Showing posts with label Mathematics. Show all posts
Showing posts with label Mathematics. Show all posts

07 June 2025

12.5 million blog readers …
but what do 12.5 million
people look like? And what do
12.5 million people need?

On the beach at Platanias near Rethymnon in Crete … Greek airports welcomed over 12.5 million passengers to Greece in the first four months last year (Photograph: Patrick Comerford)

Patrick Comerford

This blog reached yet another new peak at some stage early yesterday morning (6 June 2025), totalling up 12.5 million hits since I first began blogging about 15 years ago, back in 2010.

Yet again, I find this is both a humbling statistic and a sobering figure that leaves me not with a sense of achievement but a feeling of gratitude to all who read and support this blog and my writing.

After I began blogging, it took almost two years until July 2012 to reach half a million readers. It was over a year before this figure rose to 1 million by September 2013. It climbed steadily to 2 million, June 2015; 3 million, October 2016; 4 million, November 2019; 5 million, March 2021; 6 million, July 2022; 7 million, 13 August 2023; 8 million, April 2024; and 9 million, October 2024.

But the rise in the number of readers has been phenomenal over the past few months, reaching 9.5 million on 4 January 2025, 10 million over a week later (12 January 2025), 10.5 million two days after that (14 January 2025), 11 million a month later (12 February 2025), 11.5 million a month after that (10 March 2025), 12 million early last month (3 May 2025), and 12.5 million about a month later, early yesterday (6 June 2025).

Indeed, January 2025 was the first month this blog ever had 1 million hits in one single month – or even within a fortnight – with 1 million hits by mid-January, in the early hours of 14 January, and a total of 1,420,383 by the end of that month (31 January 2025).

In recent months, the daily figures have been overwhelming on occasions. Eight of the 10 days of busiest traffic on this blog were in January 2025 alone, and the other two of those ten busiest days were in this month (June 2025):

• 289,076 (11 January 2025)
• 285,366 (12 January 2025)
• 261,422 (13 January 2025)
• 100,291 (10 January 2025)
• 64,077 (14 January 2025)

• 55,344 (25 January 2025)
• 52,831 (27 January 2025)
• 44,134 (6 June 2025)
• 42,946 (26 January 2025)
• 39,444 (5 June 2025)

This blog has already had almost 3.1 million hits this year, over 20 per cent of all hits ever.

Joseph Heller wrote in Catch-22, ‘Just because you’re paranoid doesn’t mean they aren’t after you.’ But I have noticed that eight of these days were in the week before and after Trump’s inauguration, and that the overwhelming number of hits are not from Ireland, the UK and Greece, as I might expect, but from the US.

The bots at work in Washington must be trawling far and wide for anyone critical of the Trump regime, but I doubt my criticisms of Trump, Vance and Musk are going to make it easy to get a visa to visit the US over the next four years, should I ever want to under the present regime.

Total spending in Lichfield for work on the failed Friarsgate redevelopment and subsequent work on the Birmingham Road site has topped £12.5 million (Photograph: Patrick Comerford)

With this latest landmark figure of 12.5 million hits by yesterday, over 1.4 million hits in January alone, and half a million or more hits within the past month, I once again find myself asking questions such as:

• What do 12.5 million people look like?
• Where do we find 12.5 million people?
• What does £12.5 million, €12.5 million or $12 million mean, or what would it buy?

About 12.5 million Africans were shipped to the Americas during the transatlantic slave trade, between 1526 to 1867. About 12.5 million captured men, women, and children were put on ships in Africa, and of these, 10.7 million arrived in the Americas. The Atlantic slave trade was probably the most costly in human life of all long-distance global migrations.

There are growing concerns that 12.5 million people in the UK have not saved enough or are under-saving for their retirement. Recent research shows that 24% of UK adults, or 12.2 million people, have already missed at least one payment in the last year. More than eight million people across the UK need to get debt advice and more than 12 million more live on the edge.

Yet the Hampton by Hilton at Liverpool John Lennon Airport has been put on the market in recent days with a guide price of £12.5 million.

The Home Office says about 12.5 million people in the UK have a criminal record. The figures relate to the number of criminal records on the Police National Computer (PNC) in April 2024. This means that every year, hundreds of thousands of people face new challenges due to having a criminal record and could be excluded from getting a job, finding somewhere to live or being able to get insurance.

Countries with a population of about 12.5 million include Bolivia, Tunisia and South Sudan. The United Nations has declared South Sudan the site of the world’s largest displacement crisis, with almost 12.5 million people forced to flee their homes, including over 3.3 million refugees who have fled to neighbouring countries.

Cities with a population of about 12.5 million include Guangzhou, Los Angeles and Moscow.

The United Methodist Church, the world’s largest Methodist denomination, has about 12.5 million members.

In the first four months of 2024, Greece’s airports welcomed over 12.5 million passengers. The Greek-owned Aegean Airlines surpassed 12.5 million passengers in the first nine months of 2024, marking a 5% increase compared to the previous year. Greece has received €12.5 million in EU funding to help implement a solar power project on the island of Tilos.

The Ireland-based company behind the Six Nations rugby tournament converted its tournament success into a pretax profit of €12.5 million (£10.5 million) in its last financial year, according to a recent report in The Irish Times. Following a loss of more than £26.2 million in 2023, Six Nations Rugby Limited recorded a profit of £10,500,776 for the year ending 30 June 2024, according to filed accounts.

