Wikipedia:Reference desk/Archives/Miscellaneous/2012 July 9
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July 9
[edit]Reasonable or fallacious (and if the latter, what's the name of the formal fallacy?)
[edit]To assume, if not definitely, then almost certainly, if an idea pops into your head, that if it were a good or really valuable and workable idea, someone else has already or would already do it, and therefore pursue it no further. Statistically, this seems like a very sound assumption that would save the vast majority of people a lot of time and effort, given the unlikelihood of your idea being a great thing nobody has thought of, given the sheer quantity of H. sapiens who have been and are now, and the percentage of those that have made a world-changing idea. Therefore make zero effort to try to think of world changing ideas that would help on a worldwide scale. 69.243.220.115 (talk) 01:22, 9 July 2012 (UTC)
- Analogously, that is why I never get out of bed in the morning. Because free will is an illusion, and I will be forced to get out of bed by reality whether I want to or not. μηδείς (talk) 01:25, 9 July 2012 (UTC)
- Douglas Hofstadter, in the essays that form chapters 30 and 31 of Metamagical Themas, calls this superrationality or renormalized rationality. Looie496 (talk) 01:42, 9 July 2012 (UTC)
- Superrationality is the article about that, but Looie should have understood something wrong since the concept doesn't relate to the OP's question. OsmanRF34 (talk) 12:45, 10 July 2012 (UTC)
- Maybe Base rate fallacy? You are only looking at "number of humans who have made a difference" / "the number of humans", this fraction is undoubtedly miniscule. However you are neglecting the other, arguably more important part of the statistic, namely out of "the number of humans who changed the world and DIDN'T make zero effort" / "number of people who changed the world" is probably close to 1 (expressed as probablility, or 100% as a percentage). Vespine (talk) 02:36, 9 July 2012 (UTC)
- I don't think this is a nameable formal fallacy. The OP describes a self doubting state of mind that could arise from experience of past failure to assert one's inventions and/or inadequate knowledge of the actual state of the relevant art. Unimaginative managers can have this effect on smarter workers who will feel constricted by their NIH attitude. DriveByWire (talk) 03:16, 9 July 2012 (UTC)
- From the articles Not invented here and Invented here, it looks like NIH's meaning is "we only use what we invented" while IH actually means "we only use what others have invented." 20.137.18.53 (talk) 13:01, 9 July 2012 (UTC)
- I don't think this is a nameable formal fallacy. The OP describes a self doubting state of mind that could arise from experience of past failure to assert one's inventions and/or inadequate knowledge of the actual state of the relevant art. Unimaginative managers can have this effect on smarter workers who will feel constricted by their NIH attitude. DriveByWire (talk) 03:16, 9 July 2012 (UTC)
- Douglas Hofstadter, in the essays that form chapters 30 and 31 of Metamagical Themas, calls this superrationality or renormalized rationality. Looie496 (talk) 01:42, 9 July 2012 (UTC)
- If you really did have an exceptional idea, doubting it seems like a case of the Dunning–Kruger effect; you assume that other people have the same high ability that you do. In any case, even if your idea isn't totally original doesn't mean it's not worth pursuing; perhaps there are reasons why your idea hasn't been put into practice that you haven't thought of, or which you have thought of and can overcome. We are fortunate that we live in an age where idly researching vague notions is so easy! FiggyBee (talk) 03:42, 9 July 2012 (UTC)
- Actually, I think Vespine has the answer. μηδείς (talk) 03:59, 9 July 2012 (UTC)
- I'm not a statistician and only recently got interested in this topic but I do think I'm on the right track. It's not quite the base rate fallacy as explained in our article, which is more specifically about sensitivity and specificity in "tests".. Another fallacy based on the base rate fallacy is Prosecutor's fallacy which again, isn't qite the same thing as the op describes, but pretty close. It describes how evidence was presented in the OJ trial that "only 1 in 7500 people who bash their wife go on to kill them", so the fact that OJ bashed his wife can't be used as evidence, that's the logic they used. However, 8 out of 9 wives who are murdered by their husbands ARE previously bashed by them, so it is in fact very relavant to the trial. Similarly you could say only 1 out of 10 Million people change the world so it's pointless, BUT 9 out of 10 of people who DO change the world DO make an effort (hypothetically). Ignoring that is the base rate fallacy. I'm fairly sure. Vespine (talk) 06:01, 9 July 2012 (UTC)
- Yes, it is the Defender's fallacy, actually, which is a complicated misapplication of base rates. μηδείς (talk) 07:17, 9 July 2012 (UTC)
