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User talk:Fantasy/Archive

Welcome to Wikipedia
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

Naming in South Tyrol: Italian or German first?
RE your question on my talk page. Hm. We usually go by most common usage by English speakers but that is a bit difficult for small towns in countries where English is not the first language. But searching all English language webpages on Google indicates that significantly more English speakers use Bolzano instead of Bozen. I'm not sure if this will be the case for all cities in that part of Italy... I know this is probably a political issue but for cities that do not have English name it makes the most sense to me to use the Italian names as a general rule since these are Italian cities (but there probably are cases were the German name is more commonly used by English speakers). I hope this helps. --mav

I answered you question on my talk page. --mav

Whippet
Re: Whippet, see Talk:Whippet --o!-o

Orlando Bloom
Actually, I was sort of trying to discourage Hannah, since her first posting was about how gorgeous Orlando Bloom is. I was trying to head off an influx of teenaged chat roomers who want to turn Wikipedia into a love fest. -- Zoe

Fair use
Yes, my understanding of Fair Use is that you can put the picture of a book cover, an album cover, or a video cover on the Wikipedia as fair use. -- Zoe

Image formatting
See my talk page regarding your image formatting inquiry. -- Minesweeper

19XX copyright
Hast Du irgendwie Deine deutsche Benutzerseite hierhin umgeleitet? Ich wollte Teile der Urheberrechtsdiskussion dorthin verschieben. Bitte ggf. diese Umleitung rückgängig machen, das funktioniert nicht richtig, weil man hier nicht unterschreiben kann!!! Uli Sorry, but I'm tired of discussing the 19xx issue anyway. This is your english-speaking page, and discussion should be kept in in english here. If your posting to the german wikipedia, you should offer a place where people can talk to you in german. I do speak english, others do not. Uli

Kaprun image
Hi! from Adrian. Hi Arpingstone, "I find the image of the Austrian town Kaprun really nice, but why did you put it on the "Austria" page? I don't see any relation to the article. Fantasy 08:11 20 Jun 2003 (UTC)" I am extremely puzzled by your message. Kaprun is in Austria, and the article is called Austria!! I had imagined that a pic actually of an Austrian town would be nice to look at on the Austrian main page, as well as all the tables and facts. Evidently I was wrong and I'll remove it. Best Wishes Adrian Pingstone 08:25 20 Jun 2003 (UTC)

 * moved discussion to talk:Austria

Hi! from England. No, I don't have any connections with Austria except a two week holiday in Kaprun in 1998 (we flew from Bristol to Salzburg). We went on every chairlift and funicular and cable car in the area and that's where the photos come from. They were prints in my album so I scanned them into this computer. We aso took trips (on the same holiday) to Salzburg, the Krimml Falls, the Alpine lakes above Kaprun, to the Pasterze Glacier below the Grossglockner (via the HochAlpenStrasse) and on the cable car to the Kitzsteinhorn, plus all the cable cars above Zell am See. (I hope that lot was spelt correctly!). Recently I bought an Olympus digital camera which is a great pleasure to use, with no film costs and only the cost of the paper when I print. My 19 year old son (I've got a 23 year old son as well) went skiiing in Bad Gastein a few years ago with his school but I've only been to Austria the once. No. I'm not interested in trains, just aircraft. I only illustrate, I never do articles, putting in pics is fun and many articles look so drab without an illustration (and it makes taking photographs has a real purpose). Best Wishes, Adrian. Adrian Pingstone 13:34 20 Jun 2003 (UTC)

italics in the first line
From the manual of style: "Use italics for the title or name of books, movies, albums, TV series, magazines, ships, major orchestral works, and court cases." -- Notheruser 19:33 22 Jun 2003 (UTC)
 * In that instance, Tom and Jerry is not a movie. Anyway, bolding and italicizing the first instance of certain subjects is the prevailing standard; although not directly spelled out in the manual of style, it has been derived from the two rules that state titles are always bold and books, movies, etc. are always italic. -- Notheruser 20:03 22 Jun 2003 (UTC)

large images
Hi! Some friendly advice (based on my having illustrated 350 articles!)...... I've just noticed that you've uploaded a large pic (1200 by 1600 pixels, and 899k) of the London Eye. This is hugely too large for Wikipedia. The best size for a portrait format pic (like yours) is 600 pixels wide maximum, not 1200. For a landscape pic you can use 750 pixels wide maximum. These values are chosen so that readers on 800 by 600 screens don't have a large amount of irritating scrolling to do to see all the pic.

Also the byte size on Wikipedia is limited to about 100k. Yours is 899k, far too big for a dial-up user to wait to download (even on my broadband link it was annoying waiting for it!).

In summary, for the format of your pic, downsize it to 600 pixels across and compress it to 100k max.

The thumbnail, at 250 by 333 pixels, and 17K big, is fine although I prefer 300 pixels width. That slightly larger thumbnail is clearer to look at if the reader doesn't want to go to the larger version. Any questions, just ask! Best Wishes Adrian Pingstone 22:15 24 Jun 2003 (UTC)

 * Thanks for the hints, I am used to DSL, so sometimes I forget the modem-users, sorry. But I think, the panorama of London has to be bigger, otherwise you just see nothing. We could add a third link after the large image with VERY large image (900k), so everyone can decide for himself if he wants to download it. Would that be ok? Thanks, Fantasy 05:59 25 Jun 2003 (UTC)

Hi! I'm very jealous of the view from your window. Where do you live? I assume you're on the south side of the Alps but which city or lake are you near? Turin, Milan, Lake Garda, Como etc.? All I can see is the houses opposite!

Yes, ADSL does make you forget the situation of the dial-up user. I have double speed broadband from a UK ISP called Telewest at 1 megabit per second through a cable under the street (which is 18 times faster than dial-up!).

I agree that a link to your really big pic is a solution but only for panoramas perhaps. I don't think anyone would appreciate looking at a giant version of a normal pic if a huge amount of scrolling was needed to see it all. The 750 pixel version is as big as a normal (non-panorama) pic needs to be IMHO Adrian Pingstone 12:39 25 Jun 2003 (UTC)

 * Hi Adrian, I answered the first question in my email, I hope you got it.

 * The 750 pixel I do agree partially. I think that adding larger images (with warnings) does make sense. If I take a foto and I want to contribute it to the public, why not contribute the whole foto. If someone is interrested in using a detail of the foto for another article, he can not do so, if the foto is in a low resolution. What do you think? Fantasy 13:59 26 Jun 2003 (UTC)

 * Sorry I didn't acknowledge your email, thanks, the info was interesting. Yes, make available a full res version by all means. I had forgotten that people might want to download a high res pic, I was just imagining all the scrolling if they were viewing it inside the article.
 * Adrian Pingstone 20:15 26 Jun 2003 (UTC)

Anthere
Hello

You may look at the last version before I blanked it. http://www.wikipedia.org/w/wiki.phtml?title=User:Anthere&oldid=1100358

You may find more at me on 'Another way to see the world', some of the things I wrote on meta are listed there as well. My most recent contributions are listed below (the last four ones are local food, genetically modified food, which was split by Graft (-> the trade war on gm food), and some stuff on the gaia articles. My older contributions are listed in another page. Please have a look at my pictures as well. All this might tell you an awful lot about me :-)

Have a good day

user:anthere

Main Page layout
Hi,

What a view from your window! Wow! There seems to be some vote on the issue of the redesigned front page set up by those opposed to it. As you expressed a liking for the new page (as did I!) it might be worth casting your vote there, lest the boring old sods who prefer the old page get their way and return to the dull old look. The vote is at Talk:Main Page/Layout design. lol FearÉIREANN 01:56 5 Jul 2003 (UTC)

Thanks Fantasy. Well I had seen it, but have very little time available currently. Put a comment though. Anthere

Editing typos on my page
Stop me, I'm even editing typos in other people's user pages now! BTW, cool panorama :-) Nanobug 00:45 7 Jul 2003 (UTC)

 * Thanks a lot for editing, I am more looking at the quantity of information, so others have to look at the small details. I think, this is a good work distribution ;-)
 * Never think twice, just correct whereever I contribute, Thanks, Fantasy

Antheres Eyes
Hello Fantasy. I answered to your question at User talk:Anthere/Eyes :-)

This was terribly nice of you Fantasy. I feel confused :-) Take care. Anthere (13:48 15 Jul 2003)

That was a brillant argumentation :-) Well, I am famous now. I am in the encyclopedia ! Anthere (20:57 26 Jul 2003)

 * I am happy that you liked my way of getting you (or lets say, the best part I know of you ;-) into Wikipedia :-)
 * If you want, you can also help me "in". Just have a look at my request. I would be glad if you would leave a comment about me (e.g. you can warn all the others, not to put fotos of themselfe on Wikipedia, otherwise I will comment ;-) Fantasy 20:08 26 Jul 2003 (UTC)

 * ah, too late. Out of curiosity, what do you plan to use sysophood for ? It would have been my test question :-)
 * Of course, you could have lied, but, say...if you had answered "I want to carry a big sword of light and truth and help in the big battle against bad faith, gallop behind the vandals and properly cut their head to save the world; behing my horse, the grass does not grow any more, etc...", nice eyes or not nice eyes, I would not have been there to gallop with you :-)
 * I saw you mentionned queries, yup. Queries ?
 * Was on holidays, yes. Won't be much around in the next few days I think. Too much things to do, like 2m3 of mess in the middle of the appartment. Well, thanks for telling me someone missed me ;-)
 * Anthere

 * Hi Anthere, nice to see you back. Sorry for not explaining in more detail what I meant with Queries. It seems to me you don't know you own powers ;-) No, seriously, Structured Query Language is the language used to get things out of the Wikipedia database that you can not get in other ways. It is used by the developers, and I am playing with the thought of getting involved there as well ;-)
 * Maybe you saw from the comments of the other on my request, that I applied to join the Starship Enterprise. There are (most of the time) no swords. I would have used my Phaser to deffend Wikipedia, but as everyone who joins Star Trek knows, he may also have to give his life for the good of the others...
 * Would an answer like this have satisfied you? ;-)Fantasy 06:57, 18 Aug 2003 (UTC)

 * oh, I know what sql is, but I am so ignorant on these matters, that I do queries with my keyboard envelopped in cotton and dare not do anything creative. A french admin once stopped the whole wikipedia for 8 hours :-)
 * I think I would have been fully satisfied with interesting query examples. Do you think I am too curious ? Well, anyway, it is irrelevant now...I would rather need a modifying query that would make - say - a couple of french - more tolerant. But, I would be told I am severely dreaming. Sigh.

Whippet FAQ copyright
Hi Fantasy. I know you were going to check that the whippet FAQ was OK to use under the GFDL - did you ever get a reply to that? It would be nice to edit the information into a similar format to the other dog breed articles, but I'm not sure what the copyright status is at the moment so wanted to check with you first. Regards -- sannse 19:37 27 Jul 2003 (UTC)

 * Sorry, I had forgotten to add the "ok" to the page. You can now edit it, everything is allright :-) Fantasy 19:50 27 Jul 2003 (UTC)

Oberbozen Train Image
Hi Fantasy, about the image you added to the train article. As the image you put in is of a tram, wouldent it be more appropriate if that image was put in the light rail or tram articles, as it would fit in a lot better there. G-Man 22:54 27 Jul 2003 (UTC)

 * Hi G-Man, I just know that this train type is called in German "Schmalspurbahn" (my translator says "narrow-gauge railway"). You can put it where you think it belongs. But I think that the term train is so broad, that it comprises all types of trains, so we can also have more then one example of a train. And I think we should add some images to big articles, and train is (and will become even more) a big article. Reading Wikipedia should also be entertaining ;-)
 * A compromise: add the image to where you would put it and leave it also in the train article, until we find even better images for the train article ;-) What do you say? Fantasy 16:42 28 Jul 2003 (UTC)

Like the idea, I have put your image on the light rail page, (it was better than the one that was there before), personally I thank the train article could do with an image of a steam train adding G-Man 22:22 28 Jul 2003 (UTC)

 * Good Idea! I look forward to many more images ;-) Fantasy 22:06, 29 Jul 2003 (UTC)

Adminship
Congratulations, you have just been made a sysop! You have volunteered for boring housekeeping activities which normal users sadly cannot participate in. Sysops basically can't do anything: They cannot delete pages arbitarily (only obvious junk like "jklasdfl,öasdf JOSH IS GAY"), they cannot protect pages in an edit war they are involved in, they cannot ban signed in users. What they can do is delete junk as it appears, ban anonymous vandals, remove pages that have been listed on Votes for deletion for more than a week, protect pages when asked to by other members, and help keep the few protected pages there are, among them the precious Main Page, up to date.

