15 March 2014

The higher math needed to calculate
all possible moves in rugby and chess

How many moves are needed? How many moves are possible?

Patrick Comerford

I know of someone who was studying for a degree in math at Maynooth many years ago. He was the first in his family to get to university, and his mother was understandably proud of him.

When she was asked what he was doing in Maynooth, she replied: “A course.”

When asked what the course was, she said: “Sums.”

But I cannot afford to laugh. I got a pass on the pass paper in math in the Leaving Certificate in 1969, and counting beyond four sometimes seems to require higher calculus.

Ireland can win the Six Nations’ Championship later today [15 March 2014] at the showdown in Stade de France in Paris … but only on points difference. And the calculations for this nail-biting day of wall-to-wall rugby involve a level of math that is far higher and is far more difficult than anything I learned while I was at school.

This has happened on four times in the past 41 years, and this was a task that foiled Ireland three out of four years.

So let’s look at the permutations, combinations and calculations if Ireland is to win the title today for the first time since 2009 and for only the time since 1985.

Three sides have six points, England has already won the Triple Crown. In order of their favourable points’ difference, they are:

Ireland (81)

England (32)

France (3)

England plays Italy in the Stadio Olimpico in Rome, starting at 12.30.

If England beats Italy by any margin and later in the day Ireland and France draw in Paris, then it is impossible for England not to win the Six Nations title.

If England beats Italy by 50 points or more, then an Irish win in Stade de France by any margin means Ireland still wins.

If England beats Italy by any margin, and later in the day France wins in Paris, it seems impossible for England not to secure the Triple Crown and the Six Nations title.

I say it seems … because, when it comes to points’ difference, France is 29 points behind England. So, for every point England wins by in Rome, it ratchets up the French target of a 30-point winning margin over Ireland.

If Italy beats England, or the two sides draw, and Ireland wins in Paris, then Ireland wins the Six Nations title.

If Italy beats England, or the two sides draw, and France beats Ireland, then France wins the Six Nations title.

It all explains why Ireland had to pile on all the points possible when Ireland beat Italy last Saturday.

If all that seems difficult to calculate, then consider the calculations that have to be made in playing chess, where the possibilities are boundless, it seems.

In the G2 section of the Guardian, Stephen Moss of Kingston-upon-Thames, Surrey, posed this dilemma:

In Paul Hoffman’s book, King’s Gambit: A Son, a Father and the World’s Most Dangerous Game (published by Hyperion in New York in 2007), he states that: “In practice the possibilities in chess are boundless, although theoretically it is a mathematically finite activity – there are, for example, 988 million positions that can be reached after four moves for white and four for black.” Can that figure possibly be correct? It seems far too big a number after so few moves for each side. And is the often quoted “fact” that there are more possible moves in a chess game than there are atoms in the universe really correct?

His query has drawn a number of interesting answers in the weeks since. I was overcome by the submission from ‘ThomasD’ the Thursday before last [6 March 2013]. He points out:

“There are different answers available depending on how you define the game’s complexity, though the ‘top end’ answer was calculated by Victor Allis as 10123, which compares to estimates of 1081 for the number of atoms in the observable universe.”

More moves in chess than there are atoms in the observable universe? That is almost beyond comprehension. But it certainly illustrates that God’s love and compassion for all is not beyond comprehension.

No wonder I have been a life-long reader of the Guardian.

Meanwhile, how many moves can Brian O’Driscoll make in his last international fixture this afternoon.

It’s wall-to-wall rugby for me today.

Art for Lent (11): ‘Balaclava’ (1876)
by Lady Elizabeth Butler

‘Balaclava’ (1876), by Elizabeth Thompson (Lady Butler)

Patrick Comerford

In the middle of Lent, I am constantly reminded of the sufferings of people caught in wars and conflicts. I am thinking this morning of the people caught in the conflict between Russia and Ukraine, particularly in Crimea, and the people of Syria, who have been forgotten in the media since the conflict between Ukraine and Russia became a major international crisis.

As the West considered confronting Russia over the crisis in Crimea and Ukraine, I was reminded of the Western confrontation with Russia in this region 160 years ago, leading to the disaster that became the Crimean War in 1854.

And so, for my work of Art for Lent this morning [15 March 2014], I have chosen the painting Balaclava (1876), by Elizabeth Thompson, generally known as Lady Butler.