- I'm not a statistician and only recently got interested in this topic but I do think I'm on the right track. It's not quite the base rate fallacy as explained in our article, which is more specifically about sensitivity and specificity in "tests".. Another fallacy based on the base rate fallacy is Prosecutor's fallacy which again, isn't qite the same thing as the op describes, but pretty close. It describes how evidence was presented in the OJ trial that "only 1 in 7500 people who bash their wife go on to kill them", so the fact that OJ bashed his wife can't be used as evidence, that's the logic they used. However, 8 out of 9 wives who are murdered by their husbands ARE previously bashed by them, so it is in fact very relavant to the trial. Similarly you could say only 1 out of 10 Million people change the world so it's pointless, BUT 9 out of 10 of people who DO change the world DO make an effort (hypothetically). Ignoring that is the base rate fallacy. I'm fairly sure. Vespine (talk) 06:01, 9 July 2012 (UTC)
- Actually, I think Vespine has the answer. μηδείς (talk) 03:59, 9 July 2012 (UTC)
- OJ bashed his wife, "8 out of 9 wives who are murdered by their husbands ARE previously bashed by them", therefore OJ murdered his wife. Sounds like a fairly straightforward case of affirming the consequent to me. However, it is not actually what Gigerenzer said, according to the prosecutor's fallacy article. His actual argument is "the chances that a batterer actually murdered his partner, given that she has been killed, is about 8 in 9". FiggyBee (talk) 08:48, 9 July 2012 (UTC)
- No one said "therefore OJ murdered his wife" except you. The point made was more subtle and relevant and the same both here and in the article. μηδείς (talk) 16:52, 9 July 2012 (UTC)
- That was what the prosecutor in his trial was trying to prove, wasn't it? My point (although not that well expressed) is that Gigerenzer said "the chances that a batterer actually murdered his partner, given that she has been killed, is about 8 in 9", which boils down logically to "If you bashed her, you probably killed her". What Vespine said is "8 out of 9 wives who are murdered by their husbands ARE previously bashed by them", which boils down to "If you killed her, you probably bashed her". The implication is reversed, and only the first would be sound logical evidence. FiggyBee (talk) 09:08, 10 July 2012 (UTC)
- It seems to me FiggyBee has a point although not that well expressed. Since it hadn't been established beyond a reasonable doubt that the wife was killed by her husband, the percentage of husbands who killed their wives that bashed them isn't that important. What is perhaps the most relevent in deciding if the bashing is relevant is to establish what percentage of
married women who were murdered in similar circumstances were killed by husbands who had bashed them.edit: women who had previously been bashed by their husbands or partners and were later murdered in similar circumstances were murded by the person who bashed them. (Of course how you establish similar circumstances is a very open question.) If the percentage is small, then the fact he bashed his wive wasn't particularly relevent in deciding whether or not her murdered her. (I presume it was accepted he bashed her, I'm not familiar with the details of the case.) Or to put it a different way, since they were trying to establish whether or not her murdered her, the fact that if he had murdered her there's a good chance he would have bashed her and he did bash her isn't that significant. In fact I would go as far as to say the statistic used by the defence is more significant edit: since it tells us more about the usefulness of the fact he bashed his wife in establishing his guilt for the murder. Nil Einne (talk) 19:38, 9 July 2012 (UTC)- I think the problem is that the base rate (number of women murdered by their husbands) is ALREADY very low, so using probability to imply innocence is irrelevant at best, and misleading at worst. Imagine at another murder trial, the defence didn't mention bashing at all and isntead said that only 1 in 10,000 people commit murder, so the accused couldn't have done it because the chance they did is only 1 in 10,000! That obviously can NOT be logically used as a defence at a murder trial, but it's essentially the same thing as what the defence tried at the OJ trial. The fact that murder is a rare event to begin with is not relavant, just as the fact that men who bash their wives rarely go on to kill them. However the fact that 8 out of 9 murderers do bash their wives previous to killing them IS relavant, given that a murder has actually taken place. Put it this way: Given 2 suspects, one that bashed his wife an one that didn't, the one that did is 8 times more likely to have been the murderer. It's obviously NOT a bull's eye that conclusivley proves they did it, but a case often doesn't have such a bull's eye argument and relies instead on these lines of evidence converging until it can be proved beyond reasonable doubt. Vespine (talk) 23:51, 9 July 2012 (UTC)
