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Flag of England

The flag of England is the national flag of England, a constituent country of the United Kingdom. It is derived from Saint George's Cross (heraldic blazon: Argent, a cross gules). The association of the red cross as an emblem of England can be traced back to the Late Middle Ages when it was gradually, increasingly, used alongside the Royal Banner. It became the only saint's flag permitted to be flown in public as part of the English Reformation and at a similar time became the pre-eminent maritime flag referred to as a white ensign. It was used as a component in the design of the Union Jack in 1606.

It has been widely used since the 1990s, specifically at national sporting events, especially during the campaigns of England's national football teams.

Origins

In 1188 Henry II of England and Philip II of France agreed to go on a crusade, and that Henry would use a white cross and Philip a red cross (and not vice versa as suggested by later use).

There then follows a historiographical tradition claiming that Richard the Lionheart himself adopted the full red cross flag and the patron saint from the Republic of Genoa at some point during his crusade. This idea can be traced to the Victorian era, Perrin (1922) refers to it as a "common belief", and it is still popularly repeated today even though it cannot be substantiated. Prince Edward, Duke of Kent made a variation to this in a bilingual preface to a brochure made for the British Pavilion at Genoa Expo '92. The relevant passage read: "The St. George's flag, a red cross on a white field, was adopted by England and the City of London in 1190 for their ships entering the Mediterranean to benefit from the protection of the Genoese fleet. The English Monarch paid an annual tribute to the Doge of Genoa for this privilege"

Red crosses seem to have been used as a distinguishing mark worn by English soldiers from the reign of Edward I (1270s), or perhaps slightly earlier, in the Battle of Evesham of 1265, using a red cross on their uniforms to distinguish themselves from the white crosses used by the rebel barons at the Battle of Lewes a year earlier. Perrin notes a roll of accounts from 1277 where the purchase of cloth for the king's tailor is identified as destined for the manufacture of a large number of pennoncels (pennons attached to lances) and bracers (worn by archers on their left forearms) "of the arms of Saint George" for the use by the king's foot soldiers (pro peditibus regis). Perrin concludes from this that the introduction of the Cross of St George as a "national emblem" is originally due to Edward I. By 1300, there was also a greater "banner of Saint George", but not yet in a prominent function; the king used it among especially banners of king-saints Saint Edward the Confessor and Saint Edmund the Martyr alongside the royal banner. George had become popular as a "warrior saint" during the Crusades, but the saint most closely associated with England was Edward the Confessor. This was so until the time of Edward III, who in thanks for Saint George's supposed intervention in his favour at the Battle of Crécy gave him a special position as a patron saint of the inceptive Order of the Garter in 1348. From that time, his banner was used with increasing prominence alongside the Royal Banner and became a fixed element in the hoist of the Royal Standard. Yet the flag shown for England in the Book of All Kingdoms of 1367 is solid red (while Saint George's Cross is shown for Nice and, in a five-cross version, for Tbilisi). The Wilton Diptych from the late 1390s shows a swallow-tailed Saint George cross pennant held by an angel in between (the then reigning) King Richard II (accompanied by Edward the Confessor and Edmund the Martyr) and a scene of the Virgin and Child flanked by angels wearing Richard's own heraldic devices.

Saint George's Day was considered a "double major feast" from 1415, but George was still eclipsed by his "rivals" Saints Edward and Edmund.

John Cabot, commissioned by Henry VII to sail "under our banners, flags and ensigns", may have taken a Saint George's banner to Newfoundland in 1497.

That Saint George is the primary patron saint of England is among several lasting changes of height of the English Protestant Reformation, via the content which the teenage king and his Protestant advisors issued to all churches and clerics. These rules were the revised prayer book of 1552. Just as with the Marian persecutions (four years of counter-revolution after his natural death) all defecting clerics faced likely deprivation which was the loss of their office and if more broadly heretical, burning at the stake. The book made clear all religious flags, including saints' banners except for Saint George were abolished.

Further use of this cross as a maritime flag alongside royal banners, is found in 1545.

Henry V, the history play by William Shakespeare, believed to have been written near 1599 includes the fictitious scene of the battle of Agincourt where the king's final rally is: Cry 'God for Harry! England, and Saint George!"

[Exeunt. Alarum, and chambers go off.] thus promoting the notion that the cult or festivities specifically to the saint, or focus on the Order of the Garter put him significantly ahead of two other national saints – instead of depicting that they were approximately equal. The quote became rapidly well known in London, across social classes, and thus imagery entrenched that Saint George was "historically" the primary saint.

In 1606, after the Union of the Crowns in 1603, it was combined with the Scottish St Andrew's Cross to form the Union Jack, which James VI & I ordered be flown from the main tops of ships from both England and Scotland. The "Red Crosse" continued to be flown from the fore-top by James' subjects in "South Britaine"—i.e., the Saint George cross was used with the new union flag on English vessels.

In the 19th century, it became desirable for all nations of Europe (and later worldwide) to identify a national flag. During that time, the terms Britain and England were used largely interchangeably, the Union Flag was used as national flag de facto, even though never officially adopted. The observation that the Cross of St George is the "national flag of England" (as opposed to the Union Flag being the flag of all of the United Kingdom) was made in the context of Irish irredentism, as noted by G. K. Chesterton in 1933:

"As a very sensible Irishman said in a letter to a Dublin paper: 'The Union Jack is not the national flag of England.' The national flag of England is the Cross of St. George; and that, oddly enough, was splashed from one end of Dublin to the other; it was mostly displayed on shield-shaped banners, and may have been regarded by many as merely religious."

In 2018 the mayor of Genoa reminded that England should pay for the last 247 years for using the flag of Genoa.

Union Flag
The flag of England is one of the key components of the Union Flag. The Union Flag has been used in a variety of forms since the proclamation by Orders in Council 1606, when the flags of Scotland and England were first merged to symbolise the Union of the Crowns. (The Union of the Crowns having occurred in 1603). In Scotland, and in particular on Scottish vessels at sea, historical evidence suggests that a separate design of Union Flag was flown to that used in England. In the Acts of Union of 1707, which united the Kingdom of Scotland and the Kingdom of England to become the Kingdom of Great Britain, it was declared that "the Crosses of St. George and St. Andrew be conjoined, in such Manner as her Majesty shall think fit, and used in all Flags, Banners, Standards and Ensigns, both at Sea and Land."

From 1801, to symbolise the union of the Kingdom of Great Britain with the Kingdom of Ireland, a new design which included St Patrick's Cross was adopted for the flag of the United Kingdom of Great Britain and Ireland. The Flag of the United Kingdom, having remained unchanged following the partition of Ireland in 1921 and creation of the Irish Free State and Northern Ireland, continues to be used as the flag of the United Kingdom of Great Britain and Northern Ireland.

City of London

The flag of the City of London is based on the English flag, having a centred St George's Cross on a white background, with a red sword in the upper hoist canton (the top left quarter). The sword is believed to represent the sword that beheaded Saint Paul who is the patron saint of the city.

Royal Navy

The flag used by the British Royal Navy (the White Ensign) is also based on the flag of England, consisting of St George's Cross and a Union Flag in the canton. In addition to the United Kingdom, several countries in the Commonwealth of Nations also have variants of the White Ensign with their own national flags in the canton, with St George's Cross sometimes being replaced by a naval badge.

Church of England
Churches belonging to the Church of England which have a pole may fly St George's Cross. A desirable variant (per an order from the Earl Marshal in 1938) is for the church to fly the flag with the arms of the diocese in the left-hand upper corner.

Sporting events

The flag heavily dominates for that of England at sports events in which England competes, for example during England Cricket matches (the Cricket World Cup and The Ashes), during Rugby Union matches and in football. It is also used in icons on the internet and on the TV screen to represent teams and players from England.

For at least some decades before about 1996, most of the flags waved by supporters were Union Flags. In a sporting context, the flag is often seen being waved by supporters with the addition of 'ENGLAND' across its horizontal bar.

English nationalism
As the flag of England, it is used in English nationalism. This is largely in parallel to the use of the flag of Scotland in Scottish nationalism. However Scotland has been recognised as a nation within a nation. The flag of Scotland has been officially defined by the Scottish Parliament in 2003 and is flown there and almost universally by Scottish authorities. There is no English legislature; the entire British legislature sits in England and is only subject to very weak conventions on voting on English matters. The flag of England does not figure in legislation, and its use by English nationalists is complex as these divide among those who are far-right as heavily opposed to further immigration and seeking to distinguish between residents in the jobs market and welfare state system such as the British National Party (founded 1982) and the English Defence League (founded 2009) and those who merely seek the level of devolution of Scotland, or Wales. Underscoring this complexity, in January 2012 Simon Hughes, the deputy leader of the Liberal Democrats, supported calls for a devolved English parliament and which continues under such lobbies as the Campaign for an English Parliament, and is occasionally a minor debate subject at all of the major parties' annual conferences.

Since the flag's widespread use in sporting events since the mid-1990s, the association with far-right nationalism has waned, and the flag is now frequently flown throughout the country both privately and by local authorities.

Outside England
Due to the spread of the British Empire, the flag of England is currently, and was formerly used on various flags and coats of arms of different countries, states and provinces throughout the territories of the British Empire. St George's Cross is also used as the city flag of some northern Italian cities, such as Milan and Bologna and other countries such as Georgia.

title: Flag of England


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ABC Weekend TV

ABC Weekend TV was the popular name of the British broadcaster ABC Television Limited, which provided the weekend service in the Midlands and Northern England regions of the Independent Television (ITV) network from 1956 to 1968. It was one of the "Big Four" companies that between them produced the majority of ITV networked programmes during this period.

