15 July 2014

St Swithin

St Swithun's day if thou dost rain
For forty days it will remain
St Swithun's day if thou be fair
For forty days 'twill rain nae mare

It’s the Feast Day of St Swithin’s Day today, 15 July. At the time of his death (on 2 July 862) he was Bishop of Winchester. The legend goes that Swithin desired to be buried outside  Winchester Cathedral, and he was. However, about a century later he was reinterred inside; well mostly, for various bits of his mortal remains were buried elsewhere. He supposedly showed his displeasure at being buried inside; there was heavy rainfall, hence the saying. But of course, it might have been a coincidence, and the saying is apparently later than the time of his reinterment.

It hasn’t rained here today—so far.

14 July 2014

Black is better than Orange

On 13 July, the Royal Black Presbytery gathers and marches to Scarva for the “Sham Fight”. The RBP was founded a couple of years after the Orange Order; members are exclusively drawn from the Order, and it acts as a “senior” establishment. It’s seen as a superior society, more exclusive and less actively political, and promotes itself as a fraternal society. It proclaims:

The Royal Black Institution is totally based on the teachings of Holy Scripture and is committed to the furtherance of the Christian message of the Cross. In adhering firmly to the traditions of the Reformed Christian Faith, no offence is intended to anyone or to any group.

As 13 July 2014 was a Sunday, the demonstration will be today, 14 July.

Prince William, on his journey to the Boyne and the meeting with James, is said to have camped at Scarva, at a large chestnut tree which is still (said to be) extant. Neither type of chestnut is native to Ireland; both grow to become very large trees. The sweet chestnut is from the mediterranean and was probably introduced to Britain by the Romans; it can live for many centuries. The horse chestnut is unrelated, and not as long-lived.

The “Sham Fight”, the event for which the day is famous, is a miniature reconstruction of the Battle of the Boyne; a number of horsemen take part, as do King James and King William (“King Billy”). William always wins.

There is usually a large audience, perhaps 100,000. It’s generally peaceful, unlike the Orange processions and demonstrations which in the past have been associated with sectarian rioting.


For many years Sir Norman Stronge, 8th baronet, was the Sovereign Grand Master of the Royal Black Preceptory. He was active in politics, and was Speaker of the House of Commons in the N Ireland parliament at Stormont.

He was murdered by the IRA in 1981 at his home, Tynan Abbey, co Armagh. His only son was also murdered with him, both men being shot before the house was burnt down. It was impossible to decide which of the two men had died first; the deaths were taken to be “simultaneous”. A legal fiction recognised that in such cases, the elder of the two had died first. Thus Sir Norman’s son would have become the 9th baronet, though this remains unproven. The baronetcy now appears to be extinct. In such instances of simultaneous death, taxes on inheritance on the second death are given concessionary treatment.

13 July 2014

Just when is the 12th?

The Orange parades yesterday passed without serious sectarian trouble. I mentioned some of the myths around this celebration yesterday, particularly that it was a celebration of the Battle of the Boyne on the 12th July 1690.

But it wasn’t on 12 July. So how did this confusion arise?

At that time, there were two calendars in use in Europe. The original was the Julian calendar, but as this “ran slow” compared to easily observable celestial events, such as the solstices and equinoxes, it gave the “wrong” days for religious ceremonies. In particular, Easter, the most important event in the Christian year was clearly incorrect. Most religious festivals were on fixed days, such as 25 December for the Nativity. But Easter is different, and has to be calculated.

The Council of Nicea in 325 AD, set the method: Easter is on the Sunday after the paschal full moon, that is the full moon which falls on or soon after the spring equinox. The Church decided that the spring equinox is on 21 March (though more often it is on 20 March), and the full moon is 14 days after a new moon.

To solve the difficulty of Easter falling on the “wrong” date needed reform of the calendar; this was undertaken by Pope Gregory, and is named after him. A method of calculating Easter was then devised, and remains current. Eastern Orthodox churches still use the Julian calendar for dating Easter, so the same event is celebrated on different days. Though suggestions for a fixed date for Easter are regularly advanced, a fixed date has not been achieved.

When Britain changed to the Gregorian calendar in 1752, a method of determining Easter devised on Golden Numbers and Sunday Letters was devised, though it gives identical results to the Gregorian method. You could say that it uses entirely artificial full moons.

