User talk:Stevenj/Archive 1

Hello and Welcome! I hope you like the place. --mav

Hi, I have a hard time understanding two of your additions to Quaternion and Pauli matrix:

In quantum mechanics, the 2x2 matrices that multiply b/c/d, times i, are called the Pauli matrices (plus the identity matrix for a). Moreover, this representation of a quaternion corresponding to a spatial rotation is equivalent to the rotation operator for spin-1/2 particles.

What do you mean when you say "this representation of a quaternion as a spatial rotation"? We didn't represent it as a spatial rotation, we represented it as a 2-by-2 complex matrix. I don't think you can represent quaternions as spatial rotations; the unit quaternions of course give rise to spactial rotations, but even this representation isn't faithful.

Together with the identity matrix I (which is sometimes written as σ0), the Pauli matrices form a basis for the set of 2 × 2 complex Hermitian matrices. This basis is equivalent to quaternion numbers, and when used as the basis for the spin-1/2 rotation operator it is the same as the corresponding quaternion rotation representation.

In which sense is this basis "equivalent" to quaternion numbers? What "quaternion rotation representation" are you referring to here?

Thanks, AxelBoldt 01:24 Apr 28, 2003 (UTC)

Hi Axel, part of the misunderstanding here is that you are misquoting me. I didn't say "this representation of a quaternion as a spatial rotation," I said "this representation of a quaternion corresponding to a spatial rotation." What I meant was basically the opposite of what you're thinking: I'm referring to the representation of a rotation by a quaternion, not the other way around. Less succinctly:

Suppose you take a rotation and represent it by a quaternion, which in turn is represented in the 2x2 matrix form. Alternatively, take the same rotation and represent it by the spin-1/2 rotation operator (a 2x2 matrix). The statement is that these two matrices are, in fact, the same. See also e.g. http://www.nyu.edu/classes/tuckerman/quant.mech/lectures/lecture_5/node4.html

slight correction: they are slightly different, corresponding to a 90-degree coordinate rotation x -> y, y -> -x. They are the same if you modify the 2x2 matrix formula in the quaternion page to use the Pauli matrix mapping described below.

I think that if you parse my original sentence carefully, the meaning is correct, but perhaps we should rephrase it to be more clear. =)

Regarding the equivalence of the quaternions and the Pauli matrices, I meant that if you take the quaternion a + bi + cj + dk, and map it to the matrix a * sigma_0 - b * i * sigma_1 - c * i * sigma_2 - d * i * sigma_3, you get an isomorphism. That is, you make the identification (1,i,j,k) <-> (sigma_0, -i sigma_1, -i sigma_2, -i sigma_3).

this representation is slighly different from the 2x2 matrix representation on the quaternions page; the two are related by the isomorphism b -> c, c -> -b.

The basic point is that there is a deep connection between the algebras of quaternions and Pauli matrices, and between the use of quaternions to represent rotations and the rotation operator for spin-1/2 particles.

- Steven G. Johnson, Wed May 28 20:34:39 EDT 2003

Ah I see you spotted my "spinning particle" reference on magnetic field. Call it my little bit of rebellion -- I'm inclined to think the difference between QM spin and mechanical spin is rather exaggerated. BTW Griffiths calls B the magnetic field and H the "auxillary field", hence the article title. -- Tim Starling 02:10 10 Jun 2003 (UTC)

Hi Tim. There is an important difference between QM spin and a (classical) spinning particle: the axis of a spinning particle is a 3-vector, whereas QM spin is not (there is an observable difference in how they transform under rotations). Regarding the term magnetic induction for B, it is a historical thing. Jackson uses magnetic field initially for B, but switches to magnetic induction when he starts talking about H. It's one of those rules that's observed more in the breach, but it's important to mention. -- Steven G. Johnson, Mon Jun 9 22:31:50 EDT 2003

Just saw your home page... do you know anything about quantum many body techniques, or ab-initio quantum chemistry? -- Tim Starling 02:38 10 Jun 2003 (UTC)

Some, although it's not my speciality (my work more involves solid-state physics applied to classical electromagnetism, not quantum mechanics). -- Steven G. Johnson

