTC)
thread_title:  Minkowski Space and Time  1908 

message: One objecting that I don't have to much trouble with agreeing to is the term Euclideanist.  That was just something that I made up for lack of a better term and don't mind changing it.  The central idea is that there are two ideas at war here.
What is very well documented and a great source for this is Crowe is that at the end of the 19th century there was a knock down drag out fight, between two factions.  In fact Crowe devotes a chapter, titled the struggle for existence, to the subject.
This came right before the time when there was a major revolution in physics, with the rise of quantum mechanics, as well as further developments in geometry, like general and special relativity.  Smolin 2006 and Bertrand Russel 1925, provide great sources of the idea that the revolution of general relativity is a revolution in geometry.
Quantum mechanics and relativity (in the opinion of plenty of people that it would be easy to site sources from) still can't be unified. If I have connected a few dots on my own by seeing a connection between the turn of the century debate over notation, and the 20th century fundamental split between quantum mechanics, and relativity sorry about that, but to tell the truth I don't think I have made some break through historical interpretation here.  Quantum mechanics, and relativity use different..... let me skip a complex explanation here about the difference, but just assert that it seems to me, that there might be a connection between these two debates, in that they are over the same issue in a different context.  In other words, the argument between Gibbs and Tait has spilled over into the next century in many profound ways, so that an idea can be traced as it develops from then to now.  Smolin in his book the trouble with physics, who is really interested in history after 1970, may have some incite for us, in part one of his book, titled the unfinished revolution, where he devotes an entire chapter to The world as geometry
But hey I gotta get my homework done, so I can't really get into a point by point rebutal here.  —Preceding unsigned comment added by Hobojaks (talk • contribs) 20:29, 20 September 2008 (UTC)
thread_title:  Euclideanists? 

message: I have added some material about Penrose's book on quaternions, thanks for recommending it.  Actually I was thinking about buying and reading it before this discussion even came up.
One section that I found particularly enlightening, was on page 246 and 247, were Penrose explains that quaternions make a great representation of velocity space.
I found figure 18.11 particularly enlightening.  I had compared diagrams from Bertrand Russels 1925 book ABC of relativity with Minkowski's 1908 article on space and time and always though there was a connection there but did not really understand it as well.
Jheald, could you please check my typings for factual correctness, I have tried to do my best to render Penrose's thinking on the subject, hopefully I have it close to correct.
It is tempting for me to go back now and rework a section I tried to type on night on the application of versors to special relativity that got deleted for being OR now that I have a more recent source on the subject.
Hobojaks (talk) 03:16, 9 November 2008 (UTC)
thread_title: Having read Penrose on quaternions

message: I have to agree with Penrose that the notion of the Quaternion Dot Product which is discussed on the main page, in my opinion is problematic.  The idea of extending quaternions with a dot product was what Tate thought of as a Hermiphroditical Monstrosity.  So this is a problem that people much smarter than me have been objection to for several centurys
But you have to take the tern natural in the context of several centuries of thought here.  I think Penrose is borrowing from Minkowski's 1908 article. That is what Minkowski calls his mystic formula that the square root of -1 second is equal to the distance that light travels in a second, or 300,000 km. Penrose calls complex numbers Magical and Mysterious and calls real numbers natural at the start of the book, but I think you have to keep reading Jheald!
In my copy of Penrose's book on page 201 I have underlined the phrase Quaternically natural and scrawled in the margin, see page 1035.
In the first paragraph of page 1035, Penrose explains that while some may view real numbers as being natural and complex numbers as magical and mysterious, that it may in fact be that the complex numbers are more god given.
Hence according to Penrose complex number quantities like the square root of scalar part of the square of a quaternion\sqrt{(S.q^2)} may , while seeming unnatural to some in fact be not only magical and mysterious but also ordained by god.
Hence while the dot product may seem most natural to some, including some of the authors of the main quaternion page, who are representing a long held view, that they share with giants like Euclid, Gibbs and Heavyside, scalar part of the square of a quaternion, which is a Lorentz invariant, when used  as an element of velocity space as Penrose suggests in 18.1 -18.4 of his book.
The last sentence two sentences of the paragraph in question on page 201, explain that Hamilton did not know about special relativity, in fact it was in the year of his death that it was being discovered that light was electromagnetic, and traveled an a constant speed.
Penrose then explains in the last sentence of the paragraph in question on page 201 that he is opening a whole can of worms here.  And gives a whole list of sections that deal with this problem, the last one being in chapter 32, the chapter before the one where he introduces twister theory.
You may have noticed that a twister seems to have a quaternion part?  
Since a twister consists of an array of four complex numbers, for example you could take the real number from the first complex number and the imaginary parts from the remaining three and have a quaternion, hence a quaternion can be viewed as a special type of twister?  Or a twister as a generalization of a quaternion?
Hobojaks (talk) 03:17, 9 November 2008 (UTC)
replies: text: I think you should be careful about inferences, something that could be done but is not documented is original research. Citations are key. If you are certain all the citations mention quaternions and what's mentioned in close proximity you'll be on reasonable ground. 'You may have noticed' is not good grounds for including things in a history. Dmcq (talk) 16:12, 2 March 2009 (UTC)
thread_title: Penroses Quaternically natural form