Anyway, it was the Easter problem that required sorting using a reformed calendar. The differences between the old Julian calendar and the new Gregorian calendar are not fixed, rather they increase by 1 day every 128 years.

So, in 1690 there were 10 days difference, with 1 July being then equivalent to 11 July. In 1752, there were 11 days difference, so 1 July in the Old Style was equivalent to 12 July in the New Style. This coincidence with the Battle of Aughrim on 12 July 1691 Old Style and the New Style date then for the Battle of the Boyne probably accounts for the amalgamation of the two events, and the widespread belief that the Boyne was actually on 12 July.

There are now 13 days difference; so to recalculate the date of the Boyne today would mean it was on (the equivalent of) 14 July.

12 July 2014

The "Twelfth"

It is old but it is beautiful, and its colours they are fine
It was worn at Derry, Aughrim, Enniskillen and the Boyne.
My father wore it as a youth in bygone days of yore,
And on the Twelfth I love to wear the sash my father wore.

It’s the “Twelfth” today, July 12, and the day on which Orangemen parade to commemorate and celebrate the victory of King William over King James at the Battle of the Boyne on that day in 1690, and their part in the engagement; bands play such favourites as “The Sash”.

There certainly was a Battle of the Boyne, but it wasn’t on 12 July; if William won, it wasn’t a decisive victory—that came a year later; the battle was a minor, peripheral event in the overall picture in Europe. And there weren’t any Orangemen present; and they don’t wear sashes today.

If that’s confusing, let’s try to clear things up; it’s all very complicated and confusing, and a full explanation would take a very thick academic textbook. So, no apologies for the simplification.

King Charles II died in 1685 without legitimate offspring, though he had thirteen natural ones.[1] His brother succeeded to the throne as James II. Charles was a protestant, James a catholic—such a mixture of belief among siblings was common enough then. If James was tolerant[2] of protestants[3] (though this may have been designed to improve the position of catholics), it does seem that he nurtured a desire to return England to the ‘old religion’. James’s daughter Mary was a protestant, and was married to his nephew, the Dutch[4] Prince William of Orange.[5] William was a grandson of Charles I. At the time of James’s succession, his heir was Mary, and for many it seemed as if a protestant succession was assured. However, James then had a son, also James (the old pretender)[6] in June 1688, raising fears that England could indeed revert to catholicism, or at the very least the supremacy of the established, protestant Church of England would be seriously challenged. Charles I was, or at least thought he was, an absolute ruler, King by “Divine Right”; parliamentarians disagreed with this, engaged him in the Civil War, and executed him on 30 January 1649. There were fears that James II wanted to be an absolute ruler; his friendship with the King of France was likewise unsettling.

Meanwhile, on the European continent, King Louis XIV of France, the Sun King, an absolute monarch, was making trouble. His aim was to strengthen his borders, which meant expansion into the territory of others. He had already revoked the Edict of Nantes in 1685; this had tolerated the protestant population of France. After this, they were obliged to leave, as Huguenots, finding refuge in more friendly countries, such as Switzerland, England and the low countries, where they spread tales of Louis’s anti-protestant atrocities. Louis also gave tacit support to the Ottoman Turks, who were attacking Europe from the east.

Prince William was the prime mover in a protestant coalition against Louis, the League of Augsburg, or Grand Alliance. Even the Pope was concerned with Louis’s activities, and at times supported the League. The League fought against Louis in the Nine Years’ War[7] between 1688 and 1697; the Battle of the Boyne was just a part of this War.

William was a canny political operator. He realised that England’s help would be valuable in the fight against Louis; his acceptance of an offer of the English crown (jointly with Mary) wasn’t made out of religious sentimentality, but from cunning pragmatism. His marriage to Mary was engineered to improve his claim to the English crown.

William sailed on 11 November for England, landing on 5 November. That’s not a mistake, nor was William a time traveller. Rather, the low countries had adopted the Gregorian or New Style calendar, even if it was a Popish invention, while England remained on the Julian[8] or Old Style calendar. At that time, there were 10 days difference, with the New Style (NS) being ahead of the Old Style (OS). Britain didn’t convert to the Gregorian calendar until 1752, when there were 11 days difference. To clarify; William sailed on 1/11 November, landing of 5/15 November.