Aston Villa is monitoring the Nice goalkeeper Marcin Bulka, who would be available for about £12.5 million this summer. Under the guidance of Unai Emery, Villa has secured European football for the third consecutive season, but fell short of a second-straight Champions League campaign on the final day of the Premier League season.

Councillor Sue Woodward, Leader of the Labour group on Lichfield District Council, says the total for work on the failed Friarsgate redevelopment and subsequent work on the Birmingham Road site planning has topped £12.5 million. She says residents in many areas of the district could no longer stomach money continually being pumped into the city alone.

Sotheby’s sold a pair of rare 16th-century Ming Dynasty Chinese jars decorated with orange fish for $12.5 million last November.

The world has a population of 7.75 billion people, and 12.5 million people represent only 0.16% of all those people, a modest number I suppose.

One of the most warming figures personally in the midst of all these statistics is the one that shows how my morning prayer diary continues to reach an average of 60 or 70 people each day in the past month. It is over three years now since I retired from active parish ministry. But I think many of my priest-colleagues would be prayerfully thankful if the congregations in their churches averaged or totalled 420 to 500 people a week.

Today, I am very grateful to all 12.5 million readers and viewers of this blog to date, and for the small core group among you who join me in prayer, reading and reflection each morning.

The United Methodist Church has 12.5 million members … Barbara Heck from Limerick depicted in a window in the UMC Church in Orlando (Photograph: Patrick Comerford)

25 April 2025

Daily prayer in Easter 2025:
6, Friday 25 April 2025,
Friday in Easter Week

The Risen Christ by the shore of Tiberias with the disciples and their catch of fish (John 21: 1-14) … a fresco in Saint Constantine and Saint Helen Church, Rethymnon (Photograph: Patrick Comerford, 2025)

Patrick Comerford

Our Easter celebrations continue in the Church Calendar, and this is still Easter week. In the Orthodox Church, today is known as ‘Bright Friday’, the Friday after Easter, and the feast day of the Theotokos the Life-giving Spring (Ζωοδόχος Πηγή). It is the only feast day that may be celebrated during Bright Week – although many places, in fact, celebrated Saint George on Wednesday.

Before today begins, I am taking some quiet time this morning to give thanks, to reflect, to pray and to read in these ways:

1, reading today’s Gospel reading;

2, a short reflection;

3, a prayer from the USPG prayer diary;

4, the Collects and Post-Communion prayer of the day.

A fisherman tends his boat and his nets in the old harbour in Rethymnon (Photograph: Patrick Comerford, 2025)

John 21: 1-14 (NRSVA):

1 After these things Jesus showed himself again to the disciples by the Sea of Tiberias; and he showed himself in this way. 2 Gathered there together were Simon Peter, Thomas called the Twin, Nathanael of Cana in Galilee, the sons of Zebedee, and two others of his disciples. 3 Simon Peter said to them, ‘I am going fishing.’ They said to him, ‘We will go with you.’ They went out and got into the boat, but that night they caught nothing.

4 Just after daybreak, Jesus stood on the beach; but the disciples did not know that it was Jesus. 5 Jesus said to them, ‘Children, you have no fish, have you?’ They answered him, ‘No.’ 6 He said to them, ‘Cast the net to the right side of the boat, and you will find some.’ So they cast it, and now they were not able to haul it in because there were so many fish. 7 That disciple whom Jesus loved said to Peter, ‘It is the Lord!’ When Simon Peter heard that it was the Lord, he put on some clothes, for he was naked, and jumped into the lake. 8 But the other disciples came in the boat, dragging the net full of fish, for they were not far from the land, only about a hundred yards off.

9 When they had gone ashore, they saw a charcoal fire there, with fish on it, and bread. 10 Jesus said to them, ‘Bring some of the fish that you have just caught.’ 11 So Simon Peter went aboard and hauled the net ashore, full of large fish, a hundred and fifty-three of them; and though there were so many, the net was not torn. 12 Jesus said to them, ‘Come and have breakfast.’ Now none of the disciples dared to ask him, ‘Who are you?’ because they knew it was the Lord. 13 Jesus came and took the bread and gave it to them, and did the same with the fish. 14 This was now the third time that Jesus appeared to the disciples after he was raised from the dead.

A variety of fish in a taverna at the old harbour in Rethymnon … Aristotle taught that there were 153 different species of fish in the Mediterranean (Photograph: Patrick Comerford, 2025)

Today’s Reflection:

This morning’s Easter Gospel reading at the Eucharist (John 21: 1-14) might ask us to think about we mean by success?

The disciples that Sunday morning are not very successful, are they (John 21: 3)? So unsuccessful, indeed, that they are willing to take advice from someone they do not even recognise (verse 4 ff).

The disciples are at the Sea of Galilee or the Sea of Tiberias, back at their old jobs as fishermen. Peter, who denied Christ three times during his Passion, Thomas, who had initially doubted the stories of the Resurrection (see John 20: 24-29), Nathanael, who once wondered whether anything good could come from Nazareth (see John 1: 46), James and John, the sons of Zebedee, who once wanted to be so close to Jesus that they wanted to be seated at his right hand and his left in the kingdom, and two other disciples who remain unnamed … how about that for fame, lasting recognition and success?

They are back on the same shore where there once were so many fish, so much bread left over after feeding the multitude, that they filled 12 baskets (John 6: 1-13). There are not so many fish around this time, at first. But then John tells us that after Christ arrives 153 fish were caught that morning (verse 11).