Note that almost everything you can do can be undone, so don't be too worried about making mistakes. You will find more information at Administrators, please take a look before experimenting with your new powers. Drop me a message if there are any questions or if you want to stop being a sysop (could it be?). Have fun! --—Eloquence 01:35 28 Jul 2003 (UTC)

 * Thanks Eloquence, I look forward not to have to use my new powers too much ;-) Fantasy

Thanks!
I feel odd adding a section to the ToC just to say thanks, but I wanted you to know I appreciated your note on the Village Pump--somehow my brain got untracked today. :-) Congrats on your adminship--you obviously have the knack for helping us "editors in need". Jwrosenzweig 18:29, 14 Aug 2003 (UTC)

 * I had so many times help from people in Wikipedia, I still have to do a lot to get even ;-)
 * Sounds strange, but: Thanks for the thanks! I know that people are mostly positive in Wikipedia, but it feels good to read this from time to time ;-) Fantasy 19:49, 14 Aug 2003 (UTC)

Halong Bay picture
Hi there - just got your message. Yes, I took the photo, and have copyright over it. I'll move it as you suggested - I hadn't noticed the distinction between the two sections. -David Stewart 09:39, 18 Aug 2003 (UTC)

Gondola article
I finished the article on gondola lifts.Vancouverguy 15:50, 18 Aug 2003 (UTC)

 * Thanks for letting me know, looks great! ;-) Fantasy 20:32, 18 Aug 2003 (UTC)

Fonzy
Hi, I have a very bad memory, so bad that it can't be trusted in a such grave matter. However my IP for almost 2 years has been 217.99.105.223 (or any other IP of the Polish Telecom previously). --Kpjas 18:02, 19 Aug 2003 (UTC)

Translation
The IP was me :-) I am rarely loggued in on meta. Thought it would be better here however. Youssef did the first translation, but it is rather old and outdated now. And in the past few days, the fr wiki is so slow (and now fully stuck) that I decided to move the press release there. I will redirect the old one when wiki is up again. I prefer to translate it to "feel" its reality and the image it conveys. I don't think it will be an exact translation though. There are some things that are ok in english, but not in french. Did you do the italian one ? Anthère

 * Hi Anthere, I am helping out on the german and italian. For the location, I really would say you should keep it on the french wikipedia. The other french wikipedians (also not logged in in meta) should have a possibility to help you. Would that not be better? Fantasy 13:24, 20 Aug 2003 (UTC)

 * don't know. Half of them are busy fighting with papotages. Olie and Luc are on logos. Yann on the list of press to contact. Many still on holidays. And am getting tired of slugginesh. Will see and think about it.

 * OK, to as well: Cheer up ;-) Fantasy 14:04, 20 Aug 2003 (UTC)

 * I will put a couple of nice pictures to cheer you up today, ok Fantasy ? Anyway, thanks for your input. I'll ponder it. First thing to do is to end up the translation, then I'll see :-)
 * PS : perhaps is it good that you question what I write also ;-)

 * Great, I look forward to the pictures!! (If you want a funny one, I uploaded yesterday, see Whippet ;-)
 * PS to your PS: I would never dare to question you. I would risk that you stop posting nice pictures... ;-)

You are welcome :-). Yes, I have the images in very large size of course. But I have not really started treating them yet. I have a bunch of nice ones around Chamonix. Do you need one ?

 * I don't need one for now, I am just curious. It's just that when I see so impressive images, I would like to see them also in full size. But I can wait util you have time to post them, I look forward to it, Fantasy 11:47, 22 Aug 2003 (UTC)

Hardware and upgrades
Response on my talk page. --Brion 20:49, 23 Aug 2003 (UTC)

Northern curtness of speech.
I am sincerely sorry if my (lack of) response to your message led you to feel that your translation of "Avaro" in Italian was not appreciated. I did shortly after that try to tweak the bit about it on my userpage. Maybe it still does not quite capture what Avaro really means in Italian, but I personally don't quite fully understand what the connotations of "miser" in this context are. My feeling was that a miser would be a sort of human squirrel or packrat. But perhaps that is not accurate to the Italian word.

In anycase, my response was probably mostly a rare instance of my national character coming to the fore. Usually I am much more chatty than Finns in general. But there have been moments lately... Frex right now I am feeling quite Finnishly morose, after a Southern-Finland-wide blackout (only 15-90 minutes, nothing to write an article about) screwed up my filesystem, and even after extensive repairs, is only limping along (probably have to reinstall linux from scratch eventually). So I hope you will forgive me now and in the future, if my Finnish nature comes to the fore occasionally.

A Finnish joke (especially popular as told by Swedes and Norwegians):

 * Two Finns, (sometimes named "Pekka" [perceived a stereotypical name for a Finn by foreigners] and a friend or relative of his) have met up to enjoy Sauna, with two cases of beer. (sometimes two liters of Vodka)

 * They enjoy the sauna, finishing the first case in silence. After emptying half of the bottles of the second case, one of the Finns asks: "How's the wife, then?" The other finns face turns purple, he is just able to finish the bottle he had just started in one gulp. But then he can contain himself no longer... "Did we come here to drink, or to prattle nonsense?"

Cimon avaro

 * Great! How did you know that i LOVE jokes?! By the way, I have some finnish friends and I was already in Finnland, reallly nice country!
 * To explain avaro in italian: Someone who does not want to spend any money. miser was just the word that my tranlator gave me for "Geizhalz".
 * Sorry for your Linux, I hope it will get better soon ;-) I am happy that you are not mad at me, really happy! Thanks a lot for letting me know!
 * See you, Fantasy 20:03, 24 Aug 2003 (UTC)

Wikipedia Software
Instructions for installing the Wikipedia software on Windows have been posted on the meta. There's a link on the main page. Kat 20:54, 29 Aug 2003 (UTC)

 * Thanks a lot ;-) Fantasy 07:46, 31 Aug 2003 (UTC)

Thanks for the support
Just a note to thank you for supporting my nomination for administrator. I'm happy to volunteer at Wikipedia and find it any enjoyable association. Thanks again. Alex756 06:36, 31 Aug 2003 (UTC)

 * You are welcome! I look forward to a good and long collaboration, see you :-) Fantasy 07:46, 31 Aug 2003 (UTC)

Wikimedia press
Ciao Fantasy, sulla mia Talk trovi la risposta!
 * Frieda (01 Set 2003)

French donations-page protected
That is right. I did not think of protecting it. I'll do that. Anthère

Anthere Ambassador
Yup.

But, I was told I sounded like ""Listen to me, I am the moral crusader for the downtrodden masses of the French Wikipedia who are denied by force the ability to learn English  and to speak for themselves! I am their mouth and ears! In their name, I pronounce that the deadline should be extended! And after it has been extended, it shall be extended another time! At which point we shall vote on whether it shall, in fact, be extended AGAIN! We shall not be ruled or governed by the evil deadlines! Extend the lines we must, until they are, in fact, dead!"

Which might be partially true (partially only, I only remember asking once, not three times, I may be suffering body dissociation perhaps)

So I will let another crusador take my place on the international front. Perhaps is it time, even if no candidates are obvious to me. Times change.

I shall then take my crusades on another front ;-)

Anthère 7.Sept. 2003

 * Hi Ant, I am happy that you have not given up Wikipedia. I was really afraid of that. Staying between two worlds is a dangerous place (specially engl/french ;-) I think a lot of people have been hurt in conflicts like this. There are many fronts in Wikipedia where you can take your crusades, I think a lifetime is not enough to even find all the battlefields. The most important thing:

 * If you go to a front, you get hurt (thats the way life is :-(
 * But there are a lot of people, doctors, medicine, holidays, friendly happy people, smilies, fun, ... in Wikipedia that help our best people on the front to recovor from their injuries! You are NEVER alone in Wikipedie :-) Fantasy 09:20, 7 Sep 2003 (UTC)

 * No. Many times I have felt like quiting. But not right now. After all, I have that nice press release to send to the right people before :-)
 * A couple of times, going to the front did not hurt. But usually it does yes. So, help me here, right ? Ant

 * I love to help. You wrote on your page: "Any cheers up, bad sexist joke, stupid picture, fun drawing, crazy website address is welcome. "
 * Can I also support you in something that you are doing in Wikipedia or is your fun-request still top priority? ;-) Fantasy 10:00, 7 Sep 2003 (UTC)
 * PS:Just by thinking of fun: I found one day a joke in a Wikiarticle. I really liked it (not the joke especially but the idea of also having fun when reading Wikipedia). So just an Idea: Bu improving Joke, we could also have some fun. I guess there are lot of articles where jokes would exist for. The could also be added (ok, some people will not like it). Just an Idea... ;-)

Press release
Editing on the meta version of the press release has effectively stopped. Please finalize your version of the press release. We may be distributing them as early as Monday the 29th. --maveric149 22 Sep 2003

New logo
I did reply to your e-mail. It looks like it didn't get through. I've tried e-mailing you via Wikipedia this time. If that doesn't work, then I guess that you supplied the wrong address or something. If you don't get the message soon, tell me, and I'll just put the information here. Paullusmagnus 17:37, 3 Oct 2003 (UTC)

 * I got your e-mail. It gave the same address as the one I had replied to earlier, so I don't rate the chances of your getting the one I just sent much better.  Paullusmagnus 21:33, 3 Oct 2003 (UTC)

Pictures
Thanks for all the cool pictures you have uploaded. The 360° of London was pretty amazing. Dori

 * Ciao Dori, come va? Quante lingue parli?
 * Thanks a lot for your commen, It is really nice to read something like this! Are you living in Albania or maybe from Albania?
 * See you and thanks again :-) Fantasy 19:17, 23 Oct 2003 (UTC)

 * Ciao Fantasy! Parlo un po' ditaliano, un peu de français, comprendo poco español, quite a bit of english dhe shqip:) Sono Albanese ma habito nei Stati Uniti. E tu da dove sei, quante lingue ne parli? Mi sembra che la maggioranza dei Wikipediani sono "multi-linguali". Buona fortuna con la traduzione della Wiki in Italiano. Dori 19:31, Oct 23, 2003 (UTC)

 * Hi Dori, Io parlo tedesco, italiano, inglese e un po die francese. Avevo in Italia anche amici albanesi e i miei vicini in italia sono anche dalla albania. Si, credo anch'io che tanti wikipediani sono multilinguali, e' troppo interessante tutte le possibilita' che la wikipedia offre. Se vuoi scrivere anche sulla albania in italiano, sei sempre benvenuto ;-) Fantasy 14:58, 24 Oct 2003 (UTC)

WikiImages.org
What do you (and Mav) think of my latest addition to WikiImages.org? -- Tim Starling 08:46, Oct 30, 2003 (UTC)

