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References?

I noticed on a few occasions you mention your access to references may be limited. In the following I'm probably stating the obvious, and you're more than welcome to delete this thread, but in case it's useful...

Have you access to books on mathematics by Dover Publications? Many (not all) great works are published by them at a very affordable price (approx equivalent of £ 10 = US $ 16.64), about the same as a Schaum's outlines book. Some examples include

• Sergei Sobolev's book on partial differential equations [1],
• Maxwell's two-volume treatise on EM vol 1vol 2,
• Cartan's work on spinors (English translation),
• some of the references (Tensors, Differential Forms, and Variational Principles By David Lovelock, Hanno Rund, Tensor Calculus By J. L. Synge, A. Schild, Tensor Analysis on Manifolds By Richard L. Bishop, Samuel I. ) in the Ricci calculus and tensor articles,
• even Levi-Civita's work on tensor calculus.

(Unfortunately not all the classics seem to be available, e.g. Gibb's vector analysis, Schouten and Courant's treatise on Ricci calculus, Courant's Calculus and analysis, etc. which tend to get published in the high quality and ridiculously expensive Springer and Wiley or so on).

Two often good places to buy books online (at least in my experience) are abebooks or waterstones, rather than amazon, ebay, etc.

Best, M∧Ŝc²ħεИ_τlk 21:00, 3 April 2014 (UTC)

Thank you – this is very useful. These are prices that I can live with. I should start a list of "intended purchases". So far, I've only looked at the new book market, which is really silly of me. —Quondum 23:50, 3 April 2014 (UTC)

Willard's General Topology - much recommended. YohanN7 (talk) 02:24, 4 April 2014 (UTC)

Cool. You may also like:

• Kreyszig's Differential geometry,
• Flanders' Differential forms with application to the physical sciences,
• Rucker's Geometry, relativity, and the fourth dimension, (qualitative review like Penrose rather than a textbook)
• Pauli's Theory of relativity, (historically a standard reference, today the real drawback is his use of ict..., anyway covers SR and GR, including relativistic EM, some fluid mechanics, and thermodynamics),
• Tolman's Relativity, thermodynamics, and cosmology (similar to Pauli but more detail and better),
• March, Young, Sampanthar's The many body problem in quantum mechanics (from the 1960s, but good for historical perspective).

I have the books listed here (plus a few more on waves, fluid mechanics, and thermodynamics), but out of the ones above, only Cartan's theory of spinors. M∧Ŝc²ħεИ_τlk 12:29, 4 April 2014 (UTC)

Others I don't have (and hope to get soon), and which you may be interested in, include:

• Weyl's Theory of groups and quantum mechanics,
• Riesz and Nagy's Functional analysis,
• Knopp's Theory of functions,
• Silverman's
  • Introductory Complex Analysis,
  • Essential Calculus with Applications,
  • Complex Analysis with Applications,
• Coxeter's Regular polytopes

I'll stop here. M∧Ŝc²ħεИ_τlk 12:55, 4 April 2014 (UTC)

Okay, I'm compiling a list below. —Quondum 04:56, 4 April 2014 (UTC)

Dover:

• Sergei L. Sobolev, Partial Differential Equations of Mathematical Physics: $19.95
• Tullio Levi-Civita, The Absolute Differential Calculus (Calculus of Tensors): $30.75 (paperback + ebook)
• Stephen Willard, General Topology: $24.95
• — other books (I haven't transcribed all those on tensors above yet)

Abebooks:

• — to be compiled

Books status

Have

• James Clark Maxwell (1891). A Treatise on Electricity and Magnetism. Vol. Vol 1 (3rd ed.). {{cite book}}: |volume= has extra text (help)
• James Clark Maxwell (1891). A Treatise on Electricity and Magnetism. Vol. Vol 2 (3rd ed.). {{cite book}}: |volume= has extra text (help)
• Élie Cartan (1966). The Theory of Spinors.
• Irving Kaplansky (1974). Linear Algebra and Geometry: A Second Course.
• Pertti Lounesto (2001). Clifford Algebras and Spinors (2nd ed.).
• Roger Penrose (2004). The Road to Reality.
• Leo Dorst; Daniel Fontijne; Stephen Mann (2007). Geometric Algebra for Computer Science.

On order

JSTOR papers

Plenty of the important papers are only found at JSTOR. There you can read (all of?) them for free, only that you can have only three on your "shelf" at any one time. When you add an item to the shelf, it can be removed after 14 days. If you pay $20 per month, you can read as much as you want (don't know if they exclude much) + download 10 items per month. I think this is decent (provided you select the papers well of course). Think about 10 papers you really want. They'd probably be worth a $20 investment. Compare this to $100+ for a typical Springer GTM, which will refer you to the original papers anyway if you want the details. YohanN7 (talk) 17:52, 27 April 2014 (UTC)

Don't I have to belong to a participating library/institution? —Quondum 18:18, 27 April 2014 (UTC)

Nope. Just get an account, log in and have a look. You can't download or print, only read on the screen what you have on the "shelf", unless you pay the $20 (or you are a hacker). YohanN7 (talk) 19:06, 27 April 2014 (UTC)

A restriction of only being able to look at three papers per two-week period is pretty severe, if you just want to verify a lot of references. JRSpriggs (talk) 23:57, 28 April 2014 (UTC)

Yup, I guess so – but it's a start, and more than I've been doing... —Quondum 05:34, 29 April 2014 (UTC)

That would be the time when you take up your wallet, and cough up $20. Disclaimer: I don't know how much, and what, is excluded from these deals. I'm usually reading somewhat aged classical papers. I'd not be able to understand highly specialized 2014 research papers anyway. YohanN7 (talk) 14:58, 29 April 2014 (UTC)

I've used the "shelf" there before, and I still have access to many through my alma mater. If I can help by digging up a paper or two, just let me know. Rschwieb (talk) 17:27, 29 April 2014 (UTC)

Wikipedia:JSTOR YohanN7 (talk) 12:50, 9 November 2014 (UTC)

More refs

Hi Quondum, sorry to cut in randomly like this after such a long absence, I'll be back in business soon, but if it's ok to add more Dover refs in case you haven't seen them:

• a fantastic choice is Barut's Electrodynamics and Classical Theory of Fields & Particles. It covers relativistic mechanics, relativistic dynamics of fields, in each case in the Lagrangian and Hamiltonian formalism and uses the EM field as a prototype, also gets to the homogeneous/inhomogeneous Lorentz groups and spinors quickly, even includes the Dirac equation. Not an introductory book, it begins with the tensor formulation of SR (of course not a problem for us - we can cope with tensors now), and even develops a spinorial formulation of Maxwell's equations (yes - spinor indices and all). The book is very compact for the context it covers, and is very cheap. The typography is also very nice, sadly there are occasional printing errors (seen a few, usually obvious). Bought it recently - definitely worth every penny.
• a better reference to the many-particle theory would be Fetter and Walecka Quantum theory of many particle systems, this is a standard graduate-level ref on the topic, now in its 2nd edition. Bought this a while ago – worth it but not easy.
• another great book I still do not have, and hope to get soon, is Mattuck's Feynman diagrams in the many-body problem
• you may want to look at Borisenko, Tarapov Vector and Tensor Analysis with Applications, masterful development of vector and tensor analysis, from geometry to algebra, includes the dot and cross product not only in orthogonal coordinates but arbitrary coordinates, bought this a while ago. Unfortunately there are a few printing errors but you'll know them when you see them.

For non-Dover refs...

• You may also notice I had previous emphasis on a graduate-level QM book by Abers, although the content is generally good - I gave up on it since the section on RQM is so awful, I do not recommend it anymore...
• A far superior RQM and QFT book is Ohlsson's book, starts with RQM, goes onto QFT, covers most things/basically everything in each and the overlap at an introductory-level (late undergrad/early grad), a good start before you take on Steven Weinberg's standard 3-volume QFT books.
• A brilliant general QM book is the 2nd edition of Zettili, overall generalities, operators, Dirac notation, dynamical pictures, etc. it actually spans from the undergrad-early grad levels, only real drawback is the price.

I'll stop cluttering your page like this (I know - said this above), sorry about that, just thought to get these in at least, no more unless you ask. Best, M∧Ŝc²ħεИ_τlk 07:28, 19 August 2014 (UTC)

Hi, welcome back. Thanks, I'll look through these for my next "shopping spree". Incidentally, I've been finding JSTOR doesn't seem to have much in maths and physics – perhaps I'm not searching correctly? —Quondum 14:46, 21 August 2014 (UTC)

The priority would be Barut - absolutely reccomended.

Sorry - I've never really used JSTOR so can't help... Here I just typed "physics" in the "add field" bar, with a concrete subject like "relativity" or "particle physics" in the top search bar, leaving everything else blank, in each case ended up with loads of random papers [2][3]. You may have tried this already though... M∧Ŝc²ħεИ_τlk 23:50, 23 August 2014 (UTC)

Entropy

Hi, what do you meant with "..without more context so early in the lead, this could misleadingly imply a more direct connection than is the case: it depends on what else is kept constant" -what context are you missing exactly? Prokaryotes (talk) 17:12, 6 April 2014 (UTC)

The bald statement "The entropy of a system increases or decreases with temperature" is confusing and apparently not generally true. Consider an ideal gas as an adiabatic process: it is an isentropic process, yet its temperature increases and decreases. (I'm no expert, but I cannot see how one could escape this conclusion.) —Quondum 17:28, 6 April 2014 (UTC)

I changed the part to "Systems which are not isolated may decrease in entropy.". Prokaryotes (talk) 18:11, 6 April 2014 (UTC)

Please keep in mind that the lead of an article is for introducing the concept, not for explaining details. —Quondum 19:34, 6 April 2014 (UTC)

Bra-ket notation = square blocks

Hi Quondom. Haven't looked into this too much so thought you might be able to shine some light on it. After you changed the Bra–ket notation this morning the < and > symbols are showing as white boxes to me and at least a few others. Any idea why that might be? Thanks, Sam Walton (talk) 15:39, 2 June 2014 (UTC)

Old computer with XP like me I suppose? See section 11.1 here: [4] YohanN7 (talk) 00:41, 3 June 2014 (UTC)

(ec) I've used a "standard" template to produce the symbols. It uses mathematical Unicode symbols U+27E8 (MATHEMATICAL LEFT ANGLE BRACKET) and U+27E9 (MATHEMATICAL RIGHT ANGLE BRACKET). Wikipedia uses quite a lot of characters from the Unicode mathematical extension, so their use is pretty much a given. The {{math}} template then changes the font to serif. Browsers sometimes have fonts loaded that do not include all the math characters, and then a white square or similar might be displayed. I'd suggest loading/selecting a font to solve this. If you're missing some of the more recent Unicode characters, you'll probably be missing others. In general, I think the solution is to fix it at the browser rather than trying to use only only Unicode characters dating back to before say 2004. Try selecting Cambria as your browser's serif font. If it is a general pattern with many browsers that the default sans serif font has these characters but the serif font doesn't (though I'd be surprised), we could replace the math template with nowrap throughout – a simple global substitution. Which of the following can you see properly?

• ⟨φ|ψ⟩
• ⟨φ|ψ⟩

—Quondum 00:58, 3 June 2014 (UTC)

Unfortunately none of them. I did change to Cambria and refreshed. Think we have done this once before? I'll try to fiddle a bit with the fonts, but they are probably simply too old on my machine. YohanN7 (talk) 01:14, 3 June 2014 (UTC)

Ouch. I wonder how prevalent this problem is? On XP you should be able to download and install updated fonts, but I have little experience with this. For the article concerned, we could switch to <math>, which will solve the problem for most people there at least. What do you think? —Quondum 03:03, 3 June 2014 (UTC)

Hmm, I don't see either of those. And I'm running Windows 7 actually, on Chrome. Just tested Firefox and that seems to work fine. Will investigate further... Sam Walton (talk) 06:03, 3 June 2014 (UTC)

Yes, Firefox works on XP too. It took me only 3 years to be able to see ⟨⟩ properly Besides, Firefox is much faster than Chrome and consumes much less memory. (Google is turning into MS) YohanN7 (talk) 16:53, 18 December 2014 (UTC)

?

Hi!

Do you know what M is up to these days?

Hasn't been around for some time... YohanN7 (talk) 01:31, 4 July 2014 (UTC)

Nope, no idea. I've had no communication in the last two months. Perhaps Rschwieb might have an idea? —Quondum 01:44, 4 July 2014 (UTC)

We mean Maschen, right? I don't think I've heard anything from him in months... Rschwieb (talk) 16:44, 4 July 2014 (UTC)

And what about I M (Mr. Sunshine)? YohanN7 (talk) 19:35, 5 July 2014 (UTC)

I have had no interaction that does not appear in his edit history. One would hope that recent political events didn't play a part in his retirement. —Quondum 19:59, 5 July 2014 (UTC)

Journals

Hi Q!

I assume you have seen this: Wikipedia:Royal Society journals

I got free access and it's still possible to join the waiting list. Not all places were filled, so there's a fair chance they'll fill up to their original quota right away from the waiting list.