James soon left England, ultimately reaching Ireland where he could rely on the support of the native population; rather surprisingly, there were elements of the protestant elite who also supported him. Even more surprisingly, it is said that the Pope sent forces to fight on William’s side.

The Battle of the Boyne was fought on 1 July 1690 (OS), though some sources suggest it was 30 June; very little in Ireland is straightforward. William ‘won’, but the engagement wasn’t decisive. It wasn’t until the Battle of Aughrim, which was fought on 12 July 1691, that James’s forces were fully defeated. On that occasion the Jacobite[9] forces were commanded by a French general. After his defeat at the Boyne, James left Ireland very rapidly, earning himself the soubriquet Séamus an Chaca or James the Shit.

The original “Twelfth” actually celebrated and commemorated this final victory in Ireland. The Battle of the Boyne was on 1 July (OS), or 11 July (NS), close enough to the twelfth for the two to be amalgamated.

Fast forward a century; there were land disputes between protestant “Peep-o-Day” boys and catholic “Defenders” which resulted in a skirmish in September 1795, at which about 30 catholics were killed in the Battle of the Diamond. The Orange Order was formed later that day in nearby Loughgall, co Armagh. It was a protestant and trinitarian[10] order, with a similar structure to Masonic lodges. Depending on your sensibilities, it either upholds protestant civic and religious freedoms, or is sectarian, triumphalist and supremacist.

Orangemen today don’t wear a sash, rather they wear a “collarette” around their necks. Their uniform is completed, at least in posher lodges, by a sober suit, white gloves, a bowler hat[11] and an umbrella.

The song “The Sash” began as “Molly-o”, apparently in America; it was originally about the love of a man for his girl. Her father forbade it, he lamented it:

Tell me who is that poor stranger that lately came to town

And like a pilgrim all alone, he wanders up and down

He's a poor forlorn Glasgow lad and if you would like to know

His heart is breaking all in vain for Irish Molly-o

She is young and she is beautiful and her likes I've never known

The lily of old Ireland and the primrose of Tyrone

She's the lily of old Ireland and no matter where I go

My heart will always hunger for my Irish Molly-o

Oh but when her father heard of this a solemn vow he swore

That if she wed a foreigner, he would never see her more

He called for young MacDonald and he plainly told him so

I'll never give to such as you my Irish Molly-o

MacDonald heard the heavy news and sadly he did say

Farewell my lovely Molly, I am banished far away

Till death shall come to comfort me and to the grave I go
My heart will always hunger for my Irish Molly-o

So, William, of “glorious, pious and immortal memory” was more concerned with opposing Louis and consolidating his position on the throne; the Battle was more political that religious; Orange isn’t in Holland, the Battle of the Boyne wasn’t on 12 July, and the celebrations were originally for another battle; Orangemen weren’t present at the Boyne, and they don’t wear sashes today.

Just don’t let the facts get in the way of mythologies.

The Lodge members (Brethren) meet in a Hall such as this one. The Parish Church is in the background, beside the modern Church Hall.

1 One son, the Duke of Monmouth was a claimant to the throne after Charles’s death. Monmouth’s rebellion of 1685 was crushed, many of the participants were executed at Judge Jeffrey’s Bloody Assize. Through two other lines, the present Duke of Cambridge is a descendant.

2 Through the Declaration of Indulgence which granted religious freedom; it was vigorously resisted by Anglicans.

3 James gave the pension promised to Nell Gwynn by his brother Charles on his deathbed—“let not poor Nelly starve”. Nell was once mistaken for another of the King’s mistresses, the frenchwoman and catholic Louise de Kérouaille, by an angry mob. She responded: "Good people", she said, smiling, "you are mistaken; I am the Protestant whore."  One of her sons by Charles was created Duke of St Albans.

4 France, Holland etc are names used for convenience; they were not coterminous or politically identical to the countries as we know them today.

5 Orange was actually located in Provence in France; William was a prince of the house of Orange-Nassau, and principal Stadtholder of the United Provinces or Dutch Republic. The territory was seized by Louis XIV, ceasing to exist as a sovereign entity.