This painting depicts the aftermath of the infamous Charge of the Light Brigade, which took place during the Crimean War at the Battle of Balaclava (1854). The poet Alfred Lord Tennyson also wrote a poem about the same Charge of the Light Brigade.

Lady Butler’s war paintings portray in a blunt way the horrors and sufferings of war, and the plight of the common soldier on the frontline.

On 27 February 1854, Britain issued an ultimatum to Tsar Nicholas I of Russia, whose troops had crossed the Danube River into Turkey. Britain feared that if the Tsar’s Black Sea fleet gained access to the Mediterranean it would threaten Britain’s dominance as a sea power and its use of the Suez Canal, and so threaten its imperial interests in Africa and India.

When the Tsar was silent in the face of this ultimatum, Britain joined France and Turkey in declaring war on Russia on 28 March 1854, and so began the Crimean War. The British began bombarding the Russian naval base at Sevastopol, the home of its Black Sea Fleet. The Russians responded by bombarding the British at Balaclava.

The command of the Cavalry Division was given to the ridiculous and silly Irish peer, Lord Lucan, and his brother-in-law, Lord Cardigan, had command of the Light Brigade. Neither had ever led troops in battle before, and they had risen in the ranks and received promotion because they had bought their commissions and because of their nobility.

The Charge of the Light Brigade and the Crimean War were military disasters, and the plight and suffering of the ordinary soldiers is captured in this morning’s painting. Yet the myths surrounding the Crimean War developed quickly. The Victoria Cross, Britain’s highest accolade for bravery, was first awarded by Queen Victoria in 1856 to soldiers who fought in Crimea, and is it is said the first medals were made from artillery guns captured at Sevastopol. The words Cardigan and Balaclava have entered the English language from the knitted woolen clothing and garments sent to the soldiers from home.

Many streets in Belfast are named after characters and events in the Crimean War (1853–1856), including Crimea Street, Raglan Street (Lord Raglan), Alma Street (Battle of Alma), Balaklava Street (Battle of Balaklava), Inkerman Street (Battle of Inkerman), and Sevastopol Street (Siege of Sevastopol).

I first became aware of the work of Lady Butler while I was at school in Gormanston in the 1960s – she died in Gormanston Castle in 1933. She is one of the few female painters to achieve fame for history paintings, especially military battle scenes, at the end of that tradition. Some of her most famous military scenes depict the Napoleonic Wars, but she covered most major 19th-century wars and painted several works showing World War I.

Lest anyone think she was glorifying war in her paintings, in her autobiography in 1922 she wrote about her military paintings: “I never painted for the glory of war, but to portray its pathos and heroism.”

She was born Elizabeth Southerden Thompson on 3 November 1846 at Villa Claremont in Lausanne, Switzerland, the daughter of Thomas James Thompson (1812-1881) and his second wife Christiana Weller (1825-1910). Her sister was the noted essayist and poet Alice Meynell.

She studied at the South Kensington School of Art for two years and attended classes in Florence and Rome during her holidays. She became a Roman Catholic along with the rest of the family after they moved to Florence in 1869.

Initially she concentrated on religious subjects like The Magnificat (1872), but after moving to Paris in 1870 she was exposed to battle scenes by Jean Louis Ernest Meissonier and Édouard Detaille, and switched her focus to war paintings.

She first exhibited at the Royal Academy in 1873 with her painting Missing. With this depiction of a battle scene from the Franco-Prussian War and the suffering and heroism of common soldiers, she earned her first submission to the Royal Academy.

She became a celebrity overnight the following year after The Roll Call was shown at the Royal Academy in 1874. The painting was commissioned by a Manchester businessman who wanted her to paint a large picture of a Crimean War roll-call.

She painted Balaclava (1876, oil on canvas), depicting one of the major battles of the Crimean War. That painting represents the aftermath of the infamous Charge of the Light Brigade in 1854, when a misinterpreted order led to heavy British losses: 661 cavalrymen were reduced to 195 in 20 minutes.

The subject became a favourite for painters after Tennyson’s poem The Charge of the Light Brigade. This poem was quoted by Lady Butler in the catalogue accompanying her work’s debut at the Society of Arts. Her portrayal of the soldiers was controversial as it focused on the psychological effects of war. But the painting was seen by thousands at several venues and was further popularised by large editions of prints.