M & I M & R, if you happen to read this, why don't you grab the chance as well? YohanN7 (talk) 08:24, 8 July 2014 (UTC)

I had seen it, but passed because I felt that there were many editors that would use the limited access to references far more intensively and beneficially than I would. I have not yet demonstrated (even to myself) that I source and reference material very effectively, though of course that may change when I actually get more than the very limited access to material that I have. I have applied for JSTOR access. —Quondum 03:55, 9 July 2014 (UTC)

Here's a paper I'm sure you'll like: The octonions YohanN7 (talk) 02:43, 18 July 2014 (UTC)

Gravitoelectromagnetism

Hey Douchebag, thanks for simply deleting the section I created in that article. Next time you think about deleting someone's hard work, why don't you consider correcting it, starting a talk page entry to gather sources, or something like that. That page needs an effects section, so people can understand what gravitomagnetism does. I did your work for you and started a talk page entry instead of an edit war, even though I do actually have a source.

In short, next time consider not being a dick. Fresheneesz (talk) 20:08, 27 August 2014 (UTC)

You might consider being civil, if you wish to be constructive. You are referring to my undo of your section. —Quondum 23:09, 27 August 2014 (UTC)

Internet archive and bookzz.org

Hi, in case you haven't come across internet archive before - they're often very good for old textbooks or papers which are fully viewable, readable online and even downloadable as pdf, as opposed to google books or amazon which only allow limited preview access.

There is also bookzz.org which I just discovered yesterday. It will allow a few books to be downloaded as PDF or DJVU (which can be converted to PDF using any online DJVU-to-PDF convertor), and viewed. Without an account, only about 7 are allowed per 24 hours. If you have an account (you only need an email, password, and nickname, no payments and no need for institutional membership), apparently you can get 100 per 24 hours. If you donate money, you get even more per 24 hours. It seems you can get almost everything there, so if you have an account, I think for verifying references this is far more superior to google books or JSTOR (based on the restrictions outlined by YohanN7).

A good example for both sites is Gibb's vector analysis, at bookzz.org and at internet archive. You can also get the famous volumes of the Landau-Lifshitz (et al) Course of theoretical physics, Courant's classical works on Calculus and Analysis, a famous book on differential forms (I only recently discovered...) is Harold's Advanced Calculus: A Differential Forms Approach, and plenty of otherwise-unaffordable books published by Springer and Wiley.

Have fun! ^_^ M∧Ŝc²ħεИ_τlk 22:42, 19 September 2014 (UTC)

Wow, thanks. These seem pretty impressive in terms of what is available; plenty of material relevant to my interests. —Quondum 14:22, 20 September 2014 (UTC)

And very very illegal (in case you haven't figured that out) YohanN7 (talk) 09:39, 15 December 2014 (UTC)

Heh. Yes, copyright considerations did occur to me, and this should be used to determine what actual documents one downloads from an internet source. —Quondum 18:31, 15 December 2014 (UTC)

In what nation(s) are these illegal sites based? I thought that, since the fall of the Soviet Union, nearly all nations were agreed to enforce copyright. JRSpriggs (talk) 18:35, 15 December 2014 (UTC)

I suppose one could go into the legalities of it and I am no expert; enforcement (in the sense of blocking such sites) and law are not the same thing. My expectation is that the site would be governed by the law of the country it is in, whereas the person/client downloading material would be governed by the country in which they are. Thus, for example, possession of material in the US not in accordance with a copyright licence (e.g. through purchase of a copy), where such material is copyright-protected in the US, would be in violation of the copyright. In some cases, obtaining an electronic copy of a book already legally in a person's possession might not violate copyright law. On some documents, copyright may have expired. Hence the copyright status of individual documents is what would be relevant. —Quondum 19:33, 15 December 2014 (UTC)

Since you ask, the domain name seems to be registered in Switzerland, but my geolocation skills may not be up to scratch. And I guess one should research them before labelling them as illegal. —Quondum 19:49, 15 December 2014 (UTC)

No, you should research them before labeling them as legal. Think about it, we are talking about scanned copies here, not pdf's from source code. Chances are close to nil that a random book there is there legally, or at the very least, is there with the copyright owners consent if it happens to exist a loophole in the laws. Whether it is legal for you to download is another matter. YohanN7 (talk) 22:39, 15 December 2014 (UTC)

The accessibility of the sites caught my attention quickly on google. Indeed they are illegal, but here the suggestion was just for freely verifying references, without having to buy the books in the first place. "Downloading as a PDF" does not mean you keep the sources permanently. It would be worse to use them to forge books at a fraction of the publisher's price, which isn't exactly possible unless you have access to the resources to print, bind, and create false barcodes etc.. M∧Ŝc²ħεИ_τlk 21:06, 15 December 2014 (UTC)

Just forget about bookzz.org... recently it seems very unstable, apparently [5][6] last month they lost 25TB of storage, and user's data , but somehow not the details of subscribers (for those that choose to pay extra). Also apparently, some people have had to pay each time they download, I have never had to since I just download to view a few every other day (and have never given any of my bank details, they only have my email). M∧Ŝc²ħεИ_τlk 21:42, 15 December 2014 (UTC)

I am not passing any moral judgements. I have been known too to once in a while sneak a peek in places on the net where moral standards are questionable The bottom line from my POV is this: A real book is worth one hell a lot more than an electronic copy. The computer screen makes you utterly silly. (Sure, you can print it out, not the same thing and certainly not free.) Have you tried to tackle a hard Sudoku on-screen? I can sit an hour or more and fail. If I print it out, I usually solve it within minutes without the extra "tools" you have on-screen. YohanN7 (talk) 22:39, 15 December 2014 (UTC)

Question on light propagation

I am new to this site, so apologies if contacting you like this is wrong.

I am very interested in light propagation through glass, and trying to find out what is explained. I read the article on refraction and noted you as the most recent editor. It is easy to explain refraction in terms of an altered transmission speed and phase velocity change. It is easy to explain why wet cold air has a different speed of sound to warn dry air. I do not find any explanation for why light slows in a glass or similar medium.

Do you think that I am correct if I claim that light slows in the presence of matter and this is observed, well-documented and measured, but not explained? — Preceding unsigned comment added by Biezanek (talk • contribs) 00:44, 23 September 2014 (UTC)

I'm sure you'll get the hang of things quickly enough. For example, use the "New section" tab at the top of a talk page to add a new discussion thread, and sign your posts on talk pages by adding four tildes at the end (~~~~). Also, the most appropriate place to ask questions of this nature will be at the Science reference desk: read the banner at the top, do as it says, and and fire away! (Use the "Ready? Ask a new question!" button.) There you may get a number of editors responding, and in so doing may get a more comprehensive picture than you'd get from any one editor. Though don't expect a tutorial, either, but at least you should be pointed to relevant material and may be given explanations. Rather than answering your initial questions here, it makes sense for you to start the discussion there, and I can join in there in whatever way I feel may be helpful, rather than ending up with a fragmented conversation. —Quondum 01:24, 23 September 2014 (UTC)

The slow-down is understood. When passing through matter, light is sometimes scattered (reflected) in a slightly different direction or absorbed and after a time re-emitted by an atom (or other imperfection). When these possibilities are included, most photons experience a delay. However, there is still a small possibility that a photon will pass through unaffected, and those few photons arrive at the same time as if the matter were not present. JRSpriggs (talk) 10:12, 23 September 2014 (UTC)

This gives an outline of the picture presented by QED, which gives a rigorous quantum mechanical explanation but comes across as hand-wavy because of all the concepts that need to be understood. It also appears to suggest a delay in terms of increased path length, whereas Biezanek quite correctly refers to phase velocity as the basis of refraction. In terms of QED, one would have to explain the stationary phase behaviour along the path that becomes the direction followed (Richard Feynman's QED: The Strange Theory of Light and Matter is a stunning explanation of this). However, just as explaining sound propagation in terms of phonons may complicate things, an initial explanation using concepts from of classical electromagnetism is a good place to start, is accurate and ties in well with the concept expressed in the question. But yes, the phenomenon is well understood in detail, in a sense at a more basic level than sound is. —Quondum 14:07, 23 September 2014 (UTC)

Speaking classically then, the electric susceptibility increases the weight of the time-derivative term in the wave equation relative to the space-derivative terms. This reduces the phase velocity. This makes sense since the electric polarization is a property of the material medium which is assumed to be at rest. In other words, the light sticks to the medium and is slowed down by the fact that the medium is not moving (as much). JRSpriggs (talk) 03:58, 24 September 2014 (UTC)

Yes, the equations argument is fairly direct and allows one to calculate the phase velocity from the resulting wave equation; I guess there are a number of ways of getting a feel for this, though the "sticking" part does not give me a feel for whether the phase should be advanced or retarded. Another way of looking at it might be that when electrons move resistively (o° phase), they absorb the electromagnetic field, and when they move against the force the field applies to them (180° phase), they reinforce it. In a dielectric, they move 90° in advance of the field, which is 90° behind the movement that reinforce the field. Thus, the electrons' radiated field adds in a way to put the propagating field behind in phase, which corresponds to a slower phase velocity. —Quondum 04:20, 24 September 2014 (UTC)

It is usually assumed that the electrons (the polarization) move in-phase (0°) with E. If they lag a little, that results in attenuation (absorption) of the light rather than a slow-down.

When light moves through a medium, some of its energy and momentum are transferred (temporarily one hopes) to the medium. More momentum is transferred than energy which slows it down. JRSpriggs (talk) 05:44, 24 September 2014 (UTC)

One must be careful to distinguish between position and velocity as being what is meant be the "movement", since these are out of phase. I meant velocity as being the most mathematically convenient quantity; I agree that position is in phase in a dielectric. —Quondum 13:42, 24 September 2014 (UTC)

Ping

Figured I would ping you on another back and forth revision at spinor (this time with discussion from Rogier). I assume you watchlist this, but figured I would let you know that I value your input there, if you have the time to spare. Sławomir Biały (talk) 21:56, 26 September 2014 (UTC)

It's good to know that my input may be of use. It might help if we can formulate a plan of attack; I'm afraid that my contribution is likely to revolve around bits and pieces (particular understandable or problematic statements), since I've been unable to synthesize a coherent whole of the topic. This might not be all bad, but it might test everyone's patience. Perhaps I can help by commenting on particular points of disagreement, or highlighting what I think I do understand of what's there? —Quondum 05:14, 27 September 2014 (UTC)

Homogeneous coordinates

Hi Quondum,

You recently requested a citation on this page and I want to respond, but not on the talk page. I put that sentence in mostly to curb the effect of another editor's insistence on including links to Projective line over a ring whenever he can. I don't think that that topic is particularly notable, but I have stopped fighting with this editor over that issue. I can explain where the condition comes from, but I can't find a reference to cite basically because none of the authors I am familiar with would care enough about the topic to comment on this. The argument goes as follows: having the coordinatizing algebra be a division ring is equivalent to the geometric condition that the projective space is Desarguesian which in turn implies the existence of many collineations of the projective space. If you try to use a more general ring, you lose this property and the corresponding collineations, unless the space is one dimensional and so every map is a collineation by default. You can use more general coordinatizing algebras in non-Desarguesian planes (as soon as you hit three dimensions the space must be Desarguesian) but they are more general than rings, and as soon as you get close to having a ring, it has to be a division ring. Geometers will pretty much ignore this topic since it doesn't lead to anything, but there were a few Russian authors who saw this as a way to generalize complex numbers. I can support everything that I have said above, but I wouldn't want to do this in the article since it would be giving undue weight to an insignificant topic. I am also not keen on removing the offending link since that will bring this editor down on our necks. Suggestions? Bill Cherowitzo (talk) 17:28, 12 October 2014 (UTC)

I appreciate your response. I'm more interested in what forces the restriction to one dimension. I was concerned that the statement might be incorrect, but it sounds like it might hinge on subtleties of the definition of a projective space; if I am correct on this, it would be nice if it was more explicit about exactly what is defined as a projective space in this more general context – regardless of whether there is a citation. (For example, I would define it from a Kleinian perspective as an R-module with the general R-linear group of invertible transformations, which seems to permit any number of dimensions.)