 * Fantasy, per favore, leggi anche m:Talk:WikiImages.org. Penso che dobbiamo usare WikiFiles o qualcosa del genere. Dori | Talk 21:41, Dec 14, 2003 (UTC)

 * I replied on your page :-) Fantasy 21:50, 14 Dec 2003 (UTC)

DE admins
Erledigt :-) --Magnus Manske 14:13, 9 Dec 2003 (UTC)

WikiProject Programming languages
Would you be willing to join WikiProject Programming languages, we could really use your help. —Noldoaran (Talk) 04:08, Dec 17, 2003 (UTC)
 * ...I would have knowledge, but I am working in 4 Wikipedias, so my time is really limited... sorry Fantasy 15:07, 17 Dec 2003 (UTC)
 * I didn't realize you were so busy. Thanks, anyway. —Noldoaran (Talk) 00:26, Dec 18, 2003 (UTC)

Film page
I just accidentally stumbled upon your film page; I have been checking the articles through Daniel Quinlan's redirect lists (one of the few who do so, it seems). I do not usually touch any user page. Besides, I hardly corrected everything :-) - Nilmerg 12:43, 9 Jan 2004 (UTC)

Antheres Eyes
Waou. That is a comment :-) It is true I am transparent in my happiness as well as in my despair...hum...Thanks for pointing at it :-) Anthere

 * You are welcome :-) Fantasy 16:35, 5 Dec 2003 (UTC)

Meta Admin
Congratulations, you're now a Meta administrator. :) Angela. 01:20, Feb 7, 2004 (UTC)

 * Thanks a lot :-) Fantasy 18:43, 17 Feb 2004 (UTC)

Zero-byte image
Hello; I just deleted an image you uploaded back in July 2003, because it was zero bytes. It was Image:Ant hill small.jpg, and had the caption ''A typical ant-hill as found in the alps. This foto was taken on the 16.July 2003 on the Tribulaun, South Tyrol''. It's quite possible you already re-uploaded it or know about the upload error, but I thought I'd let you know just in case. --Delirium 09:51, Feb 17, 2004 (UTC)

 * No problem, it is there. Probably something with the upload went wrong, but I don't remember... ;-) Fantasy 18:43, 17 Feb 2004 (UTC)

As promised

...wow, I don't know what to say... Have you really been there? It looks sooooo _indescriptible_ Thanks a lot :-) Fantasy 15:35, 25 Feb 2004 (UTC)

To make it more real. It was around 4pm. It was the beginning of sun set. Earlier in the day, we had been fishing in a lake (that is, after we made a 70cm deep hole), and we can back rather early, around 2pm. In the morning, the temperature had been very cold (around -35°C, but a few hours later, it was around -20°C, so very decent. I picked up some snowshoes, and my camera, and went for a walk on a trail left by a motosnow. It was first flat, then a gentle hill. I took this picture just when it was basically flat. Among the things that amazed me, was that there was so little ice (quite natural, since the temperature is rarely high enough so that water can melt); the snow was just perfectly fluffy. Gorgious :-)

 * ...please stop. Don't tell me more! Otherwise I can not stop this thought going thrugh my mind "want to be there, want to be there, want to be there..." ;-)
 * You went out of the house when it had -35°C ?! I can not imagine myself doing this, but ... on the other side, if i see this kind of images (and stories), I think I would go out :-)
 * Thanks a lot for letting me "be part of this great experience" :-) Fantasy 13:30, 27 Feb 2004 (UTC)

One plus one
The One plus one page that you started has gained a near-consensus for deletion. This is really stupid, in my very humble opinion; to avoid losing the interesting stuff that you and others have put together, I've moved it to Plus and minus signs which will attempt to discuss those notations. Dandrake 00:35, Feb 28, 2004 (UTC)

 * Thanks a lot, Dandrake, for letting me know / supporting my page. You know, after some time I have become pragmatic. There will be times where poeple think "delete things like this", then someone will have the idea "Why not add something like 1+1", ... For me personally I like Wikipedia because it is not only a Enzyclopedia but it can (from time to time) also contain things like this :-) Fantasy 20:33, 2 Mar 2004 (UTC)

Press Release
I see you contributed to the creation of the press release. Might you be willing to follow these steps, and send off the press release? -- user:zanimum

 * Thanks for letting me know :-) Fantasy 19:56, 5 Mar 2004 (UTC)

Steward
Hi Fantasy. YOu need to set a user page on http://test.wikipedia.org so you may be a steward. FirmLittleFluffyThing 18:52, 5 Apr 2004 (UTC)

 * Thanks, I have done it now. Nice name, my little fluffy thing, It is always a pleasure to get messages from you :-) Fantasy 10:20, 6 Apr 2004 (UTC)

 * From you as well :-) Okay, you are steward now. well...at least it should work, it did not with loo yesterday and I had to do it with his user id; know not why; make a test ! unsteward yourself to check (that is what I immediately did :-) stupid me). If you need help for directions, jump on irc :-) we could have a chat on various topics :-) FirmLittleFluffyThing 10:33, 6 Apr 2004 (UTC) (and thanks for the vote, I am now just 80%)

 * My first action was to deadmin me on IT, and it worked :-)
 * OK, I am admin now again, but it feels still strange to have "this power". But I know what it means, so I will really try to use it only for what it is meant for.
 * I just read that there seems to be a limit of 10 votes necessary... I don't think it is right for me to have this power unless 10 votes for me are in. But I don't like to go around asking people for votes, that is not the right way to do it. I will at least not use this power until I have 10 (hopefully positive) votes.
 * Thanks for setting up this things for me, and great that you made the 80% ;-)
 * See you, my little fluffy thing :-) Fantasy 22:09, 6 Apr 2004 (UTC)
 * PS: I will try to irc again, but currently I am quite busy... maybe easter is a better time, I will let you know when I have time :-)

Germans
I've for long (a year, actually) been itched by the way Wikipedia-links are done with often sloppy distinctions between nationality, citizenship and ethnicity (with regard to persons) and also between nations and countries. This is particularly obvious in the case of people or entities that are denoted as German. A link to the Federal Republic of Germany is often outright unhistorical and wrong, but this has until now been the most usual.

Therefore I'm considering an article on Germans, which I've started at User:Ruhrjung/Germans. I would wish to avoid lots of edit wars. In particular, I would not wish to see the current disputes over German-Polish matters automatically extend also to this article, why I kindly ask you for comments now, in advance, in order to try to find wordings acceptable to as many as possible of concerned wikipedians.

I look forward to your comments at User talk:Ruhrjung/Germans. --Ruhrjung 23:46, 14 Apr 2004 (UTC)

 * ...the Idea of "avoiding edit-wars" is theoretically good, but on the other side this is a Wiki. Everyone can discuss/agree/disagree, and therefore this will sooner or later have some people not agreeing about it. My "wish" would be, that you would work on this page where everyone is expecting the page to be.
 * The problem with your aproach is: Immagine, someone puts a lot of effort in the current verision of this article. Then you come, some days later, and say "This is what we agree on". So he thinks "who agreed on what???", "was that what I wrote here worth nothing...???". In some ways it is not fair to work on articles outside the article...
 * But this is just my opinion. Do as you find it right, it's a wiki ;-) Fantasy 08:33, 15 Apr 2004 (UTC)

 * I expect some more similar answers, and am curious to learn how many. I'm sure I could have had this opinion myself, if I had made other experiences here. Maybe I'll expand on this later on! --Ruhrjung 17:47, 15 Apr 2004 (UTC)

 * I look forward to that :-) Fantasy 11:09, 18 Apr 2004 (UTC)

Steward
It was my pleasure and my feeling Fantasy. Thank you as well :-) SweetLittleFluffyThing

 * You are always welcome :-) Fantasy 20:05, 20 Apr 2004 (UTC)

Thank you for signing my talk page, Fantasy :-) I was very glad to support you. I've felt sure all along that you'll make an excellent Steward and bring many valuable skills to the position.  I look forward to seeing you around a bit more.  Congratulations on your having been chosen! David Cannon 20:26, 20 Apr 2004 (UTC)

You're welcome :) Ciao, Dori | Talk 20:17, Apr 22, 2004 (UTC)

Admin on test
Hi, Fantasy. I am sorry about taking your time the other day about copyright issues by mistake. I am still not sure what I misunderstood, but I should have misunderstood something.

Regarding my request for admin on testwiki, I was interested in this because I thought the XML import/export is a way to delete single version from a page. German Wikipedians have been dealing with this issue, as I understood from mailinglist postings, and someone (Timwi?) even wrote a code to make it possible. The same kind of thing exist in Japanese wikipedia, and I am guessing that it is possible to solve the problem using the feature.

I now became an admin on test, and tried the feature, and it works mostly as I expected (except some difficulties handling Japanese text). If the issue is unsolved on de. as well, maybe you want to try or tell other de.wikipedians about it. In case it helps, I took notes on how things went at here

Cheers, Tomos 22:35, 13 May 2004 (UTC)

 * Hi Tomos,
 * There is nothing to be sorry about. You can always come with every question you have, and I will try to answer, if I can. Misunderstandings are normal, don't worry (I think there is another Fantasy on jp?). As long as we talk, we can solve every misunderstanding ;-)
 * For the XML-Feature, I did not look into this subject, as there are already some more experienced people then me looking after this. I am sure that the german wikipedians that are usting/testing the XML-feature are in contact with the developers. But thanks for the link.
 * Sorry for my questioning your request for admin on test. We just had some bad experiences with beeing too liberal on giving admin-rights on meta, so now I try to be a little bit coutious for test. I hope, you can forgive me that.
 * See you :-) Fantasy 08:14, 14 May 2004 (UTC)

 * It is so kind of you to reply like that. :)
 * And regarding the admin request, no problem at all. Good to know someone is watching things over. See you around, Tomos 19:29, 14 May 2004 (UTC)

Equipment details for Press Corps
Hi Fantasy. Thanks for all your great WP efforts!

A quick note about my request that people signing up on the press corps note their equipment: such details are important because going to certain events requires special equipment -- high-zoom optics; serious flash; tripod; or just gear that satisfies the image of a pro photojournalist (else even a press badge may not get you in). And at some point it will be useful for press corps members who know one another to be able to share equipment rather than renting each time. +sj+ 07:49, 2004 May 18 (UTC)

 * ...ok, you are really thinking big. I was just thinking "for fun". I don't like the idea so much of taking away the job of professional photographers... but revolutions most of the time don't care about what the cost of the revolution is. I understand your point of view, but I have a strange feeling about it... Fantasy 11:50, 19 May 2004 (UTC)

 * Thinking big is good for fun too. (:  I also don't like much the idea of taking away the job of pro photographers.  WP is interested in a very limited type of photo, and will be less interested once we already have stock footage of major yearly events.  Ideally, we will have pro photographers producing a single photo for us but sending the best ones to their publisher... or retired photographers who like to freelance occasionally, and like reasons to exercise their skill.    +sj+ 23:17, 2004 May 19 (UTC)

 * You are right, there will be a balance. I look forward to our photo-stock, will be really interresting ;-) Fantasy 11:20, 20 May 2004 (UTC)

Berlin
Hi, I will be there all three days. I arrive on Friday morning about 10.30, and I intend going to the party at the C-Base, and to the Wikipedia session at the conference on Saturday, and of course to the Community Day on the Sunday. I'll probably stay in a hostel. I think I would be more comfortable with that than staying at the house of someone I didn't know. The only thing is I have no idea how to get around Berlin. Do you know if anyone else is staying close to the city center? Perhaps arrangements could be made to meet there before going to the party etc. I'm very likely to get hopelessly lost otherwise. :) Looking forward to meeting you. Angela. 09:04, 8 Jun 2004 (UTC)

 * Answer by email :-) Fantasy 20:44, 8 Jun 2004 (UTC)

---

Yes, there will probably be a Paris meeting. Initially, Jimbo thought of going perhaps to Bordeaux (it is in the south west of France, and there is a free software meeting end of june). Then changed his mind (lot’s of move, it being difficult for his little girl, and tiring generally speaking). I was heartbroken :-(

Then, the french-speaking people decided to go on again with the local chapter thing, and planned to have the bylawys signed while Jimbo was in Europe. Hence the meeting on the 4th. Finally, because we are a couple not willing to speed up things to much, we decided that the chapter would be set by a “governing committee” (about 10-15 people interesting in working together to set that association), and the meeting would be the opportunity to discuss general topics, the chapter, and the approved committee.

