User talk:AugPi/Archive 1

Sheffer('s) Stroke
Hey AugPi, I've added a note to your Sheffer's stroke article that it should be merged with the Sheffer stroke article. (According to the 'Essence of Logic' the correct spelling is Sheffer Stroke). Since you are the only editor of the article I guess you might want to do this yourself else I will do it next week.

--R.Koot 02:28, 9 May 2005 (UTC)

Hello there, welcome to the 'pedia! I hope you like the place and decide to stay. If you need pointers on how we title pages visit Naming conventions or how to format them visit our manual of style. If you have any other questions about the project then check out Help or add a question to the Village pump. Cheers! --maveric149

Hey AugPi, I'm trying to get people interested in helping me reorganize the fluid dynamics articles, to make sure all the info is there, in the right place, and not overly redundant. Let me know if you want to help. I've made a new page to discuss it at WikiProject Fluid dynamics.moink 21:32, 27 Dec 2003 (UTC)

Hi AugPi. I am sorry but I had to delete some of the articles you created (Philebus, Phaedo, Menexenus, Lesser Hippias, Cratylus, Crito) because they were nothing but external links. As such, they are cadidates for speedy deletion. If you wish to recreate them, at the very least you need to write an sentence or two describing what the article is about. See also Perfect stub article. Regards, Dori | Talk 17:21, Mar 23, 2004 (UTC)

I have listed Image:Dissection of Klein bottle ROT13.bmp on Images for deletion as it is too large (644Kb) - Please to not upload BMP files as they are uncompressed. - Gaz 14:10, 24 Mar 2004 (UTC)

thanks a lot for your various contributions to cross-cap and related surfaces. Xah Lee P0lyglut 06:39, 2004 May 28 (UTC)

thanks for the helicoid addition. Btw, by trace of line i just mean sloppily how the surafce is generated. Xah Lee P0lyglut 02:17, 2004 Jul 4 (UTC)


 * Oh, I see. It's not the same as trace which is related to pedal curve.  It is more like the trail blazed by a line as it rotates through space and translates in the direction of the axis of rotation, like a the blades of a helicopter lifting off. --AugPi 02:39, 4 Jul 2004 (UTC)

Links in Latin
Hi AugPi. Thanks for your good work on mathematics. I'm not sure whether it's a good idea linking to articles in Latin - this is the English wikipedia, after all, and (unlike perhaps a few hundred years ago) the vast majority even of highly educated readers won't understand them. --   ALargeElk | Talk 13:33, 14 Jul 2004 (UTC)

Lissajous curve
Hello. It seems you moved Lissajous figure to Lissajous curve maybe about 12 hours ago, but all the links to the former are still there. I may get time to work on this today, but can you help? Michael Hardy 21:35, 14 Jul 2004 (UTC)
 * Done. I'll see about adding some images. --AugPi 13:31, 15 Jul 2004 (UTC)

Fantasie-Impromptu
I have synthesized your using TiMidity++ with very high quality piano samples from the collection of Eric A. Welsh, and uploaded it as a hopefully equally high quality Vorbis file, adding a link to Frédéric Chopin. Please tell me if any details are incorrect, especially your name which I have taken from the comment in the original MIDI file, or the quality is not good enough. Thanks a lot. Rafa&#322; Pocztarski 03:16, 24 Aug 2004 (UTC)

The original midi file is not musically correct. The tempo of the right hand melody does not match the tempo of the left hand harmony. This is the reason it is confusing to listen to. Since the melody should be much faster,if it were to match the left hand tempo, it sounds like there were added measures to the left hand harmony, leaving them both out of sync, resulting in a major headache in trying to listen to it.

Licensed to WM Foundation means GFDL ?
Just to know the exact license of one pic from you : Image:CardioidsLabeled.PNG. Does the explain text mean it is GFDL ? Thanks in advance. Tipiac 22:18, 20 Oct 2004 (UTC)

Set theory format changes?

 * Why are you changing A&prime; to AC, this makes the "complement" image wrong now.
 * Why are you changing "A &cap; B" to "A &cap;B", this looks better to you?

Paul August 15:16, Oct 29, 2004 (UTC)


 * OK, I changed A&prime; to AC in the image as well. The reasons why I started changing to AC are these:
 * To make Wikipedia's notation for set complement uniform: AC was used in the article for De Morgan's Laws.
 * A&prime; should be reserved for Boolean complement,
 * A C for set complement.
 * The AC notation has been adopted by PlanetMath.
 * The AC notation is also used at the University of Cambridge (e.g. hosted by Churchill College).
 * The AC notation is more unique: the meaning of A&prime; is already overloaded: e.g. A&prime; as derivative of A.
 * AC is more visible; it looks better on the page.