Her Return from Inkerman shows a column of exhausted and wounded men of the Coldstream Guards and the 20th East Devonshire regiment returning from the heights of Inkerman on 5 November 1854.

Her career and fame peaked with her marriage on 11 June 1877 to Sir William Francis Butler (1838-1910), a distinguished general from Golden, Co Tipperary, who later questioned whether British and European colonial imperialism was in the best interest of indigenous peoples.

When he retired, they returned to Ireland and lived at Bansha Castle, Co Tipperary. She exhibited at the Royal Hibernian Academy from 1892. He died in 1910, and in 1922 she moved to live with her youngest daughter, Eileen, Viscountess Gormanston, at Gormanston Castle, Co Meath. She died there shortly before her 87th birthday on 2 October 1933 and was buried nearby in Stamullen.

Gormanston Castle ... Lady Butler lived here with her daughter from 1922 until her death in 1933 (Photograph: Patrick Comerford, 2014)

The Charge of the Light Brigade, by Alfred Lord Tennyson

Half a league, half a league,
Half a league onward,
All in the valley of Death
Rode the six hundred.
“Forward, the Light Brigade!
“Charge for the guns!” he said:
Into the valley of Death Rode the six hundred.

“Forward, the Light Brigade!
“Was there a man dismay’d?
Not tho’ the soldier knew
Someone had blunder’d:
Their’s not to make reply,
Their’s not to reason why,
Their’s but to do and die:
Into the valley of Death
Rode the six hundred.

Cannon to right of them,
Cannon to left of them,
Cannon in front of them
Volley’d and thunder’d;
Storm’d at with shot and shell,
Boldly they rode and well,
Into the jaws of Death,
Into the mouth of Hell
Rode the six hundred.

Flash’d all their sabres bare,
Flash’d as they turn’d in air,
Sabring the gunners there,
Charging an army, while
All the world wonder’d:
Plunged in the battery-smoke
Right thro’ the line they broke;
Cossack and Russian
Reel’d from the sabre stroke
Shatter’d and sunder’d.
Then they rode back, but not
Not the six hundred.

Cannon to right of them,
Cannon to left of them,
Cannon behind them
Volley’d and thunder’d;
Storm’d at with shot and shell,
While horse and hero fell,
They that had fought so well
Came thro’ the jaws of Death
Back from the mouth of Hell,
All that was left of them,
Left of six hundred.

When can their glory fade?
O the wild charge they made!
All the world wondered.
Honor the charge they made,
Honor the Light Brigade,
Noble six hundred.

Tomorrow:Christ Instructing Nicodemus,’ attributed to Crijn Hendricksz Volmarijn.

Contemplating summer sun and
sand by the beach in Greystones

The sun setting behind the beach and beyond the railway line in Greystones, Co Wicklow, late this afternoon (Photograph: Patrick Comerford, 2014)

Patrick Comerford
It’s another two weeks or more before summer time officially begins on 30 March. But Spring has truly arrived in this part of Ireland. The buds on the lawn and beneath the trees are turning into flowers, the blossom is spreading along the branches of the cherry tree outside my house, the morning birdsong starts earlier and earlier, and – as Irish people love to say this time of the year – “there’s a grand stretch in the evening.”

Although yesterday began as what one commentator from Cheltenham described as a “pea-souper,” and the heavy cloud cover in Dublin never truly lifted yesterday or today, there were striking pink and purple streaks in the sky to the west and south this evening all the way back from Greystones, Co Wicklow.

After a lengthy working week that had followed a full working weekend, two of us left south Dublin in mid-afternoon for a late lunch in the Happy Pear and a walk on the beach in Greystones.

Sea and sand ... the beach in Greystones this afternoon (Photograph: Patrick Comerford, 2014)

On the way to the Happy Pear, we picked up four holiday brochures in Phoenix Travel on Church Road, near the Dart and train station. We pored over those brochures upstairs in the Happy Pear, contemplating a week in the sun and close to sand later this year. Greece? Turkey? When? Where?

Down on the beach, there were few people on the sand as we watched the small waves lap against the shore. To the west, beyond the railway line, the sun was beginning to set slowly behind the Burnaby Estate.

Back in Greystones, it was obvious the town was looking to forward to Saint Patrick’s Day and the Bank Holiday weekend. Green flags were fluttering, and shop windows were decorated in green-white-and-orange shops and many restaurants were advertising special menus.