This number is probably a symbol meaning a complete number. The number 153 is divisible by the sum of its own digits, and it is the smallest number that can be expressed as the sum of cubes of its digits, since 153 = 13 + 53 + 33. Aristotle is said to have taught that there were 153 different species of fish in the Mediterranean.

Whatever they say, the disciples must have thought they had managed the perfect catch that morning.

But the perfect catch was Christ – and, of course, they were the perfect catch for him too. When they came ashore once again he invites them to share bread and fish, to dine with the Risen Lord (21: 12-13).

To eat with the Risen Lord and to invite others to the Heavenly Banquet, so that every creature in heaven and on earth and under the earth and in the sea can say ‘Amen’ before the Throne of God … now that is what I call success (Revelation 5: 11-14).

And when others ask us, Do we love Christ?, when others ask us, Do we love them?, when others ask us, Do we love one another?, will we hesitate, like Peter, not knowing how to answer?

Or when they ask, will the answers be obvious in the ways we worship, in the way we live our lives, in the way we respond to others?

Χριστὸς ἀνέστη!
Christ is Risen!


A lone fishing boat in the old harbour in Rethymnon (Photograph: Patrick Comerford, 2025)

Today’s Prayers (Friday 25 April 2025, Friday in Easter Week):

‘Cross-Cultural Mission at Manchester Airport’ provides the theme this week in ‘Pray With the World Church’, the Prayer Diary of the Anglican mission agency USPG (United Society Partners in the Gospel).’ This theme was introduced on Sunday with reflections by the Revd Debbie Sawyer, Pastoral Chaplain in the Church in Wales and Airport Chaplain, Manchester.

The USPG Prayer Diary today (Friday 25 April 2025, Friday in Easter Week) invites us to pray:

In the likeness of Saint Mark, we pray for ourselves, that we may be true disciples of Christ, boldly proclaiming his Gospel and living humbly with open minds and tender hearts.

The Collect:

Lord of all life and power,
who through the mighty resurrection of your Son
overcame the old order of sin and death
to make all things new in him:
grant that we, being dead to sin
and alive to you in Jesus Christ,
may reign with him in glory;
to whom with you and the Holy Spirit
be praise and honour, glory and might,
now and in all eternity.

The Post-Communion Prayer:

God of Life,
who for our redemption gave your only-begotten Son
to the death of the cross,
and by his glorious resurrection
have delivered us from the power of our enemy:
grant us so to die daily to sin,
that we may evermore live with him in the joy of his risen life;
through Jesus Christ our Lord.

Additional Collect:

God of glory,
by the raising of your Son
you have broken the chains of death and hell:
fill your Church with faith and hope;
for a new day has dawned
and the way to life stands open
in our Saviour Jesus Christ.

Yesterday’s Reflections

Continued Tomorrow

In the dim light, where would we see or recognise Jesus? … by the shores below the Fortezza in Rethymnon earlier this week (Photograph: Patrick Comerford, 2025)

Scripture quotations are from the New Revised Standard Version Bible: Anglicised Edition copyright © 1989, 1995 National Council of the Churches of Christ in the United States of America. Used by permission. All rights reserved worldwide. http://nrsvbibles.org

26 January 2025

73 is a prime number,
or a lucky prime, or even
a star number, rather than
the fading sunset or twilight

No 73 Emerald Hill, Singapore … a prime number that is also a star number (Photograph: Patrick Comerford, 2024)

Patrick Comerford

We RE on our way to the Holocaust Remembrance Day commemorations in Milton Keynes, which may not be the most joyful way to mark or celebrate my birthday this afternoon. Perhaps we shall go for a meal out later in the day, and have a drink in Stony Stratford on the way home to mark the evening.

Shakespeare talks in Sonnet 73 of

… … the twilight of such day
As after sunset fadeth in the west

But I have a lot to be thankful for on this birthday as I look back over the last 73 years.

In those 73 years, I have lived through the reign, rule or time in office of three British monarchs, seven Popes, seven (soon to be eight) Archbishops of Canterbury, eight Irish Presidents, eight Church of Ireland Archbishops of Armagh, 14 (or 15) US Presidents (depending on how you count Trum), 16 Greek heads of state, 17 Taoisigh, 18 British Prime Ministers … it almost sounds like singing out the 12 days of Christmas.

Despite Shakespeare’s words, I still feel as though I am in the prime of my life, as befits reaching yet another prime number, rather than in ‘the twilight of such day’ or even ‘after sunset fadeth in the west’.

The number 73 is a natural number, a prime number, and is what is known in mathematics as a star number, a twin prime, a lucky prime and a sexy prime. It also the number of books in the Catholic Bible, and another way of saying ‘best regards’ when signing off some conversations.

73 as a star number (up to blue dots) … 37, its dual permutable prime, is the preceding consecutive star number (up to green dots)

In mathematics, 73 is the 21st prime number, and an emirp – a prime number that results in a different prime when its decimal digits are reversed – with 37, the 12th prime number. It is also the eighth twin prime, with 71 – a twin prime is a prime number that is either 2 less or 2 more than another prime number, such as either member of the twin prime pair 17 and 19, 41 and 43, or 71 and 73.

The number 73 is the fourth star number. In mathematics, a star number is a centred figurate number, a centred hexagram (six-pointed star), such as the Star of David, or the board Chinese checkers is played on. The numbers 73 and 37 are also consecutive star numbers or equivalently consecutive centred dodecagonal (12-gonal) numbers, respectively the fourth and the third.