In my case, it would be important if a homogeneous coordinatization of higher-dimensional "geometries" were entirely excluded. Some rings fail to be division rings only because they include nonzero zero divisors, as is the case for matrix rings over a field. Yet, the construction with homogeneous coordinates being ring elements might still retain useful properties on the group of invertible transformations, and not necessarily collineations or whether it is Desarguesian. —Quondum 18:30, 12 October 2014 (UTC)

Projective space has a very simple axiomatic definition (only three axioms, only one of which has any subtlety to it) and the problem arises when you try to analytically describe the same object. Most treatments don't even attempt to get the exact fit – they'll start with a field (or if they are trying to be a little more honest, a division ring) construct an object, show that it satisfies the axioms and then move on. The question of whether everything satisfying the axioms can be obtained this way is rarely addressed. One reason for this is that the mathematics involved is just plain nasty. The algebraic structure that corresponds exactly to the axiomatic definition is something called a Planar ternary ring. These are poorly named, they certainly aren't rings and have only the most rudimentary algebraic structure (for instance, neither addition nor multiplication need be associative). As you increase the amount of geometric structure required in a projective space, you increase the amount of algebraic structure you will find in these PTRs. My point in saying all of this is that you can't divorce the geometric and algebraic structures and preserve what we want to call a projective space. For instance, if you require the projective space to be three dimensional (or higher), the algebraic structure must be a division ring. What goes wrong with using general rings is precisely the existence of nonzero zero divisors. If you are in two or more dimensions, such zero divisors will produce multiple lines passing through a pair of points, in violation of one of the axioms (unless of course there is only one line in the space so that this axiom can not be violated). The R-module construction you mention will give you something, but it won't be a projective space. (Off the cuff, I'd say you get some type of hypergraph, not likely to interest a geometer). Bill Cherowitzo (talk) 03:43, 13 October 2014 (UTC)

Okay, so the Veblen–Young theorem makes it clear for 3 dimensions and higher that projective spaces are over division rings. And you have pointed out that a projective space is defined in terms of specific axioms. Planar ternary rings presumably then only have application in under 3 dimensions, but nevertheless are associated with projective planes. If I understand you correctly, projective planes in one and two dimensions can be described algebraically in terms of division rings or planar ternary rings, but not rings that are not division rings. The wording in the article says that projective spaces over rings that are not division rings do not exist. Which is saying that the projective line over a ring is a fiction. Why then the further restriction to one dimension? Some wording change appears to be called for here. Also, the projective line over a ring, of defined slightly differently (not in using the group of units, but defining an equivalence class as when there exists a scalar multiplier that is not a zero divisor for each of two vectors such that the results are equal, they are in the same equivalence class. Under this modified definition, the projective space of any dimension over the ring of integers is none other than the projective space over the field of rational numbers (I think you could use any Ore ring). As defined in the article though, it seems to me you'd end up with something pretty useless. —Quondum 05:44, 13 October 2014 (UTC)

I think you are right about a wording change in the homogeneous coordinates article, I was being a little too cavalier with that statement. Let me recap and rephrase some things to make this clearer. I am using dimension in the geometric sense, so a one dimensional space is a single line, a two dimensional space is a plane, and so on. We are dealing here with a low dimensional problem, just dimensions one and two. PTRs are used only in the two dimensional case since they are not needed in higher dimensions and they require more than one line in order to be defined. Division rings (and fields) are PTRs with a lot of algebraic structure and these are the only rings to be found amongst the PTRs. The upshot of this is that a two dimensional structure defined over a ring can not be a projective plane unless that ring is a division ring. We turn now to the one dimensional case where our entire space is a single line (and this is where I was a little sloppy in my discussions above). In this case the three axioms which define a projective space don't put any strong limitations on what you get. The axiom about two points determining a unique line is trivially true. The Veblen-Young axiom requires two lines, so is vacuously true. The third axiom just requires that there be at least three points in the space. Essentially this says that there is no geometric structure on a projective line considered as a projective space, so the object is just a set with at least three points. If however the projective line is embedded in a higher dimensional projective space then it will inherit a geometric structure from the ambient space. The usual way to exhibit (or define) this structure uses cross ratios and that method can be mimicked using an arbitrary ring, but the embedding can not occur unless the ring is a division ring (assuming that we are starting with a ring). This is the loophole that lets you define projective lines over rings and limits them to one dimension. Ask a geometer if these objects are projective spaces and they will say no because they don't embed (however, neither do non-Desarguesian projective planes and that doesn't cause a problem). In the article I simply responded as a geometer and not as an editor and didn't quite say enough. On the other hand, as I've said before, how much space should be spent on clarifying a basically useless generalization (I fully agree with you on that point). Bill Cherowitzo (talk) 16:49, 13 October 2014 (UTC)

So basically, projective lines are not interesting as incidence structures. Any set of points all on one line will do. No need to highlight any particular case. I'll think about a rewording – I'm comfortable with the overall picture given your discussion here.

A minor quibble: Veblen's axiom is trivially rather than vacuously satisfied: the lines involved are not required to be distinct in the premise. —Quondum 02:05, 14 October 2014 (UTC)

Quibbles are what we live for . You are right, I was thinking of the diagram that usually accompanies the statement of that axiom. A separate nondegeneracy axiom is often assumed which declares that there should be at least two lines in a projective space (that sweeps the whole business under a rug). Bill Cherowitzo (talk) 03:05, 14 October 2014 (UTC)

Reading around WP a bit, it seems that there are nonequivalent way of defining projective spaces, so this wording needs thought. For example, Projective space says a projective space is the set of lines through the origin of a vector space V, which is not equivalent to the three-axiom synthetic approach (but rather apparently adds Desargues' theorem as an axiom in 2-d, but this breaks down in 1-d), even if you allow generalizations on the vector space. The axioms lead to the (possibly infinite) symmetric group acting on the chosen set as the most symmetric (or general) projective line, and I've never seen this mentioned. The projective line seems to be of interest only when there is some way of specifying the group of transformations in addition to the axioms. —Quondum 18:42, 14 October 2014 (UTC)

The real projective space of dimension 2 is actually defined as the ultimate hedgehog. YohanN7 (talk) 19:25, 14 October 2014 (UTC)

Uh? I'll have to admit you've lost me on this one. If you're alluding to the variation of definitions, at least each one is independently understandable. —Quondum 04:23, 15 October 2014 (UTC)

Geometric intuition (fantasy rather). Lines through the origin. This may even be an even better definition: Sea urchin Now make it ultimate YohanN7 (talk) 05:34, 15 October 2014 (UTC)

Ah – I'm slow. I should have made the connection. The lines-through-the-origin picture my default, nice to have a fun name for it. —Quondum 15:39, 15 October 2014 (UTC)

You've hit upon one of my pet peeves. Different subdisciplines will "define" projective spaces in ways that are most useful for themselves. Some algebraic geometers want to work exclusively over algebraically closed fields. Coxeter wants his general projective space to resemble the real projective space, so he introduces an axiom that eliminates any algebraic structure of characteristic two. Many geometers would rather not deal with those aberrant buggers in dimension two (the non-Desarguesian planes), so they use the vector space definition (lines through the origin) which eliminates them from consideration. All these approaches can be found in the literature and what ends up in a WP page pretty much depends on the traditions that the writers have been brought up in. I am a bit sensitive to this since my core research area involves projective planes over fields of characteristic two (a double whammy on topics that are often neglected or regulated to nonexistence). Your statements about the projective line could be considered a paraphrasing of Reinhold Baer's Linear Algebra and Projective Geometry. He is one of the very few authors who actually deal with the issues rather than sweeping them under the rug when they get too complicated. I would quote him except that his language is a bit too archaic but he explicitly says that a projective line is not interesting unless you restrict its transformations to those which are inherited from an ambient space. And, just a point of clarification, Desargues theorem is provable if you use the lines through the origin approach to projective spaces, you don't have to assume it as an axiom. Some axiomatic treatments which don't want to deal with the non-Desarguesian planes may assume the theorem as an axiom to get rid of them. Bill Cherowitzo (talk) 21:33, 14 October 2014 (UTC)

On WP, we should mention each approach, rather than writing from one viewpoint, else it becomes confusing for the reader. The lead of Projective space starts with the vector space definition, without mention that the synthetic axioms are different. One has to go to section § Axioms for projective space before one get the axiomatic approach, and then it is not highlighted that these are not equivalent. Can you give me a page reference to Baer? (I presume this is Volume II). —Quondum 04:23, 15 October 2014 (UTC)

Sure. {{citation|first=Reinhold|last=Baer|title=Linear Algebra and Projective Geometry|year=2005|origyear=First published 1952|publisher=Dover|isbn=9780486445656|page=71}} Volume II must refer to the Academic Press edition of 1952, it was the 2nd volume in the Pure and Applied Math series. The section in question is III.4 The Projective Geometry of a Line in Space; Cross Ratios. Bill Cherowitzo (talk) 16:35, 15 October 2014 (UTC)

Thanks, found it. I'll need to study it a bit to get the hang of it. —Quondum 05:28, 16 October 2014 (UTC)

Linearity

Why did you revert my edit of the page linearity? I may be wrong, but why can the concept of linearity not exist in a metric space? I'm not saying all functions in a metric space are linear--I'm just saying that with the definition of a linear map, it can exist in a metric space. For example a homeomorphism between X and Y, where X and why are metric spaces but not necessarily vector spaces, can be linear, no? If not can you explain why? — Preceding unsigned comment added by Rhaycock (talk • contribs) 23:18, 18 October 2014 (UTC)

All I'm saying is this: let X and Y be metric spaces, and let f:X->Y be a map. Then f is linear if it satisfies the following: 1. f(x+y) = f(x) + f(y) and 2. f(αx) = αf(x). x is an element of X. I'm not saying it's true for all functions in a metric space. I'm saying the definition can extend to it, where x is a member of a metric space.Rhaycock

It cannot if either addition or scalar multiplication are not defined on the space X. These are not generally defined in the case of metric spaces. Take geometric Euclidean space as a simple example of a metric space: addition of and scalar multiplication of points are both clearly undefined. —Quondum 23:43, 18 October 2014 (UTC)

Ahh I see. Thanks for the clarification; not sure how I overlooked that. Could we then replace vector space with the more general normed linear/vector space, since an NLS is simply a more general vector space? NLS defines addition and scalar multiplication. It might seem a little overboard for the article. Maybe it could be said "x may be an element of any vector space, and even more generally, any normed vector space. Rhaycock (talk) 00:07, 19 October 2014 (UTC)

I'm afraid that a normed vector space is a vector space with additional structure (namely a norm), and it is thus less general. Every normed vector space is a vector space, but the converse does not hold. It would be pointless restricting the generally applicable case to a special case that is not specifically relevant to the topic. —Quondum 00:49, 19 October 2014 (UTC)

Yeah, I realize an NLS is less general now. We learned it a bit differently in a general topology class I took. Thanks bud. Rhaycock — Preceding undated comment added 09:33, 19 October 2014 (UTC)

You have the following inclusions:

Hilbert spaces ⊂ Inner product spaces ⊂ Normed spaces ⊂ Translationally invariant metric vector spaces ⊂ Metric vector spaces ⊂ Topological vector spaces ⊂ Vector spaces

It is illuminating to dig up counterexamples showing that the inclusions are strict, (except that any set can be endowed with a topology). Not all topologies are metrizable, and if they are, the may not be normable (if the latter is a proper word in math lingo ). Hilbert spaces have certain completeness properties (compare rationals and reals) that general inner product spaces don't have. Merely metric spaces can be complete in this sense too, I think Frechet space is the term, not sure. Edit: It turns out that Frechet spaces are a (strict?) subset of the complete metric vector spaces. They are locally convex with an extra condition on the metric, translation invariance. Complete spaces with norm are Banach spaces. An aside: You can sign posts by typing four tildes (~). YohanN7 (talk) 12:33, 6 November 2014 (UTC)

Then we get these inclusions:

Hilbert spaces ⊂ Banach spaces ⊂ Frechet spaces ⊂ Complete metric vector spaces

Hey Q: Sorry about doing OR on your talk page. YohanN7 (talk) 14:57, 6 November 2014 (UTC)

Quite a change of direction from the original direction ;) I was wondering about the strictness of the last inclusion XXX vector spaces ⊂ Vector spaces, since one cannot exactly provide an example of a vector space that is not an element of any specific subclass: one does not exactly define subclasses by the lack of any specific structure. E.g., not all vector spaces are normable? —Quondum 15:50, 6 November 2014 (UTC)

No, not at all a change of direction. What generalizes what is the topic ;) Yes, there are qualifications that need to be pointed out. The thing is that the algebraic qualities need to cooperate with the topology. While any vector space can be made into a a topological space, it isn't certain that scalar multiplication and addition is continuous w r t the chosen topology (hence not a topological vector space). Every vector space clearly has a topology turning it into a topological vector space (take the discrete topology, in which everything is continuous). [In the string of inclusions you replied to there was a misplaced class of "locally convex metric vector spaces". I think it fits in to the left of "metric vector spaces", but I'm not sure yet.] YohanN7 (talk) 17:37, 6 November 2014 (UTC)

If every vector space can be made into a topological vector space (as you say it can), the simplest is to drop the suggestion that the inclusion is strict (in the sense that it is a proper subclass). As to the others, most of them I have not dome more than heard their names, so I would not be able to comment on the actual inclusion sequence. —Quondum 18:23, 6 November 2014 (UTC)

The inclusion is correct in that a vector space without a chosen topology (or a badly chosen topology) isn't a topological vector space. But, you are right, this inclusion is of another nature than the other ones. For instance, a vector space without a norm isn't a normed space, but the central message is that, for certain topologies, there is no norm (metric) such that the norm (metric) generates the topology, while there is always a topology such that a vector space is a topological space. YohanN7 (talk) 18:55, 6 November 2014 (UTC)

Yeah, the semantic distinction seems to be the difference between "no defined structure of this type" and "no possible structure of this type". —Quondum 21:52, 6 November 2014 (UTC)

More OR: It appears as if locally convex metric spaces are such that an open set U is characterized by that for every element u ∈ U there is an ε such that the ε-ball around U is contained in U. With a translation invariant metric, this is evident. YohanN7 (talk) 19:16, 6 November 2014 (UTC)

Since the only topology that I have any familiarity with is the intuitive one on a real manifold, this seems fair for this case (if it is indeed a locally convex metric space). Though now one has to tuck in the "vector" part somehow. Come to think of it, studying topology and geometry using vector spaces seems wrong to me: I'd expect origin-free (i.e. affine) treatments to be the natural setting. —Quondum 21:52, 6 November 2014 (UTC)

The central object of study isn't usually the topology, but either the Hilber/Fréchet/Banach space, or, more commonly, the linear operators on these spaces and related spaces (especially dual spaces). But yes, for the purpose of studying topology one might also choose to have less structure. But if the topology is on a vector space interesting in that it it isn't "the same everywhere", then the origin may come in handy as a reference point so that one can sensibly define the topology in terms of something. Even with a topology being "the same everywhere" the origin is useful in practice. One proves results for, say, neighborhoods of the origin and then concludes that the result holds for the whole space and one can then forget about all algebraic structure as far as the topology goes.