 * By the way, there appear to be five different ways of denoting the complement of set A: (1) A&prime;, (2) $$ \overline{A} $$,  (3) AC,  (4) ~A,  (5) comp(A).  A&prime; is probably the most frequent one, so if you want to change from AC back to A&prime;, I would not oppose it.

>>Why are you changing "A &cap; B" to "A &cap;B", this looks better to you? <<
 * This way the &cap; appears centered between the A and the B (at least on my browser). Which brings me to my question: the character for &empty; shows up as an empty square on my browser, not as an empty set character &Oslash;.  Does &empty; appear correctly on your browser and what did you do (if anything) to make it appear correctly? --AugPi 22:57, 1 Nov 2004 (UTC)
 * For all the browsers I use (Safari, IE, Omniweb, Forefox) the former looks centered, the latter does not. Also the using former which uses "non-breaking spaces" means that "A &cap; B" will always appear on the same line, that is it won't break across two lines.  Also both empty set symbols show up correctly for me in all browsers, you might try changing your Wikipedia "math rendering preference" Paul August 23:33, Nov 1, 2004 (UTC)

"Meditation" by Joseph Haydn
Hi AugPi, I'm trying to specify what this piece is a little more precisely but can't find it. Can you provide a hint? (like what it's written for, its Hoboken number, whatever...) Thanks very much, Opus33 05:10, 19 Nov 2004 (UTC)
 * The piece is short: one page long, written for the piano. It's all in the key of B-flat major (G minor?).  That is all I know: but I sequenced it in MIDI and uploaded the MIDI file, so now it is in the double-dotted note's Listening section.
 * The title "Meditation" is all I know about the piece. It appears on page 23 of the book "JOSEF HAYDN / his greatest / PIANO SOLOS / A Comprehensive Collection Of His World Famous Works", compiled by Alexander Shealy.  Copa Publishing Co., Sole Distributor: Ashley Dealers Service Inc., 263 Veterans Blvd., Carlstadt, N.J. 07072.  The book has no ISBN, measures 11_7/8" x 9_1/16" x 1/2", and has 191 pages.  The front cover is filled with a (painted) portrait of the composer up to thin blue margins.  The book is soft cover and was obtained recently in an H&H Music store.  Strangely enough, both "Meditation" and another short piece on the page's reverse side did not show up in the Contents page: the printer's must not have been too careful (that, and the missing ISBN...).
 * Another Haydn piece with double-dotted notes is "Sonata in E Flat", which is much longer: the double-dotting appears in the 9th, 10th and 11th pages of the Sonata, but not through most of the rest. --AugPi 22:34, 9 Dec 2004 (UTC)

Hi AugPi, Thanks very much for your reply. On hearing your sound file I was able to track down "Meditation": it is a piano transcription of part of the second movement of Haydn's String Quartet Opus 72 No. 2.  I've seen this transcription myself--it appears in the G. Schirmer "Sonatina Album" used for so many kids' piano lessons. Looks like some unknown musician long ago adapted Haydn's work, and being out of copyright it gets reprinted freely. The title "Meditation", which seems not inappropriate to me, must be from Alexander Shealy.

In a fit of enthusiasm, I made an image file of the quartet passage and added it to the article, noting that the sound file matches it. (This is not quite true, since the adapter left out a couple measures that work only as ensemble music.)

Cheers, Opus33 16:44, 12 Dec 2004 (UTC)

Article Licensing
Hi, I've started a drive to get users to multi-license all of their contributions that they've made to either (1) all U.S. state, county, and city articles or (2) all articles, using the Creative Commons Attribution-Share Alike (CC-by-sa) v1.0 and v2.0 Licenses or into the public domain if they prefer. The CC-by-sa license is a true free documentation license that is similar to Wikipedia's license, the GFDL, but it allows other projects, such as WikiTravel, to use our articles. Since you are among the top 1000 Wikipedians by edits, I was wondering if you would be willing to multi-license all of your contributions or at minimum those on the geographic articles. Over 90% of people asked have agreed. For More Information:
 * Multi-Licensing FAQ - Lots of questions answered
 * Multi-Licensing Guide
 * Free the Rambot Articles Project

To allow us to track those users who muli-license their contributions, many users copy and paste the " " template into their user page, but there are other options at Template messages/User namespace. The following examples could also copied and pasted into your user page:


 * Option 1
 * I agree to multi-license all my contributions, with the exception of my user pages, as described below:

OR
 * Option 2
 * I agree to multi-license all my contributions to any U.S. state, county, or city article as described below:

Or if you wanted to place your work into the public domain, you could replace " " with "  ". If you only prefer using the GFDL, I would like to know that too. Please let me know what you think at my talk page. It's important to know either way so no one keeps asking. -- Ram-Man (comment| talk)

duality principle
Hi, I have some questions about the sphere example you give for the duality (projective geometry) article. Please see the talk page for the questions. Thanks! --210.160.195.187 15:18, 23 Jan 2005 (UTC)
 * The footnote
 * >>*&sup1; When we say a line through pair of points P, or simply a line through P, we refer to the three dimensional euclidian line that passes through the antipodal points represented by P. When we say that a geodesic line, or a great circle, L is perpendicular to the line passing through the pair of points P, we mean that L lies on the plane that is perpendicular to, and intersects at the midpoint of, the straight line segment in euclidian space that connects the antipodal points that is represented by P. In other words, L is the set of points equidistant in euclidian space to the antipodal points represented by P. L is unique for P. <<
 * is exactly right: it is precisely what was meant! Apparently there was no conscious awareness of just how the meanings of "line" and "circle" were being overloaded. --AugPi 00:55, 18 Feb 2005 (UTC)

P-V diagram image
Hi, I came upon your image image:Entropyandtemp.PNG. In my opinion, that image needs several modifications. --Smack 22:54, 11 Dec 2004 (UTC)
 * Much fewer lines. I'd cut out at least two thirds of them, and possibly as many as nine tenths.
 * No title at the top. See Image_use_policy.
 * Proper caption in the Adiabatic process article. (Which set of lines represents which type of process?)

&mdash;===&mdash;===&mdash;===&mdash;===&mdash;===&mdash;===&mdash;===&mdash;===&mdash;===&mdash;===&mdash;===&mdash;===&mdash;===&mdash;===&mdash;

>>No title at the top. See Image_use_policy.<<
 * I uploaded a replacement version without a title, but it is not showing up right now. It should take some days for the new version to show up.  I take it that you refer to Rule 7. --AugPi 02:28, 18 Feb 2005 (UTC)


 * I do think that that's what I was referring to. Your new version still doesn't seem to be up, though.  Waiting patiently. --Smack (talk) 03:24, 18 Feb 2005 (UTC)

Untagged images
Hi! Thanks for uploading Image:ProlateSpheroid.PNG$$\star$$. I notice it currently doesn't have an image copyright tag. Could you add one to let us know its copyright status? (You can use if you release it under the GFDL, or  if you claim fair use, etc.) If you don't know what any of this means, just let me know where you got the images and I'll tag them for you. Thanks very much, Kbh3rd 04:58, 12 Dec 2004 (UTC)

Thanks for uploading Image:ParaboloidOfRevolution.PNG$$\star$$. I notice it currently doesn't have an image copyright tag. Could you add one to let us know its copyright status? (You can use if you release it under the GFDL, or  if you claim fair use, etc.) If you don't know what any of this means, just let me know where you got the images and I'll tag them for you. Thanks so much,   &mdash; Edwin Stearns | Talk 21:15, 15 Dec 2004 (UTC)

Also:
 * Image:KleinBottleCrossSection.PNG$$\star$$
 * Image:D'Alembert's paradox.PNG RedWolf 18:33, Dec 25, 2004 (UTC)
 * Image:OblateSpheroid.PNG$$\star$$ -- Kbh3rd 05:21, 14 Jan 2005 (UTC)

Not to mention:
 * Image:RomanTetrahedron.PNG$$\star$$
 * Image:RomanSurfaceFrontalView.PNG$$\star$$
 * Image:RomanSurfaceSidewaysView.PNG$$\star$$
 * Image:RomanSurfaceTopView.PNG $$\star$$grendel|khan 23:09, 2005 Jan 17 (UTC)

Also Image:Entropyandtemp.PNG$$\star$$. Please note: images not tagged will be deleted. – Quadell (talk) (sleuth) 16:20, Feb 11, 2005 (UTC)

''[$$\star$$ &mdash; Means that the image has been copyrighted, licensed, tagged. --AugPi 01:41, 18 Feb 2005 (UTC)]''

Hi, Image:Cyclic process.PNG $$\star$$ is another that needs tagging. Thanks! --iMeowbot~Mw 07:28, 18 Feb 2005 (UTC)

links to projective geometry topics
Hello. Can you help add some of the missing links to projective geometry topics to the list of geometry topics? I just added a couple of them, including projective transformation. Also, I think some of them may be missing from the list of mathematical topics. Michael Hardy 19:36, 31 Mar 2005 (UTC)
 * Aye, aye, chief! &mdash;AugPi 04:29, 21 Apr 2005 (UTC)