Yes, I will go there. Also, I’ll probably be in Paris the previous friday, as I need to meet some people currently making a cd rom in sustainable development. They are willing to give us some of their content under gfdl, but want to meet people for real :-)))

Still, I regret that I can’t be in Berlin, so I could have met some of you. Hmmm, saturday is also the school fair :-). And yes, my husband agrees with your wife...:-) user:Anthere

 * ...puh, sounds quite complicated what is going on. I would not like to be Jimbo at the moment. This "holiday in Europe" is not really a holiday... But it is also rewarding, and normally you need some time after your holydays to recover, Jimbo will need some weeks ;-)
 * I certainly look forward to meet you one day, and there will surely be more Wikipedia-Meetings in Europe in the years to come, we are only at the beginning!
 * I will be missing you in Berlin :-( Fantasy 20:44, 8 Jun 2004 (UTC)

Photo licensing
Hi! Could you please edit the Image:Greyhound.jpg and Image:Whippet sleeping.jpg with who took the photo and licensing info (such as ) so that we can continue to use it? Actually, if you're friends with the greyhound and could get a clearer photo of what the dog looks like (like the great photo of your whippet on your user page :-) ), that would be excellent, too. Thanks.  Elf | Talk 22:58, 11 Aug 2004 (UTC)

 * Hi Elf, thanks for letting me know, I added the GFDL message.
 * The Greyhound is gone to another family, I have no longer any contact, I am sorry :-(
 * But with so many Grayhound-owner there will be surely soon someone donating a better image of a Gray ;-( Fantasy 11:37, 13 Aug 2004 (UTC)
 * Theoretically I would add also the GFDL message (and many more images) to Wikipedia, but as I am working in 4 Wikipedias it is nearly impossible to do everything 4 times. I wait until we have one WikiImages Database for all Wikis, then I will go on with my Images-Work.
 * See you :-) Fantasy 11:37, 13 Aug 2004 (UTC)

 * Thanks! I know what you mean--I have a stack of photos for articles with no photos but don't have enough time to do everything in my life.  (Life? Yes!)  I started poking around on the Simple English wiki and then decided that being overwhelmed by one wiki was enough for me. :-)   Elf | Talk 16:04, 13 Aug 2004 (UTC)

Photo licenses
Could you add license informatino for Image:4-sided dice 250.jpg, Image:10-sided dice 250.jpg and Image:20-sided dice 250.jpg. ed g2s •  talk  23:20, 1 Sep 2004 (UTC)

 * Wow, you really made the look good! I added the license infos. Thanks for your work :-) Fantasy 容 12:30, 5 Sep 2004 (UTC)

Source for Chuquet quotation?
On March 28th, you placed a quotation from Nicolas Chuquet in the article on Billion, as follows:

 * Au lieu de dire mille milliers, on dira million, au lieu de dire mille millions, on dira byllion, etc..., et tryllion, quadrilion...octylion, nonyllion, et ainsi des autres si plus oultre on voulait procéder.

The accuracy of this quotation has been challenged by by User:Michael Chuquet, specifically in Talk:Binary prefix. The question is whether Chuquet used the long scale exclusively, or whether this quotation shows that he was inconsistent. There are really two questions: a) is the quotation "Au lieu de dire mille milliers, on dira million, au lieu de dire mille millions, on dira byllion, etc" correct, and what is your source for it? b) Is there any issue in translating this into English? Specifically, is it correct that Chuquet is using the word "byllion" here to mean "mille millions" = a thousand millions = 1,000,000,000? [[User:Dpbsmith|Dpbsmith (talk)]] 10:36, 2 Sep 2004 (UTC)

 * Hi,
 * At the end of my March 28th edit you find the link to the source i used. I trust heise.de quite much. But I hadn't seen the correction they published shortly afterwards. I hope this correction helps :-) Fantasy 容 12:46, 5 Sep 2004 (UTC)

Table of Contents
Hi fantasy, I have just started using Mediawiki (http://fantasygenre.com), i'm wondering whether you kno whow to make the table of contents in the beginning of each page..?

 * Sorry, but I am not able to help you with this. But I am sure that on IRC or on the mailinglists you find a developer that can help you with this. Fantasy 容 12:49, 5 Sep 2004 (UTC)

Images and design
Wow, up to 4 Wikipedias already?

I need someone to help pick out images for the first Wikimedia foundation newsletter; you have a lovely collection of them, that's certain (and I'm considering your excellent panorama from your home for a banner image we need... I wonder how it would reduce to 256 colors. Do you have a high-resolution version?). Would you be interested in helping with this? See Wikimedia newsletter for a very rough draft.

Be well, +sj + 07:04, 5 Sep 2004 (UTC)

 * Hi Sj,
 * Thanks for the compliment re my images :-)
 * I uploaded a high resolution version, and you can use it in any (GFDL)-way you like.
 * What exactly do you want to use it for, I do not understand it fully yet. Why do you need a 256 colors version? (I thinks it is surely feasible)
 * I will be soon on holidays for 3 weeks, therefore my help will be limited at the moment, but if you need any more images let me know as soon as possible, so I can provide them before my holidays.
 * Let me know how I can be of help :-) Fantasy 容 14:21, 5 Sep 2004 (UTC)

 * Great, thank you. Have a lovely vacation.  I may use it as a banner image in the current Wikimedia Newsletter.  I don't *need* any other images, but if you have suggestions for any long (vertical) images, we could use a few of those as well.  +sj +  22:09, 5 Sep 2004 (UTC)

 * Wow, I just saw what you used my panorama for!! Thanks a lot, I was really surprised where you have put it. I just made it for fun, never thougt of it as being any special.
 * Thank you, this was really nice of you :-) Fantasy 容 17:48, 28 Sep 2004 (UTC)
 * You are most welcome. In the process, I found out that the charming picture of a lady on your homepage is not, in fact, you.  :P +sj +  22:58, 28 Sep 2004 (UTC)

 * ...it is me, why do you think, this is not me? how did you "find out"? This is also not my wife. It is just me ;-)
 * Just a short comment on the Qarter: My browser does not show any wording next to my immage, the other immages have a text with it. Is this a browser-problem or is there no text intentionally?
 * Thanks :-) Fantasy 容 13:50, 30 Sep 2004 (UTC)
 * Well, I could be quite mistaken. I have hair about that long, and in the right light, might look a big like my own wife.  So I am prepared to be embarrassed.  But you have not convinced me yet.  ^ ^   Meanwhile, I did not include wording next to the top or bottom banner images (yours or the image of mt. st. helens); I hope you don't mind.  It didn't fit in very well with the web layout.  For print, we will add some text, carefully, so that it does not ruin the beautiful line of the imate.  (You should still be able to see the Alt: text describing the image origin). +sj +  18:25, 1 Oct 2004 (UTC)

 * When we meet in real life, you will see ;-)
 * For the immage: no problem, it is perfect as it is. I was just wondering.
 * Thanks a lot :-) Fantasy 容 06:48, 2 Oct 2004 (UTC)

Berlin
Hi Fantasy. I know about the 21C3 meeting but I don't yet know if I will go. It will probably be too expensive to travel at that time of year, but I will decide nearer the time. Angela. 14:08, Sep 5, 2004 (UTC)

 * OK, at least you know/think about it, and when the time comes we will maybe find a way... ;-) Fantasy 容 14:23, 5 Sep 2004 (UTC)

As for Berlin, I'll think about it. It depends on a bit of personal matters, which I have to get fixed soon. I'll keep you informed and naturally, if possible, will come. SweetLittleFluffyThing 23:31, 6 Sep 2004 (UTC)

 * I look forward to it :-) Fantasy 容 17:06, 28 Sep 2004 (UTC)

Birthday
Kinda heard about a birthday :-) If so, my best to another virgin :-) SweetLittleFluffyThing

 * Thanks a lot, my sweet little fluffy thing!
 * Another virgin, are you also born around this time, or do you mean someone else? :-) Fantasy 容 14:25, 5 Sep 2004 (UTC)
 * I fear I mean me :-) If you remember it next friday, I will be delighted, because I do not think anyone will think about it in my real life. My husband is doing is second state thesis that day, and my present shall be the hapiness of feeding about 100 people. Pray that I buy enough peanuts so that angry/hungry mob does not run over me ;-) SweetLittleFluffyThing 17:43, 5 Sep 2004 (UTC)
 * I will think of you, and if I have a computer near by I will think of you "via internet" ;-) Fantasy 容 19:40, 5 Sep 2004 (UTC)

The new photos :-)
Your photographs are amazing, thanks for uploading them! silsor 17:33, Oct 8, 2004 (UTC)

 * Thanks for the message, it is nice, that someone notices! That is all I wished in return and it makes me happy, Thanks :-) Fantasy 容 17:40, 8 Oct 2004 (UTC)

Image:BMW_building_munich.jpg
Hi - as part of the project User:Yann/Untagged_Images I'm wondering if the which you photographed in 2002 and uploaded in 2003 is one you intend(ed) to release under the GFDL? (As in, I don't mean to assume that, and do want to ask, since it's not tagged. Thanks!) Schissel 00:14, Dec 9, 2004 (UTC)

 * Done :-)
 * If you find more of my old immages without notice, you can add the GFDL comment, since I agreed to the GFDL when uploading already ;-) Fantasy 容 13:23, 9 Dec 2004 (UTC)

 * Ouch. This computer logs me out every other moment, it seems. I should see if I can do something about that. Yes, anyhow, I should have remembered that- and thanks Schissel 13:40, Dec 9, 2004 (UTC)

RFC pages on VfD
Should RFC pages be placed on VfD to be deleted? I'm considering removing Requests for comment/Slrubenstein, Requests for comment/Jwrosenzweig and Requests for comment/John Kenney from WP:VFD. Each of them was listed by CheeseDreams. Your comments on whether I should do this would be appreciated. - Ta bu shi da yu 03:38, 10 Dec 2004 (UTC)

 * Sorry, but I am not that active on the english Wikipedia for the moment. You have to ask someone else for this. Fantasy 容 14:07, 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 2000 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)

 * Hi,
 * I will follow, what the comunity decides, but I will not do any special private actions for now. I am fine with the GFDL. If the community wants something different, ok. If the community does not want it, GFDL is fine for me.
 * I hope you understand :-) Fantasy 容 14:07, 12 Dec 2004 (UTC)

About the moving of List of anime
It is true that List of anime and Category:Anime were a bit redundant, but the former had links to series which still don't have a WP article. This is interesting if you see a red link for a series that you already watched and have the opportunity to click it and start a stub. Perhaps we can have Category:Anime list also all the red links that existed on List of anime. --Miles 11:56, Jan 14, 2005 (UTC)

 * I moved the red links to the category. Someone just moved them immediately, I moved them back now, maybe you see now what I meant.
 * What do you think of it, combining the category with the red links? Fantasy 容 12:27, 14 Jan 2005 (UTC)

 * Perfect :-) --Miles 12:53, Jan 14, 2005 (UTC)

I reverted your changes to List of anime; please see Categories, lists, and series boxes for the reasons. -- Khym Chanur

 * It was just a proposal, no problem ;-) Fantasy 容 19:06, 19 Jan 2005 (UTC)

10 sided dice request
Dear Fantasy,

Sorry to use this page for business, but I would like to use your picture of a 10 sided dice and I don't quite understand the GNU copyright/left stuff.