The numbers 73 and 37 are successive lucky primes and sexy primes, both twice over. In number theory, a lucky number is a natural number in a set that is generated by a certain ‘sieve’, similar to the sieve of Eratosthenes that generates the primes, but eliminating numbers based on their position in the remaining set, instead of their value. And, in number theory, sexy primes are prime numbers that differ from each other by 6. For example, the numbers 5 and 11 are a pair of sexy primes, because both are prime and 11 – 5 = 6. In the same way, 73 - 67 = 6, and 79 - 73 = 6.

73 at a front door in Stony Stratford (Photograph: Patrick Comerford, 2025)

Amateur radio operators and other morse code users commonly use the number 73 as a ‘92 Code’ abbreviation for ‘best regards’, typically when ending a QSO or a conversation with another operator.

No 73 was a 1980s children's television programme on the ITV network that ran from 1982 to 1988.

In 1982, the TV Times summed up the show: ‘From the outside No. 73 looks like a tumbledown house, but once inside it’s a different world. The house, in the south of England, is rented by an eccentric old lady called Ethel, who is like a fairy godmother to the children in the area.

‘Each week she opens her door and is visited by superstars and famous personalities who provide a madcap spectacle of music, competitions and fun. Ethel is assisted in looking after her guests by her nephew Harry and her boyfriend Percy.’

73, paired with 75, on a front door in York (Photograph: Patrick Comerford, 2025)

In Sonnet 73, William Shakespeare focuses on the theme of old age and uses autumn, twilight and a dying fire as extended metaphors for growing older.

The poet invokes a series of metaphors to characterise the nature of what he sees as his old age. Each of the three quatrains contains a metaphor: Autumn, the passing of a day, and the dying out of a fire. Each metaphor proposes a way the younger person may see the poet.

Sonnet 73, ‘That time of year thou mayst in me behold’, by William Shakespeare:

That time of year thou mayst in me behold
When yellow leaves, or none, or few, do hang
Upon those boughs which shake against the cold,
Bare ruin’d choirs, where late the sweet birds sang.

In me thou see’st the twilight of such day
As after sunset fadeth in the west,
Which by and by black night doth take away,
Death’s second self, that seals up all in rest.

In me thou see’st the glowing of such fire
That on the ashes of his youth doth lie,
As the death-bed whereon it must expire,
Consum’d with that which it was nourish’d by.

This thou perceiv’st, which makes thy love more strong,
To love that well which thou must leave ere long.

‘As after sunset fadeth in the west’ … sunset on the Sarawak River in Kuching (Photograph: Patrick Comerford, 2024)

03 October 2024

DNA and a scientist’s
challenge to racism
show how we are all
related since 1400

The cover of ‘Clancarty: The high times and humble origins of a noble Irish family’ by Rod Smith … launched in London today

Patrick Comerford

Book Launch,
‘Clancarty: The high times and humble of a noble Irish family’
by Rod Smith

Kwanglim Room, Wesley’s Chapel,
City Road, London
2:15 pm, 3 October 2024

Genealogy goes through swings and trends in fashion.

At one time, it was the preserve of titled and landed families, families who appeared in Burke’s or Debrett’s peerage. But that was such a sad way of doing genealogy and of tracing family history. It was reduced to collecting the names and dates of lineal ancestors, often failed to look at contexts or touch the real people, and was oh so badly class laden.

Thankfully, the television series Roots in the mid-1970s created an interest in the genealogy of the oppressed, but also recognised the role of collective family memory in creating identity.

For the past 20 years or more, the television series Who Do You Think You Are? has shown us how the stories of ordinary working class families and families from diverse ethnic and cultural backgrounds have equally colourful and romantic stories to tell.

A new trend has emerged with the popularity and accessibility of cheap DNA tests, which is good for finding long-lost or discreetly hidden half-siblings and lost cousins, but very poor at telling us the real stories that went into creating that sample of spittle.

Genealogy and family trees are always dependent on collective imaginations and identities. In any family tree, some ancestors are counted in and some are counted out. All genealogists make choices that are based on the needs of a family or an individual to provide a colourful illustration of their sense of identity within community, with place and across generations and down through the centuries.

But a new aid that many genealogists are unwilling to give adequate attention to involves the use of mathematical projections.

I was perplexed by the title of Dr Adam Rutherford’s recent book, How to argue with a racist. Genealogy, when properly pursued, shows the inherent stupidity of every form of racism. And Dr Rutherford, in fact, is not arguing with racists – he is totally dismissive of racism, and points out the absurdity of all racist arguments.

One way he does this is through his critical examination of genealogy, its purposes and its methods, in Chapter 2, headed ‘Your ancestors are my ancestors’ (pp 67-107).

He points out that in the study of genetics, there is an assumed generational time of 24 to 30 years, and he points out that in every generation back through time the number of ancestors you have doubles.

What this means is that over a 500-year period, I have 1,048,576 ancestors. By 1,000 years ago, I have 1,099,511,627,776 ancestors – that is, over a trillion people, a number that is about 10 times the number of people that ever existed.

He says, ‘This apparent paradox reveals quite how incorrectly we think about our ancestry.’ Our family trees coalesce and collapse in on themselves as we go back in time. I certainly have a trillion positions on my family tree 1,000 years ago. But the further I go back, the more frequently these positions will be occupied by the same individual multiple times.

He points out that family trees coalesce with startling speed. ‘The last common ancestors of all people with longstanding European ancestries lived only 600 years ago – meaning that if we could draw a perfect family tree for all Europeans, at least one branch on each tree would pass through a single person who lived around 1400 CE. This person would appear on all our family trees, as would all of their ancestors.’