A related (but different) thing is to show existence of solutions to differential equations. Then one toplogizes the space that must contain any solution in such a way that it is compact (locally compact or whatever). Then the existence may be established, and then the topology can be thrown away (the solution exists whether there is a topology or not). YohanN7 (talk) 08:09, 7 November 2014 (UTC)

Ricci Tensor

$Ric$ is the notation of Ricci tensor. $Ric(\xi ,\eta )$ is the evaluated value given two vectors $\xi$ and $\eta$. Thus it is not fair to say $Ric(\xi ,\eta )$ is a Ricci tensor of (0,2) type.--IkamusumeFan (talk) 20:12, 5 November 2014 (UTC)

The line was poorly expressed, granted, and I see you've fixed it now. However you look at it, since the vectors used are not basis vectors, it could not properly be called a component either. I trust that in this light that you do not feel the revert was unfair, and that a better result has now been achieved. —Quondum 20:29, 5 November 2014 (UTC)

I am very happy you agree with the current edit. Sorry I did not read the context carefully. Thanks for your reminding!--IkamusumeFan (talk) 20:35, 5 November 2014 (UTC)

Finite geometry

Hi Quondum, since we were getting a bit off-topic I thought I should switch the discussion to your talk page. In essence, finite geometry is defined by a single book, Peter Dembowski's Finite Geometry (1968). This is the bible by which all of us finite geometers swear. Dembowski does not give an actual definition of finite geometry; on page one he defines an incidence structure and he takes off from there, never looking back. Dembowski's background is in combinatorics, so this approach was natural for him. The treatment is clearly synthetic. Coordinates are introduced as needed, but not until there is enough structure assumed to make this meaningful. Non-desarguesian planes do play a significant role, but he starts with such generality that you have to go a ways before you have enough structure to have a meaningful definition of dimension, and only then can you talk about planes. In this type of generality, the transformation groups only have to preserve incidence, so there is not much to them. As more structure is added, there is more that can be preserved and the groups start to get interesting. There is a book project that is nearing completion which will probably supplant Dembowski. This is written by someone with a group theory background and I am assuming that the whole area is going to have a different look after this is published. I haven't been shown any of this work, since I think the author is afraid that I would prematurely put the material on WP, stealing his thunder; but I hold him in high enough regard to know that this is going to be a very significant publication (actually it'll be several books). We haven't always agreed on foundational issues and I expect that some of this will rub me the wrong way (I expect that the current combinatorics/group theory balance will be skewed toward the group theory side), but I'll get over it. I don't know if any of this rambling clarifies anything for you, but I can get more precise if you want. Bill Cherowitzo (talk) 20:27, 21 November 2014 (UTC)

This is gives a fairly clear picture from one definitional perspective. Even Dembowski (in his introduction) does not seem to emphasize the role of constraints on the group of transformations, e.g. the constraints that distinguish a Euclidean geometry from an affine geometry, or an elliptic geometry from a projective geometry. Surely adopting one over the other (synthetic vs. Kleinian) is counterproductive? Incidence structures with added axioms presumably produces structures that the Erlangen Program does not, and likewise groups acting on spaces gives a simple way of producing certain structures that cannot be replicated with an incidence structure with axioms on this structure, i.e. without explicitly restricting the group of transformations. So, to define what constitutes a geometry, then, one cannot avoid including the group of transformations, in both the finite and non-finite cases. And bringing this back to WP, I think the distinction between the two approaches (or at the very least which one is being adopted) should be made very clear in each article. —Quondum 03:28, 22 November 2014 (UTC)

We may be looking at the same thing, but starting in different places. What I think you are saying is – start in the infinite realm where the Kleinian view is so successful and apply enough constraints to work your way down to a finite setting. This is fine, but I don't see how you can a priori assume that the procedure won't ultimately strangle the groups (putting so many constraints on that you are left with nothing but trivial groups). My preference is to build up to the groups once the structure is rich enough to support them. This process will let in more objects that are interesting combinatorially, but not group theoretically. What I think my friend the group theorist is going to do is to define "interesting", as in an interesting finite geometry, as something for which the transformation group has an infinite analogue. That is, he will admit the more combinatorial examples, but then ignore them and treat the subject from the Kleinian perspective. I do not think that he will define them away and this means that if he does give a definition of the area it won't be in Kleinian terms. (And as an aside, I can't think of any structure produced by a group that can't be replicated axiomatically. Certainly there are cases where you would not want to do that, but I see nothing that theoretically obstructs the method.) Bill Cherowitzo (talk) 22:28, 22 November 2014 (UTC)

Starting at the different ends may lead to the class of geometries being defined differently. You seem still to be arguing for one starting point; I'm not doing so, only arguing that we must be clear about the starting point (and hence what adheres to the definition of a geometry). I'm not sure the question of what is interesting actually applies: the trivial group is not "interesting", but it is still a salient example of a group. And at least the examples that I'm familiar with (those obtainable via the group of automorphisms of a module) a significant class, and should fit any starting point. (As to you axiomatically constraining a geometry, how would you restrain an affine geometry to a Euclidean geometry, other than through some mechanism to constrain the transformation group, e.g. a metric?) —Quondum 23:40, 22 November 2014 (UTC)

It's been a hectic week at home, but there are still a couple of responses that I should make. First of all, if you don't end up with the same set of objects means (to me at least) that you don't have alternate definitions. Two approaches being equivalent almost everywhere (in its technical sense) is just not going to cut it with a combinatorialist. Metaphorically, I see you asking me to fit my square pegs into your round holes. When the holes are big enough there is no problem, but when things get small ... . Also, there is no conflict with taking an axiomatic approach. Both Klein and Hilbert (not his more famous treatment) have axiomatic developments of Euclidean geometry based on transformations. Hilbert (in his more famous treatment) transitions from affine geometry to Euclidean through the Archimedean axiom and his completeness axiom (and you need both, one or the other will not suffice). I would say that the reason there are several approaches to these topics is pedagogically driven. It is just easier to introduce and explain many concepts in a non-axiomatic way. And finally, I certainly meant no disrespect for the vitally important but still uninteresting trivial group . Bill Cherowitzo (talk) 22:05, 30 November 2014 (UTC)

I wasn't being clear. Let me try again: the definitions produce nonequivalent classes. On WP, we seem to have no clear definition of the class of objects we might choose to call geometries. The problem is more obvious with what are defined as projective geometries: the definitions used are incompatible, and the reader is not even alerted to this. More concretely:

• Projective geometry, Projective space and Projective line define it as, in effect, something that preserves cross ratios.
• Projective plane seems to be mixed up: it gives the axiomatic definition on points and lines, but then goes on to speak of vector space constructions that are nonequivalent without clarifying the nonequivalence.
• Collineation seems to adhere to the axiomatic definition.

I agree that "almost everywhere" is the same the same as "nonequivalent" in this context; this is indeed my point. If we insist on using the same name for different things, we must make it clear which case we are referring to. And if the vector space construction is being used for pedagogical reasons (which doesn't cut it on WP), but what is being illustrated axiomatically allows all collineations, the incompleteness of the illustration must be made clear.

You almost seem to be agreeing with me that the axiomatic treatment requires the concept of transformations to define a Euclidean geometry. —Quondum 22:58, 30 November 2014 (UTC)

Neutron proof details

Hi, Quondum! How do you consider the info presented in the Franz N. D. Kurie article pertaining to the disproof of the proton-electron composition of the neutron? Some essential quantitative details seem to be missing from there.--5.15.58.108 (talk) 09:32, 29 November 2014 (UTC)

There is so little information as to be almost nonexistent, and what is there is merely a passing mention in a popular science journal. The linked article refers to only two specific proton–electron models, and uses the words "he concludes that", which is not a particularly strong statement. I would only conclude that he did some work in the area. The statement "Consequently, and until the discovery of the quark structure of hadrons, the neutron was assumed to be an elementary particle" in Franz N. D. Kurie seems inappropriate, given only this reference. IMO, it is not enough to merit inclusion in the Neutron article. —Quondum 15:45, 29 November 2014 (UTC)

I agree that for the moment this info should not be mentioned. The important issue is, I think, how to find the original article(s) by Kurie before 1933 where he gives the details of disproof. Perhaps some other wikipedians could help? 5.15.187.201 (talk) 21:24, 29 November 2014 (UTC)

The best place to mention it that I can think of would be would be at Talk:Neutron. The suggestion will not get much exposure on my talk page. —Quondum 16:03, 30 November 2014 (UTC)

degenerate matter

I know that it does apply to other states of matter. I know because I clearly stated it 'as it happens with plasma'. I am trying to turn his article into one which is useful to more than 0.00000001% of the world population. Also raising interest in science while doing it. — Preceding unsigned comment added by 177.16.206.4 (talk) 18:35, 2 December 2014 (UTC)

My talk page is not the place to discuss this. Raise the matter at Talk:Degenerate matter. —Quondum 19:17, 2 December 2014 (UTC)

numerology

I'd be happy to provide the source for these remarkable equations for lepton mass ratios. However, forgive my skepticism but your reaction seems like you may be something less than open-minded. How do you define numerology? I think of numerology as an algorithmic based search for ways to combine terms in haphazard but methodical ways to find a combination that will meet observed values. The opposite of numerology is starting with a specific, coherent model for the universe, and then applying known laws in transparent calculations that reach an easily verified result. Numerology is not a valid for description for a calculation that someone may dislike because they disagree with the initial model. However, I will point out that even if I had used numerology to find the mu/electron ratio, doesn't it appear odd that the tau/mu ratio uses nearly identical terms? Not saying it couldn't be done, but it certainly makes the challenge that much harder. Anyway, if we can agree on a definition of numerology, and you're willing to take seriously the idea that at least a couple of ideas of how you think the universe works are dead wrong, then I'd be happy to give you a pointer or two. KnowMoreThanU (talk) 13:55, 16 December 2014 (UTC)

I think my reaction was sufficiently open and accommodating. This is the wrong forum for original research, and I'm not personally interested. —Quondum 15:02, 16 December 2014 (UTC)

Talk:The Spy Who Loved Me (novel)

I saw your contributions (to Wikipedia:Manual of Style in section MOS:LQ. I value your expertise. Perhaps you would like to contribute to a discussion now taking place at Talk:The Spy Who Loved Me (novel)#Logical quotation. —Anomalocaris (talk) 03:12, 23 December 2014 (UTC)

Quaternion Rotations: A Request for Feedback

Hi. I'm new here. An editor and I are having a disagreement about something I wanted to add to this quaternion page. You were active there recently, so I was wondering if I could perhaps get your feedback? The topic in the talk page is here — Preceding unsigned comment added by Patrick.rutkowski (talk • contribs) 04:44, 6 January 2015 (UTC)

You surprise me

Ha. You are usually the first to condemn original research. But this time you have set off on a flurry of your own on orientations, projective spacess, CPT-symmetry, wave function collapses, expanding universes and god knows what else. I'd say you have set a new world record in OR without supplying sources All of this is imo totally irrelevant to proper time as (it should be, haven't read it) discussed in the article. You also seem to agree with the ip, i.e. that proper time is a pseudo-scalar, at the very least that it is an arbitrary choice whether proper time is a scalar or a pseudo-scalar. Proper time for an event on a world line is what the clock passing through that event along the world line displays. No transformation in the world can change that.

I write here because I have no interest in posting every hour over there. We can discuss this at a slower pace, say once per day here if you feel like it? YohanN7 (talk) 00:26, 9 January 2015 (UTC)

I am quick to condemn OR inserted into an article (at least when I disagree with it!). Trying to get onto the same wavelength with fellow editors on a talk page is another matter. But you'll have to admit I'm pretty consistent in seldomly supplying references . I do not favour a definition that leads to proper time being a pseudo-scalar; your L&L quote is an unfortunate one in this respect. Don't mistake my pointing out holes in logic or for showing the implications of a premise for disagreement with a conclusion.