Damn. I thought you might be able to help me with my PhD project, because my supervisor seems to be incapable. Your comment about spin hit my misconception dead-on -- let's just say I was rather humbled. You must be a very good lecturer, not to mention an exceptional physicist. Don't waste too much time hanging around Wikipedia, okay? -- Tim Starling 03:11 10 Jun 2003 (UTC)

Hi there. What's the the handedness of the universe? (seen on Pseudovector) -- Tarquin 20:29 12 Jun 2003 (UTC)

You can't really define an absolute "handedness". If you want a left-hand rule for cross-products, you just slightly change your definitions of things like the magnetic field. The real question is whether the laws of physics are invariant under inversion; for classical physics they are, but for weak interactions they are not. To take a more simplistic example, suppose that some observable quantity depended upon the sum E+B (assuming compatible units). After inversion, this becomes B-E, and this is not just a change of definitions because Maxwell's equations (which are invariant) also relate E and B...so an experiment measuring that quantity could determine whether the inverted or non-inverted version was correct, but you can still always define things to use a right-hand rule. -- Steven G. Johnson

Regarding your cross-product edit on handedness: does that mean that in a LH system, a ^ b is still defined as a RH triple? I know of at least one programming language where that is not the case. -- Tarquin 09:01 13 Jun 2003 (UTC)

Howdy ....

I am writting you concerning the Maxwell equations.

... as you are a post-doctoral associate in theoretical physics, I'd appreciate it if you's locate and read:

T. W. Barrett, "Electromagnetic Phenomena Not Explained by Maxwell's Equations," in A. Lakhtakia (ed.), Essays on the Formal Aspects of Electromagnetic Theory, World Scientific, River Edge, NJ, 1993, p. 6-86.

... also .... Doug sweetser explains quaternions .... [something that Gibbs and Heaviside did not understand or neglected to address]

http://world.std.com/%7Esweetser/quaternions/intro/scalarsvectors/scalarsvectors.html

There is the electromagnetic potential, which has a scalar field phi and a 3-vector potential A.

To do calculus with only information contained in events requires that a scalar and a 3-vector form a field. According to a theorem by Frobenius on finite dimensional fields, the only fields that fit are isomorphic to the quaternions .... requirement and an identical solution. This is the logical foundation for doing physics with quaternions.

http://world.std.com/%7Esweetser/quaternions/EandM/gauges/gauges.html

-- It's not hard to understand the quaternion notation that Maxwell used, it's quite simple. I'm sure Gibbs etc. was able to follow it. They just didn't like it. User:Stevenj

In the quaternion representation, the gauge is a scalar generated in such a way as to not alter the 3-vector.

http://world.std.com/%7Esweetser/quaternions/classical/sho/sho.html

-- Maxwell originally (even before quaternions), chose to use the vector potential explicitly, and he picked a particular gauge (the Coulomb gauge I believe, div A = 0). Nothing special here; people use vector potentials and pick gauges all the time in modern notation as well. User:Stevenj

In fact, the four Maxwell equations appear to be one nonhomogeneous quaternion wave equation, and the structure of the simple harmonic oscillator appears in the Klein-Gordon equation.

... mabey more later ...

Thanx for reading .... reddi 03:23 7 Jul 2003 (UTC)

Thought you might find this useful: User:Tim Starling/Reddi watchlist -- Tim Starling 02:25 27 Jul 2003 (UTC)

I'm not certain which "Russian school" is referred to in the "real number" discussion page, but it's probably something about constructivism, which is a philosophy that holds that an existence proof is not valid unless it "constructs" the object whose existence is to be proved. For example, if you were to deduce a contradiction from the proposition that every even number greater than 2 is a sum of two primes, that would not be taken by constructivists to be a proof of the existence of a counterexample. Michael Hardy 00:19, 22 Oct 2003 (UTC)

I have made some minor changes to Curie point, with the aim to incorporate your ideas in a user-friendly description. I noticed you altered my earlier description of the Curie point to make it read (now) as if it were an infinitely abrupt change to paramagnetism. That is not my understanding of the Curie point. Would you mind if I altered your words slightly in this regard? Cheers, Humanist 08:59, 14 Nov 2003 (UTC)