message: Section 5 is some old material that was cut and pasted out of the Classical Quaternions article because it really did not belong there.
There is an important section in the main article about the relationship between R^3 and the vector part of a quaternion.
When the content of section 5 was written that section in the main article did not exist yet, in fact the idea that a
quaternion had both a vector and a scalar part did not really exist in the main article.  So we have come a long way.
Some of section 5 the who and when part, needs to be in the history article.
The "what" the technical details of how the vector part of a quaternion and a vector in R^3 and the relationship 
between the scalar product of two R^3 vectors, and the scalar of the product of two right quaternions, that is
two quaternions which have a zero scalar part, and between the vector of the product of two right quaternions and
the vector product of two vectors in R^3 needs a clear explanation in the main article.  Since many readers will
already know about dot and cross products this information will draw a line between what they know and what 
they don't know.
Can someone please help me with Merge tags????  So that it reflects the suggested merging between what and what.  —Preceding unsigned comment added by Hobojaks (talk • contribs) 19:00, 1 March 2009 (UTC)
thread_title:  Merging section 5 

message: Section 6 has some really great information.  All of it belongs somewhere!
There are some really technical parts in this section that in my opinion belong in the main article on quaternions.
But when did this modern synthesis happen.  What were important dates?  Who had he ideas?
I don't know all the history, but I don't think that the names Clifford and Grassmann even appear in the current
article.  Who in the 20th century was responsible for the synthesis?  When did these ideas begin to be understood.
Needs to be in the history article.
Hobojaks (talk) 19:06, 1 March 2009 (UTC)
replies: text: No, this contains Original Synthesis. Septentrionalis PMAnderson 23:40, 4 March 2009 (UTC)
thread_title:  Merge section 6 

message: Wikiquette alert here  - seems only polite to mention it seeing as the complainer has not bothered.  pablohablo. 16:51, 5 March 2009 (UTC)
thread_title:  Wikiquette alert 

message: http://en.wikipedia.org/wiki/Wikipedia:Administrators%27_noticeboard/Incidents#AFD_consensus_was_keep.2C_but_some_editors_keep_deleting_and_redirecting_instead
I was told to take the issue there, so did so.  And I forgot to post a link previously.  Everyone is encouraged to participated, and state their opinions, of course.  Dream Focus 17:56, 5 March 2009 (UTC)
replies: text: Any contributions to make as far as cleaning up/rewriting go?  pablohablo. 20:02, 5 March 2009 (UTC)