I concur that there is little value in spending undue energy there. My purpose has hopefully been achieved, though: to make it clear that the edits do not belong in the article, if for no other reason than that there are many ways to skin that cat.

I think we are in agreement that proper time should be defined so that it matches what a "real" clock would measure along a world line, whatever L&L says. So while you're welcome to debate, I'm not too sure whether there'd be much debate between agreeing parties. —Quondum 00:58, 9 January 2015 (UTC)

Let's first agree to a good nights sleep That integral over there is not relativistically invariant (as seen from its asymmetry in space and time (but it is still correct). That is why it has to be treated the way I did. But you may be right in that it didn't prove anything. YohanN7 (talk) 01:08, 9 January 2015 (UTC)

You're not helping by suggesting that the integral formulation is equivalent to a clock. It is not. Best to leave it in words: a real clock measures time in one direction, and all observers agree on what it reads at a given event. —Quondum 17:18, 9 January 2015 (UTC)

The integral integrates what the clock shows. In the other direction, define a perfect clock to show what the integral yields. Conceptual clocks are useless for a formalized theory. Mathematical definitions are not. You probably doubt me as you automatically always do, but try to find the reference I gave, and you will see that exact definition (disclaimer:don't have the book here) of proper time (with clocks thrown away). If any definition should stay, it is the integral. It is manifestly invariant and coordinate independent. YohanN7 (talk) 17:56, 9 January 2015 (UTC)

Let's leave aside what either of us has said on this particular point here; whether we agree on this is immaterial. My point is that throwing it in only invites further confusion. —Quondum 18:02, 9 January 2015 (UTC)

No, it clarifies. Q, please do your homework first, then reply. Your post above indicates that you do not understand. You have absolutely no sense about when it is appropriate to be rigorous, and when not to be rigorous. You are usually extremely rigorous when totally unwarranted (informal discussions on talk pages). In this case it is the other way around. It has gone so far that the lot of you have accused me of fucking up. It makes me a bit sick because the whole subject is the ABC of relativity (its very simplest concept). It is very appropriate to become rigorous on my part. The last post is as rigorous as fits at all on a talk page. Never again I will engage in proving the obvious. I'll take a break here and not reply until tomorrow. It costs too much frustration. YohanN7 (talk) 18:40, 9 January 2015 (UTC)

And naturally, the troll over there puts a lot of confidence in you. But the idiot distrusts me. Nice work. YohanN7 (talk) 04:32, 10 January 2015 (UTC)

I look forward to reading your reply to the troll to the question he now has. I'm sure it will be entertaining. the troll must have liked very much the post by you that begins with YohanN7, I'd say you have this exactly wrong. ... Come to think of it, the majority of your posts in reply to me begins with something to that effect. Then a lecture follows. YohanN7 (talk) 13:02, 10 January 2015 (UTC)

Several of us are frustrated by this interaction. It's time for all of us to take a break. I will almost immediately be archiving most of the content of this page, including this thread; I'm sure you'll find this via the history. I would appreciate it if you wait a week or more before reopening this discussion. —Quondum 16:26, 10 January 2015 (UTC)

Breit Rabi 1934

Ive transcribed the interesting commentary by Breit and Rabi from 1934 on the state of measurement of the neutron's magnetic moment and on the proton/electron composition of the neutron here. A copy paste from the reference PDF file. The reference is: Breit, G.; Rabi, I.I. (1934). "On the interpretation of present values of nuclear moments". Physical Review 46, p. 230. Thought you'd be interested. Bdushaw (talk) 22:51, 30 January 2015 (UTC)

Thanks. One gets a sense that there were a whole bunch of incompatible results that they had to extract sense from. I note an interesting comment: "The attempt at a conclusion that the neutron is not an elementary particle from the sign of its g factor appears to be premature. It is well known that interaction terms of Pauli's type can describe a particle with an arbitrary magnetic moment so that either sign of the g factor is in agreement with the view that the neutron is an elementary particle." I wonder what this meant. OTOH, the neutrino is considered to be an elementary particle, yet due to its nonzero rest mass apparently may have a tiny magnetic moment. Confusing. —Quondum 02:01, 31 January 2015 (UTC)

Gamma matrices

You should probably take the chance now to save your face. Think it over before you consider reverting. The statement, aside from being trivial, is now the best referenced statement in the article. Classification of Clifford algebras has nothing to do with this. YohanN7 (talk) 19:14, 8 March 2015 (UTC)

Speed of light

Hi, Quondum!I have noticed your recent edits to speed of light. I want to ask in this context about the possibility of expressing the speed of an object relatively to speed of light by comparison to the way it is done with the speed of sounds in relative Mach units.--94.53.199.249 (talk) 08:24, 13 January 2015 (UTC)

It is quite normal for physicists to use the speed of light as a unit in many contexts, for example by refering to a particle travelling at 0.999999 c. The further simplification may be made where this unit is omitted, or equivalently treated as equal to 1. You may be interested in reading articles such as Fundamental unit, Natural units and Geometrized units. This would seem to me to be comparable to how the Mach unit is used. —Quondum 15:24, 13 January 2015 (UTC)

Often "β" is used for the ratio of the speed of an object divided by the speed of light, $\beta ={\frac {v}{c}}\,.$ JRSpriggs (talk) 06:19, 14 January 2015 (UTC)

Is there a name for this beta in analogy to Mach number, like perhaps Einstein number of Photo-Mach?--94.53.199.249 (talk) 16:19, 17 February 2015 (UTC)

According to Lorentz transformation, β is called the velocity coefficient, and the vector equivalent is called the relative velocity vector, but don't take that as given. Simply "c" seems to be common as a "unit", as in my example above. Perhaps one could regard the symbol as 'c', and the name of the of the unit as 'celeritas'? There is a quantity closely related to β, called rapidity φ = artanh(β). —Quondum 19:49, 17 February 2015 (UTC)

Can this velocity coefficient β as a quantity be applied to the speed of sound? It seems that Mach unit is/can be a dimensionless unit for the speed of sound velocity coefficient.--94.53.199.249 (talk) 14:15, 14 March 2015 (UTC)

This seems to be going in circles. The Mach number is essentially that, except being defined in relation to the speed of sound in a medium. If you mean β in relation to the speed of light, yes, technically it can, though something at the speed of sound would then have β ≈ 10⁻⁶. —Quondum 15:11, 14 March 2015 (UTC)

Thanks

Thanks for your perceptive guidance at Talk:International System of Units/Archives/04/2015#The SI and the ISQ. NebY (talk) 16:32, 30 March 2015 (UTC)

My pleasure, though I just thought of it as chipping in my opinion (which is not always received well). I've actually learned a bit about the ISQ in the process. Thank you for polishing up that niggling issue of cross-dependence. —Quondum 16:52, 30 March 2015 (UTC)

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Troublesome editor

I ran out of patience...

There is currently a discussion at Wikipedia:Administrators' noticeboard/Incidents regarding an issue with which you may have been involved. Thank you.

Bdushaw (talk) 06:56, 31 March 2015 (UTC)

You should not run out of patience, Bdushaw. These emotional reactions are not advisable (I'm also tempted to be irritated by Bdushaw's irritation/lack of cooperation, but that would be contrary to my own demand of advisability). Please familiarize yourself with relevant wikipolicies before making edits that on the verge of tendentiousness. The troublesome is certainly not me.--5.15.185.197 (talk) 07:51, 31 March 2015 (UTC)

The new speed of light section

Hi, I think it is right to be very careful there. The source does not seem to be very neutral - I cannot check the translations, their interpretations seem to be very favorable for the old texts. Like being surprised that they knew the ratio of the Moon's diameter to its distance to earth - a simple angle measurement. And you have to subtract the radius of earth from the semi-major axis to get that value of 108. --mfb (talk) 01:10, 4 April 2015 (UTC)

I was trying to make it as non-misleading and unobtrusive as possible while placating the person whose agenda it is to place it in the article, hoping to stop the edit warring. Your description is IMO very charitable. —Quondum 02:34, 4 April 2015 (UTC)

Your revert of my changes to Diffie-Hellman

Wikipedia is not the place for personal opinions. When the reason for you revert starts with "I disagree" you are admitting that it is personal opinion, not verifiable from reputable sources. I have re-edited the page to add CN for this statement. There's a huge difference between an algorithm used by public-key crypto and being an instance of public-key crypto.

I also aded a note that "some people" consider this to be public-key cryptography although I don't know any people other than you that believe that. If there are reputable sources other than your personal opinion, please cite them. Otherwise, please reconsider your revert of my changes. --- Vroo (talk) 18:54, 4 April 2015 (UTC)

My edits were immediately reverted by an "anonymous" user. Please see discussion on the talk page. --- Vroo (talk) 20:13, 4 April 2015 (UTC)

I removed my latest comment here as I realized I was not replying to you but to that anonymous user. --- Vroo (talk) 06:04, 5 April 2015 (UTC)

Request for mediation rejected

The request for formal mediation concerning Vectors are not tensors, to which you were listed as a party, has been declined. To read an explanation by the Mediation Committee for the rejection of this request, see the mediation request page, which will be deleted by an administrator after a reasonable time. Please direct questions relating to this request to the Chairman of the Committee, or to the mailing list. For more information on forms of dispute resolution, other than formal mediation, that are available, see Wikipedia:Dispute resolution.

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Move review for Carbon (fiber)

An editor has asked for a Move review of Carbon (fiber). Because you participated in the move discussion for this page, you might want to participate in the move review. Srnec (talk) 22:41, 17 April 2015 (UTC)

Sesquilinear form

Hi Quondum. With the two of us working on this page simultaneously it has been a bit of a challenge to keep the formatting consistent - but I'm not complaining. Just wanted to let you know that I'm only planning on adding a little something about dual modules to the last section so that I can get a tie in to projective geometry dualities and then I'm done with this page (unless you see some glaring omission that I should patch up). I only have one quibble with your edits - in the finite field example I'd like to go back to the specific automorphism that I used instead of the generic name for that automorphism. I think that if an example is going to help someone understand a passage in an article, it should really be as concrete as possible. That was the reason I set the example in 3-space rather than n-space and why I prefer the qth power way of writing it. Bill Cherowitzo (talk) 23:22, 4 May 2015 (UTC)

Sorry, I am sometimes a little impulsive – I should not be getting under your feet while you're editing. I was trying only to make formatting consistent with what seems to be the dominant convention in the article, but that is something that should wait if it makes your life difficult. I'm not particularly stuck on any format, though I tend to try to keep MoS consistency (e.g. roman named objects, italic variables). If you have a preference on formatting, just say. I've changed back to the qth power; I have no objection, though I may be tempted to reorder the statements slightly to provide a smoother flow, along the lines of "Here is a mapping defined on two vectors defined in terms of their components, and given that the map σ to the qth power is an involutory automorphism, it follows that the given map on the vectors is a σ-sesquilinear form." —Quondum 02:23, 5 May 2015 (UTC)

Rings commutative every day of the year?

Here is an edit (look at the motivation) that you might be the right person to handle: [Orthogonal group]. It might be right and it might be wrong. Best! YohanN7 (talk) 11:32, 19 May 2015 (UTC) Hm... Associative, not commutative. Sorry, not awake yet. too little coffee. but the Q perhaps remains? YohanN7 (talk) 11:43, 19 May 2015 (UTC)

The edit is perfectly legitimate. It's established that "division algebras" can refer to nonassociative algebras, but certainly "division ring" is not used outside of associative rings. Strange, I know. Rschwieb (talk) 12:49, 19 May 2015 (UTC)

Yeah, Y noted that. But the concept of a projective line over a non-ring (the octonions) is foreign to me, so Incnis's earlier edit may be suspect (or at least someone with an understanding of this construction would have to look at it – it is beyond me). —Quondum 14:03, 19 May 2015 (UTC)

Beltrami–Klein model‎;

hi, I created a new section in the Beltrami–Klein model‎ especially about the 2 dimensional case as discussed on the talk page.