- Only if they are married to the same dead woman, of course. μηδείς (talk) 01:51, 10 July 2012 (UTC)
- Yes, it's purely a hypothetical example. Another way of putting it might be, the defence said only 1 out of 7500 men who batter their wives go on to kill them, BUT they don't mention that only one out of 67,000 men who DON'T batter their wives go on to kill them (the number is a rough guess). Vespine (talk) 01:59, 10 July 2012 (UTC)
- Only if they are married to the same dead woman, of course. μηδείς (talk) 01:51, 10 July 2012 (UTC)
- I think the problem is that the base rate (number of women murdered by their husbands) is ALREADY very low, so using probability to imply innocence is irrelevant at best, and misleading at worst. Imagine at another murder trial, the defence didn't mention bashing at all and isntead said that only 1 in 10,000 people commit murder, so the accused couldn't have done it because the chance they did is only 1 in 10,000! That obviously can NOT be logically used as a defence at a murder trial, but it's essentially the same thing as what the defence tried at the OJ trial. The fact that murder is a rare event to begin with is not relavant, just as the fact that men who bash their wives rarely go on to kill them. However the fact that 8 out of 9 murderers do bash their wives previous to killing them IS relavant, given that a murder has actually taken place. Put it this way: Given 2 suspects, one that bashed his wife an one that didn't, the one that did is 8 times more likely to have been the murderer. It's obviously NOT a bull's eye that conclusivley proves they did it, but a case often doesn't have such a bull's eye argument and relies instead on these lines of evidence converging until it can be proved beyond reasonable doubt. Vespine (talk) 23:51, 9 July 2012 (UTC)
- It seems to me FiggyBee has a point although not that well expressed. Since it hadn't been established beyond a reasonable doubt that the wife was killed by her husband, the percentage of husbands who killed their wives that bashed them isn't that important. What is perhaps the most relevent in deciding if the bashing is relevant is to establish what percentage of
The suspect thing is largely irrelevant, and there's no reason to think of only 2 suspects. In other words, the fact that he was 8 times more likely to have been the murderer then some other random person in the hypothetical example is largely irrelevent (as there are a lot more random people then OJ Simpsons).(Ignore this may have confused self and too tired to think about it.) The 67k figure islikewiseirrelevent since as I said before, what they were trying to establish that he murdered his wife, not that he bashed her.- Again, I don't know the details of the case, and I'm not that interested to read but you seem to be missing the point (with your 1 in 10k comments etc) which was I presume not to establish innocence, but to demonstrate the fact he bashed his wife should not play much, if any of a factor in determing his guilt beyond a resonable doubt. I presume either the prosecution entered the evidence of domestic violence in to play or wanted to, hence the statistics the defence used to demonstrate the bashing was largely irrelevent in establishing guilt beyond a resonable doubt. Definitely once the defence brought up such a statistic, there was nothing I presume stopping the prosecution pointing out it didn't establish innocence, simply suggested they shouldn't read too much in to the bashing if they felt the jury may be mislead by it in that way.
- As I mentioned, I'm not saying the defences statistics are great, but they are far better then anything you or μηδείς have brought up. As I also mentioned the much more significant factor was the percentage of "women who had previously been bashed by their husbands or partners and were later murdered in similar circumstances (edit: and) their murdered was the person who bashed them". The fact the prosecution didn't I presume bring up these figures either means they didn't have them, or they further demonstrated the bashing was largely irrelevent in establishing guilt beyond a resonable doubt so the prosecution had no desire for them to be known. (The defence of course had no reason to bring them up if they felt they could confuse the jury with other statistics.)
- To put it a different way, establishing guilt beyond a resonable doubt is actually a very high standard. Certain details are so meaningless in a wider context yet are easily over-relied on by juries in establishing guilty beyond a resonable doubt, hence a number of countries who still rely entirely on juries greatly limit the introduction of evidence likely to be unduly prejudicial, from the statistics presented so far, it sounds like the bashing could potentially be one such statistic (particularly in the absence of a wider context).