I have taken part in some of the programmes in the series Who Do You Think You Are?. Alan Rutherford recalls an episode in which the actor Danny Dyer found he was 22 generations in direct descent from King Edward III in the 14th century. But, as he points out, ‘the chances of anyone with long-standing British ancestry being similarly descended from Edward III is effectively 100 per cent. It is true for Danny Dyer, and it is true for the majority of British people too.’

It is true for everyone in this room, and it is true for everyone in this new book by Rod Smith that we are celebrating this afternoon.

But it goes so much wider than that. In conversation, a Muslim theologian asked me did I know that as humans we share 50 percent of the same DNA as bananas. Actually, there is some truth to that startling statistic, although it is not the whole truth.

This idea may have originated in a programme in the US run by the National Human Genome Research Institute in 2013 and led by a genetics expert, Dr Lawrence Brody, as part of an educational video from Smithsonian Museum of Natural History, The Animated Genome. That video noted that DNA between a human and a banana is ‘41 percent similar.’

The scientists working with Dr Brody compared the protein sequence from each banana gene to every human gene. Essentially, they took all of the banana genes and compared them one at a time to human genes. Their study shows that about 60 percent of our genes have a recognisable counterpart in the banana genome. ‘Of those 60 percent, the proteins encoded by them are roughly 40 percent identical when we compare the amino acid sequence of the human protein to its equivalent in the banana.’

It may seem shocking that so many genes are similar in two such vastly different things as a person and a banana. But actually, it’s not. ‘If you think about what we do for living and what a banana does there’s a lot of things we do the same way, like consuming oxygen. A lot of those genes are just fundamental to life,’ Dr Brody says.

As humans, we not only just share a high percentage of DNA with bananas – we also share 85 percent DNA with a mouse and 61 percent with a fruit fly. The remarkable thing is that, despite being very far apart in evolutionary time, we can still find a common signature in the genome of a common ancestor. And all of this is because all life that exists on earth has evolved from a single cell that originated about 1.6 billion years ago.

As Dr Brody says gleefully, ‘In a sense, we are all relatives!’

We are all related, but for a long time we have told our stories in different ways, not realising that your story is my story too.

It is a delight to be part of this book, and not just because I have written one of the forewords, taken one of the photographs, and am quoted on the back cover. But there is a way in which the story of the Trench family – and the story of the Guinness family in Rod’s previous book ( Guinness Down Under) – is your story and my story too … and not simply because of DNA tests or mathematical projections.

As Rod points out, the members of the Trench family not special because of an accident of birth or perceptions of inherited privilege. They lived a mixture of high and humble lives. They are part of the broad canvas of Irish history, and they must not be relegated to the margins and the footnotes of Irish social and political history to the footnotes of Irish history.

As I say in my foreword, the way we understand the place of landed, titled families in Ireland and their contribution to Irish life has changed profoundly in recent years.

This reappraisal has been helped, in part, by the Lthe works in refer to at the University of Galway and Maynooth University, and the work of historians in response to the ‘Decade of Centenaries’, including the Easter Rising in 1916, the War of Independence and the Irish Civil War.

In the past, writers were often dismissive of the roles of families such as these, caricaturing them as oppressive or capricious landlords, portraying them as quaint or eccentric, or finding them relative to nation-building narratives only when they included writers such as William Butler Yeats or George Bernard Shaw, or identified with nationalist causes, as with Henry Grattan, William Smith O’Brien or Douglas Hyde.

Too often, the Irish identity of these families was easily questioned or traduced, with pejorative labels such as ‘planters’ or hyphenated stereotyping such as ‘Anglo-Irish’ that doubted their identity and that implied Irish identity depends on particular cultural, linguistic or supposed ethnic backgrounds.

The recent and unsettling rise of populist racism in Ireland is a consequence of cultivating a definition of Irish identity that is neither broad enough nor tolerant enough, that is not visionary enough, to embrace the variety and breadth of ethnicity and culture that contributes to the mosaic making up the full, beautiful, diverse and rich picture of Irish identity.

The contribution of the Trench family to that mosaic is both rich and beautiful in its scope. They were French Huguenots in their origins, so offering an early contribution to linguistic and religious pluralism in Ireland. And their lives have embraced church life, and the cultural, political, architectural, educational and social life of Ireland.

Thankfully, this new book, lavishly illustrated, thoroughly researched and beautifully produced, introduces the truth that the stories of families such as this must never be confined to the margins and the footnotes of Irish social and political history.

In a blog posting last week, I quoted Leo Tolstoy (1828-1910) and his opening sentence in Anna Karenina: ‘All happy families are alike; each unhappy family is unhappy in its own way.’

As you read this book, you will find, contrary to Tolstoy’s oft-quoted saying, that the Trench family has, at times, been a happy family, like all happy families, and at times an unhappy family, ‘in its own way’ too.

But is that not so with all families? It is certainly true of the different branches of Comerford family too, as I know – at times, a happy family, like all happy families, and at times an unhappy family, ‘in its own way’ too.

But then, why should we be surprised? We all share many common ancestors, somewhere in the recent past – recent in terms of European and human history. Enjoy this book, for it offers insights into the stories of your family, and your story too.