text: You seriously need to drop this and respect the AFD consensus. Wikipedia is not a battleground, sometimes decisions are made that you might not agree with. Deal with it and move on. Use your time to improve the article instead.  --neon white talk 04:39, 6 March 2009 (UTC)
replies: text: (Apparently the above comment is addressed to Dream Focus).  I wholehearted agree with this.  The consensus was to burn this article down and start anew.  That's what is being done.  --C S (talk) 05:03, 6 March 2009 (UTC)
replies: text: Strange, from Neon White's contributions, it really seems like s/he was commenting to me!  Well, not that I don't appreciate being chastised, but comments like Neon White's are out of line.  I would suggest Neon White point out to Dream Focus that distracting people here with antics on WQA, AN/I (and who knows where else since the AN/I thread didn't go his/her way), is not "improving the article".  Indeed, Pmanderson has asked for my help on working on this article, but every time I look at it, there's somebody trying to stir up drama.  --C S (talk) 05:14, 6 March 2009 (UTC)
replies: text:  No, my advice is good and you need to follow it. Continually denying the afd consensus to a disruptive level is only going to lead to blocks. The ANI alert was recommended by volunteers at the WQA board because it was decided that was the best place to deal with it. It was the correct course of action considering the edit warring on this article. It should not have been necessary but sadly do the poor behaviour of a few editors it was. --neon white talk 20:46, 6 March 2009 (UTC)
replies: text: Your "help" here is not needed, so get off your high horse.  I know people like you get their jollies from acting like the police, but you aren't helping anything.   Go away.  Shoo. --C S (talk) 01:56, 7 March 2009 (UTC)
replies: text: The article is being improved, and it isn't redirected any more. Can we call this thread closed? — Carl (CBM · talk) 02:06, 7 March 2009 (UTC)
thread_title:  Administrator noticeboards incident 

message: By this I mean a list of important dates, listed in order.
At one time I tried to start one, but I didn't contribute very much material to it.
What I mean is a list of events, in order of their date?
The Birth and death of Hamilton, should be included, and the date of the first discovery of quaternions.  Perhaps the dates of the births and deaths of Clifford, Grassman, and Gibbs should be included.  That might help to give readers a better idea of how the idea of quaternions and extensions and alternatives to it evolved, in a linear time like manner.
Perhaps, we can postpone a discussion of what should go into a time line, till after we agree that there should at least be a time line.
*I don't think there should be; the birth and death dates of the protagonists should be in parentheses (if needed, that's one of the things links are for). Please note that Conway's account of the history begins with Euler. Septentrionalis PMAnderson 23:28, 5 March 2009 (UTC)
thread_title:  It would be nice to have a cronology! 

message: I have added a note on the mathematical uses of quaternions, and the couple of sentences from Conway/Smith themselves on quaternions. 
That leaves what they say on octonions, if we want octonions here, and John Baez's paper, which is probably the source of what we now say insofar as it was taken from Quaternion#history. I encourage others to attack Baez, since the source is readily available. Septentrionalis PMAnderson 19:48, 6 March 2009 (UTC)
thread_title: Baez

message: Currently the article states, "for many years Hamilton had known how to add and multiply triples of numbers. But he had been stuck on the problem of division: He did not know how to take the quotient of two points in space."  However, according to Baez's octonions articles, and indeed, this is a very famous story, up until the month of his discovery of the quaternion relations, he did not know how to multiply triples.  Indeed, the story goes that his two boys would ask him at breakfast every day, "Can you multiply triples, daddy?"  And his answer would be "no" until that fateful day.  --C S (talk) 02:13, 7 March 2009 (UTC)
replies: text: That's Bell, and he may be right, especially if Baez supports him. Let me see if I can find a life of Hamilton. Septentrionalis PMAnderson 18:30, 7 March 2009 (UTC)
thread_title:  Can you multiply triples? 