I did do some editing on the other parts of the page (renaming the Poincare disk model to the poincare ball model and maybe others as well )

Will try later to add some pictures to it, I am wondering about some statements used at the rest of the page (for example that the two disk models are projections ofeachother, it is not that simple) can you check and where nescessary improve them. (please continue this discussion on the talk page of the beltrami klein model when needed.WillemienH (talk) 10:20, 21 May 2015 (UTC)

Neutron magnetic moment reviewed

You may have noticed that we have a review of Neutron magnetic moment as a "good article". The reviewer has raised some issues which I've been thinking about. I've gone about as far as I can with the article, but I am a little too close to it, so solicit your wiser input. The main sticking point (not really sticking though) seems to be whether there is original research or not - I've done what I can to redress the issue (maybe its ok now?). Perhaps a fresh set of eyes will provide a better resolution. ("Thirty years in the wilderness" is on the cutting room floor; too bad. :) ) That failed pion theory is not really discussed much in the modern sources; it just didn't work. It leaves a curious 30-year hole in the theoretical history that people do wonder about! Bdushaw (talk) 04:48, 8 May 2015 (UTC)

Thanks for your assistance and moral support in bringing this article up to "Good Article" status. It was a good exercise, I thought. Cheers, Bdushaw (talk) 19:28, 11 May 2015 (UTC)

Congrats. You did a good job there – you have a lot more energy than I have. You've improved the referencing massively, and added some key points. Your attention to sourcing of the detail is great – a definite quality factor in WP. I enjoyed the interaction (as also with Neutron and related), though in some ways I felt that I was running interference more than anything with my opinionated approach ;). —Quondum 19:42, 11 May 2015 (UTC)

To editor Bdushaw: Is the pion theory really so "failed"? I glanced at some apparently recent material about it, suggesting that it is a coherent quantitative approach, and that it is being revived. AFAIK it has always been strong in models of inter-nucleon forces, and presumably in nuclear decay mechanisms. —Quondum 02:55, 24 May 2015 (UTC)

You are correct, the notion still seems to have some theoretical correctness. I mentioned this on the neutron magnetic moment talk page - viz, the moment seems to be the contribution from quarks, plus a correction due to pions - I had run out of steam by then, and wasn't sure what was the accepted theory. The references I found were to original pubs - in this technical field I would be nervous taking some of those articles and writing an encyclopedia article about it. There is a "cloud" of pions, but what is the contribution to the magnetic moment? What has been verified by experiment and what is the accepted theory? I am likely to be mostly away from Wikipedia in coming weeks; distractions loom. Bdushaw (talk) 05:59, 24 May 2015 (UTC)

Well, yes: what we can actually say about the contribution to the magnetic moment is very little, in WP. That is not what most people will be focusing on. But nevertheless, intuitively it might have a significant effect, because charged and uncharged pions "leak" into a larger radius than the nucleon's radius, affecting the mass and charge distribution. At moment, the only mention of pions is a theory that failed because of the incorrect "bare" neutron hypothesis. The newer quarks-and-pions could be given a mention, if either of us comes across suitable material. —Quondum 06:18, 24 May 2015 (UTC)

Velocity

Hi. There is an ongoing discussion on the velocity talk page attempting to clarify position and displacement. Please explain there why you want to switch from velocity to instantaneous velocity, and from displacement to position. It would be helpful if you would refer to a calculus text where velocity is developed, or to the path of a frightened fly in a closed glass box. Change of 'position' seems particularly misleading. Thanks, BlueMist (talk) 23:08, 23 May 2015 (UTC)

The thread Talk:Velocity#Position and Displacement seems a bit inactive to be called "an ongoing discussion". If you would like to discuss detail, open a thread there rather than here. I'll make a note there about "instantaneous velocity". —Quondum 23:38, 23 May 2015 (UTC)

I've added comments on both issues on the talk page. Feel free to respond there. —Quondum 02:48, 24 May 2015 (UTC)

Thank you for the clarification. BlueMist (talk) 06:41, 24 May 2015 (UTC)

template:Dimanalysis

Good work on the template (and the related subtemplate)! Although sometimes I have seen square brackets used around the dimension symbols, so kept the possibility in the original creation, but if it's nonstandard then feel free to leave out. Thanks M∧Ŝc²ħεИ_τlk 18:55, 24 May 2015 (UTC)

The standards bodies seem to be quite firm in the "roman sans-serif type" for dimension symbols. Are you sure the brackets are not a confusion by various parties? Brackets are defined (in the document that I linked in the template documentation) to mean "units of", as in [5 kg] = kg, so I can see where it may have crept in. I think leaving them in as an option (and hence as a suggestion that it might be standard and as an invitation to use it) is dangerous: it risks creating a badly confusing usage on WP. I realize I've stripped out something that must have been a hard work to produce (heck, I barely understand the template syntax), but c'est la vie. —Quondum 19:08, 24 May 2015 (UTC)

You're likely correct, I can't remember where I saw brackets used for dimensions, maybe just confusing them with what you're describing [square brackets around quantity meaning "units of"]. M∧Ŝc²ħεИ_τlk 21:27, 24 May 2015 (UTC)

Speed of light

Re: An interesting choice of normalization would be to put 1 = −c².
Or 1 = −c² = (ic)². An interesting choice, indeed! Thanks for that. — Preceding unsigned comment added by Rjowsey (talk • contribs) 2015-06-04T10:39:55

You might want to understand the rest of the footnote. One can have many distinct quantities κ_j with the property that κ_j² = ±1, so the traditional use of the simple imaginary unit i can lead one down a rabbit hole. —Quondum 13:21, 4 June 2015 (UTC)

Indeed! Even down a Wormhole... Rjowsey (talk) 20:08, 4 June 2015 (UTC)

Fundamental physics: dimensional analysis

	Well done!!!
	Thanks for your edits. They're very helpful. :D Rjowsey (talk) 09:47, 31 May 2015 (UTC)

Thanks. I see you've done a lot of work there; the topic deserves more exposure. I've left a comment on the talk page of the article. —Quondum 14:17, 31 May 2015 (UTC)

I've come to realise that you're entirely right about removing my L/T material from the Dimensional Analysis article. Although it's all a very natural extension of Maxwell's toolkit (he would've absolutely loved it!), it's going way too far, too fast, to be useful in terms of understanding the fundamentals of traditional DA. Because I live, eat, sleep and breathe imaginary space/time dimensions, they've come to feel very "real" to me. But they really don't for the vast majority of people (except for a few quantum physicists, perhaps). So I've come round to an understanding of the point you're making, and am moving all my L/T contributions onto a new page. Once it's cleaned up, it can be linked from the main DA page. Rjowsey (talk) 23:32, 2 June 2015 (UTC)

That sounds like a good idea. It is a related rather than the same topic, a specialization and application of dimensional analysis. So as you say, it is not "traditional DA", which is what the DA article's topic is.

As a topic in its own right, of course it will need the usual notability, referencing etc. I only only saw one reference (Wesson), and have not looked through it (Maxwell does not count for that topic; he preceded it.) But that side is up to you – if you can adequately outline and reference sources for the particular development in physics (you'll also need an article name), that would be great. Linking to such an article from the DA article would be natural.

My interpretation of Maxwell was that he was simply headed down the route that culminated in Planck units, which in a sense is the very opposite of dimensional analysis. His speed of electromagnetic waves was maybe just too new for him to normalize it too. Also, space and time were such familiar quantities that he probably was happy once he'd expressed everything in terms of them.

Since you refer to "imaginary space/time dimensions", it seems to me that the distinction (in a sense the factor i) is what is important to you, rather than L and T. Is this the case? That way, you'd get rid of T via T = iL, and still keep what you need. I like to deal with that in a different way, which in the DA way of thinking would translate to the directional units 1_t, 1_x, 1_y, 1_z. The exterior algebra over a vector space with a Minkowski form is what I naturally think of here. —Quondum 01:46, 3 June 2015 (UTC)

As a physics history geek, I'm deeply interested in how certain concepts, styles of thinking, and mathematical techniques/tools have, over time (particularly the past century), brought us to an impasse, the so-called "crisis in physics". So, in my new topic (tentatively titled Complex Spacetime), I intend to trace this history in some depth. Beginning with the little-known fact that Maxwell's ideas about spacetime were instinctively complex, i.e. his geometry had two invisible imaginary dimensions to accommodate the E and H potentials, plus another for gravity (the complex conjugate of time), all three being orthogonal to real Euclidean space. In his mind, and in his math, these comprised 6 distinct and different orthogonal spatial dimensions. Thus, he used a "heretical form" of quaternion math, stating emphatically that tensors and vectors were inadequate for encapsulating his EM fields and forces. He also quietly discussed with colleagues how one might detect and measure "non-observable" or "hidden" spatial dimensions, which he conceived of as "storing energy", both kinetic and potential, in the very fabric of space itself. His quaternion notation was eliminated from the Treatise at the insistence of his publisher, over his strenuous objections, because very few people could understood the math (so his book wasn't selling well). His equations were then butchered by Heaviside, who tossed out Maxwell's potentials, stating them to be "mystical" and "metaphysical". Minkowski was a mathematician, not a physicist, so he pressured Einstein to eliminate the imaginary unit from GR. Thereby, for the past 100 years, while QM dived deeply into complexity, SR and GR remained stuck with Minkowski's 4-dimensional approximation. Which works extremely well (although the math is hideously complicated), right up to the event horizon of black holes, where it goes to infinity, and results in impossible singularities at the center. I predict (with complete confidence) that 21st century relativity will be based on a 6D complex spacetime, which seamlessly merges with QM, at all scales. From such a complex geometry (plus phasors), electromagnetism naturally falls out, the Planck units fall out, special and general relativity fall out, and quantum spin falls out, including the spin-0 and spin-2 bosons! Then, there's E8 Theory for the particle zoo... but now I've fallen right down the rabbit hole, so I'd best stop babbling! LOL —Rjowsey (talk) 05:15, 3 June 2015 (UTC)

As I commence writing up this topic, I'm constantly asking myself "how would an intelligent 17-year-old (or a median IQ 35-year-old, with a reasonable education) understand this sentence?" Would they immediately go "WTF?!", and hit the back button? What questions would they ask? Can they easily drill-down into any of the technical terms and definitions, and access any mathematical concepts that aren't transparently obvious to a 9th-grader? Does the narrative make gut-level sense, as an easily-absorbed story about human curiosity, exploration, and discovery? I'm trying to ignore my inner admonitions about "academic credibility", and "peer acceptance", because those voices have absolutely no relevance to Wikipedia's target audience. Curious, intelligent, educated people are the audience, not academics or professional researchers. Your thoughts? —Rjowsey (talk) 10:06, 3 June 2015 (UTC)

As a style for writing, your criteria here make perfect sense, but is at the same time a challenge. But documenting the thoughts of others as a historian and putting together a consistent theory from it are two completely different things. I like to get to understand the mathematical tools, and their correspondence with whatg is being modelled. In particular, I like to understand where the model adds structure that does not occur in what is being modelled, and is thus in a sense arbitrary, or more importantly, can lead one to conclusions that do not follow from the premises. An example is the choice of a basis: one of the great insights of tensors is that nothing of what is being represented can depend on this choice. This sort of approach applies to anything involving complex numbers too, or they can be treated as a vector space with no "real" part. For example, the complex numbers can be embedded in the quaternions, but it is useful to understand that there is not a unique embedding. One needs to distinguish between a spacetime (a manifold) and the quantities that are associated with points in space (some of which may be tangent to the manifold). In what you say above, it is unclear which if these you are referring to, though you seem to want to identify the two, which cannot be done (a manifold and the tangent space at each point do not have a natural identification, if any). —Quondum 13:59, 3 June 2015 (UTC)

Re: "documenting the thoughts of others as a historian and putting together a consistent theory from it are two completely different things." I agree 100%, but here's the thing: I'm not trying to construct any theory. My point is that 6-dimensional complex spacetime was Maxwell's idea (perhaps Faraday's too, but he had zero math chops). Maxwell struggled valiantly to communicate this key concept to his peers (using quaternion math), but tragically died before he could clarify it further. History has amnesia about that fact, because Heaviside simply didn't grok it. Let me ask, why do you think GR doesn't play well with QM? What's missing? Rjowsey (talk) 20:52, 3 June 2015 (UTC)

You'd have to articulate what the "6-dimensional complex spacetime" in such a way that it hangs together. Can we even work out what was intended? Was it in any sense complete? I'd have to ask many questions before forming an idea of roughly what is intended.