Green lights in Temple Bar herald the arrival of the Saint Patrick’s Weekend (Photograph: Patrick Comerford, 2014)

The previous evening, we had strolled though Temple Bar after dinner in the Italian Corner. There too, there were green lights strung across the narrow streets, and buskers and street artists regaled in forty shades of green. The large number of tourists whose faces were filled with anticipation, and who had their hair streaked in green, indicates that if the weather holds up or even improves this could be a wonderful weekend in Dublin.

And an Irish win in Paris tomorrow [Saturday] would add to the joy and the glory.

Meanwhile, as we returned to Dublin this evening, it was still bright after 6.30. This is a blessed season to enjoy and to be thankful for prayerfully.

Pink and purple streaks in evening sky in Co Wicklow this evening (Photograph: Patrick Comerford, 2014)

Εορτασμός εθνικών επετείων και
συμπαράσταση προς την Κεφαλλονιά.

A photograph from Corfu on the wall of Corfu in Parliament Street

Αγαπητά μέλη και φίλοι

Η Ελληνική Κοινότητα Ιρλανδίας και η Ελληνορθόδοξη Κοινότητα Ιρλανδίας διοργανώνουν εορταστικό δείπνο με την ευκαιρία των Εθνικών Επετείων της Ελλάδας (25η Μαρτίου, ημέρα εθνικής παλιγγενεσίας και ξεσηκωμού κατά του Οθωμανικού ζυγού) και της Κύπρου (1η Απριλίου, επέτειος της έναρξης του εθνικοαπελευθερωτικού αγώνα της Κύπρου κατά των Βρεττανών κατακτητών). Παράλληλα αισθανόμαστε πως είναι χρέος μας σαν παροικία της Διασποράς να συμπαραστεκόμαστε στα αδέλφια μας στην Ελλάδα και Κύπρο. Έτσι τα έσοδα που θα συλλεχθούν από την αυτήν την εκδήλωση θα σταλούν στην Κεφαλλονιά προς βοήθεια των κατοίκων μετά τους πρόσφατους καταστρεπτικούς σεισμούς.

Η εκδήλωση θα λάβει χώρα την Κυριακή 30 Μαρτίου 2014 στις 6:30 μμ στο Ελληνικό εστιατόριο Corfu, 12 Parliament Street, Dublin.

Η τιμή του εισητηρίου θα είναι 25 ευρώ το άτομο, από τα οποία τα 16.5 ευρω θα διατεθούν για την πληρωμή του εκάστου γεύματος ενώ τα υπόλοιπα 8.5 ευρώ από κάθε εισητήριο θα διατεθούν υπέρ των σεισμοπαθών της Κεφαλλονιάς. Τα παιδιά κάτω των 12 ετών θα εισέρχονται με 15 ευρώ εκ των οποίων τα 9 ευρω θα διατείθενται για το γεύμα και τα εναπομείναντα 6 ευρώ θα συλλεχθούν για τον έρανο. Τα πολύ μικρά παιδάκια, βρέφη και νήπια θα εισέρχονται δωρεάν.

Επίσης θα υπάρξει και λαχειοφόρος για την περαιτέρω ενίσχυση του εράνου και ευχαριστούμε τον φίλο και συμπατριώτη μας Πέτρο Κόνσουλα που ήδη έχει προσφέρει μια από τις καλλιτεχνικές του δημιουργίες. Κάθε άλλη προσφορά για τη λαχειοφόρο από όλους μας θα ήταν ευπρόσδεκτη. Ευχαριστούμε επίσης τη διεύθυνση του εστιατορίου που προσέφεραν το χώρο τους και τα γεύματα σε τιμή κόστους. Λεπτομέρειες για τα μενού προσεχώς.

Για την κράτηση θέσεων παρακαλούμε να αποστείλετε ηλεκτρονικό μήνυμα στη διεύθυνση thomae.kakouli_at_itcarlow.ie μέχρι την Τετάρτη 26 Μαρτίου 2014. Παρακαλούμε να κάνετε τις κρατήσεις σας εγκαίρως για να αποφύγετε απογοήτευση.

Με εκτίμηση

Το Εκκλησιαστικό Συμβούλιο και το ΔΣ της Ελληνικής Κοινότητας