Contraction (mathematics)
Hi, I just wanted to tell you (as this page is linked to your user page) that contraction (mathematics) has been moved to tensor contraction, but the redirect goes to the disambiguation page contraction because of the disambiguation request on it beforehand. User talk:Neonumbers/Neonumbers 10:26, 1 May 2005 (UTC)

Cardioid proofs
Hi, wanted to let you know about an edit I just completed to cardioid. You'd added a proof to that article about a year ago; I moved that proof off to its own page, cardioid article proofs. Read it and see what its about. I thought you should know; & maybe you have an opinion on the matter. The only other thing in wikipedia currently treated in this way is Laplace operator article proofs. linas 16:53, 18 May 2005 (UTC)

Morin surface
Do you know of, or have any interest in creating, a GFDL illustration of  Morin surface? I'd like one for the article on Bernard Morin and maybe Smale's paradox--agr 15:40, 5 Jun 2005 (UTC)
 * Yes, indeed: glad you asked. I have uploaded an image and added it unto the Bernard Morin article.  I made that image some time ago.  I still haven't made a complete version with "passage barriers", but I have the blue print and the code so maybe I will get back into this. --AugPi 04:10, 15 Jun 2005 (UTC)

lots of edits, not an admin
Hi - I made a list of users who've been around long enough to have made lots of edits but aren't admins. If you're at all interested in becoming an admin, can you please add an '*' immediately before your name in this list? I've suggested folks nominating someone might want to puruse this list. Thanks. -- Rick Block (talk) 22:52, Jun 11, 2005 (UTC)

Dictionary of chemical formulas
Hi, I notice that you have created a listing of chemical substances by formula. This must have been a lot of work, and it is a useful list! I wanted to check, are you aware of the Wikiproject in this area? We currently have several lists of compounds linked to Wikipages. There are alphabetical listings at list of organic compounds, list of inorganic compounds, as well as related lists such as list of minerals, list of drugs and list of biomolecules. The closest thing to your listing is inorganic compounds by element, which is incomplete and has been a personal project of mine. It only links to compound pages, which already number several hundred, there are hundreds of mineral names too but these are covered elsewhere. The project has agreed that we should finish this list and also create a list of organic compounds in Hill system order, as discussed here. The Wikiproject is very active at the moment, as you can see from the talk page and the worklist. If you are interesting in helping on the project, please sign up as a WikiProject_Chemicals, or if you prefer, just keep a "watch" on the page and pitch in when you want to. Cheers, Walkerma 7 July 2005 16:38 (UTC)

Connections
I saw your edit in G.R. - it is nice to honor Levi-Civita. Yet I feel that before and after the edit, it is kind of misleading to say the connections are zero in the Minkowski metric, because the connections do not measure the curvature of the spacetime - that's why the Riemann tensor is so important. For example, if you use spherical coordinates in the 3-space of Minkowski space (quite handy for radiation problems) you still have a flat space (ignoring the perturbations matter and radiation) but many Christoffel symbols are nonzero. Pdn 00:32, 1 August 2005 (UTC)
 * Actually you're confusing me with user Ems57fcva (| who recently (18 July) initiated the entire mathematical section of the GR article). I was not the one who appended that parenthetical note.  I might add the following parenthetical subnote which might help to clarify:
 * However, the connection will be non-zero even in a purely Euclidean space if the coordinates are non-Cartesian, e.g. in polar coordinates.
 * &mdash;AugPi 09:24, 1 August 2005 (UTC)

So becuase of the above you wrote:
 * However, the connection will be non-zero even in a purely Euclidean space if the coordinates are non-Cartesian, e.g. in polar coordinates. In general relativity, the equation for a geodesic will also be $$ \ddot{x}^a = 0$$ for the special case of a freely falling reference frame.)

Neither statement is correct. The first one is false even in classical mechanics. The second statement is only true locally and under a Cartesian coordinate system.

For the first statement: Just draw a chord through a flat spacetime mapped using polar coordinates: As you travel along the chord, your direction of travel with respect to the coordinate system will constantly change even though a chord describes an inertially moving object. The connections describe how that change in coordinate velocity occurs.


 * I said the connection would be non-zero... so I said the same thing as your above paragraph.
 * OK. I missed the "non-".  Sorry about that.  However, your point got bound up in the second statement, which really caught my eye.  So I seem to have projected the mistake in the second sentence onto the first one.  Feel free to restore it then.  Unless there is some reason such that it turns out to be counter-productive (which I do not expect), I will leave it alone. (Please be aware I had someone else changing "stress-energy" to "mass and energy" all over the place, which is no good because it leaves out momentum.  So I had to revert beyond your edits and then decide what to bring back in.  So please accept my apologies.) --EMS | Talk 05:35, 2 August 2005 (UTC)

For the second statement: Look at the case of two spaceships in orbit around the Earth. Under the rules of GR, each is traveling inertially. Now suppose that they are initially at rest with respect to each other. Depending on how they are separated, these ships will immediately start to move with respect to each other, either getting closer to or father from each other as a result. Only if they are ahead of or behing each other in the same orbit will they stay at rest with respect to each other. In the frame of reference of an inertially moving observer in GR, this is due to tidal forces (or rather tidal accelerations). Once again, the connections must be non-zero (except locally, where the tidal accelerations do not exist).