What I had planned to say at today’s book launch (Patrick Comerford)

Daily prayer in Ordinary Time 2024:
145, Thursday 3 October 2024

72 on a front door in St Albans … but is this a significant number? (Photograph: Patrick Comerford, 2024)

Patrick Comerford

We are continuing in Ordinary Time in the Church Calendar. The week began with the Eighteenth Sunday after Trinity (Trinity XVIII), and the calendar of the Church of England in Common Worship today remembers the life and ministry of George Bell (1881-1958), Bishop of Chichester, Ecumenist and Peacemaker.

I have a busy day ahead, speaking in Wesley’s Chapel, London, later this afternoon at the launch of Rod Smith’s new book, Clancarty: The high times and humble origins of a noble Irish family. But, before today gets busy, I am taking some quiet time this morning to give thanks, and for reflection, prayer and reading in these ways:

1, today’s Gospel reading;

2, a reflection on the Gospel reading;

3, a prayer from the USPG prayer diary;

4, the Collects and Post-Communion prayer of the day.

Tradition says the degrees of Jacob’s Ladder were 72 in number

Luke 10: 1-12 (NRSVA):

1 After this the Lord appointed seventy others and sent them on ahead of him in pairs to every town and place where he himself intended to go. 2 He said to them, ‘The harvest is plentiful, but the labourers are few; therefore ask the Lord of the harvest to send out labourers into his harvest. 3 Go on your way. See, I am sending you out like lambs into the midst of wolves. 4 Carry no purse, no bag, no sandals; and greet no one on the road. 5 Whatever house you enter, first say, “Peace to this house!” 6 And if anyone is there who shares in peace, your peace will rest on that person; but if not, it will return to you. 7 Remain in the same house, eating and drinking whatever they provide, for the labourer deserves to be paid. Do not move about from house to house. 8 Whenever you enter a town and its people welcome you, eat what is set before you; 9 cure the sick who are there, and say to them, “The kingdom of God has come near to you.” 10 But whenever you enter a town and they do not welcome you, go out into its streets and say, 11 “Even the dust of your town that clings to our feet, we wipe off in protest against you. Yet know this: the kingdom of God has come near.” 12 I tell you, on that day it will be more tolerable for Sodom than for that town.’

Shanah Tovah … the Jewish New Year celebrates the birthday of the universe

‘Celebrating the birthday of the universe’

Rosh Hashanah (רֹאשׁ הַשָּׁנָה‎), the Jewish New Year, celebrates the birthday of the universe, the day God created Adam and Eve. This year, Rosh Hashanah 5785 began yesterday evening at sundown on the eve of Tishrei 1 (2 October 2024) and ends tomorrow evening after nightfall on Tishrei 2 (4 October 2024). Together with Kol Nidrei (Friday 11 October) and Yom Kippur (Saturday 12 October), it is part of the Yamim Nora’im, the Days of Awe or High Holidays, and the 10 Days of Repentance.

Most synagogues and Jewish communities held Erev Rosh Hashanah services yesterday evening (Wednesday) and are holding Rosh Hashanah services today (Thursday). The central observance of Rosh Hashanah is blowing the shofar (ram’s horn), normally blown in synagogues as part of today’s services. Tashlich, in which people stand near a body of water and ask God to cast away sins, takes place in the late afternoon on the first day of Rosh Hashanah.

Rosh Hashanah traditions include round challah bread studded with raisins and apples dipped in honey, as well as other foods that symbolise wishes for a sweet year. Other Rosh Hashanah observances include candle lighting in the evenings and refraining from creative work.

Tonight is the second night of Rosh Hashanah, when the traditions include: prayer services in the synagogue, just like the first night; holiday candles, with the added blessing of Shehecheyanu; Kiddush over wine, with Shehecheyanu, if it was not said when lighting candles; a new fruit, enjoyed immediately after Kiddush; and a round challah, often studded with raisins. The festive meal, which is prepared after nightfall, typically does not include apples in honey, fish head, and the other symbolic foods enjoyed the night before.

The Number 72 on a garden fence in the Coffee Hall estate in Milton Keynes (Photograph: Patrick Comerford, 2024)

Today’s Reflection:

The Gospel reading at the Eucharist today (Luke 10: 1-12) tells of the sending out of the 72, or the 70, depending on which translation we are reading and which manuscripts the translations give greater weight to. In the Eastern Christian traditions, they are known as the 70 or 72 apostles, while in Western Christianity they are usually described as disciples.

The number 70 may derive from the 70 nations in Genesis 10, but the number 72 may represent the 12 tribes, as in the significance of the number of translators of the Septuagint, the symbolism of three days (24 x 3), and understanding the meaning of 144 (12 x 12), to appear again in the 144,000 in the Book of Revelation.

In translating the Vulgate, Jerome selected the reading of 72. In modern translations, the number 72 is preferred in the NRSV, NIV, ESV and the New Catholic Bible, for example, but 70 figures in the NRSV Anglicised (NRSVA) and the Authorised or King James Version.

In number theory, 72 is the natural number after 71 and before 73, prime numbers. It is a pronic number, as it is the product of 8 and 9, it is the smallest Achilles number, as it is a powerful number that is not itself a power.

The number 72 is an abundant number. With exactly 12 positive divisors, including 12 (one of only two sublime numbers), 72 is also the twelfth member in the sequence of refactorable numbers. It has a Euler totient of 24, which makes it a highly totient number, as there are 17 solutions to the equation φ(x) = 72, more than any integer below 72. It is equal to the sum of its preceding smaller highly totient numbers, 24 and 48, and contains the first six highly totient numbers 1, 2, 4, 8, 12 and 24 as a subset of its proper divisors.