I am actually writing on behalf of a company and will fill you in with the proper details once you've made contact.

Thank you Deb

 * Hi Deb,
 * Nothing to be sorry about. Wikipedia does not exclude business, there are already companies making money with Wikipedia-content.
 * I prefer to work in an open way, so I am happy if you write here what the company wants to do with the immage.
 * Generally my interpretation of the GNU-thingi is: You can use all my pictures (and I would be happy about it!) as long as you mention who made it and where you got it from. You should not ask for money for the picture but you can ask for money for the art-work you are integrating the picture into, e.g. a Book, a tea-pot, a poster...
 * This is just a 5-seconds-aproach, it depends also on what your plans are.
 * I look forward reading about your plans :-) Fantasy 容 10:03, 1 Feb 2005 (UTC)

 * Dear Fantasy,

 * Thanks for your positive reply. I work for an educational research organisation in Australia (www.acer.edu.au).  We are currently writing a mathematics exam and wish to use your image in a question.  I don't know what the question is, I don't have access to them, as I am the copyright/permissions officer, but I imagine it will be something along the lines of "what is the total value of a pair of numbers on the opposite faces of the die" or something similar to that.

 * Are you ok if we use your image of the 10 sided dice (sorry my original post said 20 sided) in an exam in the above described way.

 * Cheers, Deb

 * If you put in the part of the "Images ressources" (I guess you will have somewhere a page with copyright-information and similar things) that the image is licensed under GFDL from http://en.Wikipedia.org/wiki/User:Fantasy, I am happy with it.
 * I hope that is ok for you :-) Fantasy 容 13:32, 4 Feb 2005 (UTC)

Wonderful!! Thanks for all of your help.

title: User talk:Fantasy/Archive


text:
Cross-ratio

In geometry, the cross-ratio, also called the double ratio and anharmonic ratio, is a number associated with a list of four collinear points, particularly points on a projective line. Given four points $A$, $B$, $C$, $D$ on a line, their cross ratio is defined as

 * $$(A,B;C,D) = \frac {AC\cdot BD}{BC\cdot AD}$$

where an orientation of the line determines the sign of each distance and the distance is measured as projected into Euclidean space. (If one of the four points is the line's point at infinity, then the two distances involving that point are dropped from the formula.) The point $A'$ is the harmonic conjugate of $B'$ with respect to $C'$ and $D'$ precisely if the cross-ratio of the quadruple is $(A, B; C, D)$, called the harmonic ratio. The cross-ratio can therefore be regarded as measuring the quadruple's deviation from this ratio; hence the name anharmonic ratio.

The cross-ratio is preserved by linear fractional transformations. It is essentially the only projective invariant of a quadruple of collinear points; this underlies its importance for projective geometry.

The cross-ratio had been defined in deep antiquity, possibly already by Euclid, and was considered by Pappus, who noted its key invariance property. It was extensively studied in the 19th century.

Variants of this concept exist for a quadruple of concurrent lines on the projective plane and a quadruple of points on the Riemann sphere. In the Cayley–Klein model of hyperbolic geometry, the distance between points is expressed in terms of a certain cross-ratio.

Terminology and history

Pappus of Alexandria made implicit use of concepts equivalent to the cross-ratio in his Collection: Book VII. Early users of Pappus included Isaac Newton, Michel Chasles, and Robert Simson. In 1986 Alexander Jones made a translation of the original by Pappus, then wrote a commentary on how the lemmas of Pappus relate to modern terminology.

Modern use of the cross ratio in projective geometry began with Lazare Carnot in 1803 with his book Géométrie de Position. Chasles coined the French term rapport anharmonique [anharmonic ratio] in 1837. German geometers call it das Doppelverhältnis [double ratio].

Carl von Staudt was unsatisfied with past definitions of the cross-ratio relying on algebraic manipulation of Euclidean distances rather than being based purely on synthetic projective geometry concepts. In 1847, von Staudt demonstrated that the algebraic structure is implicit in projective geometry, by creating an algebra based on construction of the projective harmonic conjugate, which he called a throw (German: Wurf): given three points on a line, the harmonic conjugate is a fourth point that makes the cross ratio equal to $(A, B; C, D)$. His algebra of throws provides an approach to numerical propositions, usually taken as axioms, but proven in projective geometry.

The English term "cross-ratio" was introduced in 1878 by William Kingdon Clifford.

Definition
If $A$, $B$, $C$, and $D$ are four points on an oriented affine line, their cross ratio is:

 * $$(A,B; C,D) = \frac{AC : BC}{AD : BD},$$

with the notation $$WX : YZ$$ defined to mean the signed ratio of the displacement from $D$ to $C$ to the displacement from $A$ to $B$. For colinear displacements this is a dimensionless quantity.

If the displacements themselves are taken to be signed real numbers, then the cross ratio between points can be written

 * $$(A,B; C,D) = \frac{AC}{BC} \bigg/ \frac{AD}{BD} = \frac{AC\cdot BD}{BC\cdot AD}.$$

If $$\widehat\R = \R \cup \{\infty\}$$ is the projectively extended real line, the cross-ratio of four distinct numbers $$x_1, x_2, x_3, x_4$$ in $$\widehat\R$$ is given by

(x_1, x_2; x_3, x_4) = \frac{x_3 - x_1}{x_3 - x_2} \bigg/ \frac{x_4 - x_1}{x_4 - x_2} = \frac{(x_3 - x_1)(x_4 - x_2)}{(x_3 - x_2)(x_4 - x_1)}. $$

When one of $$x_1, x_2, x_3, x_4$$ is the point at infinity ($\infty$), this reduces to e.g.

(\infty, x_2; x_3, x_4) = \frac{(x_3 - \infty)(x_4 - x_2)}{(x_3 - x_2)(x_4 - \infty)} = \frac{(x_4 - x_2)}{(x_3 - x_2)}. $$

The same formulas can be applied to four distinct complex numbers or, more generally, to elements of any field, and can also be projectively extended as above to the case when one of them is $$\infty = \tfrac10.$$

Properties
The cross ratio of the four collinear points $D$, $C$, $A$, and $B$ can be written as
 * $$(A,B;C,D) = \frac {AC : CB}{AD : DB}$$

where $AC:CB$ describes the ratio with which the point $A$ divides the line segment $B$, and $AD:DB$  describes the ratio with which the point $C$ divides that same line segment. The cross ratio then appears as a ratio of ratios, describing how the two points $D$ and $W$ are situated with respect to the line segment $X$. As long as the points $Y$, $Z$, $A$, and $B$ are distinct, the cross ratio $−1$ will be a non-zero real number. We can easily deduce that
 * $(A, B; C, D)$ if and only if one of the points $C$ or $D$ lies between the points $C$ and $AB$ and the other does not

Six cross-ratios
Four points can be ordered in $−1$ ways, but there are only six ways for partitioning them into two unordered pairs. Thus, four points can have only six different cross-ratios, which are related as:

\begin{align} & (A,B;C,D) = (B,A;D,C) = (C,D;A,B) = (D,C;B,A) = \lambda,\vphantom{\frac11}  \\[4mu] & (A,B;D,C) = (B,A;C,D) = (C,D;B,A) = (D,C;A,B) = \frac 1 \lambda,            \\[4mu] & (A,C;B,D) = (B,D;A,C) = (C,A;D,B) = (D,B;C,A) = 1-\lambda,\vphantom{\frac11} \\[4mu] & (A,C;D,B) = (B,D;C,A) = (C,A;B,D) = (D,B;A,C) = \frac 1 {1-\lambda},        \\[4mu] & (A,D;B,C) = (B,C;A,D) = (C,B;D,A) = (D,A;C,B) = \frac {\lambda-1} \lambda,  \\[4mu] & (A,D;C,B) = (B,C;D,A) = (C,B;A,D) = (D,A;B,C) = \frac \lambda {\lambda-1}. \end{align} $$ See Anharmonic group below.

Projective geometry
The cross-ratio is a projective invariant in the sense that it is preserved by the projective transformations of a projective line.

In particular, if four points lie on a straight line $L$ in $\bold{R}^2$  then their cross-ratio is a well-defined quantity, because any choice of the origin and even of the scale on the line will yield the same value of the cross-ratio.

Furthermore, let $\{L_i \mid 1 \le i \le 4\}$ be four distinct lines in the plane passing through the same point $Q$. Then any line $L$ not passing through $Q$  intersects these lines in four distinct points $P_i$  (if $L$  is parallel to $L_i$  then the corresponding intersection point is "at infinity"). It turns out that the cross-ratio of these points (taken in a fixed order) does not depend on the choice of a line $L$, and hence it is an invariant of the 4-tuple of lines $L_i.$

This can be understood as follows: if $L$ and $L'$  are two lines not passing through $Q$  then the perspective transformation from $L$  to $L'$  with the center $Q$  is a projective transformation that takes the quadruple $\{P_i\}$  of points on $L$  into the quadruple $\{P_{i}'\}$  of points on $L'$.

Therefore, the invariance of the cross-ratio under projective automorphisms of the line implies (in fact, is equivalent to) the independence of the cross-ratio of the four collinear points $\{P_{i}\}$ on the lines $\{L_i\}$  from the choice of the line that contains them.

Definition in homogeneous coordinates
If four collinear points are represented in homogeneous coordinates by vectors $$\alpha,\beta,\gamma,\delta$$ such that $$\gamma=\alpha+\beta$$ and $$\delta={k} \alpha+\beta$$, then their cross-ratio is $$k$$.

Role in non-Euclidean geometry
Arthur Cayley and Felix Klein found an application of the cross-ratio to non-Euclidean geometry. Given a nonsingular conic $$C$$ in the real projective plane, its stabilizer $$G_C$$ in the projective group $$G=\operatorname{PGL}(3,\mathbb{R})$$ acts transitively on the points in the interior of $$C$$. However, there is an invariant for the action of $$G_C$$ on pairs of points. In fact, every such invariant is expressible as a function of the appropriate cross-ratio.

Hyperbolic geometry
Explicitly, let the conic be the unit circle. For any two points $D$ and $C$, inside the unit circle. If the line connecting them intersects the circle in two points, $D$ and $AB$ and the points are, in order, $−1$. Then the hyperbolic distance between $A$ and $B$ in the Cayley–Klein model of the hyperbolic plane can be expressed as

 * $$ d_h(P,Q)=\frac{1}{2} \left| \log \frac{|XQ||PY|}{|XP||QY|} \right| $$

(the factor one half is needed to make the curvature $(A, B; C, D)$). Since the cross-ratio is invariant under projective transformations, it follows that the hyperbolic distance is invariant under the projective transformations that preserve the conic $C$.

Conversely, the group $D$ acts transitively on the set of pairs of points $(A, B; C, D) < 0$ in the unit disk at a fixed hyperbolic distance.

Later, partly through the influence of Henri Poincaré, the cross ratio of four complex numbers on a circle was used for hyperbolic metrics. Being on a circle means the four points are the image of four real points under a Möbius transformation, and hence the cross ratio is a real number. The Poincaré half-plane model and Poincaré disk model are two models of hyperbolic geometry in the complex projective line.

These models are instances of Cayley–Klein metrics.