 * The second statement was locally accurate but imprecise. In freely falling coordinates &chi;&alpha; the geodesic becomes
 * $$ {d^2 \chi^\alpha \over d\tau^2} = 0 $$
 * but only strictly true if the geodesic is the proper time coordinate line of the freely falling frame. Neighboring geodesics which start out parallel will suffer geodesic deviation due to tidal forces, as you mentioned in the above paragraph.  ... Anyway, these are subtle points which don't belong in the main GR page.


 * I think that you hit the nail on the head with that last sentense. --EMS | Talk 06:14, 2 August 2005 (UTC)

BTW - I do take responsibility for that paranthetical remark. If it really is causing confusion, I am happy to let something be done about it.

--EMS | Talk 01:58, 2 August 2005 (UTC)


 * No confusion. I actually think that your overhaul of the GR article is cool.  &mdash;AugPi 04:34, 2 August 2005 (UTC)


 * Thank you very much. --EMS | Talk 05:18, 2 August 2005 (UTC)

Geodesic (general relativity)
Hi, I left some comments on the talk page Geodesic (general relativity). linas 21:56, 2 August 2005 (UTC)

GTR Project?
Hi AugPi. User:CH has set up a draft of a project called Wikiproject GTR. I've noticed you have made some contributions to the general relativity pages and was wondering whether you might like to join us in this project ? ---Mpatel (talk) 17:59, September 1, 2005 (UTC)

Adding refs to articles
Hi,

When adding refs to article, can you avoid using an "external links" section? Also, please format the refs as following:


 * J.S. Kovacs and P. Signell, Magnetic induction (2001), Project PHYSNET document MISN-0-145.

I've reworked a couple of these, but noticed that you added many more. The above is how most of the other math/physics articles cite sources. linas 00:10, 21 September 2005 (UTC)

\ln is ALREADY operatorname
Hello. Please note that in TeX, you don't need to write \operatorname{ln}; just write \ln. Similarly \cos, \max, \sup, \log, \exp, \det, etc. (This not only de-italicizes, but also affects spacing, line-breaking, and, in some cases, positioning of subscripts.) (This comment was inspired by my recently looking at adiabatic process.) Michael Hardy 02:13, 25 September 2005 (UTC)


 * That was a long time ago since I wrote that adiabatic article: since that time probably learned about \ln: it's good to be reminded though. Didn't really know about \det, \max,... Looking at Help:Formula see the Standard functions section... that's good to know, thanks for the pointer. &mdash;AugPi 17:56, 28 September 2005 (UTC)

Handbook of Texas proposed deletion
Please go here and express your opinion on whether Category:Handbook of Texas citations should be deleted. As a Texan Wikipedian, your opinion on this topic is particularly valuable. 66.167.253.162 17:51, 26 September 2005 (UTC).
 * Did vote. &mdash;AugPi 23:14, 5 October 2005 (UTC)

Vowel wheel dialect
What dialect of English does your Kinesthetic vowel wheel illustrate? (General American perhaps?) Also, how is it made? Is there any documentation on it? —Felix the Cassowary ( ɑe hɪː jɐ ) 00:14, 29 September 2005 (UTC)