- P.S. One of the problems is that for readers, we're often more interested in whether someone commited a crime or not. So we tend to look at things from that POV. And forget juries are never (supposed) to look at it from that POV, instead only decide whether they're convinced beyond a resonable doubt the person commited the crime of which they're accused according to the standards the law requires for such a crime.
- The fact that OJ (allegedly?) bashed his wife may make him a nasty person, and may mean he was more likely to have been a murderer then a husband who didn't bash his wife, but it may not mean the bashing should be much, if any, of a factor in deciding that he was guilty beyond a resonable doubt of being his wife's murderer, which is all that should matter to the jury.
- Remember the defence and prosecution aren't on the same footing. The prosecution is interested in proving guilt beyond a resonable doubt. Any competent defence, whatever they or their client may say isn't actually that interested in establishing innocence yet alone innocence beyond a resonable doubt (sure it's nice), only in showing the prosecution hasn't established guilt beyond a resonable, so anything they say should be read in this context, which may include demonstrating that the jury shouldn't read too much into an instance of bashing.
- Nil Einne (talk) 17:55, 15 July 2012 (UTC)
- I read the linked article and noticed it actually says "the chances that a batterer actually murdered his partner, given that she has been killed, is about 8 in 9 or approximately 90%" which is not what Vespine said and is far closer to the statistic which I said is what really mattered. The only thing it lacks is 'similar circumstances' which I included to acknowledge this is still fairly complicated since you could legitimate argue that other cases, e.g. where the killer killed his wife during a bout of domestic violence and didn't try to deny it either saying she deserved it or expressing regret are perhaps too dissimilar to be taken in to account in determined the statistic.
- I haven't read the source but from the wording, it sounds like the author/s do understand why this statistics matters and is different from what Vespine suggested.
- P.S. I just noticed FiggyBee also noted this above. I hope I don't offend anyone (nothing that this includes me as evidenced by the strikesouts) in saying this discussion IMO demonstrates why (IMO again) juries need to be molly-coddled so much.
- Nil Einne (talk) 18:08, 15 July 2012 (UTC)
Gaelic Football and marriage
[edit]I have a couple of questions
- Why is Gaelic Football exclusively Irish? I am told that Scotland is a Gaelic country as well
- Why is marrying close relatives so innapropriate? 212.183.128.73 (talk) 20:23, 9 July 2012 (UTC)
- 2) Closely related individuals have a higher chance of having children with dual recessive genetic disorders. They also tend to have exaggerated features (if parents are tall, the children are really tall, etc.), which can be good or bad. StuRat (talk) 20:44, 9 July 2012 (UTC)
- 1) The Gaelic Athletic Association defines itself as a native Irish organization and has (as far as I know) no grounds or offices outside Ireland. The article Gaelic football gives the sport's history which dates back over 300 years in Ireland, and it has been spread outside Ireland only by amateur players of the Irish diaspora. The Gaelic known in Scotland has deviated from Irish Gaelic and is spoken by only 1.2% of the population. Clearly the Scots would rather beat the English at their own game than import the Irish game. DriveByWire (talk) 21:37, 9 July 2012 (UTC)
- Of those hundreds of years of history, most of it comprises that rather ill-defined generic game simply called football (a hodge-podge of kicking, dribbling, carrying, throwing, scrumming, and punching). It wasn't until the 19th century that various formal codifications of that sport arose, which gave rise to the various codes of "football" that dominate today - rugby football in 1823, association football in 1948, Australian rules football (the most traditional adherent to the punching ethos) in 1859, and American football shortly thereafter. All drew lines between classes and nations which hadn't been so formally delimited until then. This was particularly the case for Gaelic football, which was formalised in around 1887 as a specific rejection of the British codes and a deliberate statement of Irishness. Ever since it's been very strongly associated with Irish identity and Irish nationalism: playing Gaelic football (and other Gaelic games) was tantamount to declaring you were Irish. Gaelic football was thus inextricably enmeshed with the torments of the Irish independence struggle (e.g. Bloody Sunday (1920)) and its own rules and practices (such as rule 27) meant it was unlikely to take off outside the community of people who identified as Irish. Until relatively recently Gaelic football made little attempt to evangelise itself outside Ireland and those of Irish extraction. Compare that to association football and to a lesser extent American football, which have tried very hard to spread their appeal. -- Finlay McWalterჷTalk 01:08, 10 July 2012 (UTC)
- Isn't Scotland Gaelic as well? Shouldn't it have Gaelic stuff like Gaelic Football too? — Preceding unsigned comment added by 212.183.128.152 (talk) 19:35, 10 July 2012 (UTC)
- Gaelic is not a single language - Irish Gaelic (Gaeilge) is different from Scots Gaelic - (Gàidhlig). So Scotland isn't "Gaelic as well": despite having languages with a common ancestor, and to some extent having cultural crossover, they are as separate as England and France. As for why there is no 'native' football game in Scotland, the game that would go on to become Gaelic Football in Ireland (Medieval football - which developed separately and in parallel throughout Europe) was called the Ba game in Scotland, and is still with us as Association football - the game invented on the playing fields of Eton and Harrow was influenced by Mob football games from across the UK, and the Scots were involved in the codification and playing from the outset - see History of Scottish football. Apart (as Finlay points out above) from the Irish having more desire for a game that was not invented by the British, the game in Ireland just took a different direction, that's all. - Cucumber Mike (talk) 19:53, 10 July 2012 (UTC)
- Why doesn't Scotland have its own version of Football?