Yes, we can work out "what was intended", by carefully studying his conversations with colleagues, and his mathematics. Over the past 40+ years, I've done exactly that. It wasn't "complete", but then, neither is GR. And, I assert, Maxwell's forgotten ideas about complex 3r+3i spacetime provide the golden key to unlock unification of GR+QM, and to completing GR so it works "inside" black holes and at the big bang. Not with any new theory, nor any particular interpretation, but with a simple, elegant, unified 6D mathematical framework for both, plus EM and the Planck Units. Rjowsey (talk) 03:02, 4 June 2015 (UTC)

The GR/GM incompatibility is a whole discussion, but if you at least have a moderate understand MWI, it should be obvious. In GR, the geometry of space is determined by the content, which is in a superposition of states according to QM, and thus the spacetime manifold itself must be in a superposition of states. But QM is formulated in a single spacetime continuum, not in a superposition of spacetimes – the very concept of a linear superposition of the wavefunction at a point of spacetime becomes ill-defined. —Quondum 22:27, 3 June 2015 (UTC)

6D math implies that Hestene's "Zitterbewegung interpretation" [D. Hestenes, The Zitterbewegung Interpretation of Quantum Mechanics, Foundations of Physics 20: 1213–1232 (1990)] is closest to reality. Hard on its heels would be Cramer's "Transactional interpretation" [The Transactional Interpretation of Quantum Mechanics by John Cramer. Reviews of Modern Physics 58, 647–688, July (1986)]. The truth is out there! ;-) Rjowsey (talk) 21:55, 4 June 2015 (UTC)

The problem I see in unifying GR with QM is that in QM one must be able to recombine different histories of the system to determine whether the interference is constructive or destructive, but that requires a common background (metric or coordinates) which can be used to match the different parts of the histories while GR has no such background. JRSpriggs (talk) 03:59, 5 June 2015 (UTC)

Damn good point! The key to unpacking your statement is the word "histories": if you burrow into the Dirac equation deeply enough, you'll see that one of the spinors is oscillating in time, so it's going forward, then backward, in both space and time. So the notions of post-causality and retro-causality become fundamentally moot points in QM. "Time is suspect" said Einstein, famously. Then his good bud Kurt Gödel turns up with Closed Timeline Loops on his 70th birthday, bit of a fun prank I guess, but Gödel was making an important point, mathematically. There's no common background spacetime metric. SR/GR sits atop a classical 4D spacetime; QM inhabits a Hilbert configuration space, which is intrinsically complex. The Dirac bispinor oscillates in 6 dimensions, 3 real (x,y,z space) and 3 imaginary (i,j,k space/time). So, the only way to have these worlds play nicely together would be to refactor special/general relativity into a 6D complex spacetime, like the one a particle's wavefunction inhabits. Good news is, it can be done. Rjowsey (talk) 08:48, 5 June 2015 (UTC)

JRSpriggs has rephrased the superposition problem well. But rephrasing a 4-d spacetime background in terms of a 6-d spacetime background does not appear to me to solve this particular issue. Reinterpreting in terms of Hilbert space makes sense to me; I'm not sure that there is any contradiction here, and this is the space in which superposition really applies. The transactional interpretation and zitterbewegung seem to me to add nothing and to draw mathematically false conclusions if they are in any sense claimed to be distinguishable, akin to that saying that 7 = 4 + 3, but not 7 = 2 + 5. —Quondum 13:32, 5 June 2015 (UTC)

Let's get ourselves on the same page, mathematically speaking. Soak yourselves in this graphic for a while: https://upload.wikimedia.org/wikipedia/commons/3/34/SpinZero.gif — It's the 6D wavefunction of the Higgs boson, in supercooled vacuum. Top-left quadrant is the classic 4D Minkowski diagram; time is up the y-axis, space lies along the x-axis. The bottom-left projection pertains to momentum, aka kinetic energy; the top-right projection pertains to imaginary time and potential energy (kinda-sorta). The bottom-right quadrant shows the cross-product of the kinetic and potential energy sinusoidals. This bispinor represents ground-state spacetime, an elemental vibrating space/time string, aka "spin-foam". Then let's talk some more about time, and superposition, and probabilistic truthiness... :D Rjowsey (talk) 22:49, 5 June 2015 (UTC)

BTW, unity density is Planck density, and 0.25 density is an event horizon, like you'd find around a black hole. By way of contrast, have a looksee at the wavefunction for a spin-2 boson, which has phase offset of PI radians (180°), and whose bispinor, you'll notice, never oscillates into real time and real space at the same time. https://upload.wikimedia.org/wikipedia/commons/6/62/SpinTwo.gif — It's a CPT-inverted Higgs, and although purely imaginary, actually exists, because gravity. Rjowsey (talk) 04:54, 6 June 2015 (UTC)

The ground state of a canonical spin-1 boson's wavefunction, with phase offset of π/2 (↑-spin, R chirality), oscillates like so: https://upload.wikimedia.org/wikipedia/commons/e/eb/SpinOneUp.gif Its CPT-inverted (↓-spin, L-chiral) sibling, with a phase offset of 3π/2, oscillates like this: https://upload.wikimedia.org/wikipedia/commons/b/be/SpinOneDown.gif In 6D spacetime geometry, these "wavicles" manifest as massless photons propagating in null-time. At the next energy level, thus inhabiting an 8D or (3r+5i)-dimensional geometry, these bispinor wavefunctions manifest as gluons, (metaphorically) arranging themselves at the 8 vertices of a cuboctahedron, therefore congruent with String/E8 Theory. But that's way down the rabbit hole... ;-) Rjowsey (talk) 08:13, 6 June 2015 (UTC)

Finally, there's the spin-half fermions, e.g. the ground-state massless neutrino (my favourite invisible lepton). There are two L- and R-chiral fermions, plus two L/R-chiral anti-fermions, so the 4 fermionic wavefunctions having phase offsets of nπ/4 (where n = 1, 3, 5, or 7) oscillate like so:

https://upload.wikimedia.org/wikipedia/commons/1/10/SpinHalfUp.gif

https://upload.wikimedia.org/wikipedia/commons/e/e7/SpinHalfUpAnti.gif

https://upload.wikimedia.org/wikipedia/commons/9/98/SpinHalfDownAnti.gif

https://upload.wikimedia.org/wikipedia/commons/4/46/SpinHalfDown.gif

Isn't this skipping over too much? There is no conceptual framework to hang this on. You've said nothing about the manifold of spacetime points, its tangent space and where in the exterior algebra of this tangent space the wavefunction belongs. —Quondum 12:45, 6 June 2015 (UTC)

You're absolutely right, and thanks for that!! Very, very useful. I tried to unpack your questions starting with "the manifold of spacetime points", as if I were tutoring a bunch of 16-year-olds. And that led me to the core concept in Einstein's interpretation of Poincaré's work on the Lorentz transformation, which Einstein conceptualised as the "mixing" of space and time, in special relativity and in GR. I've always felt uneasy about that notion, because I couldn't explain it simply, to kids, without complicated math and a bunch of hand-waving. Ditto for GR, where we find a 4D Minkowski "manifold", and a "metric", and x₀ being rotated into x_mumble. That same "space-time mixing" thing. And it works, perfectly well, right up to the event horizon of a black hole. Einstein realised, when Schwarzschild's solution predicted an impossible singularity inside a black hole, that his general relativity was "incomplete". Then Kaluza and Klein came along with a nifty 5D solution for GR, out of which fell Maxwell's equations, quite naturally. Einstein spent the next 30 years trying to find a way to fix his theory of relativity, and, reading his last few papers, he came very close. Meanwhile, Pauli, Dirac, Schrödinger, et al were burrowing into QM, using Hilbert's complex configuration/state space, which is very similar, mathematically, to the quaternion-based (3r+3i) space that Maxwell was (sorta-kinda) using behind his electromagnetics equations. Kids don't know anything about "manifolds", so they never ask that question. However, they intuitively understand what a "point of spacetime" is, so I begin there, by describing an infinitesimal volume of space, a Planck volume. It's utterly empty (vacuum), and absolutely cold (zero degrees K). It has Planck length (~10^—43 metres) in x, y and z dimensions; you'd probably want to label those x₁, x₂, and x₃, because you're thinking in a more abstract coordinate frame. Then you'd probably add a time dimension, labelled x₀, as did I until a few years ago, when I found another way to understand special relativity. Geometrically. In Maxwell's 3r+3i space, the Lorentz rotation becomes a phase angle φ, on an imaginary plane, and β = v/c becomes sin(φ). The Lorentz gamma becomes cos(φ), because sin²φ + cos²φ = 1. There's no "mixing" of space into time. Space is what rulers measure, and time is what clocks measure. These fundamental dimensions don't get mixed up, so we don't actually need any kind of "manifold". Plus, that geometrical solution works perfectly all the way through a BH's event horizon, and keeps on working perfectly, all the way down to φ = 2π (= 0). The fundamental "manifold" is simply empty, flat, vacuum, with 5 dimensions. If we put some mass into this space, its phase angle increases as φ/2π = (Gm/rc²)², which 16-year-olds can easily use to calculate what you'd think of as "curvature". In fact, they're able to derive that equation from first principles, from Newton's Law of gravity, once I show them how φ goes to π/2 at the Schwarzschild radius. They can understand that Einstein's "spacetime curvature" is actually an illusion at the "conformal boundary" of 5-dimensional space, because we can only observe its 3-dimensional surface. I explain to the kids that this is like a 3-dimensional hologram, because they want analogies, and examples, and simple animated graphics. Then, if we introduce some energy into this space, we can see that a harmonic oscillation happens, that there's an observable vibration in the fabric of spacetime, at some frequency f = E/h. If I were teaching this stuff to kids, I'd also mention that if we squeeze an entire Planck unit of energy E_P (a Gigajoule) into this Planck volume of vacuum, we just made ourselves an infinitesimal black hole, because they love that idea! I'd also point out that the oscillation of this microscopic black hole is at Planck frequency ω_P = E_P/h (~10⁴³ Hz), because that would make sense to them. The Dirac equation tells us that this fundamental harmonic oscillation has (at least) 2 orthogonal sinusoidal waveforms (functions of e^iθ), one pertaining to kinetic energy, the other to potential energy. But these equations need 5 spatial dimensions and one of time, so I'd introduce Maxwell's ideas about imaginary spatial dimensions (which exist, but aren't exactly "real"). The analogy I'd use might be that of a sphere passing through a flat 2D surface, or I'd show them an animated tesseract, because that would help them visualise an imaginary volume "behind" or "inside" every point in space. Since now we have a simple 6-dimensional spacetime, they're able to understand those wavefunction animations, like ripples on a pond, like vibrations of a field. The unified one that Einstein was looking for. Rjowsey (talk) 04:20, 7 June 2015 (UTC)

So you have a 6-dimensional real differentiable manifold. All that says us that each spacetime point (event) can be coordinatized by six real parameters in a continuous fashion, irrespective of whether some dimensions might be "imaginary", since that is determined by additional structure (such as a metric). This is already enough to do a lot: one can form the tangent space at each event, and differentiate and integrate. One can consider an open region, and thus not need to worry about the global topology. We do not need to consider metric/flatness/curvature or the distinction between space, time, not-so-real dimensions, and "mixing" (yet). But for intuition's sake, how does our visble set of four real dimensions map into this? As an embedded 4-d submanifold, or do points map to entire 2-d submanifolds? —Quondum 04:58, 7 June 2015 (UTC)

I don't know. An embedded submanifold, I guess. What do you think? Rjowsey (talk) 05:49, 7 June 2015 (UTC)

How should I know? I'm not the one saying that this produces good results. I'm simply trying to fill in the gaps where I cannot put a coherent and complete interpretation to what has been said so far. I like to pare everything down to the minimum structure for clarity of thought and conceptualization. As you can see, I've stripped it down to the barest structure that fits the description "six-dimensional spacetime". One way to hide the additional dimensions is to wrap them very small, as I understand is done in Kaluza–Klein theory. Unless one has some idea of how the additional dimensions become invisible, it is difficult to proceed. If the mapping is to an embedded manifold as a slice across a "large" dimension, there needs to be a mechanism that confines the observable world to that submanifold. —Quondum 06:03, 7 June 2015 (UTC)

OK, now I understand, I think. First, forget compactified dimensions — that's an very obsolete notion that belongs in the dustbin of history. There's no experimental evidence. Paul Wesson wrote a paper a few years back which described 3 different ways of understanding KK's extra dimension; one of them had some resonance with the way I'm thinking, namely "projection" mumble-something. I'd have to dig out the paper. Essentially, as I understood him, if you have extra (imaginary, whatever) dimensions, you can project from a certain point of view onto a 2D plane surface (or into a 3D volume), and move your "camera angle" around-about in the hyperspace, like you're projecting a shadow of an n-dimensional shape onto a 2D screen. And Garrett Lisi uses this technique with his E8 Theory applet, which is very neat, so that you can rotate the 8-dimensional hypervolume around various axes, and thereby visualise (in 2D) the pattern of particles, whatever, in the 8D geometry. Math says that the imaginary spatial dimensions are infinitely large, as are the 3 real spatial dimensions, and there are (potentially) an infinite number of them. But we can't interact directly with, nor observe, nor measure them. So it's really difficult to describe what they are, exactly, except mathematically. They're not real, they're imaginary. But they exist, because gravity and electromagnetism and Planck units. This projection idea is what I used to build those 8 spin animations. I wish there was some better way to answer your question (which, as usual, is a good one). Maybe somebody much smarter than me could chime in, and help us both out. My brain is fried. Later... Rjowsey (talk) 08:56, 7 June 2015 (UTC)

Time is an imaginary dimension, indistinguishable from your imaginary space dimensions. Yet it clearly has a different physical significance. You need a mechanism to spearate these. —Quondum 16:44, 7 June 2015 (UTC)

In a 6D framework, time is what clocks measure. In Einstein's 4D Riemannian geometry, time is dimensioned as a distance (ct), and "spacetime" is a unitary object. Thus, a Lorentz rotation appears to mix time into space, to explain time dilation and length contraction. That's the way I learned to think about special and general relativity, and it's taken me many years to unravel that idea, and learn how to think in 5 spatial dimensions, evolving through time. In a (5+1)D geometry, distance is measured in metres, and time returns to being just time, measured in seconds. Time is what clocks measure; time is not a distance. The way I'd explain this to 16-year-olds would use the analogy of a world map, like the one on the wall in their classroom. Comparing the size of, say, Antarctica on this map to the continent at the bottom of a spherical globe, we can see that its size has become highly distorted when the mapmaker "projected" the surface of a sphere onto a flat piece of paper. This exact same distortion happens when we reduce the imaginary spatial dimensions of a 5D hypersphere into 3D Euclidean space, at the boundaries or edges we call an "event horizon". We see the distortion (at such conformal boundaries) as a warping of spacetime. This illusory effect happens at the "horizons" of our 3D hologram, so time appears to stop at the event horizon of a black hole, and conversely, time appears to be exponentially accelerated at the event horizon we call the big bang (according to the math at time-zero). The same distortion can be seen at a temperature near absolute zero, when time appears to stop, so light stops moving. This event horizon marks out a conformal boundary between our positive energy/forward time "3D universe" and a negative energy/reverse time "5D universe". Just like a hologram with blurry edges. That's the only way I can understand what the math is saying. I follow where it leads, down the rabbit hole...