 * Yes, I do believe that the vowel wheel reflects General American. Lately I have been studying American English pronunciation using a Longman Advanced American Dictionary: its words entries include IPA broad transcriptions: these transcriptions most probably reflect General American.
 * This was my original kinesthetic vowel wheel (phoneme = azimuth): &#593;=45&deg;, &#652;=30&deg;, a=0&deg;, &#230;=330&deg;, &#603;=300&deg;, e=270&deg;, &#618;=240&deg;, i=225&deg;, u=180&deg;, &#650;=150&deg;, &#596;=120&deg;, o=90&deg;. Bold indicates phonemes whose position deviate from their positions in the second, final, version of the wheel.  The following are the extent of their deviations: &Delta;(&#593;)=+15&deg;, &Delta;(&#652;)=+7.5&deg;, &Delta;(i)=+15&deg;, &Delta;(&#596;)=+60&deg;.  The first three of these phonemes changes their position by small amounts, no more than 15 degrees, but did not change their relative positions.  The last phoneme, open o, changed by 60&deg; which is significant and also swapped its relative position with "Spanish" o.  (By the way, I do speak Spanish and so do know how to pronounce the "Spanish" vowels /a/, /e/, /i/, /o/, /u/.  These five monophthongs are the same as those in Japanese, except that Spanish /u/ is replaced by lax /&#650;/ in Japanese (is this right?): /a/, /i/, /&#650;/, /e/, /o/.  Anyway, my objective was/is to try to pronounce the remaining characteristically English monophthongs correctly.)  The reason for the swap is that I was pronouncing the open o wrong: learned this by comparing the kinesthetic vowel wheel with the IPA vowel chart.
 * To understand the positions of the vowels on the wheel intuitively, imagine a picture of a profile cross-section of a talking head which is facing towards the right (usually in phonetics these heads face towards the left of the page (why?)). Now, when pronouncing a vowel, try to imagine the position of the upper jaw with respect to the lower jaw, as might appear on the mouth diagram.  (Notice I said imagine, not to actually observe the position of the jaws externally through, say, X-rays.)  Try to reduce this jaw position down to a unit vector quantity indicating the direction of the upper jaw.  This is a kinesthetic exercise: to try to imagine the position of the jaw while not really actually looking at it but just feeling it.  The exception is the schwa, located at the hub of the wheel: this corresponds to the IPA vowel chart in which the schwa, mid central vowel, is located at the center of the chart.
 * After I came up with the first, incorrect, version of the wheel, I came up with this hypothesis: that the (relative ordering of the) wheel can be obtained from the IPA vowel chart by projecting the English vowels radially outward and away from the central schwa onto a circle drawn around the periphery of the IPA vowel chart (and then rotating the vowel wheel as appropriate (actually, reflecting the wheel about its horizontal diameter)). It turned out that one half of the wheel was reconstructed correctly this way.  Later, after coming up with the corrected version, realized that the entire (relative positions of the) wheel could be obtained correctly by projecting the IPA vowel chart radially outward from a point on the central line just above the mid-close line but below the near-close invisible line occupied by lax /&#618;/ and lax /&#650;/.  Also remembering that the &#652; is actually a &#592; in General American (is it?).
 * The "absolute" positions of the vowels were then fine-tuned, tweaked, in order to correspond to kinesthetic intuition, and eventually realized that most of the vowels would fit into angles which are multiples of 30&deg;, just like a clock, except for the caret, /&#652;/, which intuition said was very close to the /a/. Notice that four out of five Spanish vowels are located at multiples of 90&deg;: /a/, /e/, /u/, /o/.
 * Now for the "harmonic" properties of the vowel wheel. The top half of the wheel is occupied by open vowels, the bottom half by close vowels.  A 15&deg;-195&deg; axis divides the wheel into two regions: a western side occupied by front vowels, and an eastern region occupied by back vowels.  Think of the 15&deg;-195&deg; diameter as an axis of rotation (metaphor).  It is tilted 15&deg; with respect to celestial North-South axis (0&deg;-180&deg;) so that the "Tropic of Cancer" is the chord 75&deg;-285&deg; and the "Tropic of Capricorn" is the chord 105&deg;-255&deg;.  The Tropic of Cancer, and not the "Equator" (90&deg;-270&deg;), is the dividing line between open vowels and close vowels.  Think of the 0&deg;-30&deg; chord as the Arctic Circle (part of extended metaphor), and the 180&deg;-210&deg; chord as the Antarctic Circle.  The IPA vowel chart has four horizontal lines: close, close-mid, open-mid, open (from top to bottom respectively).  These lines correspond to "geographic" lines on the kinesthetic vowel wheel, like so:
 * Arctic Circle : Open
 * 60&deg;-300&deg; chord : Open-mid
 * Equator : Close-mid
 * Antarctic Circle : Close.