Originally created as Associated British Cinemas (Television) Ltd, ABC was one of a number of commercial television companies established during the 1950s by cinema chain companies, in an attempt to safeguard their business by becoming involved with television, which was taking away their cinema audiences. In this case, the parent company was the Associated British Picture Corporation (ABPC) — owner of ABC Cinemas — which initially did not wish to become involved with the new broadcasting system, but was persuaded to do so by the Independent Television Authority (ITA) and the manager of its Pathé News subsidiary Howard Thomas, who became the new company's managing director.

ABC operated two franchises, one in the Midlands, which was the fourth ITA franchise to go on air, in 1956, and the other in the North of England, which was the sixth franchise to go on air, later the same year. It lost both its franchises in 1968, but merged with another franchisee to form Thames Television, which held the London weekday franchise for 24 years.

From 1967, ABC's sister company, ABC Television Films, used the name Associated British Corporation on its exports to the US, such as the last two series of The Avengers.

Formation
When Kemsley-Winnick, one of the consortia that had been awarded two franchises in the new Independent Television network in 1954, collapsed, the ITA approached ABPC to step into the breach. The Corporation agreed to assume the franchises to broadcast on Saturdays and Sundays to the Midlands and the North of England. The contract agreeing to do so was signed on 21 September 1955, the day before Independent Television (ITV) began in London.

This left the new ABC five months to begin broadcasting in the Midlands, the service beginning on 18 February 1956. Soon afterwards, it was also up and running in the North; it began broadcasting in the North West on 5 May 1956, and in Yorkshire on 3 November 1956. It was aided in part by the failure of the original contractor; Kelmsley-Winnick had ordered over £1 million (equivalent to £ million today) of production equipment from manufacturer Pye, which it sold to ABC at a much-discounted price.

ATV
The London weekend contractor had launched under the name "Associated Broadcasting Company" (ABC), but ABPC wanted to use the ABC brand for its own service, to match its existing ABC Cinemas brand, so it took legal action against the Associated Broadcasting Company who subsequently agreed to rename as Associated Television (ATV) after broadcasting for three weeks as "ABC". This allowed ABPC to launch its own station as "ABC".

ITN
ABC's late entry into Independent Television meant that some of the details of how the new system would run were already agreed between the ITA regulator and the other three contractors. ABC felt that some of these details were unfair on itself as the smallest contractor, and the only contractor that broadcast only at weekends.

In particular, ABC objected to paying one-quarter of the costs for ITN, provider of national news broadcasts for the network, as there would be fewer news programmes at the weekend than on weekdays. ABC's managing director Howard Thomas, former head of Pathé News, felt that ABC could provide its own news for a fraction of ITN's price, but the ITA would not allow this: regional companies were responsible only for regional news, and national news should be independent of the regional companies. ABC lobbied both ITN and the ITA for change, which eventually resulted in a cutback to the amount of programming to be provided by ITN to the network and a substantial reduction in ITN's costs.

Presentation
Once the "Big Four" companies were in profit, the ITA reviewed the performance each of them. ABC escaped with little criticism, except for its presentation, which was considered to be dull and too closely aligned with its sister "ABC Cinemas" brand. ABC took this to heart and launched a new look in September 1959.

ATV again
Of the original four ITV contractors, ABC had difficulty getting its programmes shown in the London region, which was hampering its reputation. Two of the other contractors had London franchises, and Granada seemed to have a good working relationship with Associated-Rediffusion to show its programmes. ABC found itself in a head-to-head battle with ATV, as, in the early years, these were the only two companies whose franchises operated at the weekend.

ATV had close connections with the Moss Empires theatre chain (through ATV's Val Parnell) and the Grade Organisation theatrical talent agency (through ATV's Lew Grade and his brother Leslie) and felt they had the expertise to make expensive, high-status drama, variety and comedy shows, and leave the cheaper "provincial" off-peak weekend programming to ABC. This would have been to ABC's financial disadvantage, since ABC (with its two regions to ATV's one region at the weekends) would have to pay two-thirds of the expensive costs of ATV London's shows, while ATV would pay only one-third of the costs of ABC's cheaper shows.

ABC fought back, first of all, by selling some of its pre-recorded shows to Associated-Rediffusion (instead of ATV) to broadcast to London on weekdays. Secondly, it refused to buy some of ATV's top-rated shows such as Sunday Night at the London Palladium and broadcast its own alternatives such as Blackpool Night Out. Eventually ATV gave way and agreed to buy more of ABC's shows.

Loss of franchise
Structural changes in the regional contract areas meant that ABC no longer had a contract to reapply for in 1967. The Northern area (split into North West and Yorkshire) was to become a seven-day operation, as would the Midlands. Existing weekday contractors (Granada and ATV respectively) were correctly considered the favourites. ABC consequently submitted two applications: one for the service for London at the weekend, the other for the Midlands seven-day operation, although it favoured the first contract.

It was expected that ABC would be awarded the weekend London licence, but the strength of another application (from the London Weekend Television consortium) ruled this out. This led to a situation where a successful company could be closed down through no fault of its own. To prevent this, the governing body of ITV, the Independent Television Authority, ordered a merger with the existing London weekday company Rediffusion, with ABC having majority control of the new operation.

Despite protests from Rediffusion, the two companies eventually became Thames Television. ABC ceased weekend broadcasting in the North and Midlands regions on Sunday 28 July 1968 and resumed on Tuesday 30 July in the London region as weekday company Thames.

Studios

ABC operated three production sites and had a further sales office. The main production facilities were the former Warner Studios in Teddington, Middlesex. Although this was outside its contract area, ABC wanted a London base, as many performers could not venture outside of the capital to record programmes because they were often committed to runs of theatre plays in the West End. Upon the merger with Rediffusion, this site became the main production base for the new company Thames Television.

In the Midlands, ABC formed a joint venture with Midlands weekday licensee ATV to oversee the running of a production and transmission facility to be used by both. Alpha Television purchased a former cinema in Aston, near Birmingham, and extended it by the construction of additional studios and office space; the site was known as the Alpha Studios.

ABC operated a northern studio centre in Manchester and a sales office based in Television House in the city centre. The production facility was converted from a former Capitol cinema in Didsbury. ABC vacated both premises during 1968. ABC also made some entertainment shows such as Blackpool Night Out and The Blackpool Show at the ABC Theatre in Blackpool (owned by ABC-TV's sister company ABC Cinemas). For its pre-filmed series, such as The Avengers (from 1965), ABC used its parent company's Associated British Elstree Studios.

Identity
When ABC first went on the air, it used the branding of its sister company ABC Cinemas. This featured a triangular shield with the letters ABC upon it, and a bar across it with the caption 'Television'. This lasted from the station's launch in 1956 until September 1959. The ITA had criticised ABC's original presentation style for being bland and too much attached to the existing ABC Cinemas chain.

As a result, ABC created a new brand ident featuring three arrows pointing to the bottom of the screen to reveal the letters ABC in turn and leaving a triangle behind and on top of the letters. At the end of this, the three triangles would snap together into the new ABC logo. This ident lasted until 1964 when the lettering font was altered slightly from a serif font to the latest bold used by the company, this revision lasting until the company's demise.

The logo uses the notion of threes, three triangles making another triangle, with the points of a triangle often being labelled 'A', 'B' and 'C' in geometry. The tune that was used for all of ABC's idents was a vibraphone playing the notes A-B-C (la-te-doh). Out of this look, ABC Television developed a strong corporate identity, effectively becoming the first British TV station to recognise the importance of corporate branding.

The company itself was originally called Associated British Cinemas (Television) Limited, which by 1957 had been shortened to A.B.C. Television Limited. However, from about 1967, on exports made by its sister company A.B.C. Television Films Ltd. (such as the last two series of The Avengers), the name 'Associated British Corporation' was used, to avoid confusion with the US ABC network. As for on-air, the name was for a few months 'Associated British', before becoming 'ABC Television', or just 'ABC'. The names 'ABC Television Network' and 'ABC Weekend Network' were also used, for example in TV Times listings. The station received a joke nickname from Bob Monkhouse, namely "All Bloody Commercials".

The station's spoken slogan varied through time, starting off as "ABC – Associated British in the North/Midlands" before being replaced in 1958 to "ABC, your weekend TV" and again changed in 1964 to "ABC, your weekend television in the North/Midlands".

Continuity announcers
The following who have served as announcers for ABC Weekend TV include:
 * Jill Bechley,
 * John Benson
 * Sidonie Bond
 * John Braban
 * John Duncanson
 * John Edmunds
 * Philip Elsmore
 * David Hamilton
 * Sheila Kennedy
 * Keith Martin
 * John McGavin
 * Mel Oxley
 * Owen Oyston
 * Bill Steel
 * Julie Stevens
 * Clifford Swindells

Programming
Networked programmes from ABC included the drama series Police Surgeon, The Human Jungle, Undermind, Redcap, The Avengers, the Armchair Theatre series of single plays, the Habatales cartoons, the popular shows Thank Your Lucky Stars, Opportunity Knocks, Big Night Out, Doddy's Music Box and Oh Boy!, Tommy Cooper's shows Cooperama and Life with Cooper, the children's science fiction serials Emerald Soup, Target Luna and its sequels Pathfinders in Space, Pathfinders to Mars and Pathfinders to Venus, and the gritty drama series Callan and Public Eye (both of which continued as Thames productions after 1968). ITV's first weekly series devoted to the arts, Tempo, was introduced by ABC, as was its first hidden camera show, Candid Camera, and its first attempt to challenge the BBC's dominance of television sport, with World of Sport. ABC also introduced British television's first late night chat show, The Eamonn Andrews Show and, together with ATV, British television's first regular weekly series of adult education programmes.