6 James I’s grandson was Charles Edward Stuart, Bonnie Prince Charlie, the young pretender.

7 Not to be confused with another Nine Years’ War, or Tyrone’s Rebellion a century before. This rebellion was against the English rule, and was supported by the Spanish. Its defeat resulted in the Flight of the Earls in 1607, and the Plantation of Ulster.

8 The Julian calendar is named after Julius Caesar who introduced it. It was calculated by Sosigenes, Cleopatra’s scientific adviser. It was accurate to 10 days in 1500 years. In the Gregorian calendar, the new year began on 1 January, rather than 25 March.

9 James is from an anglicisation of the French variation of the Latin Iacobus or Jacob. Hence, James’s supporters were called Jacobites, as were James’s successors.

10 The Order is more tolerant of protestant variation today.

11 The bowler hat was originally protective headwear for servants, only later being adopted by the upper echelons.

11 July 2014

11 July—the Eleventh Night

Traditionally, on 11 July bonfires (pronounced “bone-fires”) are lit in Belfast and other places in N Ireland. They are said to commemorate the signal fires lit for William of Orange on his passage to and through N Ireland before his engagement with King James II at the Battle of the Boyne.

In recent years, such bonfires have become vast pyramids of wooden pallets and sometimes tyres, and may be adorned with viciously anti-catholic sectarian slogans.

Wikipedia has a short article about the eleventh night, here. The date of the Battle of the Boyne, given there as 12 July 1690, is wrong; see here. The French troops who supported William were protestant Huguenots, for the catholic King Louis XIV supported James politically and militarily. 

09 July 2014

On this day; 9 July 1921

On 9 July 1921 a truce was agreed between the Irish Republican Army and the British government.

The pressures for Home Rule in Ireland had been present for decades, if partially put into abeyance during the Great War. There was the Easter Rising in 1916, when an Irish Republic was declared, but this rebellion was soon ended. Even in the fateful weeks before the declaration of war against Germany on 4 August 1914, the British government was at least as much concerned with the Irish Problem as they were with far-away difficulties on the European continent.

At the end of the Great War negotiations continued against a continuing background of resistance to Home Rule in the north-east of the Ireland. There, loyalists were as prepared to fight to remain within the United Kingdom as their fellow islanders further south were prepared to fight for independence.

The chronology of the period is confusing and confused, with assorted groups of republicans having differing ideas of what Home Rule might actually mean. Originally, it implied self-determination, without any clear indication of either independence or a republic, and these political differences persisted. Further, many if not all republicans envisaged a republic that encompassed the entire island.

The UK parliament passed the Government of Ireland Act 1920, creating two entities, one in the north, one in the south. The intention was that both entities would remain part of the United Kingdom, and foresaw the eventual reunification of the island.

In the general election of 1918, Sein Féin won a landslide of the votes in the south, and promptly withdrew from the UK parliament at Westminster, forming their own government, the Dáil Éireann, and declaring independence, UDI—a “unilateral declaration of independence”. Almost simultaneously, a guerilla war against the British began, mostly in the south. To counter this, and the Royal Irish Constabulary who were often the main focus of the attacks, the British government recruited ex-army veterans in Britain, and sent them to Ireland. These troops were called the “Black and Tans” after the colour of their uniforms. Both sides in this War of Independence were responsible for considerable violence, atrocities and reprisals; the war persisted without a clear winner well into 1921.

Established under the provisions of the Government of Ireland Act, the parliament of Northern Ireland was convened, with the official opening on 22 June 1921, by King George V. The King was a man of modest intellectual abilities, a man who seemed to prefer stamp collecting to almost anything else; he had previously refused his cousin, Tsar Nicholas, refuge in the country, even though the tsar had been offered safe passage by the Russian revolutionaries. However, the activities of the Black and Tans were bad enough to concern the King’s sensibilities. He was originally to have delivered an anodyne speech; but with the assistance of his friend Jan Smuts, the prime minister of the Union of South Africa, what he actually delivered was as different as it was well received by all sides; it was, effectively, a fait accompli. At one point he asked,

all Irishmen to pause, to stretch out the hand of forbearance and conciliation, to forgive and to forget, and to join in making for the land they love a new era of peace, contentment, and good will

The British prime minister, David Lloyd George wrote to the leader of Sinn Féin, Éamon de Valera suggesting a conference, which the latter agreed to. A truce was agreed upon, on 9 July, to come into effect on 11 July.