If you define a paramagnet as having a spin-based magnetization in response to an applied field, but no spontaneous magnetization in the absence of an applied field, then indeed the material suddenly becomes a paramagnet at the Curie point. Below the Curie point, the spontaneous magnetization increases continuously from zero (although the slope is discontinuous at the Curie point). Of course, even below the Curie point, an applied magnetic field will have an effect on the magnetization, but this magnetization follows a hysteresis curve, unlike a paramagnet. On the other hand, the mechanism for the magnetic field to affect the magnetization is the same both above and below the Curie point, so in that sense there is paramagnetism everywhere (becoming weaker as temperature goes to zero and the hysteresis increases). Steven G. Johnson 19:12, 14 Nov 2003 (UTC)

Responding to your changes on the pages African-American and Role of women in Judaism, I must reply that I did not make these changes. My dad did it because I wouldn't let him get on to check his E-mail. Sorry. MattSal 23:22, Nov 18, 2003 (UTC)

Thanks for your additions to Laocoon and his Sons. My only problem with them is that your reference to "some accounts" makes it sound like a news story, whereas it is a mythological event described by various ancient authors. Can you identify which sources attribute the sending of the serpents to which gods? Adam 04:49, 4 Feb 2004 (UTC)

Apparently, the various ancient authors/storytellers were not very consistent. Virgil sort of implies that Athena did it, but he's not very explicit; my memory of that made me look around on the web and found agreement in things like Bartleby. Various accounts are quoted here. The version blaming Apollo is attributed to Euphorion here. It's also given in Hyginus' account here. I'm anything but an expert on the subject, though; I'd love to see a well-researched description in the Laocoon article of who said what and when. Steven G. Johnson

Well done on your work on making Linux halfway readable. I just went the hack on Linux distribution, but I think I've died of bad writing fatigue. It's got some content, it just needs severe editing ... want a go? - David Gerard 12:26, Feb 5, 2004 (UTC)

Steven,

Nearly all of the litigation material you removed was mine. I agree that there are overlaps with the SCO v IBM article, but my intent in modifying the existing litigation text here was distinguishable, and I thought, useful to readers. Your impulse toward optimal parsimony is admirable, but not in a legal / user quandry context, I fear. Perspective is important in the WP, especially in considering the expected reader. This is, after all, an article of first reference, and for many will be an article of last reference as well. Its treatment should be commensurate.

Encyclopedia articles should be summaries, with side topics as pointers to other articles. It doesn't hurt people to click on a link if they want more information, but it does hurt to have a deluge of stuff about one set of events in 2003/2004 overshadowing an article about an operating system that spans decades. Moreover, it makes no sense to have the same material duplicated in two articles. Steven G. Johnson

I meant to summarize the legal situation in terms understandable to the ordinary user considering Linux (hence the location in the Linux article), and to do so in such a way that the history (the source of SCOG's claim) is not left entirely opaque (as it almost is to those of us who have been following the Unix genetic tree with special interest since the '70s). Furthermore, I attempted to bring out -- in a technical programming sense -- the cross pollination of algorithms, code fragments, public domain material, etc for the technically inclined new_to_Linuxer. And for those more concerned with the commercial side of things, to bring some of that out not overly opaquely as well. That I was unable to do so in so brief a paragraph as you have left is a function of the underlying messy reality, I think. I necessarily made many choices in the text I left, and many of them were conscioulsy to avoid leaving out stuff that was (1) understandable to a non-lawyer, (2) potentially significant to someone who might be considering where the litigation left him/her/them as a Linux user or potential user, or (3) useful in understanding the damage IP litigation can cause. I didn't want to 'dumb it down' too much.

As the article is currently, a reader of the Linux article -- perhaps coming to the WP to make some sense of (the nearly always incompetent journalistic coverage) what appears to be a Big Deal in regard to Linux -- is left with what is, to my eye, far too little and that little appearing, and too some extent, being, too legally technical. The linked article is, in my view, 'too legal' altogether.