Service areas
Areas are described in terms of the county boundaries at the time. After ABC's closure there were significant county boundary changes in 1974, and ITV's regional boundaries have also changed over time.

ABC's two franchise regions each had their own continuity announcers, advertisements and regional programmes (mainly news and weather, and the magazine shows ABC of the Midlands and ABC of the North). Apart from those exceptions, both regions usually showed the same programmes simultaneously.

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

title: ABC Weekend TV


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Talk:Chaitin's constant

Prohibition of Certain Programming Languages
"The definition of a halting probability relies on the existence of a prefix-free universal computable function. Such a function, intuitively, represents a programming language with the property that no valid program can be obtained as a proper extension of another valid program."

Chaitin added this requirement when someone pointed out that Chaitin's "constant" a.k.a. "Halting Probability" could be greater than 1. However, adding this to reduce its size eliminates any programming language that I am aware of as a computer programmer. A computer program is a sequence of commands. So you can always add additional commands, i.e. another program, to extend a valid program.

Invariance Theorem
Chaitin's Invariance Theorem, added to respond to the problem of programming languages with varying size for the same function, states that there is a finite bound to the difference in the sizes of the minimum programs to calculate a given number in any two programming languages. However, consider two programming languages, one of whose programs differ from the other programming language only in that every character is repeated to occur twice in a row. For example, it might be designed for unreliable communications over the internet and the second occurrence of every character serves as a check bit (byte) for verification.

If you follow through the proof of the Invariance Theorem with this in mind, you see that the problem is where they assume that the lengths of the representations of a numeric literal in two programming languages are the same, which is not the case.

Calculation of the Chaitin constant...?
Calculation of the start of a Chaitin Ω

Calude, Dinneen, and Shu have calculated the first 64 bits of a Chaitin ΩU for a particular machine. These are, in binary notation

0.0000001000000100000110001000011010001111110010111011101000010000...

or in decimal notation

0.0078749969978123844...

Note that the notion of whether a specific digit of Ω can be correctly calculated is different from the notion of computability: any specific digit of any number is computable since for any integer there is a program printing it.
 * Do you mean that there is something wrong with the "Relationship to the halting problem" section stating that only the first few digits can be calculated? ΩU is uncomputable so there is no finite list of instructions such that if you give a computer that list of instructions, it will out put an arbitraily large number of digits of ΩU provided that the computer is big enough, but the first 64 digits of it have been calculated. Does that mean a brain is better than a computer, though there may have been partial use of a computer with constant human intervention to calculate those digits of ΩU even though a computer can't do it alone? Blackbombchu (talk) 16:29, 19 August 2013 (UTC)

What is this? Who are Calude, Dinneen, and Shu? What particular machine is being talked about? What references are there to back up this statement?

And more importantly, this little bit:

"Note that the notion of whether a specific digit of Ω can be correctly calculated is different from the notion of computability: any specific digit of any number is computable since for any integer there is a program printing it."

is wrong. If all of the digits of Ω could be correctly calculated, then the number would be computable, as that function would then compute all of Ω. The reason given, that "for any integer there would be a program printing it" doesn't make sense and is unclear. I think we should remove this from the article.

192.88.124.204 (talk) 22:11, 12 April 2008 (UTC)

 * That particular bit comes from the Calude, Dinneen and Shu paper "Computing a Glimpse of Randomness" and I agree that it is incorrect as worded. A "specific digit of any number" is not something to which computability applies; computability applies to the entire number up through that particular digit.  Calude, et al were reinforcing the point that their particular method of calculating a portion of Chaitin's constant doesn't violate the basic tenants of the uncomputability of the constant itself.  Regardless, it's incorrect and not necessary to the article. 76.99.236.216 (talk) 04:54, 16 May 2008 (UTC)

 * I took a look at the paper and it seems they where able to calculate an upper bound on Chaitin Ω, because it is possible to decide the halting problem for very short programs (<=84 bits). The language they use has only primitive operations like shift left (=add 1) and shift right (=subtract 1). Even conditional jump (=a,0,L1) requires atleast 6 characters (=42 bits). I estimated that goldbach's conjecture takes about 1200 bits.
 * The first 21 bits are 0.000000100000010000011. There's exactly one program of 7 bits (HALT). There's exactly one program of 14 bits (DUMP, HALT). There's exactly 3 programs of 21 bits (DUMP, DUMP, HALT), (JUMP 1, HALT), (dunno, HALT). There's nothing random in the first 64 bits.
 * I'll delete this section, but leave the reference to the paper. Tlepp (talk) 01:00, 21 June 2008 (UTC)

The Omega defined in their paper is kind of defective. Each bit of data read by a program contributes 7 bits to its size (see end of section 5 of their paper), making it impossible to prove their Omega incompressible. In fact, the more data one of these program reads, the more compressible it is according to proper definitions like Chaitin's. John Tromp. —Preceding undated comment was added at 00:20, 10 February 2009 (UTC).

comments by exa
It is a normal and transcendental number which can be defined but cannot be computed

I really doubt that this fact is proven yet. Both (the normalness and the transcendence) is quite likely, but I have never seen a proven for either of that. I would be surprised if the irrationality of the number is already proven, which I doubt again due to the incomputableness of the number.

(The constant N heavily depends on the encoding choices and does not reflect the complexity of the axiomatic system in any way.)

Where did you get this terrible idea?.... Do you know the invariance theorem? Do you know Theorem C in AIT that shows the relation between the axiomatic complexity of a FAS to the number of digits that can be proven? exa 16 Sep, 2004

Proof of normalness: Omega is ML-random. Every ML-random is normal. QED.

Proof of transcendence: Omega is non-computable. Every algebraic number is computable. QED.

 * ... then there exists a constant N such that no digit of Ω after the N-th can be proven to be one or zero within that system.

Is this true? It seems like this states that there are at most a finite number of Turing machines that can be proven to either halt or not halt (given some system of enumeration, etc.). Chas zzz brown 02:06 Feb 5, 2003 (UTC)

Ooops! In the words of emily latella, "never mind". I misread that the nth digit of Ω was 1 iff Turing machine n halts. Chas zzz brown 09:00 Feb 5, 2003 (UTC)

 * The proof of the transcendence of Chaitin's number for any particular encoding could rely on the following indirect argument. If Chaitin's number is algebraic, then it is computable. But we can prove it isn't computable as this leads to a contradiction with the undecidability of the halting problem. However, does this argument hold water if Chaitin's number is algebraic, but it is absolutely impossible to determine which one it is? At 3am, I'm not sure... Elroch 02:11, 27 March 2006 (UTC)

I have rewritten the introduction to this article and added some headings to divide it into sections. I am not sure if this belongs to algorithmic information theory so perhaps someone can put it in the right category. MathMartin 17:44, 20 Jul 2004 (UTC)

What does the statement "Ω is uncompressible" mean? Is compressible number defined anywhere in the Wikipedia? - Mike Rosoft 16:55, 8 Dec 2004 (UTC)

Oops! I thought the link I had supplied to Data compression would clear it up. It means that it is impossible to supply a program + infinite "compressed" sequence such that for any $$n$$, the program can return the first $$n$$ bits of Ω using the first $$f(n)$$ bits of the compressed sequence, and for any $$k$$ there exists $$n_0$$ such that for $$n>n_0$$, $$f(n)<n-k$$. I couldn't find this definition anywhere in the data compression category. Lev 20:15, 9 Dec 2004 (UTC)

I have included a summary of the definition for incompressible number. Rattle 09:00, 1 Jun 2005 (UTC)

Certainly there may be an algorithm that computes Chaitin's constant. There is just no way to prove that any algorithm does so.