The number 144, or twice 72, is also highly totient, as is 576, the square of 24. While 17 different integers have a totient value of 72, the sum of Euler’s totient function φ(x) over the first 15 integers is 72. It also is a perfect indexed Harshad number in decimal (28th), as it is divisible by the sum of its digits (9).

In addition, 72 is the second multiple of 12, after 48, that is not a sum of twin primes. It is, however, the sum of four consecutive primes (13 + 17 + 19 + 23), as well as the sum of six consecutive primes (5 + 7 + 11 + 13 + 17 + 19). Also, 72 is the first number that can be expressed as the difference of the squares of primes in just two distinct ways: 112 − 72 = 192 − 172.

In science, 72 is the atomic number of hafnium, and in degrees Fahrenheit 72 is 22.22 Celsius and is considered to be room temperature.

Biblically, tradition says 72 is the number of languages spoken at the Tower of Babylon. The degrees of Jacob’s Ladder (Genesis 28:10-19) were 72 in number, according to the Zohar, a foundational work of Kabbalistic literature.

The conventional number of scholars involved in translating the Septuagint was 72, not 70, with six Hebrew scholars drawn from each of the 12 tribes. According to tradition, Ptolemy II Philadelphus sent 72 Hebrew scholars and translators from Jerusalem to Alexandria to translate the Tanakh from Biblical Hebrew into Koine Greek, for inclusion in his library.

According to Kabbalah, 72 is the number of names of God. In Kaballah, the Shem HaMephorash (שֵׁם הַמְּפֹרָשׁ) or ‘the explicit name’ of God is composed of 72 letters. The 72-fold name is derived from a reading of Exodus 14:19-21. Kabbalist legend says the 72-fold name was used by Moses to cross the Red Sea, and that it could grant later holy men the power to cast out demons, heal the sick, prevent natural disasters, and even kill enemies. This, of course, relates directly to the commission of the 72 in Saint Luke’s Gospel.

So, having turned 72 earlier this year, having arrived at my prime – or, at least, between two prime numbers – perhaps I am best served at room temperature. I am now a powerful number, suited to translation, ready to be sent out.

I once stayed at the Tamworth Arms at 71-72 Lichfield Street, almost directly across the street from the Moat House, the former Comberford family home. The Cock Hotel in Stony Stratford, where the choir of Saint Mary and Saint Giles Church regularly adjourns after Wednesday evening rehearsals, is at 72 High Street.

But what is there to look forward after 72?

When the long-serving Labour MP for Rochdale Sir Tony Lloyd earlier this year at the age of 73, the Guardian reported him as saying some years ago: ‘There’s this recognition that you only have a certain time left … I’m 70, and as such you think, “Well, I’m probably not going to be around in X years’ time, so use these years wisely. Use these days wisely.” That’s good advice for us all.’

Of course that’s good advice for us all. But surely there is more to look forward to than merely counting the X number of years ahead, to something that has more meaning than what is left of my mere temporal existence.

The Tamworth Arms at 71-72 Lichfield Street, Tamworth … known locally as ‘The Bottom House’ (Photograph: Patrick Comerford)

Today’s Prayers (Thursday 3 October 2024):

The theme this week in ‘Pray With the World Church’, the Prayer Diary of the Anglican mission agency USPG (United Society Partners in the Gospel), is ‘One God: many languages.’ This theme was introduced on Sunday in reflections by Rachel Weller, Communications Officer, USPG.

The USPG Prayer Diary today (Thursday 3 October 2024) invites us to pray:

Let us pray for a world where language diversity is celebrated as a testament to the beauty of God’s creation, and where people of all languages and cultures come together in solidarity, recognising that we are all children of the same divine creator.

The Collect:

Almighty and everlasting God,
increase in us your gift of faith
that, forsaking what lies behind
and reaching out to that which is before,
we may run the way of your commandments
and win the crown of everlasting joy;
through Jesus Christ your Son our Lord,
who is alive and reigns with you,
in the unity of the Holy Spirit,
one God, now and for ever.

The Post Communion Prayer:

We praise and thank you, O Christ, for this sacred feast:
for here we receive you,
here the memory of your passion is renewed,
here our minds are filled with grace,
and here a pledge of future glory is given,
when we shall feast at that table where you reign
with all your saints for ever.

Additional Collect:

God, our judge and saviour,
teach us to be open to your truth
and to trust in your love,
that we may live each day
with confidence in the salvation which is given
through Jesus Christ our Lord.

Yesterday’s reflection

Continued tomorrow

The Cock Hotel at 72 High Street, Stony Stratford … where the choir of Saint Mary and Saint Giles Church regularly adjourns after Wednesday rehearsals (Photograph: Patrick Comerford, 2024)

Scripture quotations are from the New Revised Standard Version Bible: Anglicised Edition copyright © 1989, 1995 National Council of the Churches of Christ in the United States of America. Used by permission. All rights reserved worldwide. http://nrsvbibles.org

25 January 2024

Being served at room
temperature at 72,
defending the poor, and
crushing the oppressor

72 on a front door in St Albans … but is this a significant number? (Photograph: Patrick Comerford, 2024)

Patrick Comerford

I have spent much of the day in Birmingham at a training day in Acocks Green for the trustees of almshouses. It has been a long day, beginning with long train journeys, and this evening I am on my way back by train again and bus to Stony Stratford.

I have had time on these journeys to think about my birthday tomorrow and to reflect on the significance of reaching the age of 72.