Negotiations began soon afterwards, leading to the Anglo-Irish Treaty. However, this was not acceptable to some, the anti-treaty group; the Irish Civil war between them and the pro-treaty lobby was inevitable. This lasted until the middle of 1923, when the anti-treaty group were defeated.

Matters didn’t end there; the south of Ireland only became a fully independent state in 1949; the problem of the border between the two parts of Ireland was never properly resolved; political tensions remained between the two parts; and even the name of this new country remained—and remains—problematic.

05 July 2014

On this day, 1948: the NHS

On 5 July 1948 the National Health Service was born. It aimed to provide comprehensive medical treatment to all which was fee at the point of service. If the birth was straightforward, the gestation certainly wasn’t.

Previously, medical care had to be paid for, if you were sufficiently rich; if you were poor, you might end up in a Voluntary hospital, effectively a charitable institution at which consultants worked for “the honour”, usually appearing for a couple of half-days a week. The rest of their time their business was the business of making money. If you could afford to, you could attend a general practitioner; and if you were poor you usually had to do without.

In the Welsh valleys, the local population formed associations and opened community hospitals from the early part of the 20th century. These provided care for all members of the community. The best known now was at Tredegar; Tredegar was also the birthplace of Aneurin Bevan, and the system of the funding and provision of the community hospital there was the model for the future NHS; the NHS was conceived in Tredegar.

The system of voluntary hospitals had to be considerably strengthened during WW2 because of the numbers of civilian casualties; at the same time it was recognised that the voluntary hospitals were largely bankrupt.

The Beveridge report was published in 1942. It was an enquiry into social conditions in the UK, and identified five “giant evils”, squalor, ignorance, want, idleness, and disease.

There was strong medical opposition to the concept of an NHS initially; many feared the loss of their independence, becoming merely functionaries of the state, and their earnings. General practitioners did not become employees of the state, rather they became self-employed contractors to the NHS. Their NHS earnings had been estimated from their income tax returns. Unfortunately, many GPs were paid not in cash but in kind, and did not represent this on their returns. It’s quite possible that many had also been economical with the actualitié, but they could hardly complain. The remuneration of hospital consultants was worked out on the back of a fag packet (literally) by Bevan and Lord Moran, the president of the Royal College of Physicians, and a man largely removed from the realities of everyday life, even though his brother was a GP in Barrow-in-Furness. Bevan later confided that he had been willing to pay up to three times the rate agreed with Lord Moran. If this wasn’t enough, Bevan also agreed a system of “merit awards”, by which consultants could enrich themselves; or as Bevan himself put it, he “stuffed their mouths with gold”.

These pecuniary inducements, along with general sensibilities, were enough to overturn the British Medical Association’s views, and the profession accepted the NHS.

Originally, there was a totally naive view that the vast health improvements would lead to a decrease in the cost of the NHS budget; this never happened, and funding for the service has remained a difficult political problem.

In infancy, childhood and now maturity the NHS has been subject to many “reforms”. “Reform” in NHS-speak does not mean improvement, rather it is synonymous with “saving money” or doing something political for the sake of it, or to enhance politicians’ egos. If the service that the NHS supplies must now be “evidence-based”, such an evidence base is unnecessary for politicians to speak of “reform”.

The infant that was born with such promise 66 years ago did indeed grow into a pretty healthy child and young adult. In its early forties, it suffered a classic mid-life crises with the advent of “managers”, an administrative layer previously unnecessary. And now, as an old age pensioner, there are the inevitable signs of all the stresses and strains of the years: what was once, perhaps, the envy of the world is now seen as such only by the unsighted.

04 July 2014

Today, 4 July: A boat beneath a sunny sky

Today is the 4th July; it is celebrated as Independence Day in the United States.

It’s also the anniversary of a boat trip, “all in the golden afternoon”, along the River Thames in 1862. Three young girls were taken on the journey by two clerics. A book of the story that was told to the girls was subsequently published, followed by a companion volume a few years later. This second books ends with an untitled poem, one of the poet's finest:

A boat beneath a sunny sky,
Lingering onward dreamily
In an evening of July—

Children three that nestle near,
Eager eye and willing ear,
Pleased a simple tale to hear—

Long has paled that sunny sky:
Echoes fade and memories die.
Autumn frosts have slain July.