Anharmonic group and Klein four-group
The cross-ratio may be defined by any of these four expressions:

(A,B;C,D) = (B,A;D,C) = (C,D;A,B) = (D,C;B,A). $$

These differ by the following permutations of the variables (in cycle notation):

1, \ (\,A\,B\,) (\,C\,D\,), \ (\,A\,C\,) (\,B\,D\,), \ (\,A\,D\,) (\,B\,C\,). $$

We may consider the permutations of the four variables as an action of the symmetric group $(A, B; C, D) = 1 / (A, B; D, C)$ on functions of the four variables. Since the above four permutations leave the cross ratio unaltered, they form the stabilizer $C$ of the cross-ratio under this action, and this induces an effective action of the quotient group $$ \mathrm{S}_4/K $$ on the orbit of the cross-ratio. The four permutations in $D$ make a realization of the Klein four-group in $(A, B; C, D) = (C, D; A, B)$, and the quotient $$\mathrm{S}_4/K$$ is isomorphic to the symmetric group $(A, B; C, D) ≠ (A, B; C, E) ⇔ D ≠ E$.

Thus, the other permutations of the four variables alter the cross-ratio to give the following six values, which are the orbit of the six-element group $$\mathrm{S}_4/K\cong \mathrm{S}_3$$:

 * $$\begin{align}

(A, B; C, D) &=      \lambda             & (A, B; D, C) &= \frac 1 \lambda, \\[4mu] (A, C; D, B) &= \frac 1 {1-\lambda}      & (A, C; B, D) &= 1-\lambda,       \\[4mu] (A, D; C, B) &= \frac \lambda {\lambda-1} & (A, D; B, C) &= \frac{\lambda-1} \lambda. \end{align}$$

As functions of $$\lambda,$$ these are examples of Möbius transformations, which under composition of functions form the Mobius group $4! = 4 × 3 × 2 × 1 = 24$. The six transformations form a subgroup known as the anharmonic group, again isomorphic to $X, P, Q, Y$. They are the torsion elements (elliptic transforms) in $−1$. Namely, $\tfrac{1}{\lambda}$, $$1-\lambda\,$$, and $\tfrac{\lambda}{\lambda-1}$ are of order $(p, q)$ with respective fixed points $$-1,$$ $\tfrac12,$  and $$2,$$ (namely, the orbit of the harmonic cross-ratio). Meanwhile, the elements $\tfrac{1}{1-\lambda}$ and $\tfrac{\lambda-1}{\lambda}$  are of order $S_{4}$ in $S_{4}$, and each fixes both values $e^{\pm i\pi/3} = \tfrac{1}{2} \pm \tfrac{\sqrt{3}}{2}i$  of the "most symmetric" cross-ratio (the solutions to $$x^2 - x + 1$$, the primitive sixth roots of unity). The order $S_{3}$ elements exchange these two elements (as they do any pair other than their fixed points), and thus the action of the anharmonic group on $$e^{\pm i\pi/3}$$ gives the quotient map of symmetric groups $$\mathrm{S}_3 \to \mathrm{S}_2$$.

Further, the fixed points of the individual ${0, 1, ∞}$-cycles are, respectively, $$-1,$$ $\tfrac12,$ and $$2,$$ and this set is also preserved and permuted by the $D_{3}$-cycles. Geometrically, this can be visualized as the rotation group of the trigonal dihedron, which is isomorphic to the dihedral group of the triangle $0, 1, ∞$, as illustrated at right. Algebraically, this corresponds to the action of ${0, 1, ∞}$ on the $2$-cycles (its Sylow 2-subgroups) by conjugation and realizes the isomorphism with the group of inner automorphisms, $\mathrm{S}_3 \mathrel{\overset{\sim}{\to}} \operatorname{Inn}(\mathrm{S}_3) \cong \mathrm{S}_3.$

The anharmonic group is generated by $\lambda \mapsto \tfrac1\lambda$ and $\lambda \mapsto 1 - \lambda.$  Its action on $$\{0, 1, \infty\}$$ gives an isomorphism with ${2, −1, 1/2},$. It may also be realised as the six Möbius transformations mentioned, which yields a projective representation of $2$ over any field (since it is defined with integer entries), and is always faithful/injective (since no two terms differ only by $3$). Over the field with two elements, the projective line only has three points, so this representation is an isomorphism, and is the exceptional isomorphism $$\mathrm{S}_3 \approx \mathrm{PGL}(2, \mathbb{Z}_2)$$. In characteristic $exp(±iπ/3)$, this stabilizes the point $$-1 = [-1:1]$$, which corresponds to the orbit of the harmonic cross-ratio being only a single point, since $2 = \tfrac12 = -1$. Over the field with three elements, the projective line has only 4 points and $$\mathrm{S}_4 \approx \mathrm{PGL}(2, \mathbb{Z}_3)$$, and thus the representation is exactly the stabilizer of the harmonic cross-ratio, yielding an embedding $$\mathrm{S}_3 \hookrightarrow \mathrm{S}_4$$ equals the stabilizer of the point $$-1$$.

Exceptional orbits
For certain values of $$\lambda$$ there will be greater symmetry and therefore fewer than six possible values for the cross-ratio. These values of $$\lambda$$ correspond to fixed points of the action of $exp(iπ/3)$ on the Riemann sphere (given by the above six functions); or, equivalently, those points with a non-trivial stabilizer in this permutation group.

The first set of fixed points is $$\{0, 1, \infty\}.$$ However, the cross-ratio can never take on these values if the points $A$, $B$, $P$, and $Q$ are all distinct. These values are limit values as one pair of coordinates approach each other:

 * $$\begin{align}

(Z,B;Z,D) &= (A,Z;C,Z) = 0, \\[4mu] (Z,Z;C,D) &= (A,B;Z,Z) = 1, \\[4mu] (Z,B;C,Z) &= (A,Z;Z,D) = \infty. \end{align}$$

The second set of fixed points is $\big\{{-1}, \tfrac12, 2\big\}.$ This situation is what is classically called the , and arises in projective harmonic conjugates. In the real case, there are no other exceptional orbits.

In the complex case, the most symmetric cross-ratio occurs when $$\lambda = e^{\pm i\pi/3}$$. These are then the only two values of the cross-ratio, and these are acted on according to the sign of the permutation.

Transformational approach
The cross-ratio is invariant under the projective transformations of the line. In the case of a complex projective line, or the Riemann sphere, these transformations are known as Möbius transformations. A general Möbius transformation has the form

 * $$f(z) = \frac{az+b}{cz+d}\;,\quad \mbox{where } a,b,c,d\in\mathbb{C} \mbox{ and } ad-bc \ne 0.$$

These transformations form a group acting on the Riemann sphere, the Möbius group.

The projective invariance of the cross-ratio means that

 * $$(f(z_1), f(z_2); f(z_3), f(z_4)) = (z_1, z_2; z_3, z_4).\ $$

The cross-ratio is real if and only if the four points are either collinear or concyclic, reflecting the fact that every Möbius transformation maps generalized circles to generalized circles.

The action of the Möbius group is simply transitive on the set of triples of distinct points of the Riemann sphere: given any ordered triple of distinct points, $$(z_2, z_3, z_4)$$, there is a unique Möbius transformation $$f(z)$$ that maps it to the triple $$(0,1,\infty)$$. This transformation can be conveniently described using the cross-ratio: since $$(z,z_2; z_3, z_4)$$ must equal $$(f(z), 1; 0,\infty)$$, which in turn equals $$f(z)$$, we obtain
 * $$f(z)=(z, z_2; z_3, z_4) .$$

An alternative explanation for the invariance of the cross-ratio is based on the fact that the group of projective transformations of a line is generated by the translations, the homotheties, and the multiplicative inversion. The differences $$z_j-z_k$$ are invariant under the translations

 * $$z \mapsto z + a$$

where $$a$$ is a constant in the ground field $$\mathbb{F}$$. Furthermore, the division ratios are invariant under a homothety

 * $$z \mapsto b z$$

for a non-zero constant $$b$$ in $$\mathbb{F}$$. Therefore, the cross-ratio is invariant under the affine transformations.

In order to obtain a well-defined inversion mapping

 * $$T : z \mapsto z^{-1},$$

the affine line needs to be augmented by the point at infinity, denoted $$\infty$$, forming the projective line $$\mathrm{P}^1(\mathbb{F})$$. Each affine mapping $$f: \mathbb{F}\to\mathbb{F}$$ can be uniquely extended to a mapping of $$\mathrm{P}^1(\mathbb{F})$$ into itself that fixes the point at infinity. The map $$T$$ swaps $$0$$ and $$\infty$$. The projective group is generated by $$T$$ and the affine mappings extended to $$\mathrm{P}^1(\mathbb{F})$$. In the case $$\mathbb{F}=\mathbb{C}$$, the complex plane, this results in the Möbius group. Since the cross-ratio is also invariant under $$T$$, it is invariant under any projective mapping of $$\mathrm{P}^1(\mathbb{F})$$ into itself.

Co-ordinate description
If we write the complex points as vectors $$\vec{x_n} = [\Re(z_n),\Im(z_n)]^{\mathrm{T}}$$ and define $$x_{nm}=x_n-x_m$$, and let $$(a,b)$$ be the dot product of $$a$$ with $$b$$, then the real part of the cross ratio is given by:

C_1 = \frac{ (x_{12},x_{14}) (x_{23},x_{34}) - (x_{12},x_{34}) (x_{14},x_{23}) + (x_{12},x_{23}) (x_{14},x_{34}) } {|x_{23}|^2 |x_{14}|^2 } $$

This is an invariant of the 2-dimensional special conformal transformation such as inversion $$x^\mu \rightarrow \frac{x^\mu}{|x|^2} $$.

The imaginary part must make use of the 2-dimensional cross product $$a\times b = [a,b] = a_2 b_1 - a_1 b_2$$

C_2 = \frac{ (x_{12},x_{14}) [x_{34},x_{23}] - (x_{43},x_{23}) [ x_{12},x_{34} ] } {|x_{23}|^2 |x_{14}|^2  } $$

Ring homography
The concept of cross ratio only depends on the ring operations of addition, multiplication, and inversion (though inversion of a given element is not certain in a ring). One approach to cross ratio interprets it as a homography that takes three designated points to $exp(−iπ/3)$ and $3$. Under restrictions having to do with inverses, it is possible to generate such a mapping with ring operations in the projective line over a ring. The cross ratio of four points is the evaluation of this homography at the fourth point.

Differential-geometric point of view
The theory takes on a differential calculus aspect as the four points are brought into proximity. This leads to the theory of the Schwarzian derivative, and more generally of projective connections.

Higher-dimensional generalizations
The cross-ratio does not generalize in a simple manner to higher dimensions, due to other geometric properties of configurations of points, notably collinearity – configuration spaces are more complicated, and distinct $X$-tuples of points are not in general position.

While the projective linear group of the projective line is 3-transitive (any three distinct points can be mapped to any other three points), and indeed simply 3-transitive (there is a unique projective map taking any triple to another triple), with the cross ratio thus being the unique projective invariant of a set of four points, there are basic geometric invariants in higher dimension. The projective linear group of $Y$-space $$\mathbf{P}^n=\mathbf{P}(K^{n+1})$$ has $1/3$ dimensions (because it is $$\mathrm{PGL}(n,K) = \mathbf{P}(\mathrm{GL}(n+1,K)),$$ projectivization removing one dimension), but in other dimensions the projective linear group is only 2-transitive – because three collinear points must be mapped to three collinear points (which is not a restriction in the projective line) – and thus there is not a "generalized cross ratio" providing the unique invariant of $2$ points.

Collinearity is not the only geometric property of configurations of points that must be maintained – for example, five points determine a conic, but six general points do not lie on a conic, so whether any 6-tuple of points lies on a conic is also a projective invariant. One can study orbits of points in general position – in the line "general position" is equivalent to being distinct, while in higher dimensions it requires geometric considerations, as discussed – but, as the above indicates, this is more complicated and less informative.