message: It will matter less to readers studying Hamilton's ideas who made up names for concepts, and matter more the history of the concepts.
I have looked at that half page before when it used to be at cornell, but I suspect that there has been enough interest in the subject that wikipedia was driving to much traffic over to cornell so they shut us down.
Hamilton did speak before the Royal Irish what ever they called it, on the subject of octonains, he did suggest a name for them to the society, and he did say that Graves thought of them first.
His idea was for the basis vectors to be i,j,k,l,m,n,o
The key concept here is that there are two possible double quaternions.  One is the bi-quaternion, that Hamilton did a lot of work on, that the other one is what ever you want to call it, but not much work has ever really been done on it.
To construct the bi-quaternion in Hamilton's alter work suggested the letter h be used.
h is just the plain old imaginary from scalar algebra.  It is both commutative and associative.  l,m,n and o are not commutative or associative, but I believe that it is possible to construct a double quaternion in two ways so that it does not have a geometrically imaginary part.  This means that all the coefficients except 1,i,j and k are zero.  Also looks like to me that given l one could construct m n and o as li,lj and lk.
Here is the thing, as far as I can tell there really are no credible sources on non-associative double quaternions, since I hate the idea of the norm, I would be inclined to construct one that wasn't a normed division algebra.
Also it is pure fiction to suggest that Bi-quaternions can't be divided, Hamilton showed that they can, unless that is tensor a new word some of us are learning has meanings in Hamilton's context, is zero.
I don't really understand the reasoning behind saying that the biquaternons are not a normed division algebra, other than the fact that it is possible for them to have an imaginary tensor.
So well, attribute the term double quaternion to Penrose if you must, we can verify that and that will let us explain a key concept, that is needed for anyone reading this history because they are tracing the development of mathematical ideas back to their origina.  —Preceding unsigned comment added by Taits Wrath (talk • contribs) 11:37, 14 March 2009 (UTC)
thread_title:  Double quaternion is key concept. 

message: A large section of text was recently deleted from classical hamiltonian quaternions and the fact that clue bot and then even a live person accused me of vandalism got me to thinking.  Even with out this text of this section, that article is 63K long, so this article seems the logical place to put this text.
So here is some old text written by a beginning user who does not exist any more, pasted into this article one more time.  Actually there might actually be some good material in there some place, but it definitely needs a major rewrite.  I notice that the slash and burn, and then build back up approach to this article basically left it devoid of content.
Some history in this section is that when the article tensor of a quaternion was voted as deleted and merged part of the content of the article to be merged contained content regarding the concept that Hamilton uses the word tensor in a different context from other users.  Given the laborious nature of the task at hand, that content was merged back in as an early version of the main article.  Hence some of this material has made the long trip from classical hamiltonian quaternions to the articles tensor of a quaternion and the vector of a quaternion.
There are some important concepts, but it needs to be reworded to remove both the essay and OR problems.  I could eventually help with sourcing but right now, most of us interested in working on the subject of quaternions are focused on bickering over other issues, so I would have to come back to this subject at some later date after other chores were completed.  —Preceding unsigned comment added by Robotics lab (talk • contribs) 20:36, 15 April 2009 (UTC)
replies: text: I have no idea or opinion on your motivation for deleting this material somewhere else, but it certainly does not belong in this history article. This is about the history of quaternions, not about how to read historical texts on quaternions. The original location, classical hamiltonian quaternions, or a new article, seem better suited (if this essay is appropriate material for Wikipedia). -- Crowsnest (talk) 21:31, 15 April 2009 (UTC)
thread_title:  I don't generally work on this page but 

message: The reference to the thesis of Johannes C. Familton is a continuous narrative of the development of quaternions and related representations of rotation. The reference was moved here from another article for which it was less appropriate. The value of the thesis is its survey of algebraic rotation representations spanning several decades. Such a broad survey is rare and might be compared to History of Lorentz transformations in its scope. However, Familton's thesis for a Department of Mathematical Education fails to meet standards expected in research mathematics. Examples include a deficient definition of simple groups (pages 77,8), and assertion that Pauli matrices form an algebra isomorphic to quaternions (page 80). Some of the historical sketch appears to be parody, and for the insightful reader of this article, such commentary can be taken as humorous. — Rgdboer (talk) 19:06, 30 March 2018 (UTC)
thread_title: Familton