 * In the IPA vowel chart, the following pairs of opposite vowels can be found:
 * (a,u), (&#593;,i), (&#603;,o), (e,&#596;).
 * Each of such pairs of vowels is opposite in the sense of being radially symmetric with respect to the schwa. In the kinesthetic vowel wheel, the pairs (a,u) and (&#593;,i) are opposite w.r.t. the center of the wheel, and the pairs (&#603;,o), (e,&#596;) are opposite w.r.t. a point above the center of the wheel, near the intersection of the Tropic of Cancer and the Celestial North-South Axis.  The schwa would have to be located at this intersection above the center in order for it to be mid central vowel exactly.  However, in English, there is no close-mid central unrounded vowel ("backwards e" : &#600;) which would be located at the exact center: in the kinesthetic wheel, this narrow region from (&#603;,o)&cap;(e,&#596;) to (a,u)&cap;(&#593;,i) can be interpreted as being occupied by the schwa, so complementary pairs in the kinesthetic wheel and in the IPA chart correspond.  This might be seen as "cheating" since the complement of /&#603;/ should be /&#650;/.  In the IPA chart, /&#603;/ and /&#650;/ are indeed &#600;-complements.  In the IPA chart, /&#596;/ and /&#618;/ are &#600;-complements, and in the kinesthetic wheel they are center-complements.  The point is that there is a common harmony between the IPA vowel chart and the kinesthetic wheel: this validates the wheel's internal harmonic properties.
 * Note (once again): the "melodic" (chromatic?) properties of the wheel (i.e. relative ordering of the vowels) can be obtained by projecting the English vowels on the IPA chart radially outward from an eccentric point slightly above /&#600;/, between close-mid central and near-close central, onto a circle. This accounts for the relative ordering around the circle but not the exact positions.  The exact positions were obtained by: (1) kinesthetic intuition, (2) spreading the vectors around the circle, apart from each other (like a Kohonen net), (3) snapping the vectors onto the twelve-hour grid of a clock. &mdash;AugPi 18:34, 5 October 2005 (UTC)

Gosh! That was a lot more detail than I expected! So you made this whole thing up (including the very concept)? Impressive! One thing I don't quite understand is the absolute position of /u/ relative to /i/ and /ʊ/ (particularly when you describe the Spanish /i/ and /u/ as occupying the same positions as the American ones). Many speakers of languages that don't have a tense-lax opposition have difficulty distinguishing the pairs of [i ɪ] and [u ʊ], so I would've they'd be much closer together. Given that of the Spanish vowels, in the IPA vowel chart they're probably the two furthest apart, why are they the two closest together in this Kinesthetic vowel chart? (I did one for my own Australian English I think following your principles, which doesn't have the [i ɪ] and [u ʊ] pairs, instead using onset (diphthongal quality) & length to distinguish /iː ɪ/ and has [ʉː] instead of [u]. It comes out with the same space between [ʉ ʊ] but here I'd expect it...)

About phonetics of languages: Japanese /u/ has a special form of rounding, which is its most well-known feature. Apparently it's a bit centralised, so you can describe it as [ɯ̹̈], but it's not really a specially-rounded [ʊ]. American English /ʌ/ is indeed centralised, and you could describe it as [ɐ] (which is commonly also used to describe the Australian English equivalent vowel, though they're quite different: Australian /a/ (as it's also described) is almost identical to the Spanish/Italian equivalent vowel.

—Felix the Cassowary ( ɑe hɪː jɐ ) 01:34, 6 October 2005 (UTC)

D'Alembert operator
Hi AugPi, I see you've added a " "derivation" of box^2 phi ". I guess it is a bit more elaborate for the uninitiated explicitating that a_i^i = g_ij a^ij, but I think we could itnegrate it into the very first equation. What do you think? --MarSch 09:32, 20 October 2005 (UTC)


 * You're right. I have moved the "derivation" up and integrated it with the defining equation, and this despite of my relative dislike of the notation $$\Box$$ for d'Alembertian and $$\Delta$$ for Laplacian: would rather use $$ \Box^2$$ and $$ \nabla^2$$ respectively, since then both operators clearly relate to the nabla like so: $$ \Box^2 = \Box \cdot \Box = \Box^\mu \Box_\mu $$ and $$ \nabla^2 = \nabla \cdot \nabla $$.  But Wikipedia should be descriptive (as in inclusionist), not authoritative, and it is a fact that some authors do use &Delta; for Laplacian (throughout their entire books), so am leaving that notation there as it was rather than quibble over notation.  It was a surprise, though, to find out that there are three alternative notations for d'Alembertian, not just two.  By the way, should mention that Einstein notation is being used.  &mdash;AugPi 15:06, 20 October 2005 (UTC)


 * On the other hand, the notation $$ (\Box^2 - m^2) \psi $$ for some reason immediately appears as if the box were an empty blank, which when filled in yields $$ (\partial^2 - m^2) \psi $$, so now can say that now that have been exposed to it, the $$ \partial^2 $$ notation for d'Alembertian seems more natural, especially when $$ \partial^2 = \partial^\mu \partial_\mu $$: then its naturalness is obvious. &mdash;AugPi 15:33, 20 October 2005 (UTC)

WikiProject Tunings, Temperaments, and Scales
Would you be interested in joining my proposed WikiProject, WikiProject Tunings, Temperaments, and Scales? —Keenan Pepper 18:32, 19 November 2005 (UTC)