- Can't answer that. But Scotland and Ireland both have games that resemble what was at some stage codified as field hockey: Shinty and Hurling.--Shirt58 (talk) 09:44, 12 July 2012 (UTC)
- To note a few things which may be relevent to the discussion, and to highlight and expand upon what others have already stated. First of all, Gaelic (and the closely related term "Celtic") refer to a somewhat broad group of related cultures. There has certainly been a history of attempts at a sort of Pan-Celticism, but these attempts haven't generally gotten very far, somewhat due to the physical seperation between the peoples. While there have been significant cultural exchanges, notably the development of the distinctive Scots-Irish culture, which a an ethnic group is somewhat distinct from the Scottish or the Irish. By-and-large, Scotland and Ireland diverged in their cultural development over history, despite having an ancient common culture. For a good parallel, consider that the English people evolved from the Anglo-Saxons; modern English don't, however, share a common culture with modern Saxons (central Germany). Also, consider that the relationship between Scotland and the U.K. is very different than that between Ireland and the U.K. It would not be entirely inaccurate to say that Scotland annexed England, as the merger of their crowns occured when a Scot, James I and VI, assumed the throne of England on the death of the Tudor line (a Welsh dynasty, not an English one, it should be noted); which would lead to the eventual Act of Union 1707. It was a relatively peaceful merger of the two formerly independent countries. Ireland, on the other hand, was essentially forcably annexed by the U.K., which has led to some bad feelings, and a greater tendency to form a distinctive Irish culture which is decidedly not British. Though Scottish Nationalism is a real thing, it is less of an issue, as many Scots think of themselves as British as well as Scottish. Few Irish would consider such an idea. Which is why Scotland readily adopted British football, as Scotland is British. Ireland, on the other hand, rather proudly is not, and thus has developed its own native game (though they do, also, play all three British versions (association, Rugby Union, and Rugby League) as well). To sum up: There is a distinctive Scottish culture, but Scottish culture is not so fiercely anti-British (as the Scottish are British, no less than Texans are American), while the Irish culture tends to be moreso, including the development of its own code of Football, which it fiercely protects. Don't get too hung up on the word Gaelic. --Jayron32 06:12, 13 July 2012 (UTC)
- Can't answer that. But Scotland and Ireland both have games that resemble what was at some stage codified as field hockey: Shinty and Hurling.--Shirt58 (talk) 09:44, 12 July 2012 (UTC)
- Why doesn't Scotland have its own version of Football?