Well, this doesn't give me many hooks to hang concepts on. —Quondum 03:28, 8 June 2015 (UTC)

Sorry about that, Chief. My main point is that 5D space is perfectly flat in every dimension, so simple Euclidean geometry rules. All that complicated partial differential calculus and those metrics and manifolds and tensors and Christoffel gammas and index acrobatics of Einstein-Minkowski's GR will (eventually) be replaced by a much simpler mathematical framework, based in pure geometry, just as Einstein's intuition told him was in there somewhere. He was right. Which particular concept did you want a hook for? Rjowsey (talk) 04:30, 8 June 2015 (UTC)

So, we have a "flat" space in all 6 dimensions. At least conceptually, since a distance metric has yet to be clarified. The "imaginariness" of two if the dimensions has not been given any meaning, nor has a way of mapping our perception of coordinates into this space, although you've implied you might be thinking of a privileged subspace (or "brane"?) that would be what we "inhabit". You also seem to want to define a distance measure, but this is difficult to reconcile: you seem to want to define distance in a Euclidean sense √(Δx₁² + Δx₂² + Δx₃² + Δx₄² + Δx₅²), but this conflicts with the idea that two of them are imaginary, which would suggest √(Δx₁² + Δx₂² + Δx₃² − Δx₄² − Δx₅²). So where do particles and fields fit into this structure? And gravity? These are things I need hooks for, and for someone who seems to think this is all but sewn up, you're amazingly short on detail. If you want to convince me you even have anything, you need to provide detail that has substance. If you want be secretive, fine, but then don't proclaim that the theory is about to take the world by storm. —Quondum 05:08, 8 June 2015 (UTC)

The hyperspace I'm describing is flat in 5 spatial dimensions, two of which are (mathematically) imaginary, so they are unmeasurable by any real ruler; they're non-observable, hidden, invisible. They're not compactified, nor rolled up. Time is just imaginary time, so it, not ict. We inhabit 3D space, moving through time, and we observe event horizons at the conformal boundaries, which are demarcation horizons between our 3D reality and 5D hyperspace. There's also a 7D hyperspace, where we find the quarks and gluons, inhabiting a cuboctahedral geometry (see E8 Theory for details). Then there's a 9D hyperspace, and so on, apparently ad infinitum. Gravity is the complex conjugate of time in n-dimensional hyperspace. When a gravitational "field" couples to mass, it imparts negative momentum, so that gravitating masses attract other masses, just like positive charges impart negative momentum to negative charges via the electrostatic "field". Alternatively, we can conceptualise this energy as being transferred via "virtual particles", e.g. gravitons and photons. These concepts are equivalent, just as "particles" and "waves" are equivalent concepts. The 6D metric you seek probably looks more like √(Δx₁² + Δx₂² + Δx₃² ± Δx₄² ± Δx₅²), but I'm focussed on unification and QM at present, and such metrics aren't particularly relevant to 6D geometrical algebra. I'm giving you details of this hyperspatial math, e.g. those wavefunction animations for the Higgs, leptons, photons, anti-leptons and the graviton. I don't have a "theory"; I have a mathematical framework, based on Maxwell's mathematics and the Planck Units, which appears to be a thoroughly robust foundation for the main currently-accepted theories of physics, viz. electromagnetism, special and general relativity, and quantum mechanics. It's also congruent with Loop Quantum Gravity, String Theory, the Holographic Hypothesis, E8 Theory, etc. I'm not trying to "convince" you about anything. If you're interested in the math, and how I understand the math, I'm happy to answer any questions. I've made no claim whatsoever about "taking the world by storm". I could care less about that; I've had my 15 minutes of fame, and I certainly don't need to be in any spotlight. I simply want to write an easily-understood article on Complex Space/time into WP, to help the next generation of scientists. Because they asked. Rjowsey (talk) 06:42, 8 June 2015 (UTC)

No, your article on Complex spacetime is not easily understood. What motivates physical complex dimensions? Have you tried to explain this to other than 16-year-olds and succeeded?

Yes. Rjowsey (talk) 22:25, 8 June 2015 (UTC)

In a 6D framework, time is what clocks measure. In Einstein's 4D Riemannian geometry, time is dimensioned as a distance (ct), and "spacetime" is a unitary object. Thus, a Lorentz rotation appears to mix time into space,...

To me, this indicates that you don't approve even of special relativity. But this is not important. What is important is whether your article belongs in Wikipedia. Though you can find scattered scientific publications on 6D complex spacetime, it seems fringe. Then, if it belongs, it is still not your forum to "educate the next generation of scientists" about your ideas, or even Maxwell's ideas. YohanN7 (talk) 08:51, 8 June 2015 (UTC)

Regarding special relativity, here's an animation in 6D hyperspace showing a test particle of Planck mass being accelerated to the speed of light, where it has Planck momentum and Planck kinetic energy (or would have, but for gravitational radiation). The Minkowski diagram at top-left shows the "4D Lorentz rotation" of the moving frame of reference inhabited by the particle. The top-right projection shows time dilation approaching infinity at light speed, and the bottom-left projection shows length contraction in the moving frame of reference. https://upload.wikimedia.org/wikipedia/commons/1/11/6D_Special_Relativity.gif Rjowsey (talk) 01:38, 10 June 2015 (UTC)

The Lorentz factor is the inverse-cosine of the phase angle (0 < φ < π/2), i.e. γ = 1/cos(φ), and the ratio of the particle's velocity to light speed is β = v/c = sin(φ). Rjowsey (talk) 02:10, 10 June 2015 (UTC)

Time dilation and length contraction simplify to τᵩ = t∙cos(φ) and ʀᵩ = r∙cos(φ). The y-axis in the bottom-right projection represents the imaginary component of the particle's kinetic energy, while the x-axis represents the imaginary component of its potential energy mc², in units of Planck energy (E_P). Thus, the particle's total energy Eᵩ is a function of √((t∙sin(φ))² + (r∙sin(φ))²). At light speed, the particle's rest-mass energy and its momentum can be seen as inhabiting two imaginary spatial dimensions. Thus, a Planck mass at velocity v = c has total energy of √2∙E_P, assuming no losses due to gravitational radiation. The particle's matter-wave now has a Compton wavelength λᵩ = unit Planck length, and is oscillating at Planck frequency. Rjowsey (talk) 03:39, 10 June 2015 (UTC)

The references given in the article are certainly not fringe. But I fail to see the connection with the content of the article. See the article talk page. YohanN7 (talk) 22:00, 8 June 2015 (UTC)

The article needs a lot more work. Have patience. I'm a newb WP/science writer. Rjowsey (talk) 22:25, 8 June 2015 (UTC)

hey Q, i'm beginning to really like your edits.

most recently at Fine-structure constant. i used to protect objectivity on Wikipedia, too, until they kicked me out. they have limits to how objective they wanna be here. Wikipedia definitely is biased in the direction of "political correctness". bestest wishes in your editing here. r b-j — Preceding unsigned comment added by 71.169.187.7 (talk) 01:48, 23 June 2015 (UTC)

hyperbolic Geometry - Geometry of the universe (including relativity) references

hi

Sometime ago you said you would look for some references for hyperbolic Geometry#Geometry of the universe (including relativity) (I believe you twice wrote you would do that) Have you found some to add? (I want to nominate hyperbolic Geometry for Good Article status but without references in this section it would fail straight away. WillemienH (talk) 09:32, 25 June 2015 (UTC)

I added a couple. There will be no shortage of physics texts that deal with this. Someone else who might want to add references or clean up what I added is Maschen. —Quondum 04:45, 26 June 2015 (UTC)

I'll look into this tomorrow. M∧Ŝc²ħεИ_τlk 21:47, 26 June 2015 (UTC)

Thanks, I like your rewording of the paragraph. —Quondum 00:39, 28 June 2015 (UTC)

No problem, though I made a slight tweak to better reflect what the sources say. M∧Ŝc²ħεИ_τlk 06:50, 28 June 2015 (UTC)

As you'll see from my tag, I see that tweak as problematic. —Quondum 15:16, 28 June 2015 (UTC)

Planck constant

hastemplate:val insource:/\{[Vv]al\|[^}]+\*/ lists articles that use * in Val. Should we should document how to do this at Val/units? — CpiralCpiral 18:29, 20 June 2015 (UTC)

Dang. Fooled by my own cleverness. I thought I'd fixed that article, not realizing that there were two more instances in the same article. Thanks for pointing it out; fixed now.

Yes, I think that this is worth documenting this there; it is the kind of clean-up maintenance that will be regularly necessary, and a cut-and-paste quick reference for this will be handy. The regex will have to become a little more sophisticated (allowing whitespace, e.g. searching for a substring in only the \|u[^=]*\= parameter (I probably messed partial regex up), but any start in documenting it is a good start, to be tweaked as we use it and gain experience. —Quondum 21:20, 20 June 2015 (UTC)

OK, check out the new documentation at {{Val/units}}. I mention a new template {{Val/find}} that can be used before removing unit codes. See you there. Once you get a search results list of particular uses of a Val instance, even if its hundreds of pages, you can change them all using WP:AWB or AutoWikiBrowser script. — CpiralCpiral 23:00, 22 June 2015 (UTC)

The guidance of a detailed "how to" guide is valuable. But I'm going to confess something: I've completely stepped back from much of this by removing pretty much everything related to WP: (MoS in particular) and Template: namespaces from my watchlist and am carefully refraining from even looking at the WP: space, mainly to keep my blood pressure in check. The shoot-first-and-ask-questions-later mentality, along with a few other things was getting to me. Keep up the excellent work. —Quondum 00:10, 23 June 2015 (UTC)

Thank you, Quondum. I started on a few of those work spurts on Val because of you on the talk page. When you are ready to come back, you can practice peace under fire. There's no better way. Think about it. It's the best way to practice.

My experience at the MoS is disheartening too. After implementing my proposal comprising several weeks of work on the talk page of MoS Dates and numbers, Kwamikagami comes along a week into its online life and just machine guns the page with a bewildering amt of energy blasting away at edits, ignoring the talk page pace, saying things like "gibberish", "nonsense", and "silly", and other blood pressure raisers. For now I prefer the template work over the MoS, although they go together somewhat as you know. I'd like to start on the Lua rewrite of Val, but I gotta ramp up on some other things in real life. Keep up the good work in the article space. Peace out. — CpiralCpiral 03:10, 23 June 2015 (UTC)

OK, its now moved from template Val/find to {{Template usage}}. I hope you like it as a way to enumerate precice template usage patterns. I'm diving back into RL, but I'm keeping my pared-down Watchlist under observation. Later — CpiralCpiral 02:21, 1 July 2015 (UTC)

Great. I've added it to my useful wikilinks list. This may spawn more of the same ;) —Quondum 05:20, 1 July 2015 (UTC)

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Send on behalf of The Wikipedia Library using MediaWiki message delivery (talk) 04:31, 7 July 2015 (UTC)

Fermi paradox

Given your interests, I wonder if you might have a look at Fermi paradox, especially [7], which could use some scrutiny. Thanks, Isambard Kingdom (talk) 08:34, 14 July 2015 (UTC)

I'll go through it, but don't expect much. I'm not sure what impression you have of my interests – they tend towards rigorous and fundamental rather than speculative topics. —Quondum 14:17, 14 July 2015 (UTC)

Okay, perhaps my invitation wasn't quite on target. I'm just trying to encourage critical involvement, but I unerstand that the FP article may not be quite aligned with your interests. Sincerely, Isambard Kingdom (talk) 15:42, 14 July 2015 (UTC)

Your edit is being discussed

Hi there, one of your edits is being discussed. Fnagaton 14:13, 17 July 2015 (UTC)

Thanks for the notification. I realize that one of my edits and the (lack of visible) reasoning features in the discussion; it may have been a different talk page that triggered my edit. I am strongly disinclined to get involved in the discussion. —Quondum 04:28, 18 July 2015 (UTC)