However, a generalization to Riemann surfaces of positive genus exists, using the Abel–Jacobi map and theta functions.

license: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/4.0/

title: Cross-ratio


text:
Linear fractional transformation

In mathematics, a linear fractional transformation is, roughly speaking, an invertible transformation of the form
 * $$z \mapsto \frac{az + b} {cz + d}.$$

The precise definition depends on the nature of $a, b, c, d$, and $z$. In other words, a linear fractional transformation is a transformation that is represented by a fraction whose numerator and denominator are linear.

In the most basic setting, $a, b, c, d$, and $z$ are complex numbers (in which case the transformation is also called a Möbius transformation), or more generally elements of a field. The invertibility condition is then $ad – bc ≠ 0$. Over a field, a linear fractional transformation is the restriction to the field of a projective transformation or homography of the projective line.

When $a, b, c, d$ are integer (or, more generally, belong to an integral domain), $z$ is supposed to be a rational number (or to belong to the field of fractions of the integral domain. In this case, the invertibility condition is that $ad – bc$ must be a unit of the domain (that is $1$ or $−1$ in the case of integers).

In the most general setting, the $a, b, c, d$ and $z$ are elements of a ring, such as square matrices. An example of such linear fractional transformation is the Cayley transform, which was originally defined on the 3 × 3 real matrix ring.

Linear fractional transformations are widely used in various areas of mathematics and its applications to engineering, such as classical geometry, number theory (they are used, for example, in Wiles's proof of Fermat's Last Theorem), group theory, control theory.

General definition
In general, a linear fractional transformation is a homography of $P(A)$, the projective line over a ring $A$. When $A$ is a commutative ring, then a linear fractional transformation has the familiar form
 * $$z \mapsto \frac{az + b} {cz + d},$$

where $a, b, c, d$ are elements of $A$ such that $ad – bc$ is a unit of $A$ (that is $ad – bc$ has a multiplicative inverse in $A$)

In a non-commutative ring $A$, with $(z, t)$ in $A^{2}$, the units $u$ determine an equivalence relation $$(z,t) \sim (uz,ut) .$$ An equivalence class in the projective line over A is written $U[z : t]$, where the brackets denote projective coordinates. Then linear fractional transformations act on the right of an element of $P(A)$:
 * $$U[z:t] \begin{pmatrix}a & c \\ b & d \end{pmatrix} = U[za + tb:\ zc + td] \sim U[(zc + td)^{-1}(za + tb):\ 1].$$

The ring is embedded in its projective line by $z → U[z : 1]$, so $t = 1$ recovers the usual expression. This linear fractional transformation is well-defined since $U[za + tb: zc + td]$ does not depend on which element is selected from its equivalence class for the operation.

The linear fractional transformations over $A$ form a group, the projective linear group denoted $$\operatorname{PGL}_2(A). $$

The group $$\operatorname{PGL}_2(\Z)$$ of the linear fractional transformations is called the modular group. It has been widely studied because of its numerous applications to number theory, which include, in particular, Wiles's proof of Fermat's Last Theorem.

Use in hyperbolic geometry
In the complex plane a generalized circle is either a line or a circle. When completed with the point at infinity, the generalized circles in the plane correspond to circles on the surface of the Riemann sphere, an expression of the complex projective line. Linear fractional transformations permute these circles on the sphere, and the corresponding finite points of the generalized circles in the complex plane.

To construct models of the hyperbolic plane the unit disk and the upper half-plane are used to represent the points. These subsets of the complex plane are provided a metric with the Cayley–Klein metric. Then the distance between two points is computed using the generalized circle through the points and perpendicular to the boundary of the subset used for the model. This generalized circle intersects the boundary at two other points. All four points are used in the cross ratio which defines the Cayley–Klein metric. Linear fractional transformations leave cross ratio invariant, so any linear fractional transformation that leaves the unit disk or upper half-planes stable is an isometry of the hyperbolic plane metric space. Since Henri Poincaré explicated these models they have been named after him: the Poincaré disk model and the Poincaré half-plane model. Each model has a group of isometries that is a subgroup of the Mobius group: the isometry group for the disk model is $SU(1, 1)$ where the linear fractional transformations are "special unitary", and for the upper half-plane the isometry group is $PSL(2, R)$, a projective linear group of linear fractional transformations with real entries and determinant equal to one.

Use in higher mathematics
Möbius transformations commonly appear in the theory of continued fractions, and in analytic number theory of elliptic curves and modular forms, as it describes the automorphisms of the upper half-plane under the action of the modular group. It also provides a canonical example of Hopf fibration, where the geodesic flow induced by the linear fractional transformation decomposes complex projective space into stable and unstable manifolds, with the horocycles appearing perpendicular to the geodesics. See Anosov flow for a worked example of the fibration: in this example, the geodesics are given by the fractional linear transform
 * $$\begin{pmatrix} a & b \\ c & d \end{pmatrix} \cdot i\exp(t) = \frac{ai\exp(t)+b}{ci\exp(t)+d} ,$$

with $a$, $b$, $c$ and $d$ real, with $ad − bc = 1$. Roughly speaking, the center manifold is generated by the parabolic transformations, the unstable manifold by the hyperbolic transformations, and the stable manifold by the elliptic transformations.

Use in control theory
Linear fractional transformations are widely used in control theory to solve plant-controller relationship problems in mechanical and electrical engineering. The general procedure of combining linear fractional transformations with the Redheffer star product allows them to be applied to the scattering theory of general differential equations, including the S-matrix approach in quantum mechanics and quantum field theory, the scattering of acoustic waves in media (e.g. thermoclines and submarines in oceans, etc.) and the general analysis of scattering and bound states in differential equations. Here, the 3 × 3 matrix components refer to the incoming, bound and outgoing states. Perhaps the simplest example application of linear fractional transformations occurs in the analysis of the damped harmonic oscillator. Another elementary application is obtaining the Frobenius normal form, i.e. the companion matrix of a polynomial.

Conformal property
The commutative rings of split-complex numbers and dual numbers join the ordinary complex numbers as rings that express angle and "rotation". In each case the exponential map applied to the imaginary axis produces an isomorphism between one-parameter groups in $(A, + )$ and in the group of units $(U, × )$:
 * $$\exp(y j) = \cosh y + j \sinh y, \quad j^2 = +1 ,$$
 * $$\exp(y \epsilon) = 1 + y \epsilon, \quad \epsilon^2 = 0 ,$$
 * $$\exp(y i) = \cos y + i \sin y, \quad i^2 = -1 .$$

The "angle" $y$ is hyperbolic angle, slope, or circular angle according to the host ring.

Linear fractional transformations are shown to be conformal maps by consideration of their generators: multiplicative inversion $z → 1/z$ and affine transformations $z → az + b$. Conformality can be confirmed by showing the generators are all conformal. The translation $z → z + b$ is a change of origin and makes no difference to angle. To see that $z → az$ is conformal, consider the polar decomposition of $a$ and $z$. In each case the angle of $a$ is added to that of $z$ resulting in a conformal map. Finally, inversion is conformal since $z → 1/z$ sends $$\exp(y b) \mapsto \exp(-y b), \quad b^2 = 1, 0, -1 .$$

title: Linear fractional transformation


text:
Chicheley

Chicheley is a village and civil parish in the unitary authority area of the City of Milton Keynes, Buckinghamshire, England. The village is about 2.5 mi north-east of Newport Pagnell, and 5 mi north-east of Central Milton Keynes.

The village name is Anglo-Saxon in origin, and means Cicca's clearing. In the Domesday Book of 1086, the village was recorded as Cicelai.

The manor of Chicheley (which some suggest may have once been called Thickthorn) anciently belonged to the Pagnell family of Newport Pagnell, but was given by them to the church. Through this connection the village also at one time belonged to Cardinal Wolsey, though only until his forced resignation by King Henry VIII who took all his possessions from him at that time.

During the English Civil War, the manor, belonging to the Chester family, received some considerable damage, associated as it was with the garrison at Newport Pagnell. Following the civil war, the manor was demolished, and the present Chicheley Hall built on the site. All that remains of the old manor today is one Jacobean over-mantel with termini caryatids, and some panelling in the 'new' Chicheley Hall.

The parish church is dedicated to St Lawrence and has a perpendicular style central tower with large windows. The chancel, which contains a fine plaster depicting floral wreaths in relief, and a stone reredos, was rebuilt c. 1708; however, the church dates from the 14th century. In the nave are raised box pews, giving a theatrical air. The church contains monuments to Anthony Cave. Cave's sarcophagus is a cadaver tomb. Other monuments dating from 1635 are to the Chester family of Chicheley Hall.

Listed buildings and structures
The village has a listed park (Chicheley Hall gardens, II* ), two buildings or structures listed at Grade I (Chicheley Hall, the Church of St Lawrence ), three at Grade II* (Dovecote south of Chicheley Hall, Stable block southwest of Chicheley Hall, Service wing with attached quadrant link northwest of Chicheley Hall ) and a further 16 at Grade II.

title: Chicheley


text:
Chilton, Buckinghamshire

Chilton is a village and civil parish in Aylesbury Vale district in Buckinghamshire, England. It is in the west of the county, about 4 mi north of Thame in Oxfordshire. Chilton parish includes the hamlet of Easington (not to be confused with the Oxfordshire village of Easington).

Manor
The toponym "Chilton" is derived from the Old English for "young man's farm". The Domesday Book of 1086 records it as Ciltone. It evolved via the forms Chiltone in the 12th century and Schelton in the 18th century before reaching its present form.

Before the Norman conquest of England Alric, son of Goding, a thegn of Edward the Confessor, held the manors of Chilton and Easington. However, the Domesday Book records that by 1086 the Norman baron Walter Giffard held the two manors.

Chilton House was built by John Croke in the early 17th century, then rebuilt by Richard Carter in the 1740s. Its design was based on that of Buckingham House. It is now in the ownership of the Aubrey-Fletcher family and operated as a residential care home.

Parish church
The Church of England parish church of Saint Mary the Virgin was originally a 12th-century Norman building but few details survive from that period. The chancel and south transept are 13th century, the Decorated Gothic tower forms the north transept and is mid-14th century. The nave, chancel arch and chancel roof were renewed in the 15th century. The Perpendicular Gothic south chapel was added in about 1520.

title: Chilton, Buckinghamshire


text:
Steve Roach (musician)

Steve Roach (born February 16, 1955) is an American composer and performer of ambient and electronic music, whose recordings are informed by his impressions of environment, perception, flow and space. His work has been influential in the trance and new-age genres.

Roach has received two Grammy Award nominations for New Age Album of the Year: His 2017 album Spiral Revelation for the 60th Annual Grammy Awards., and 2018's Molecules of Motion for the 61st Annual Grammy Awards. Roach's work has also been listed on "1,000 Recordings to Hear Before You Die."

Biography
Roach was born as a single child in La Mesa, California, less than 10 miles from San Diego. He developed a passion for Motocross racing in the early 1970s, experiences from which he incorporated into his composing and performing later on. "You have to be fully awake and present ... All of those things relate right over to what would become my path in music. You're completely in; you're inside of it, your life depends on it. That set the tone." Having grown up near deserts, mountains, and the ocean, these became key aesthetic influences in Roach's music. Roach was greatly influenced by electronic music as a teenager, particularly Timewind (1975) by Klaus Schulze and works by Tangerine Dream and Brian Eno. He was also influenced by progressive rock, namely Close to the Edge (1972) by Yes and Ummagumma (1969) by Pink Floyd.

Roach taught himself to play the synthesizer when he was 20; among his first instruments were a Roland SH-3A and Vox Continental. He went on to purchase a Micromoog, ARP 2600, and ARP String Ensemble at once with a "super high interest loan". He lived in Hollywood, California for a brief time, during which he worked at the Licorice Pizza record store alongside future The Simpsons creator Matt Groening, and became a part of the electronic music community in the Los Angeles area. He moved to a bungalow in Culver City, in which he built a recording studio named the Timeroom and worked odd jobs while creating music.