 * Nope. If there were such an algorithm, it could be used to solve the halting problem (even though we would not be able to prove it). But there is no algorithm, provable or not, that solves it. – Lev 10:35, 10 August 2005 (UTC)

 * To clarify this a bit: There is no algorithm that computes ALL bits of Chaitin's constant. Otherwise, it could be used to solve the halting problem: We would try to compute Omega by running all possible programs in parallel (we would have to launch them one by one, of course). Then we would sum up 2^-(length) for every program that would terminate. Now one of two things would happen: either the prog in question would terminate, or the sum would eventually excede Omega-2^(-our prog's length), proving by contradiction that the answer is no.
 * Now if there were an algorithm for computing Omega but we didn't know which it was, the above meta-algorithm would give us an algorithm for solving the halting problem, but we still wouldn't know what it was. But there is no solution to the halting problem, not even one we can't find.
 * Certainly, for any finite N there is an algorithm that computes the first N bits of Omega, but we don't always know which it is. And there might (for all I know) be an algorithm that computes an infinite number of bits, but still leaves an infinite number of bits unknown.
 * Lev 12:33, 21 December 2005 (UTC)
 * I think the last remark here is wrong, or at least it contradicts to the last sentence of this article: from some N the digits cannot be computed algorithmically, i.e. the algorithm does not exist. From my experience with automatic theorem provers, I'd like to add a metaphor: the automated theorem proving can algorithmically prove quite a lot and help automate proving that certain algorithms do halt or do not halt, but at some (more complicated) point it needs human assistance. There are even more complicated problems than the halting problem, so the later numbers of Chaitin's constant will be even harder to compute.
 * Lev is right. For any finite N, you can just print out a string which happens to be the relevant bit of omega :).  Beyond a certain N, you cannot prove that you are right, as the article states.
 * One candidate for an algorithm that produces an infinite number of bits is the program which starts simulating every Turing machine (cascaded, so that you're not trying to do an infinite number of things at once), and records those that halt. This machine can produce a sequence that limits to omega from below.  IIRC, all of the `1's it produces are correct digits of omega.  To prove that such a machine produces infinitely many bits of omega, it only remains to be shown that it keeps on producing 1s (I don't know if that can be done; it might depend on the model of computation/distribution of programs). -- pde 00:16, 14 March 2006 (UTC)

On the probability interpretation
The following two sentences don't agree; the first one doesn't make sense. It can then be shown that Ω represents the probability that a randomly produced bit string will encode a halting program. This means that if you start flipping coins, always recording a head as a one and a tail as a zero, the probability is Ω that you will eventually reach the encoding of  a syntactically correct halting program. It is true that Omega is the probability that a randomly chosen infinite sequence of 0s and 1s begins with a string that is a halting program. This makes sense, because there is a probability measure (Lebesgue measure) on the set of such infinite sequences, and the set of sequences that begin with a string encoding a halting program is a measurable set. But there cannot be a randomly chosen bit string because there is no nontrivial probability measure on the set of finite bit strings. CMummert 04:37, 16 June 2006 (UTC)
 * Yeah, it shold be probability that randomly chosen infinite bit string begins with a proper program which stops after finite time.

I'm not sure will it make things more clear... But the way it is now is correct with some explanations. After all you can assume that you randomly chose bits of a string until (if ever) you reach a valid program string. In such random experiment probability of obtaining program that stops is exactly \Omega. Macieksk 09:28, 24 June 2006 (UTC)

Merge
The article "Omega (computer science)" is very similar to this one. I suggest that they be merged.P.L.A.R. 21:41, 29 June 2006 (UTC)

 * See my comments on the other article's discussion page. This page should stay, the other one should go, since this is not the only omega in use in computer science, and perhaps not even the most common. There doesn't seem to be much info on the current Omega (computer science) page that should be brought over here. --Dantheox 23:40, 29 June 2006 (UTC)

Omega (computer science) now redirects to this page.P.L.A.R. 21:00, 30 June 2006 (UTC)

Properties of Chaitin's constant
Shouldn't some reference be made to the fact that one can use Chaitin's constant to determine the answer to any possible phrasable question? Jenigmat429 03:16, 13 February 2007 (UTC)

 * That "fact" is not true. Chaitin's omega is at level Sigma_1 of the arithmetical hierarchy.  Complete knowledge of it cannot even determine the truth of Pi_2 sentences of Peano arithmetic, much less more complicated questions.  Chaitin's constant is Turing equivalent to the Halting problem, and nothing more. CMummert · talk 03:24, 13 February 2007 (UTC)

 * Ok, more accurately, couldn't you use it to determine the provability of a proposition L in a formal system F? Because, if there's a program that's sufficiently small that will halt if L is provable in F, and if you know enough of chaitin's constant, one could use Chaitin's omega to determine L's provability in F. Or maybe I'm interpreting Chaitin's omega wrong. Jenigmat429 14:16, 13 February 2007 (UTC)

 * Yes, you can use a Chaitin constant to do that. But this is because these constants are equivalent to the Halting problem, not in particular because of their randomness. CMummert · talk 16:56, 13 February 2007 (UTC)

rewrite
I expanded and rewrote the article this morning. Feel free to hack away at it, I'm done for a while. CMummert · talk 17:48, 13 February 2007 (UTC)

more rewrite
Currently the article says: "Each halting probability is a normal and transcendental real number which is definable but not computable, which means that there is no algorithm that enumerates its digits." But there is a non-halting algorithm that does enumerate its digits - Omega can be approximated from below. Eventually the first n digits will be correct. I'll correct this: "which means that there is no halting algorithm that enumerates its digits." Algorithms 20:25, 23 June 2007 (UTC)

Super Omega
One should mention the "Super Omega" of Jürgen Schmidhuber: http://www.idsia.ch/~juergen/kolmogorov.html. The first n bits of Gregory Chaitin's constant Omega are incompressible in the sense that we cannot compute them by a halting algorithm with fewer than n-O(1) bits. Hoewever, consider the short but never halting algorithm which lists and runs all possible programs; whenever one of them halts its probability gets added to the output (initialized by zero). After finite time the first n bits of the output will not change any more (it does not matter that this time itself is not computable by a halting program). So there is a short non-halting algorithm whose output converges (after finite time) on the first n bits of Omega, for any n. In other words, the enumerable first n bits of Omega are highly compressible in the sense that they are limit-computable by a very short algorithm; they are not random with respect to the set of enumerating algorithms. Schmidhuber constructed a Super Omega which is still limit-computable, but more random than Omega, as one cannot significantly compress it with an enumerating algorithm. Algorithms 15:43, 8 July 2007 (UTC)

---

If there exists a non-halting program that will converge to the first N-bits of Omega in a finite amount of time, it can be written in the form of an infinite loop:

omega=0 while(TRUE) /*LOOP BODY*/ end while

It is very easy to convert this infinite loop into a finite loop:

constant ITERATIONS = ___ omega=0 while ( a< ITERATIONS) /*LOOP BODY*/ a++ end while

The value ITERATIONS can be set to any arbitrarily high value, allowing this loop to execute for an arbitrary long amount of time. Since the non-halting version of the program can converge to any N number of bits you want in a finite amount of time, so can this one, assuming ITERATIONS is a large enough integer.

Suppose the non-halting version can compute X digits in Y iterations. The halting version, if ITERATIONS is set equal Y at the beginning of the program, will also produce the same X number of digits as the non-halting version. However ITERATIONS can be arbitrarily large. You could set ITERATIONS to larger and larger values, and compute more and more digits of Omega. You can set it as large as you want and compute as many digits of Omega as you want. But this seems to violate the property of incompressibility? —Preceding unsigned comment added by 64.162.134.186 (talk) 20:47, 8 October 2007 (UTC)

It would seem that way at first, but it turns out that the bits you determine via that non-halting algorithm may be innaccurate until it completes (which of course never happens) - see the reference "Computing a Glimpse of Randomness" in the article. —Preceding unsigned comment added by 76.99.236.216 (talk) 04:46, 16 May 2008 (UTC)

Yes the problem is obviously the "carry problem". Add a 1 in the googleplexth position to a binary fraction and it may flip all the lower order bits, even the first one. Indeed Solvay has shown that ZFC cannot determine even a single bit of certain Omegas. They come from certain specifically designed Universal machines usually called Solvay machines. Moreover Calude has shown that every computably enumerable random real is the halting probability of some Solvay machine. So the value of even a single bit of such random numbers (after an initial sequence of 0s) is neither computable nor decidable in standard (ZFC) formal mathematics —Preceding unsigned comment added by 38.104.189.46 (talk) 16:21, 14 March 2011 (UTC)

Also to further clarify, while there is a simple program that run for some number k steps will output the first n bits of Omega, this does not imply that it can be compressed. Yes by "dovetailing" one gets better and better approximations of Omega (this is the definition of a C.E. random real). In fact the number k would have to be part of the program (as a bound on a for loop, say, or a parameter to the primitive recursive STEP function). After k steps the values of the first n bits of Omega would have stabilized. But the incompressibilty of Omega implies that the length of k in bits would be proportional to n itself! So there is no contradiction, or way around it. And the super-Omegas have the property that they are not even computably enumerable, i.e., they can't be approximated from below in this way. —Preceding unsigned comment added by 207.237.121.70 (talk) 10:09, 15 March 2011 (UTC)

Errata
In the Background section, shouldn't say "f = λ x.F(p,x)" instead of "f(x) = λ x.F(p,x)"?

Clarification in lead section requested
For the benefit of people like me, for whom the technical details later in the article are a bit tough to digest, a couple of clarifications in the lead section would be helpful

 * In the computer science subfield of algorithmic information theory a Chaitin constant or halting probability is a real number that informally represents the probability that a randomly-chosen program will halt. These numbers are formed from a construction due to Gregory Chaitin.

How is it possible, even in principle, to randomly choose a program, given that "a program" can be of unlimited length? Do you not need to choose randomly from all N-bit programs (or maybe all programs of <= N bits)?

 * Although there are infinitely many halting probabilities, it is common to use the letter Ω to refer to them as if there were only one. Because Ω depends on the program encoding used, it is sometimes called Chaitin's construction instead of Chaitin's constant when not referring to any specific encoding.

I don't understand what this is saying. Is it saying:

 * There are infinitely many individual halting probabilities because there are infinitely many programs?
 * There are infinitely many halting probabilities for a randomly chosen program, one for each of infinitely many encoding schemes?
 * There are infinitely many halting probabilities for a randomly chosen program, one for each of infinitely many program lengths?
 * Something else?