Still she haunts me, phantomwise,
Alice moving under skies
Never seen by waking eyes.

Children yet, the tale to hear,
Eager eye and willing ear,
Lovingly shall nestle near.

In a Wonderland they lie,
Dreaming as the days go by,
Dreaming as the summers die:

Ever drifting down the stream—
Lingering in the golden gleam—
Life, what is it but a dream?

The poem does refer to the original trip. It’s an acrostic; take the initial letter of each line to discover who is being referenced.

03 July 2014

Cot death, Sally Clark and the prosecutor's fallacy

Sally Clark was an English solicitor who was prosecuted for the murder of two of her infant children. Her defence was that the deaths were both “cot death”, also known as “Sudden Infant Death Syndrome” or SIDS.

She was initially convicted. Much weight was given to the evidence of a medical expert, Sir Roy Meadow. He was a paediatrician and an expert in child abuse. He wasn’t a statistician. Using statistics from reports about SIDS, he estimated the chance of a cot death was 1:8543, and therefore the chance of a second was about 1:73,000,000. He arrived at this latter figure by multiplying 8543 by itself, squaring it.

Her conviction was upheld at a first appeal. However, at a second appeal she was acquitted, not because the statistics and calculations were incorrect (which they were), but because there was evidence of bacterial infection in the second child, information which was previously withheld from the defence. Sadly, the story does not have a happy ending; Sally Clark was found dead from acute alcoholic poisoning about four years after her acquittal.

I followed the first trial in the newspapers. I remember being distinctly disturbed by what I read; an intuition if you like, that there was something wrong, even though I understood that intuition is often a very poor guide to the results of mathematical calculations. It has taken me to now to understand what was going on.

I was reminded of the case of Sally Clark by reading Math on Trial by the mother and daughter Leila Schneps and Coralie Colmez. They are both mathematicians, and their book concentrates on the uses and abuses of maths in court cases. As such, it concentrates on the mathematics used in trials; the mathematics are often statistics and probability, and at times I found it really hard going.


SIDS is a description, not a cause. It is applied to cases of natural death in infants, where no definite cause has been found. The causes of SIDS are usually felt to be a combination of genetic and environmental factors, even if these are either unknown or poorly understood. It hardly needs saying, that even if the cause or causes or SIDS are not known, this does not mean that there are no causes.

At the time of her first trial there were known associations with SIDS, such as smoking, maternal age and unemployment. As ever, an association is nothing more than that, it is not causation. Further, it was found that SIDS was rare in Hong Kong; the explanation was that there infants sleep on their backs, rather than face down. The subsequent “Back to Sleep” is said to have reduced the SIDS rate by about 50%. Again, the sleeping position is an association, not a causation. (The mechanism may relate to breathing patterns and brain wave activity which differ depending on the infants’ sleeping position.)

Murder is the unlawful killing of a human with malice aforethought (that is, intent). Usually, the prosecution must actively show and prove the means, method and opportunity of the perpetrator.

The Trial

Essentially, the prosecution argument was: either the deaths were due to SIDS, or murder. We will show, they implied, that SIDS is so mathematically unlikely, that the infants must have been murdered. That is, we will prove her guilt, not by proving her guilt, but by proving that she could not be innocent. This is a reversal of the usual ‘innocent until proven guilty’ rule. This distinction seems not to have been apparent at the time.

Professor Sir Roy Meadow was a paediatrician, famous for his descriptions of Munchausen’s Syndrome by Proxy, and child abuse. The original Munchausen’s Syndrome was described by Richard Asher; he found that there were patients who would self-harm to gain attention and satisfy their inner desires. Sir Roy extended this to parents (usually mothers) who harmed their children to satisfy their (maternal) needs. In child abuse, he is said to have coined “Meadow’s Law”, which is that “one death is a tragedy, two are suspicious, and three are murder”. This is almost a restatement of the quotation attributed to Joseph Stalin, that “one death is a tragedy, a million is a statistic”.