Then fix the linked article.

Accordingly, I would suggest returning the material (or some version of it -- this being a Wiki my immortal prose is hardly the final say) to this article.

My minor edits to the existing paragraph on FUD were intended for more or less the same purpose. FUD exists and has existed and is $ignificant in the marketing of many things. Computers and computer software are the most commercially significant of these, I suppose. Some anti-Linuxers have been caught spreading FUD (ie, financing bogus research reports and issuing peurile press releases) and that is a fact those new to Linux should at least be told. It is not POV (or anti any particular vendor -- and surely we all know the vendor who's most prominent in this matter) to say so in a non accusatory way. Even if some of the accusation has been publicly demonstrated. Political correctness, as I remember it developing, was intended to reduce personal pain, to 'proactively' avoid hurt feelings. Since commercial interests don't have feelings, being persons only in legal fiction, it shouldn't be, in my view extended to them. I would retain the FUD paragraph as I last edited it.

General accusations of FUD, without citations or quotations or facts, are advocacy, and/or are so vague as to be meaningless. Nor do long analyses of particular Microsoft etc. statements belong in the article. Steven G. Johnson

On to other points.

I remember a post from the early '90s (and I cannot find it after a brief search) from Linus, or Lars, attributing world domination to Tux. Thus you may conclude that that also was my contribution. I would argue it is not POV to explain something that resulted from the POV (in this case, a disdain for MS and its practices and engineering quality) of the players involved. Besides, it's funny. Recall that Linus has spoken and posted at some length on the espression that Tux is supposed to have -- fat and happy after a (burp!) large meal of herring. It may help to have a Scandinavian approach on this -- lutefisk is popular in Norway and I don't get that either. But so it goes...

That quote is not widely attributed to the mascot. It is a common joke among Linux users, but this would be better expressed via a direct quote. And even then, inside jokes don't really belong in the introductory paragraph about an OS. Nor should the encyclopedia text itself be making snide obscure references to Microsoft as "a certain large software company". Steven G. Johnson

As for 'around some words' as opposed to "around others", the subject of one of your edits, I use ' ' in my writing as a marker for something that I am not "quoting directly", but am stressing an unusual use of. A usage "...up with which I will not put.", if we can extend one of Winston's peeves a bit. In short, it's a warning to the reader not to take 'this material' exactly straight. In my case it's usually a marker of irony or sardonicism (if this is not a 'word', I apologize.) To wit, I really abhor 'proactive', hence its flagging above. Miss Fidditch surely didn't like ee cummings, nor probably archie the cockroach either, and she gave me some grief too. But since I ditched school and don't have to listen to her anymore, I've found the language's clothes a comfortable fit, including this instance. Our rules, in this shared anarchy that is and has been English, aren't (shouldn't be?) too tight for such comfort. Do you think they should be tighter than I would wear them?

Double-quotes to indicate special usage or irony are the standard punctuation in English, not single quotes. Gratuitous substitution of one glyph for a nonstandard one is distracting and unnecessary. (I'm a fan of cummings, too, but that doesn't mean that I think encyclopedia articles should be written like he wrote his novel Eimi, which is nevertheless a remarkable work.) Steven G. Johnson

Reactions?

Please continue discussions on Talk:Linux if you feel it necessary.

ww

PS: Congratulations -- too long delayed -- on the Wilkenson. I'm not current with numerical software, and so learned about it from your home page. Good work!

Could you check Maxwell's equations article. Somebody changed a 90 degrees out of fase to in phase for E & M waves, and I'm ashamed to say that I do not recall (and don't have time to derive) which one is correct. --AstroNomer 21:12, Mar 18, 2004 (UTC)

The current version is correct: the electric and magnetic fields are in phase for a plane wave. (From Maxwell's equations, the spatial derivative of one must equal the time derivative of the other, so e.g. they have to be both cosine or both sine curves.) —Steven G. Johnson 22:37, 18 Mar 2004 (UTC)

Hello, Steven. Please have a look at Talk:Trigonometric function where I'm challenging you etymology of the word sine in English.
—Herbee 20:57, 2004 Mar 25 (UTC)