86.133.243.133 (talk) 03:52, 11 November 2008 (UTC)

There are infinitely many halting probabilities, because there are infinitely many different programming languages. Each has its own halting probability.

You select a random program by flipping a balanced coin forever. This produces an infinite bit string. Since the programs are self-delimiting, if some initial sequence of this string is a valid program, that is the one selected. Then the probability of a program is just the probability that you get the program in this way or just 1/2^n, where n is the length of the program. Requiring that programs be "self-delimiting", as they are in the real world, was the key insight that led to this beautiful theory. Kolmogorv made the mistake of not counting "blank" characters on his Turing Machine tapes as information, but they clearly provide information, namely where input (a program) begins and ends. —Preceding unsigned comment added by 207.237.121.70 (talk) 10:21, 15 March 2011 (UTC)

More Errata
The page contains several inaccuracies, that I hope to address in the nearby future. For starters, I have fixed an error in the Goldbach conjecture argument, Running all <= N bit programs doesn't suffice, since their joint halting probability is not guaranteed to match Ω in the first N bits. The formulation 'on the other hand' is particularly misleading, since the two cases mentioned are not mutually exclusive.

A bigger problem is the definition of universality in terms of machines with two inputs. This fails to guarantee algorithmic randomness of the halting probability. For instance, an F that only accepts programs consisting of 2^i zeroes, could still be universal, but would obviously lead to a very non-random halting probability.

I changed the definition of universality. A proof of Omega's randomness, now possible, should be added next. John Tromp

Use of Chaitin's constant in proving unsolved problems in number theory
The section 'Use of Chaitin's constant in proving unsolved problems in number theory' makes no sense to me. How is that different from saying that a program that does that iteration will eventually say if the conjecture is false?. So, how many digits of Omega do we need to know to know wether Goldbach conjecture is true or false? Chaitin himself though that Fermat Last theorem is "true with no reason", before the proof in the 90's. Did he say also that Omega can help in that problem? —Preceding unsigned comment added by 76.193.219.199 (talk) 21:17, 9 July 2009 (UTC)

 * I agree. That section is simply the observation that the halting problem can settle any \Pi_1 sentence in number theory. While true, it has very little to do with the constant.  —Preceding unsigned comment added by 130.195.86.40 (talk) 04:05, 16 October 2009 (UTC)

 * Yes; this is just a consequence of the binary expansion of the constant being Turing equivalent to the Halting problem, nothing more. That section should be reworked to that it doesn't imply this would be a practical method of solution. — Carl (CBM · talk) 12:43, 16 October 2009 (UTC)

 * Per WP:BB I have partly rewritten that section and renamed it to Relationship between the knowledge of Chaitin's constant and the halting problem. The first paragraph contains, now in generalized form, the fact that one could use knowledge of the constant to solve the halting problem. The second paragraph mentions the relationship between the number theory problems and the halting problem while dismissing the possibility of solving these problems this way. Hope that helps. X127 (talk) 18:40, 22 June 2011 (UTC)

 * Yes. This can be supported (I do believe . . .) by Chaitin's book MetaMath!. Take a look at the last sentence, though; it seems to be misconstructed. But this is minor. It's a pleasure to encounter an editor who is coherent and who knows their stuff. (Please register as an official wikipedian. We need all the help we can get.) Bill Wvbailey (talk) 21:59, 22 June 2011 (UTC)

Proving Riemann Hypothesis
Don't you need peer review to claim that you have a method for proving Goldbach's Conjecture and the Riemann Hypothesis? I mean really, a hypothetical proof is not a proof and a verification by imagination alone is no guarantee in such a case. You are still left with the need for a leap of faith based upon something far less reliable than the character of God. —Preceding unsigned comment added by 99.156.205.151 (talk • contribs) 17:56, 12 September 2010

Possible unproven statement in the article
The Properties section states that all chaitin numbers are normal. How is it that chaitin constants have been proven using their randomness that they're normal and yet we can't use the very random nature of π to prove that π is normal or use the very random nature of the set of prime numbers to prove the twin prime conjecture. π is simpler do define than any of the chaitin numbers and yet it's harder to prove normality of that number. Did any of the refrences in this article prove the normality of chaitin numbers or state their normality, sourcing another source that stated the same thing. I'm sure that any chaitin number can be trivially proven to be normal from being computationally random, but have they really been proven to be computationally random, which is a much harder property to prove than uncomputability. Blackbombchu (talk) 03:14, 16 August 2013 (UTC)
 * This bothers me. There are a number of similar "numbers" for which it can be proved that many individual bits are non-computable, but that the number is normal.  ("This" number doesn't appear to be "computationally random" in the sense that I would mean it; in fact, with little effort, one could replace Ω with $$\frac {d+\Omega}{2^n}$$ where d is any nonnegative integer less than 2n.  — Arthur Rubin  (talk) 20:15, 14 January 2014 (UTC)

Getting the digits of Omega ?
Good evening,

Am I right : given F, there is no algorithm taking an integer n as argument and returning the n-th digit of $$\Omega_{F}$$ (or, equivalently, an infinite-time looping algorithm writing all its digits in order), but there is, for all n, an algorithm giving the n-th digit ? 86.196.217.126 (talk) 17:57, 12 October 2013 (UTC)
 * Well, since the nth digit is one of a finite number of possibilities, there is an algorithm producing that number. There isn't a computable function from n to the nth algorithm, though, as that would compute the number.  Perhaps this might be noted in the article, but I don't really see the point.  — Arthur Rubin  (talk) 20:23, 14 January 2014 (UTC)

Clarification for the general reader
The section 'Relationship to the halting problem' does not explicitly state that if p is a member of the domain of F, this is equivalent to saying that p halts. This may be confusing for the mathematically-literate general reader. Would it be possible to add a little more explanation to that section?

My apologies if I have just misunderstood the article - I am a general reader who has not touched computability theory for decades! Booleanmattock (talk) 16:39, 15 March 2014 (UTC)

The value
Every computer has its Chaitin's constant, does there exist a computer whose Chaitin's constant Ω is exactly 0.03? If no, why not? — Preceding unsigned comment added by 140.115.189.24 (talk) 06:16, 11 August 2015 (UTC)
 * Nope. See intro: all values of Ω are transcendental. 0.03 is rational. ~ CZeke (talk) 14:08, 29 November 2015 (UTC)

Super Omega section formatting issue
At, the last sentence doesn't seem to make sense (though the subject is way beyond my decades-dusty engineering math ). Is it missing a word or two? Also, the parenthetical:

 * 0``` = 0^{(3)}

seems like it should be something like:

 * O‴ = O(3)

(3 backticks → triple-prime, zero → letter "O", "^" → superscript) or is it O(3) or ... —[  Alan M 1  (talk) ]— 09:49, 14 August 2018 (UTC)

Definition not compatible with algorithmic randomness
I don't see how the definition would exclude usage of a prefix-free universal computable function which e.g. outputs the empty string for input $$\mathtt{0}^{2n}\mathtt{1}$$ and simulates the $$n$$th turing machine (in some computable enumeration) for input $$\mathtt{0}^{2n+1}\mathtt{1}$$. The Chaitin's constant for this $$F$$ would not be algorithmically random, as we know already all the even bits. I think the missing part is 'additively optimal universal partial recursive prefix function' here, as taken from this book. The proof for algorithmic randomness goes like this: If you know $$\Omega_F^{<n}$$, the first $$n$$ digits of $$\Omega_F$$, then you know the halting property of every $$F$$-program of length at most $$n$$. Call the smallest string not expressible by such a program $$\phi(n)$$. Since you can compute $$\phi(n)$$ from $$\Omega_F^{<n}$$, you expect the complexity of $$\Omega_F^{<n}$$ to differ from $$\phi(n)$$ only by a fixed constant. But to make sure this argument translates into the actual $$F$$-complexities, you want $$F$$ to be additively optimal.

Why "informally speaking"?
The first sentence of the article is the following:

"In the computer science subfield of algorithmic information theory, a Chaitin constant (Chaitin omega number) or halting probability is a real number that, informally speaking, represents the probability that a randomly constructed program will halt."

But the section Interpretation as a probability appears to make it clear that the Chaitin omega in fact is a probability.

Am I mistaken about this? If it really is a probability, then it should not be described as representing a probability only "informally speaking". 2601:200:C000:1A0:68A1:236F:AC0B:9D14 (talk) 20:47, 26 August 2022 (UTC)

"Chaitin`s number" listed at Redirects for discussion
An editor has identified a potential problem with the redirect Chaitin`s number and has thus listed it for discussion. This discussion will occur at Redirects for discussion/Log/2022 October 15 until a consensus is reached, and readers of this page are welcome to contribute to the discussion. 1234qwer1234qwer4 15:29, 15 October 2022 (UTC)

title: Talk:Chaitin's constant


text:
Flag of Scotland

The flag of Scotland (bratach na h-Alba; Banner o Scotland, also known as St Andrew's Cross or the Saltire) is the national flag of Scotland, which consists of a white saltire defacing a blue field. The Saltire, rather than the Royal Standard of Scotland, is the correct flag for all private individuals and corporate bodies to fly. It is also, where possible, flown from Scottish Government buildings every day from 8:00 am until sunset, with certain exceptions.