Sir Roy produced the 1:8543 incidence from a report; he did not accept the rather different figures from a similar report. This incidence relates to people in Sally Clark’s socio-economic group, and who aren’t smokers, unemployed or below 27 years of age. Boys are also more likely to die of SIDS than girls, compounding the overall possibilities. The real overall incidence of SIDS at that time seems to be 1:1300. “Seems” because the Back to Sleep campaign may have had an influence, and because if a registered cause of death is given as SIDS, and later information indicates a different diagnosis, the Registrar-General’s records will be changed. A subsequent search of the records may therefore not be complete, and reports and statistics on SIDS are often compiled retrospectively.

Sir Roy squared the 1:8543 figure to get 1;73,000,000. By itself this arithmetic is correct. But the (hidden) assumption is that two cot deaths are entirely unrelated, and this is incorrect. They are neither independent or “non-conditional”,  rather they are two events in which common factors (genetic and environmental) cannot be excluded Technically, two such events are described as a conditional probability. The mathematics underlying this is really very difficult for a non-expert.

Neither Sir Roy or the prosecution produced any statistics about double murders of infants.  The correct use of statistics in this case would be a comparison of the probabilities of double murder and the probabilities of double SIDS, not the presentation of only one “side” of the argument. There are other possibilities, such as one murder and one SIDS.

This misuse of statistics is known as the prosecutor’s fallacy, and is an example of Berkson’s paradox. This paradox arises when conditional probability is mistaken for unconditional probability.

Determining how often a second infant dies of SIDS is not easy. The best evidence I can find suggests that there is a dependency of between 5 and 10 in the case of a second death; that is, there is such an increased chance of a second death from SIDS. Intuitively, I would expect that a second death would be more common after a first, even if I could not quantify it. I would base this intuition on similar genetic and environmental conditions. Further, the possibility of a second murder does seem to be much less common after a first, and much less common than a double SIDS. In part, this may be because the murderer is likely to be imprisoned.

The figures of “5” and “10” have been produced from data relating to the incidence of SIDS. They have not been produced by “pure” mathematics, that is where there is a known correlation between two things, this has been factored in.

Evidence of the frequency of double murder was not given at the first trial; if it had, and a proper comparison of the rates of double murder and SIDS had been made available, it is very unlikely that she would have been convicted on statistical evidence alone. The medical evidence was not conclusive, showing no definite evidence of abuse or the lack of abuse. The infection that the second infant had was not disclosed; ultimately this proved vital.

If you are like me, you are probably finding all this statistical stuff confusing. Let us go through the logic and statistics step-by-step. I have rounded the figures to make the calculations more obvious.

The 1:8543 ratio (hereafter 1:8000) refers to a subset of people whose babies had died from SIDS. About 400,000 babies are born in the UK every year. Thus, if we take 1:8000 and divide this into 400,000 we find that 50 babies die of SIDS in a year. But, it is known that around 200 babies die of SIDS annually. We can only use the figure of 1:8000 if we know what subset of 400,000 it refers to—and we don’t. Overall, 200 babies in a population of 400,000 is 1:2000. So, you might say that Sally Clark’s subset had only a quarter of cases of SIDS compared to the general population. This isn’t relevant.

Around 20 to 30 infants were known to have been murdered annually. This represents 1:20,000 to (about) 1:13300. Thus, an infant is more likely to die from SIDS than to be murdered by a factor between 7 and 10.

Sir Roy squared 1:8000 to get 1:64,000,000 (actually 1:8543 to get 1:73 million). If we square 1:2000 we get 4,000,000. Likewise from 1:20,000 we get 1:400,000,000; and from 1:13300 we get about 177,000,000. Now, which is the most likely scenario?

So, even if we treat the two events as totally independent, which they aren’t, we can still show that SIDS is more likely than murder. We should realise that the events aren’t independent, but we cannot anyway easily quantify this. We might say that the dependency between two cases of SIDS and two murders are likely to be similar; but this is an unsupported supposition.


This picture, via Reuters, shows Sally Clark at the time of her release from prison; it speaks for itself:

Sir Roy Meadow was later struck off the General Medical Register, but reinstated on appeal.

The pathologist who performed the post mortem on the second infant was found guilty of serious professional misconduct by the General Medical Council.