- Gaelic is not a single language - Irish Gaelic (Gaeilge) is different from Scots Gaelic - (Gàidhlig). So Scotland isn't "Gaelic as well": despite having languages with a common ancestor, and to some extent having cultural crossover, they are as separate as England and France. As for why there is no 'native' football game in Scotland, the game that would go on to become Gaelic Football in Ireland (Medieval football - which developed separately and in parallel throughout Europe) was called the Ba game in Scotland, and is still with us as Association football - the game invented on the playing fields of Eton and Harrow was influenced by Mob football games from across the UK, and the Scots were involved in the codification and playing from the outset - see History of Scottish football. Apart (as Finlay points out above) from the Irish having more desire for a game that was not invented by the British, the game in Ireland just took a different direction, that's all. - Cucumber Mike (talk) 19:53, 10 July 2012 (UTC)
- Isn't Scotland Gaelic as well? Shouldn't it have Gaelic stuff like Gaelic Football too? — Preceding unsigned comment added by 212.183.128.152 (talk) 19:35, 10 July 2012 (UTC)
- 2) There is also the question of genetic diversity. From a species survival point of view, inbreeding makes a population less diverse and thus less robust. Karenjc 22:41, 9 July 2012 (UTC)
- For question 2, please note that it is legal in the UK to marry your cousin. --TammyMoet (talk) 09:14, 10 July 2012 (UTC)
- Marrying close relatives is not necessarily 'inappropriate'. As cousin marriage points out, in some cultures it is extremely common. Genetic disorders aren't really the whole story - nowadays, due to the existence of contraception, lots of married couples choose not to have children (or adopt children or use donors), and most people are not so opposed to the idea of, say, haemophiliacs having children and passing on a genetic disorder. Social norm and disgust might be relevant. 130.88.73.65 (talk) 16:04, 10 July 2012 (UTC)
- Why is marrying your sibling illegal?
- Is it illegal everywhere? It certainly hasn't been in the past. Sibling relationship says "John M. Goggin and William C. Sturtevant (1964) listed eight societies which generally allowed sibling marriage, and thirty-five societies where sibling marriage was permissible among the upper classes (nobility) only." The Ptolemaic dynasty is famous for having several examples of sibling marriage. 81.98.43.107 (talk) 21:40, 10 July 2012 (UTC)
- Why is marrying your sibling illegal?
Algebraic chess notation in other alphabets
[edit]The article on algebraic chess notation does a fine job listing how the pieces are abbreviated in other languages. But it got me to wondering if the files on the board are always labeled with the Latin alphabet letters a b c d e f g h . If a game were being recorded in Cyrillic, for example, in addition to changing the abbreviations for the pieces, would the files become а б в г д е ж з ? Or in Greek, would α β γ δ ε ζ η θ be used? → Michael J Ⓣ Ⓒ Ⓜ 23:45, 9 July 2012 (UTC)
- It would appear that in Russian the Latin script is still used (at least in this book, which appears to be an introduction to chess). Unfortunately the Russian Wikipedia is on strike today, so the thing I'd normally recommend (find some detailed en.wikipedia articles on chess minutiae and then compare against their Russian language equivalents) isn't available, today at least. -- Finlay McWalterჷTalk 00:19, 10 July 2012 (UTC)
- Eating my own dogfood and looking at Sicilian Defence it seems that Bulgarian, Chinese, and Japanese stick with Latin (bearing in mind that some non-en articles are incomplete translations from en, and so this isn't very strong evidence) but Hebrew does not. I've yet to find an Arabic or Farsi example that's instructive. -- Finlay McWalterჷTalk 00:28, 10 July 2012 (UTC)
- Dimitris Sisopoulos has coded a program to convert games from English to Greek chess σκάκι. I have not tried the program but it is free and Dimitris can be contacted with questions. DriveByWire (talk) 09:15, 10 July 2012 (UTC)
This chart shows quite a few languages that use their own script for the pieces. Not sure about the columns. --Dweller (talk) 11:07, 10 July 2012 (UTC)
- The very last paragraph of sr:Шах#Шаховска нотација states that one can use either script for algebraic chess notation in Serbia, and that the Central Serbia Chess Frederation refereeing commission recommends the usage of the Cyrillic. Notice that in that case, the files (columns) on the board are labelled with the corresponding Cyrillic equivalents of the Latin letters A through H, that is, they are а б ц д е ф г х, and not а б в г д ђ е ж, which is the way the Serbian Cyrillic alphabetical order begins. In Russia, Bulgaria and other Cyrillic-using countries, files on the chessboard are never labelled with Cyrillic characters. --Theurgist (talk) 11:47, 10 July 2012 (UTC)
- Russian Wikipedia isn't on strike anymore, and its article on chess notation (шахматная нотация, šakhmatnaja notatsija) appears to use Latin letters consistently. dalahäst (let's talk!) 03:56, 11 July 2012 (UTC)