Use of the flag is first recorded with the illustration of a heraldic flag in Sir David Lyndsay of the Mount's Register of Scottish Arms, c. 1542. It is possible that this is based on a precedent of the late 15th century, the use of a white saltire in the canton of a blue flag reputedly made by Queen Margaret, wife of James III (1451–1488).

Design
The heraldic term for an X-shaped cross is a 'saltire', from the old French word saultoir or salteur (itself derived from the Latin saltatorium), a word for both a type of stile constructed from two cross pieces and a type of cross-shaped stirrup-cord. In heraldic language, the Scottish flag may be blazoned azure, a saltire argent. The tincture of the Saltire can appear as either silver (argent) or white. However, the term azure does not refer to a particular shade of blue.

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These variations in shade eventually led to calls to standardise the colour of Scotland's national flag, and in 2003 a committee of the Scottish Parliament met to examine a petition that the Scottish Executive adopt the Pantone 300 colour as a standard (this blue is of a lighter shade than the Pantone 280 of the Union Flag). Having taken advice from a number of sources, including the office of the Lord Lyon King of Arms, the committee recommended that the optimum shade of blue for the Saltire be Pantone 300. Recent versions of the Saltire have therefore largely converged on this official recommendation (Pantone 300 is #005EB8 as a web colour). The flag proportions are not fixed but 3:5 is most commonly used, as with other flags of the countries of the United Kingdom (flag manufacturers themselves may adopt alternative ratios, including 1:2 or 2:3). Lord Lyon King of Arms states that 4:5 is suitable. The ratio of the width of the bars of the saltire in relation to the width of the field is specified in heraldry in relation to shield width rather than flag width. However, this ratio, though not rigid, is specified as one-third to one-fifth of the width of the field.

History

The 1320 Declaration of Arbroath cites Scotland's conversion to Christianity by St. Andrew, "the first to be an Apostle". Depiction of the saint being crucified on a decussate cross was seen on seals in Scotland from 1180 onwards and was used on a seal of the Guardians of Scotland, dated 1286. Bishop William de Lamberton (r. 1297–1328) also used the crucified figure of the saint in his seal.

The saltire (decussate cross, diagonal cross) was used as a field sign in the medieval period without any connection to Saint Andrew. The connection between the field sign and the legendary mode of crucifixion of the saint may originate in Scotland, in the late 14th century. The Parliament of Scotland decreed in 1385 that every Scottish and French soldier (fighting against the English under Richard II) "shall have a sign before and behind, namely a white St. Andrew's Cross".

James Douglas, 2nd Earl of Douglas at the Battle of Otterburn (1388) reportedly used a pennon with a saltire at the hoist. Similarly, white saltire was shown in the canton of the "Blue Blanket of the Trades of Edinburgh", reputedly made by Queen Margaret, wife of James III (1451–1488). This is the flag of the Incorporated Trades of Edinburgh, and the focal point of the Riding of the Marches ceremony held in the city each year.

Use of the white "Sanct Androis cors" on blue as a naval flag is recorded for 1507, for the carrack Great Michael. As a heraldic flag, the white saltire on a blue field is first shown in 1542, in the armorial of David Lyndsay. Here, the royal arms are supported by two unicorns, each holding the saltire banner.

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The seven British Army Infantry battalions of the Scottish Division, plus the Scots Guards and Royal Scots Dragoon Guards regiments, use the Saltire in a variety of forms. Combat and transport vehicles of these Army units may be adorned with a small, (130x80mm approx.), representation of the Saltire; such decals being displayed on the front and/or rear of the vehicle (on tanks these may also be displayed on the vehicle turret). In Iraq, during both Operation Granby and the subsequent Operation Telic, the Saltire was seen to be flown from the communications whip antenna of vehicles belonging to these units. Funerals, conducted with full military honours, of casualties of these operations in Iraq, plus those killed in operations in Afghanistan, have also been seen to include the Saltire being draped over the coffin of the deceased on such occasions.

In the battle for "hearts and minds" in Iraq, the Saltire was again used by the British Army as a means of distinguishing troops belonging to Scottish regiments from other coalition forces, in the hope of fostering better relations with the civilian population in the area south west of Baghdad. Leaflets were distributed to Iraqi civilians, by members of the Black Watch, depicting troops and vehicles set against a backdrop of the Saltire.

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Other uses of the Saltire by the Army include the cap badge design of the Royal Regiment of Scotland, which consists of a (silver) Saltire, surmounted by a (gilt) lion rampant and ensigned with a representation of the Crown of Scotland (this same design, save for the Crown, is used on both the Regimental flag and tactical recognition flash of the Royal Regiment of Scotland). The badge of the No. 679 (The Duke of Connaught's) Squadron Army Air Corps bears a Saltire between two wreaths ensigned 'Scottish Horse', an honour they received in 1971 which originated through their links with the Royal Artillery. The Officer Training Corps units attached to universities in Edinburgh and Glasgow, plus the Tayforth University OTC, all feature the Saltire in their cap badge designs.

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Use of the Saltire at sea as a Jack or courtesy flag has been observed, including as a Jack on the Scottish Government's Marine Patrol Vessel (MPV) Jura. The ferry operator Caledonian MacBrayne routinely flies the Saltire as a Jack on vessels which have a bow staff, including when such vessels are underway. This practice has also been observed on the Paddle Steamer Waverley when operating in and around the Firth of Clyde. The practice of maritime vessels adopting the Saltire, for use as a jack or courtesy flag, may lead to possible confusion in that the Saltire closely resembles the maritime signal flag M, "MIKE", which is used to indicate "My vessel is stopped; making no way." For the benefit of Scottish seafarers wishing to display a Scottish flag other than the Saltire, thereby avoiding confusion and a possible fine, a campaign was launched in November 2007 seeking official recognition for the historic Scottish Red Ensign. Despite having last been used officially by the pre-Union Royal Scots Navy and merchant marine fleets in the 18th century, the flag continues to be produced by flag manufacturers and its unofficial use by private citizens on water has been observed.

In 2017 the Unicode Consortium approved emoji support for the Flag of Scotland following a proposal from Jeremy Burge of Emojipedia and Owen Williams of BBC Wales in 2016. This was added to major smartphone platforms alongside the flags of England and Wales in the same year. Prior to this update, The Telegraph reported that users had "been able to send emojis of the Union Flag, but not of the individual nations".

Incorporation into the Union Flag
The Saltire is one of the key components of the Union Flag which, since its creation in 1606, has appeared in various forms following the Flag of Scotland and Flag of England first being merged to mark the Union of the Crowns, an event occurred in 1603 when James VI, King of Scots, acceded to the thrones of both England and Ireland upon the death of Elizabeth I of England. The proclamation by King James, made on 12 April 1606, which led to the creation of the Union Flag states:

"By the King: Whereas, some differences hath arisen between Our subjects of South and North Britaine travelling by Seas, about the bearing of their Flagges: For the avoiding of all contentions hereafter. We have, with the advice of our Council, ordered: That from henceforth all our Subjects of this Isle and Kingdome of Great Britaine, and all our members thereof, shall beare in their main-toppe the Red Crosse, commonly called St. George's Crosse, and the White Crosse, commonly called St. Andrew's Crosse, joyned together according to the forme made by our heralds, and sent by Us to our Admerall to be published to our Subjects: and in their fore-toppe our Subjects of South Britaine shall weare the Red Crosse onely as they were wont, and our Subjects of North Britaine in their fore-toppe the White Crosse onely as they were accustomed. – 1606."

However, in objecting strongly to the form and pattern of Union Flag designed by the College of Arms and approved by King James, whereby the cross of Saint George surmounted that of Saint Andrew, regarded in Scotland as a slight upon the Scottish nation, a great number of shipmasters and ship-owners in Scotland took up the matter with John Erskine, 19th Earl of Mar, and encouraged him to send a letter of complaint, dated 7 August 1606, to James VI, via the Privy Council of Scotland, stating:

"Most sacred Soverayne. A greate nomber of the maisteris and awnaris of the schippis of this your Majesteis kingdome hes verie havelie compleint to your Majesteis Counsell that the form and patrone of the flaggis of schippis, send doun heir and commandit to be ressavit and used be the subjectis of boith kingdomes, is very prejudiciall to the fredome and dignitie of this Estate and will gif occasioun of reprotche to this natioun quhairevir the said flage sal happin to be worne beyond sea becaus, as your sacred majestie may persave, the Scottis Croce, callit Sanctandrois Croce is twyse divydit, and the Inglishe Croce, callit Sanct George, haldin haill and drawne through the Scottis Croce, whiche is thairby obscurit and no takin nor merk to be seen of the Scottis Armes. This will breid some heit and miscontentment betwix your Majesteis subjectis, and it is to be ferit that some inconvenientis sall fall out betwix thame, for oure seyfairing men cannot be inducit to ressave that flag as it is set doun. They haif drawne two new drauchtis and patronis as most indifferent for boith kingdomes which they present to the Counsell, and craved our approbatioun of the same; bot we haif reserved that to you Majesteis princelie determination."

Despite the drawings described in this letter as showing drafts of the two new patterns, together with any royal response to the complaint which may have accompanied them, having been lost, (possibly in the 1834 Burning of Parliament), other evidence exists, at least on paper, of a Scottish variant whereby the Scottish cross appears uppermost. Whilst, in the absence of evidence to the contrary, this design is considered by most vexillologists to have been unofficial, there is reason to believe that such flags were employed during the 17th century for use on Scottish vessels at sea. This flag's design is also described in the 1704 edition of The Present State of the Universe by John Beaumont, Junior, which contains as an appendix The Ensigns, Colours or Flags of the Ships at Sea: Belonging to The several Princes and States in the World.