The rules for expert witnesses were made more explicit; the expert was to provide a report for the benefit of the court; no matter whether instructed by the prosecution or the defence, the report should be unbiased. Expert witnesses were not expected to go further than their area of expertise. The evidence of an expert witness alone was no longer sufficient for a successful prosecution.

The cases of other women who had been convicted of murder were investigated; two had the conviction released, a third was acquitted.

DNA databases have been used as a “cold” trawl, trying to find matches. If there is no other evidence, this again is a prosecutor’s fallacy. If the evidence is confirmatory, the confirmation is likely to be correct. Prosecutors have been made aware of this problem, and to treat conclusions from DNA trawls cautiously.

And I, who was so disturbed by the initial conviction, did little about it until now.


In this instance, the court clearly didn’t fully understand why the statistics were wrong. The judge did warn the jury to use them with caution; understandably, the apparent conclusiveness of 1:73,000,000 must have played a large part in their determinations. It was a majority verdict, with two jurors not convinced.

Still, statistics and their misuse isn’t an easy subject. While advocates pride themselves on their ability to master a brief in a very short time, it cannot be possible for anyone to attain the level of knowledge and expertise that an expert has gained over years of study and work. Further, advocates and courts seem to have problems with “science” as a discipline. Either they seem to be overawed by it, or they find the ramifications to be so complicated that they ignore them as being not relevant.

The common law system is adversarial, that is, one side pits its strengths against the other. You can almost see it as a descendant of a trial by strength, or a joust. And at the end, despite the statue of Justicia and the designation, courts in this system do not dispense justice, they give law. The Code Napoleon is used as the basis of the legal system in many European countries; it is investigative, and certainly seems to be designed to discover the “truth”. As such, it might be regarded as superior to common law, but it’s unclear if it is actually any more accurate.

There’s another problem with courts. Giving evidence is straightforward, but cross examination is more difficult. To be a successful witness requires the ability to think rapidly to the questions that are put. It’s often said that advocates in court only ask questions to which they already know the answers, or think they know the answers. Yet, as their understanding is likely to be incomplete, their questions can be “para-relevant”, ones that cannot be easily answered in a sentence, rather they require considerable explanation. The perceived need for rapid answers is potentially dangerous; while “fast” thinking is useful for everyday problems, ones that we have previously encountered, “slow” thinking is much more appropriate to difficult problems, including ones that we haven’t previously met. But courts like certainty; a witness who is direct and who can answer questions without needing to think about them is likely to be favoured over one who is hesitant, who seems unable to provide a “yes or no” answer, and who needs time to think.

Some evidence was withheld at the first trial. There are rules about what is allowable and what is not allowable at trials. But the active withholding of evidence is not one of them. It is arguable that the pathologist who found bacterial infection, but didn’t reveal it, exhibited confirmation bias. Confirmation bias occurs when the conclusion is predetermined, and (subsequent) findings contrary to the conclusion are ignored. Confirmation bias is one reason for cross-examination.

Judges are supposed to be able to weigh evidence, and to base their conclusions on this. They also provide a summary at the end of a jury case, indicating, inter alia, areas of greater or lesser certainty; but what if they don’t really understand the evidence? Is a summary or judgement based on incomplete understanding of evidence which may be incomplete really valuable or reliable? Are judges able to think logically; above all, do they see faults in logic which bias their findings?

Resources and references

For a fuller account of Sally Clark’s trial, see the Wikipedia page here.

Math on Trial is available from amazon, here.

Both these sources indicate the cultural background at the time of the first trial.

For considerably more detail on the mathematics and statistics, see Dawid’s opinion, here; and Hill’s calculation of the probability of two cot deaths, here.

Wikipedia has details of the prosecutor’s fallacy here, and details of Berkson’s paradox here.

NB: be aware that these mathematical positions are very technical in parts, and are not easy to understand. I found it equally difficult to render their exactitude into common language.

Thinking, Fast and Slow, by Daniel Kahneman is also available from amazon, here.

Members of math.stackexchange.com helped with the mathematics, and supplied references.


As a former medical professional, I understand the medical issues here, even if my memory of statistics is rusty. As a parent of a daughter who died from cot death, I’m not an unbiased observer.