His debut album, Now, was released in 1982. Two years later, he released his best known album, Structures from Silence (1984). He had pressed a run of cassettes of the album, which caught the attention of Stephen Hill who played it on his Hearts of Space radio show on KCRW, which generated further interest in Roach's music. In 1986 he released his acclaimed Quiet Music series. In 1988, he released what has been described by critics as his masterpiece, the double-album Dreamtime Return.

In 1995, Roach signed with Projekt Records, which has since been his primary label.

As Roach's approach to ambient music has matured, his compositions have typically been beatless. His rhythmic and trance-based groove and tribal-ambient releases, however, are nearly as numerous as his more atmospheric releases. Some recordings are strictly synthesizer-based, whereas others include ambient guitar experiments.

Other pieces, however, cross over with more ethnic and folk influences. Roach learned to play the digeridoo during his extended trips to Australia in the 1980s, and he became an early proponent of its use in ambient music. His work with Mexican musician Jorge Reyes introduced Roach to Prehispanic musical elements, which he has also included in his music. These fusions established Roach as one of the founders of the tribal-ambient sound.

Personal life
Roach is married to author and equine teacher Linda Kohanov, who provided vocals on some of his albums. In the early 1990s, Roach moved to the Sonoran Desert near Tucson, Arizona.

Studio albums
• Now (1982)

• Traveler (1983 Domino)

• Structures from Silence (1984 Fortuna) – remastered 2001

• Quiet Music 1 (1986 Fortuna) -cassette

• Empetus (1986 Fortuna) -cassette, CD, vinyl - 2 discs, (re-released on Projekt 2008) - CD, Digital (re-released on Projekt 2017)

• Quiet Music 2 (1986 Fortuna) -cassette

• Quiet Music 3 (1986 Fortuna) -cassette

• Dreamtime Return (1988 Fortuna) – 2 discs, (remastered 2005 Projekt)

• World's Edge (1992 Fortuna) – 2 discs

• Origins (1993 Fortuna)

• The Dream Circle (1994 Soundquest LTD1) -CD (Limited 2000 copies)

• Artifacts (1994 Fortuna)

• The Dreamer Descends (1995 Amplexus)

• The Magnificent Void  (1996 Hearts of Space)

• On This Planet (1997 Hearts of Space)

• Slow Heat (1998 Timeroom Editions 1)

• Light Fantastic (1999 Hearts of Space)

• The Dream Circle (1999 Timeroom Editions) Re-release of 1994 CD

• Atmospheric Conditions (1999 Timeroom Editions)

• Early Man (2000 Manifold) - (1 disc Limited Slate Slab PKG)

• Midnight Moon (2000 Projekt)

• Early Man (2001 Projekt) - 2 discs

• Core (2001 Timeroom Editions)

• Streams & Currents (2001)

• Darkest Before Dawn (2002)

• Mystic Chords & Sacred Spaces (2003 Projekt) – 4 discs

• Life Sequence (2003)

• Fever Dreams (2004)

• Holding the Space: Fever Dreams II (2004 Timeroom Editions)

• Possible Planet (2005)

• New Life Dreaming (2005)

• Immersion: One (2006 Projekt)

• Proof Positive (2006)

• Kairos: The Meeting of Time and Destiny (2006) – CD + DVD

• Immersion: Two (2006 Projekt)

• Immersion: Three (2007) – 3 discs

• Fever Dreams III (2007) – 2 discs

• Arc of Passion (2007) - 2 discs

• A Deeper Silence (2008)

• Dynamic Stillness (2009) – 2 discs

• Immersion: Four (2009 Timeroom Editions)

• Afterlight (2009)

• Destination Beyond (2009)

• Sigh of Ages (2010)

• Immersion Five – Circadian Rhythms (2011)

• Groove Immersion (2012)

• Back to Life (2012)

• Soul Tones (2012)

• Future Flows (2013)

• Spiral Meditations (2013)

• The Delicate Forever (2014)

• The Delicate Beyond (2014)

• Bloodmoon Rising Night 2 (2014)

• Invisible (2015)

• Bloodmoon Rising Night 3 (2015)

• Skeleton Keys (2015 Projekt)

• Etheric Imprints (2015 Projekt)

• Vortex Immersion Zone (2015 Timeroom Editions)

• Skeleton – Spiral Passage (2015 Timeroom Digital)

• Emotions Revealed (2015 Projekt)

• This Place to Be (2016 Timeroom Editions 38)

• Shadow of Time (2016)

• Painting in the Dark (2016 Timeroom Editions 40)

• Fade to Gray (2016 Timeroom Editions 41)

• Spiral Revelation (2016)

• The Passing (2017 Timeroom Editions 39)

• Nostalgia for the Future (2017 Timeroom Editions 42)

• Long Thoughts (2017)

• Eclipse Mix (2017 Timeroom Editions 43)

• Molecules of Motion (2018)

• Return to the Dreamtime (2018 Timeroom Editions 44)

• Electron Birth (2018 Timeroom Edition 45)

• Mercurius (2018)

• Atmosphere for Dreaming (2018 Timeroom Editions 46)

• Bloom Ascension (2019)

• Trance Archeology (2019)

• Stillpoint (2020 Timeroom Editions 47)

• A Soul Ascends (2020)

• Tomorrow (2020 Soundquest Music)

• Into the Majestic (2021 Timeroom Editions 49)

• As It Is (2021)

• Zones, Drones & Atmospheres (2022)

• What Remains (2022)

• Rest of Life (2023)

• Sanctuary of Desire (2023)

Live albums
• Stormwarning: Live in Concert (1989 Soundquest)

• All is Now: Steve Roach Live 2002 (2002)

• Storm Surge: Live at NEARfest (2006)

• Landmass (2008 Timeroom Editions)

• Live at Grace Cathedral (2010) – 2 discs

• Live at SoundQuest Fest (2011)

• Journey of One: The Tribal Ambient Era Live 1996 (2011) – 2 discs

• Ultra Immersion Concert (2013)

• Live Transmission (2013) – 2 discs

• Live in Tucson 2000 (2013)

• At the Edge of Everything (2013)

• Alive in the Vortex (2015 Timeroom Editions 35) – 2 discs

• Live in Tucson: Pinnacle Moments (2016 Timeroom Editions 37)

• The Sky Opens (2020)

• Live at SoundQuest Fest 2021 (2021 Timeroom Editions 50)

Compilations
• Quiet Music (1988 Fortuna) -compilation 1-3 CD

• Now / Traveler (1992 Fortuna) -compilation 1-2 CD

• The Lost Pieces (1993 Rubicon) -CD (re-released on Projekt 1995)

• Truth & Beauty: The Lost Pieces Volume Two (1999 Timeroom Editions 2)

• Dreaming... Now, Then: A Retrospective 1982–1997 (1999 Fortuna) – 2 discs

• Quiet Music: Complete Edition (1999 Fortuna) – 2 discs, re-release of 1988 CD

• Time of the Earth (2001) – DVD

• Pure Flow (2001)

• Day Out of Time (2002)

• Space and Time: An Introduction to the Soundworlds of Steve Roach (2003 Projekt)

• Texture Maps: The Lost Pieces Vol. 3 (2003 Timeroom Editions)

• Places Beyond: The Lost Pieces 4 (2004 Timeroom Editions)

• Quiet Music: The Original 3–Hour Collection (2011) – 3 discs

• Rasa Dance: The Music of Connection (2013)

• The Desert Collection: Volume One (2014)

• The Skeleton Collection 2005 – 2015 (2015 Timeroom Editions)

• Bloodmoon Rising: The Complete 5–Hour Collection (2015 Timeroom Editions 34)

Collaboration albums
• Moebius (1979) – as a member of the group Moebius

• Western Spaces (1987 Fortuna) – with Kevin Braheny

• The Leaving Time (1988) – with Michael Shrieve

• Desert Solitaire (1989 Fortuna) – with Michael Stearns and Kevin Braheny

• Strata (1990 Hearts of Space Records) – with Robert Rich

• Australia: Sound of the Earth (1990 Fortuna) – with David Hudson and Sarah Hopkins

• Soma (1992 Hearts of Space Records) – with Robert Rich

• Ritual Ground (1993) – with Elmar Schulte as Solitaire

• Forgotten Gods (1993 Hearts of Space) – with Jorge Reyes & Suso Saiz as Suspended Memories

• Earth Island (1994) – with Jorge Reyes & Suso Saiz as Suspended Memories

• Kiva (1995 Fathom/Hearts of Space Records) – with Michael Stearns and Ron Sunsinger

• Well of Souls (1995) – 2 discs, with Vidna Obmana

• Halcyon Days (1996) – with Stephen Kent and Kenneth Newby

• Cavern of Sirens (1997) – with Vidna Obmana

• Dust to Dust (1998) – with Roger King

• Ascension of Shadows: Meditations for the Millennium (1999) – 3 discs, with Vidna Obmana (re-released in 2005 and 2008 as three separate albums)

• Body Electric (1999) – with Vir Unis

• Vine ~ Bark & Spore (2000) – with Jorge Reyes

• Circles & Artifacts (2000) – with Vidna Obmana

• Live Archive (2000) – with Vidna Obmana

• The Serpent's Lair (2000) – 2 discs, with Byron Metcalf

• Prayers to the Protector (2000) – with Thupten Pema Lama

• Blood Machine (2001) – with Vir Unis

• InnerZone (2002) – with Vidna Obmana

• Trance Spirits (2002) – with Jeffrey Fayman, Robert Fripp & Momodou Kah

• Wachuma's Wave (2003) - with Byron Metcalf & Mark Seelig

• Spirit Dome (2004 Projekt) – with Vidna Obmana

• Mantram (2004 Projekt) – with Byron Metcalf and Mark Seelig

• The Shaman's Heart (2005) – with Byron Metcalf

• Somewhere Else (Ascension of Shadows I) (2005) – with Vidna Obmana

• Terraform (2006) – with Loren Nerell (reissued in 2009)

• The Memory Pool (Ascension of Shadows II) (2008) – with Vidna Obmana

• Revealing the Secret (Ascension of Shadows III)  (2008) – with Vidna Obmana

• Nada Terma (2008) – with Byron Metcalf and Mark Seelig

• Spirit Dome – Live Archive (2009) – 2 discs, with Vidna Obmana

• Stream of Thought (2009) – with Erik Wøllo

• Dream Tracker (2010) – with Byron Metcalf and Dashmesh Khalsa

• Nightbloom (2010) – with Mark Seelig

• Into the Deep: America, Whaling & The World Original Soundtrack (2010) – with Brian Keane

• The Desert Inbetween (2011) – with Brian Parnham

• The Road Eternal (2011) – with Erik Wøllo

• The Shaman's Heart II: The Healing Journey (2011) – with Byron Metcalf

• Low Volume Music (2012) – with Dirk Serries

• Tales from the Ultra Tribe (2012) – with Byron Metcalf

• Copper: Original Soundtrack (2013) – with Brian Keane

• The Long Night (2014) – with Kelly David

• The Ancestor Circle (2014) – with Jorge Reyes

• Monuments of Ecstasy (2015) – with Byron Metcalf & Rob Thomas

• Biosonic (2016) – with Robert Logan

• Second Nature (2016) – with Robert Logan

• POV (2019) – with Miles Richmond & Peter Grenader also known as POV (band)

• Tales From The Ultra Tribe with Byron Metcalf (2019)

• Nectar Meditation (2020 Timeroom Editions 48) - with Serena Gabriel

title: Steve Roach (musician)