On land, evidence suggesting use of this flag appears in the depiction of Edinburgh Castle by John Slezer, in his series of engravings entitled Theatrum Scotiae, c. 1693. Appearing in later editions of Theatrum Scotiae, the North East View of Edinburgh Castle engraving depicts the Scotch (to use the appropriate adjective of that period) version of the Union Flag flying from the Castle Clock Tower. A reduced view of this engraving, with the flag similarly detailed, also appears on the Plan of Edenburgh, Exactly Done. However, on the engraving entitled North Prospect of the City of Edenburgh the detail of the flag, when compared to the aforementioned engravings, appears indistinct and lacks any element resembling a saltire. The reduced version of the North Prospect ..., as shown on the Plan of Edenburgh, Exactly Done, does however display the undivided arm of a saltire and is thereby suggestive of the Scottish variant. On 17 April 1707, just two weeks prior to the Acts of Union coming into effect, Sir Henry St George, Garter King of Arms, presented several designs to Queen Anne and her Privy Council for consideration as the flag of the soon to be unified Kingdom of Great Britain. At the request of the Scots representatives, the designs for consideration included that version of Union Flag showing the Cross of Saint Andrew uppermost; identified as being the "Scots union flagg as said to be used by the Scots". However, Queen Anne and her Privy Council approved Sir Henry's original effort (pattern "one") showing the Cross of Saint George uppermost.

From 1801, in order to symbolise the union of the Kingdom of Great Britain with the Kingdom of Ireland a new design, which included the St Patrick's Cross, was adopted for the flag of the United Kingdom of Great Britain and Ireland. A manuscript compiled from 1785 by William Fox, and in possession of the Flag Research Center, includes a full plate showing "the scoth [sic] union" flag with the addition of the cross of St. Patrick. This could imply that there was still some insistence on a Scottish variant after 1801.

Despite its unofficial and historic status the Scottish Union Flag continues to be produced by flag manufacturers, and its unofficial use by private citizens on land has been observed. In 2006 historian David R. Ross called for Scotland to once again adopt this design in order to "reflect separate national identities across the UK". However, the 1801 design of the Union Flag remains the official flag of the entire United Kingdom of Great Britain and Northern Ireland.

Related flags
The flag of the Church of Scotland is the flag of Scotland defaced with the burning bush.

Several flags outside of the United Kingdom are based on the Scottish saltire. In Canada, an inverse representation of the flag (i.e. a blue saltire on a white field), combined with the shield from the royal arms of the Kingdom of Scotland, forms the modern flag of the province of Nova Scotia. Nova Scotia (Latin for "New Scotland") was the first colonial venture of the Kingdom of Scotland in the Americas. By contrast, the saltire logo of St. Andrew's First Aid is red on white rather than white on blue, in alteration of the Red Cross. Also, the Colombian department of the Archipelago of San Andrés, Providencia and Santa Catalina uses a pale-blue version because the name of principal island (San Andrés, Saint Andrew), though also by the first settlers from Scottish origin.

The Dutch municipality of Sint-Oedenrode, named after the Scottish princess Saint Oda, uses a version of the flag of Scotland, defaced with a gold castle having on both sides a battlement.

Royal Standard of Scotland

The Royal Standard of Scotland, also known as the Banner of the King of Scots or more commonly the Lion Rampant of Scotland, is the Scottish Royal Banner of Arms. Used historically by the King of Scots, the Royal Standard of Scotland differs from Scotland's national flag, the Saltire, in that its correct use is restricted by an Act of the Parliament of Scotland to only a few Great Officers of State who officially represent The Sovereign in Scotland. However, a 1934 Royal Warrant for George V's silver jubilee which authorised waving of hand-held versions continues to be relied upon by fans at sports events and other public occasions. It is also used in an official capacity at Royal residences in Scotland when the Sovereign is not present.

title: Flag of Scotland


text:
Peig Sayers

Máiréad "Peig" Sayers (29 March 1873 – 8 December 1958) was an Irish author and seanchaí ( or ) born in Dún Chaoin, County Kerry, Ireland. Seán Ó Súilleabháin, the former Chief archivist for the Irish Folklore Commission, described her as "one of the greatest woman storytellers of recent times".

Biography
She was born Máiréad Sayers in the townland of Vicarstown, Dunquin, Corca Dhuibhne, County Kerry, the youngest child of the family. She was called Peig after her mother, Margaret "Peig" Brosnan, from Castleisland. Her father Tomás Sayers was a locally renowned expert on the oral tradition and passed on many of his tales to Peig.

Through her father's influence, Peig also grew up upon a rich oral tradition of Irish folklore, mythology, and local history, including local folk heroes like Piaras Feiritéar, faction fights at pattern days and market fairs before the Great Famine, and the lingering memory of Mass rocks and priest hunters under the Penal Laws.

At the age of 12, she was taken out of the National school and went to work as a domestic servant for the Curran family in the nearby town of Dingle. The Currans were members of the growing Irish Catholic middle class produced by the Government-funded breakup and sale of the Anglo-Irish landlords' estates after the Land War. Peig later recalled that the Curran family were kind employers and treated her very well. The Curran children, however, were forbidden by their parents, who desired for them to move up in the world, to learn the Irish language and so, at the children's request, Peig taught the local vernacular to them in secret.

After she grew to adulthood, Peig was promised during the "American wake" of her childhood best friend, Cáit Boland, that Peig would soon join her as part of the Irish diaspora in the United States. Cáit later wrote, however, that she had had an accident and could not forward the cost of Peig's passage.

Instead, Peig moved to the Great Blasket Island after her brother arranged for her to marry Pádraig Ó Guithín, a fisherman and native of the island, on 13 February 1892. Pádraig and Peig had eleven children, of whom only six survived their mother.

Norwegian linguist and Celticist Carl Marstrander stayed on the island while studying the Corca Dhuibhne dialect of Munster Irish in 1907 and later persuaded Robin Flower of the British Museum to similarly visit the Blaskets. Flower was keenly appreciative of Peig Sayers' storytelling skills. He recorded her and brought her stories to the attention of the academic world.

After the Easter Rising of 1916, Peig hung up a framed picture of the 16 executed Irish Volunteers and Irish Citizen Army leaders in the family's cottage in Great Blasket island. During a search of the island by the Black and Tans during the subsequent Irish War of Independence, a terrified Pádraig Ó Guithín ordered his wife to take the picture down before she got them all killed. Even though Peig indignantly refused, the search party did not harm anyone in their family.

During the 1930s a Dublin teacher, Máire Ní Chinnéide, who was also a regular visitor to the Blaskets, urged Peig to tell her life story to her son Mícheál. Peig was illiterate in the Irish language, having received her early schooling only through the medium of English. She dictated her biography to Mícheál, who then sent the manuscript pages to Máire Ní Chinnéide in Dublin. Ní Chinnéide then edited the manuscript for its publication in 1936.

Over several years from 1938 Peig dictated 350 ancient legends, ghost stories, folktales, and religious stories to Seosamh Ó Dálaigh of the Irish Folklore Commission (while another source tallies 432 items collected by Ó Dálaigh from her, some 5,000 pages of material). Peig had a vast repertoire of tales, ranging from the Fenian Cycle of Irish mythology to romantic and supernatural stories.

She continued to live on the island until 1942, when she returned to her native place, Dunquin. She was moved to a hospital in Dingle, County Kerry where she died in 1958. She is buried in the Dún Chaoin Burial Ground, Corca Dhuibhne, Ireland. All her surviving children except Mícheál emigrated to the United States to live with their descendants in Springfield, Massachusetts.

Books
Sayers is most famous for her autobiography Peig (ISBN 0-8156-0258-8), but also for the folklore and stories which were recorded in Machnamh Seanmhná (An Old Woman's Reflections, ISBN 978-0-19-281239-1). The books were not written down by Peig, but were dictated to others.

Sayers' memoir Peig describes her childhood immersed in traditional Munster Irish-speaking culture, which was still surviving despite rackrenting Anglo-Irish landlords, the resulting extreme poverty, and the coercive Anglicisation of the educational system. Another theme was devout Catholicism and mass emigration to the New World following a ceremonial ceilidh called an "American wake".

Even though Peig Sayers' memoir at first received high praise, Máire Ní Chinnéide has since received very harsh criticism and accusations of censorship. Máire Ní Chinnéide did so, however, to make Peig's life story conform to the idealised vision of the Irish peasantry favoured by the ruling Fianna Fáil political party, which owed more to 19th century Romantic nationalism than to the reality of daily life or the culture of the Gaeltachtaí.

One matter of speculation is whether there was delicate material that a female informant such as she would have refrained from recounting to a male collector (Irish Folklore Commission's policy being to hire only male collectors), though there was evidently close rapport established between the two individuals, which perhaps overrode such hypothetical barriers. She was also among the informants not comfortable with being recorded mechanically on the Ediphone, so the material had to be taken down on pen and paper.

In the 1966 University of Chicago volume Folktales of Ireland, three uncensored folktales collected from Peig Sayers, as translated by Seán Ó Súilleabháin, appeared in English for the first time.