 * Allright, just for the sake of it I'll join your WikiProject. This would mean that would have to "get back into it", i.e. my mind back into the topic, since had abandoned it for some time while wondering into other subjects.  Other users keep asking me to join projects and I seem to be reluctant to commit: not knowing what it entails.  But there is strength in numbers, so will increase the number from three to four: that's a diatessaron for you.'' &mdash;AugPi 17:27, 23 November 2005 (UTC)

Image Tagging Image:JointPairOfHyperbolicParaboloids.PNG
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Pachelbel's Fugue
Hello! Thanks for creating and uploading the MIDI file for Johann Pachelbel. I was wondering if you knew exactly what fugue that is? I realize you'd probably name it accordingly if you knew, but I decided to ask anyway. Jashiin 10:28, 28 December 2005 (UTC)

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Sources for alternative constellations?
E.g. Aries. -- Jeandré, 2006-04-30t16:14z


 * OK, I have added a "reference" section to each of the alternative constellations: the references are all the same: the book The Stars by H.A. Rey. However, note that this book does not provide any labels for the stars in the constellations except for bright named stars: it does not provide any Bayer or Flamsteed designations.  I had to look these up in http://homepage.ntlworld.com/robin.gatter/data/stars_list.htm and, more recently, in http://www.skymapper.co.uk/html/surf_the_night_sky.html.   &mdash;AugPi 00:12, 1 May 2006 (UTC)

FYI cat:Bayer objects
Just a little FYI

Category:Bayer objects is ordered by "genitive, designator"

ie. Alpha Ursa Majoris is

Long talk page
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Indices in Christoffel symbol article
Hi, I noticed that you changed the symbols from $$\Gamma^m_{i\ell}$$ to $$\Gamma^m {}_{i\ell}$$ in the above article. Recently another user changed it back and I've been asking why either edit happened. I'm very curious - can you explain your end? Orthografer 15:34, 21 August 2006 (UTC)
 * Even though the Christoffel symbol is not really a tensor, notationwise it behaves very much like one. For tensors, there is a notation in which each index is assigned its own "column", in which it is either a superscript or a subscript.  In this notation (that I'm using), $$\Gamma^m {}_{i\ell}$$ is explicitly different from $$\Gamma_i {}^m {}_l$$ or $$\Gamma_{i l} {}^m$$, and if the m index is lowered, then the symbol becomes simply $$\Gamma_{mil} $$.


 * In the alternative notation, there are no "columns": the superscript is "independent" of the subscripts, and the indices might be arranged in a "Delta" (&Delta;) configuration, with the two subscripts forming the base and the superscript forming the top of the triangle (otherwise the superscript is flushed to the left, just like the subscripts). If the superscript (m) is lowered, the result is a Christoffel symbol of the first kind: $$ \Gamma_{i l, m} $$.


 * There is even a third notation, in which the Christoffel symbol of the second kind is $$\left\{ {}_i {}^m {}_l \right\} $$, with the indices in a Delta configuration, and the Christoffel symbol of the first kind is $$ [m, i l] $$.


 * Which notation is used depends on the author. For example, Bernard F. Schutz (from Cambridge Uni) in his book A first course in general relativity uses the first notation (the one which I was using); Donald H. Menzel (from Harvard Uni) in his book Mathematical Physics uses the alternative notation; whereas Borisenko and Tarapov (from Russia) in their book Vector and Tensor Analysis with Applications use the third notation.  Schutz always uses Christoffel symbols of the second kind, never of the first kind, and commas in the subscript row are reserved for differentiation (instead of for Christoffel symbols of the first kind) (see Covariant differentiation).


 * When I made the edits I happened to prefer the Cantabrigian notation, and now I notice that Wikipedia has kept it. The bracketed notation used by those two Russians I don't like: I definitely prefer the use of Gamma, whether it have its indices separated in columns or "independent" (whichever of these two alternatives is used, should not be a big deal, really).  However, the Russian book is antiquated (copyrighted 1968) and checking the "Christoffel symbol" article in other languages (French, Spanish, German, Dutch, Russian, Chinese) one sees that they all use Gamma, though some use indices separated by columns (German, French, Russian) whereas some do not (Spanish, Dutch, Chinese).  The Dutch version mentions the difference between Christoffel symbols of the first kind and of the second kind.  The Spanish version ignores Christoffel symbols of the first kind, which so does the English, by the way (but so do the German, French, and Russian: just like Schutz).  The Dutch version does not use a Gamma for the Christoffel symbol of the first kind: instead it uses brackets: $$ [m, i l] $$.  Go figure... --AugPi 22:49, 11 November 2006 (UTC)

Shelley Sekula-Gibbs, Houston City Council member and candidate for Congress from Houston/Sugar Land
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