Peig
Peig is among the most famous expressions of a late Gaelic Revival genre of personal histories by and about inhabitants of the Blasket Islands and other remote Gaeltacht locations. Tomás Ó Criomhthain's similarly censored memoir an tOileánach ("the Islandman", 1929) and Muiris Ó Súilleabháin's Fiche Bliain ag Fás, and Robert J. Flaherty's documentary film Man of Aran address similar subjects.

The often bleak tone of the book is established from its opening words:

"I am an old woman now, with one foot in the grave and the other on its edge. I have experienced much ease and much hardship from the day I was born until this very day. Had I known in advance half, or even one-third, of what the future had in store for me, my heart wouldn't have been as gay or as courageous as it was in the beginning of my days."

Ironically, the standard cliches of Peig's memoirs and those censored similarly to hers swiftly found themselves the object of contempt and mockery – especially among the cosmopolitan middle class intelligentsia and the often covertly literary Irish civil service – for their often extremely depressing accounts of rural poverty, starvation, family tragedies, and bereavements. In Modern literature in Irish, mockery of the Gaeltacht memoir genre reached its peak with Flann O'Brien's parody of An tOileánach; the novel An Béal Bocht ("The Poor Mouth").

Despite this fact, Peig's book was widely used as a text for teaching and examining Irish in many secondary schools. As a book with arguably sombre and depressing themes and its latter half cataloguing a string of heartbreaking family tragedies, its presence on the Irish syllabus has often been harshly criticised.

It led, for example, to the following comment from Progressive Democrat Seanadóir John Minihan in the Seanad Éireann in 2006 when discussing improvements to the curriculum:

"No matter what our personal view of the book might be, there is a sense that one has only to mention the name Peig Sayers to a certain age group and one will see a dramatic rolling of the eyes, or worse."

According to Blasket Islands literary scholar Cole Moreton, however, this was not Peig's fault, but that of her censors, "Some of her stories were very funny, some savage, some wise, some earthy; but very few made it into the pages of her autobiography. The words were dictated to her son, then edited by the wife of a Dublin school inspector, and both collaborators sanitized the text a little in turn so that it was homely and pious, a book fit to be taken up as a set text in Irish schools. The image of Peig's broad face smiling out from beneath a headscarf, hands clasped in her lap, became familiar to generations of schoolchildren who were bored rigid by this holy peasant woman who had been forced upon them. They grew up loathing Peig... without hearing the stories as they were intended."

Peig was eventually replaced by Maidhc Dainín Ó Sé's A Thig Ná Tit Orm during the mid-1990s.

Popular culture
In Paddywhackery, a television show from 2007 on the Irish language on television channel TG4, Fionnula Flanagan plays the ghost of Peig Sayers, sent to Dublin to restore faith in the Irish language revival.

A stage play, Peig: The Musical! (co-written by Julian Gough, Gary MacSweeney and the Flying Pig Comedy Troupe) was also loosely based on Peig's autobiography.

title: Peig Sayers


text:
Talk:Peig Sayers

More about the bio?
Is there something remarkable about her biography? Is it sad, happy, adventures, sentimental, what focus?

 * It is core reading for generations of youth :)

 * Perhaps note could be made of how she was sent to school even as a young girl, because her mother was weakened from many years of pregnancy...

 * Sad is understating it - depressing is a lot closer! Autarch 20:15, 17 May 2006 (UTC)

question
quote: "Peig was illiterate, but dictated many of her stories to Seosamh Ó Dálaigh of the Irish Folklore Commission and Dr. Robin Flower of the British Museum."

I thought she was literate in English but not in Irish, and dictated her stories to her son. EamonnPKeane (talk) 13:40, 10 January 2008 (UTC)

 * I couldn't comment on the "illiterate" bit, but Peig dictated to many people. There is no conflict in the quote above. She dictated much of the folklore and stories that are referenced in Machnamh seanmhná to the folklorists AND her son, and much of the content for Peig to her son, (Mícheál Ó Gaoithín, Micheal O'Guiheen, Maidhc File). I don't think that there is anything in what is included in the sentence above that is self conflicting or incorrect. Cheers. Guliolopez (talk) 20:44, 17 January 2008 (UTC)

 * FYI - Máire Ní Chinnéide is often referenced as the "author" of Peig. Not Maidhc. This is largely because, while Maidhc "recorded" the stories, Ní Chinnéide wrote them down, editted them, and saw them published. Similarly, while Maidhc recorded the stories that were ultimately published in Machnamh seanmhná, Peig herself is credited as "author", with Séamus Ennis as "translator", and Pádraig Ua Maoileoin & Máire Ní Chinnéide with additional pub/editing credits. The folklore commission and British Museum types that recorded Peig's stories published, but not with a focus on Peig entirely. Mr. Flower for example (as a "Celticist") published on the Irish/Blasket tradition's of storytelling and poetry in general. Again, there's nothing in any of this that impacts the accuracy of what we have in the article. (And in a way, including it would just confuse matters.) Guliolopez (talk) 20:56, 17 January 2008 (UTC)

Book
It doesn't really make it clear in the opening paragraph what she is most famous for (her book, Peig) or the fact that it's written in Irish - which is probably the most important aspect considering it's the first thing most Irish people would think of. --Tuzapicabit (talk) 18:27, 17 September 2008 (UTC)

Merge
I have suggested that An Old Woman's Reflections be merged into this article because the book is apparently not notable enough for its own wikipeida article apart from the context of this article. -- Mikeblas (talk) 00:29, 30 December 2009 (UTC)
 * Support: The Old Woman's Reflections article is a badly-written and bitty stub that doesn't stand on its own feet. It contains such silly statements as "the story is of monumental simplicity", "collecting turf for roots" (which is meaningless), and the book "has been accused of scarring a whole generation of young Irish people" (it merely bored children). This should be absorbed into the main article about Peig. I have rewritten the stub to purge the most daft text. --174.16.17.42 (talk) 22:50, 10 February 2010 (UTC)go

Is é Peig: A Scéal Féin an leabhar a bhí ar shillobas an Ardteistiméarachta ó na 60í go dtí na90í. Is leabhar eile de chuid Pheig é Machtnamh

Article An Injustice to Sayers
Unfortunately the article gives no hint of why Sayers' stories fascinated generations of folklorists and ordinary readers, which they did; and by the way, not ALL those schoolchildren who were required to read her works were bored. The article is a slack, lazy piece of work whose author was not perceptive enough to see that those who dismissed Sayers work as "boring", or old-fashioned, now seem far more dated than her timeless stories.

I'm baffled at the shallowness of those who are offended because a woman who lived a very hard life, in dark and bitter times, sometimes said as much in her stories. Would they have preferred it if she lied? Younggoldchip (talk) 21:36, 21 February 2010 (UTC)

 * I agree with your sentiment however the wikipedia rules say one needs to find a published instance of someone sayiing so before it can go in the article. 86.166.75.231 (talk) 19:47, 16 November 2017 (UTC)

Dates please?
Checking the Irish 1901 and 1911 censuses online, and there are no "Ó Guithín"s listed in Kerry. Could someone add her year of marriage to him? The 1901 census lists a 26-year-old Margaret Sayers at Drumquin, unmarried, who however could read and write in Irish and English. Come someone point us researchers in the right direction please?78.16.95.94 (talk) 12:51, 6 January 2017 (UTC)

title: Talk:Peig Sayers


text:
Talk:Flag of England

Features
"Features"? That would apply to a flag that was quartered with it too, or one that bore marks of cadency etc. the description probably needs more. PML. —Preceding unsigned comment added by 203.202.5.75 (talk • contribs)

Flag of England <> St George's Cross
St George's Cross is a model of cross, and not a flag. The St George's Cross is present also in other flags. I think the two pages mustn't be merged. —the preceding comment is by 84.222.1.86 (talk • contribs) : Please sign your posts!.

Battle of Poitiers, 1356, who is using the red cross as field badge?
It's John II of France who is using the red cross..."https://fr.wikipedia.org/wiki/Drapeau_de_la_France#/media/File:R%C3%A9dition_de_Jean_le_Bon.jpg"...unless the painter made a mistake, and John, with a sword, is in fact Edward.

The figures on the left look victorious. The figures on the right defeated. The left is woods, the right is plains. Given that England won at Poitiers by attacking through the woods, I wonder if a later artist added incorrect captions? Ariehkovler (talk) 16:23, 11 July 2021 (UTC)

 * @Ariehkovler there are multiple paintings of those battles and every time France used the 🏴. Until the English took Paris and red was seen as the color of the enemy, then started to use a white cross. Esteban Outeiral Dias (talk) 09:54, 5 March 2023 (UTC)

Citations for St George and France
I've seen the mark saying "citation needed". I'm also surprised by how there is barely any mention of it at all. One paragraph then that's it.

For the sources there is hundreds of them and with a detailed overview of the switch from France's 🏴 and England's 🇩🇰 to France's 🏴rotated and England's 🏴. There is sources but also paintings, on the wikipédia page for French flags in French: https://fr.wikipedia.org/wiki/Drapeau_de_la_France?wprov=sfla1

If no one wants to do the work I'll understand it'd take time, so maybe I'll eventually help later. Esteban Outeiral Dias (talk) 09:57, 5 March 2023 (UTC)

Hawaii; East India Company
I think you should the Flag of Hawaii under "Elswhere - Commonly". Also the Flag of the East India Company under "Historically". 68.100.121.207 (talk) 14:38, 18 May 2023 (UTC)

title: Talk:Flag of England