In number theory, 72 is the natural number after 71 and before 73, both prime numbers. It is a pronic number, as it is the product of 8 and 9, it is the smallest Achilles number, as it is a powerful number that is not itself a power.

The number 72 is an abundant number. With exactly 12 positive divisors, including 12 (one of only two sublime numbers), 72 is also the twelfth member in the sequence of refactorable numbers. It has a Euler totient of 24, which makes it a highly totient number, as there are 17 solutions to the equation φ(x) = 72, more than any integer below 72. It is equal to the sum of its preceding smaller highly totient numbers, 24 and 48, and contains the first six highly totient numbers 1, 2, 4, 8, 12 and 24 as a subset of its proper divisors.

The number 144, or twice 72, is also highly totient, as is 576, the square of 24. While 17 different integers have a totient value of 72, the sum of Euler’s totient function φ(x) over the first 15 integers is 72. It also is a perfect indexed Harshad number in decimal (28th), as it is divisible by the sum of its digits (9).

In addition, 72 is the second multiple of 12, after 48, that is not a sum of twin primes. It is, however, the sum of four consecutive primes (13 + 17 + 19 + 23), as well as the sum of six consecutive primes (5 + 7 + 11 + 13 + 17 + 19). Also, 72 is the first number that can be expressed as the difference of the squares of primes in just two distinct ways: 112 − 72 = 192 − 172.

In science, 72 is the atomic number of hafnium, and in degrees Fahrenheit 72 is 22.22 Celsius and is considered to be room temperature.

Tradition says the degrees of Jacob’s Ladder were 72 in number

Biblically, tradition says 72 is the number of languages spoken at the Tower of Babylon. The degrees of Jacob’s Ladder (Genesis 28:10–19) were 72 in number, according to the Zohar, a foundational work of Kabbalistic literature.

The conventional number of scholars involved in translating the Septuagint was 72, not 70, with six Hebrew scholars drawn from each of the 12 tribes. According to tradition, Ptolemy II Philadelphus sent 72 Hebrew scholars and translators from Jerusalem to Alexandria to translate the Tanakh from Biblical Hebrew into Koine Greek, for inclusion in his library.

The Gospel reading tomorrow for the Feast of Saint Timothy and Saint Titus, (Luke 10: 1-9), tells of the sending out of the 72, or the 70, depending on which translation you are reading. In the Eastern Christian traditions, they are known as the 70 or 72 apostles, while in Western Christianity they are usually described as disciples. Tradionally they are said to include Saint Timothy and Saint Titus.

The number 70 may derive from the 70 nations in Genesis 10, but the number 72 may represent the 12 tribes, as in the significance of the number of translators of the Septuagint, the symbolism of three days, and understanding the meaning of 144 (12 x 12), to appear again in the 144,000 in the Book of Revelation.

In translating the Vulgate, Jerome selected the reading of 72. In modern translations, the number 72 is preferred in the NRSV, NIV, ESV and the New Catholic Bible, for example, but 70 in the NRSV Anglicised and the Authorised or King James Version.

According to Kabbalah, 72 is the number of names of God. In Kaballah, the Shem HaMephorash (שֵׁם הַמְּפֹרָשׁ) or ‘the explicit name’ of God is composed of 72 letters. The 72-fold name is derived from a reading of Exodus 14:19-21. Kabbalist legends say the 72-fold name was used by Moses to cross the Red Sea, and that it could grant later holy men the power to cast out demons, heal the sick, prevent natural disasters, and even kill enemies. This, of course, relates directly to the commission of the 72 in Saint Luke’s Gospel.

So, at 72, having arrived at my prime – or, at least, between two prime numbers – perhaps I am best served at room temperature. I am now a powerful number, suited to translation, ready to be sent out.

The Tamworth Arms at 71-72 Lichfield Street, Tamworth is known locally as ‘The Bottom House’ (Photograph: Patrick Comerford)

I once stayed at the Tamworth Arms at 71-72 Lichfield Street, almost directly across the street from the Moat House, the former Comberford family home. The Cock Hotel in Stony Stratford, where the choir of Saint Mary and Saint Giles Church regularly adjourns after Wednesday evening rehearsals, is at 72 High Street.

But what is there to look forward after 72?

When the long-serving Labour MP for Rochdale Sir Tony Lloyd last week at the age of 73, the Guardian reported him as saying some years ago: ‘There’s this recognition that you only have a certain time left … I’m 70, and as such you think, “Well, I’m probably not going to be around in X years’ time, so use these years wisely. Use these days wisely.” That’s good advice for us all.’

Of course that’s good advice for us all. But surely there is more to look forward to than merely counting the X number of years ahead, to something that has more meaning than what is left of my mere temporal existence.

My life is filled with love and with a sense of purpose. I am looking forward not only to my 72nd birthday tomorrow, but, in the words of Psalm 72, to something beyond my own interest at my own age, including justice, righteousness and long life, so that that those with power and in government may defend the poor, deliver the needy and crush the oppressor, so that righteousness may flourish and peace abound. Perhaps the expected general election later this year will result in a promise of that future. I live in hope.

‘May the kings of Tarshish and of the isles render him tribute, may the kings of Sheba and Seba bring gifts’ (Psalm 72: 10) … the visit of the Magi in the Basilica of Sant’Apollinare Nuovo in Ravenna (Photograph: Patrick Comerford)

Psalm 72 is a prayer for eternal life, for God’s blessings for ever. It is a song praying for gifts for ‘the king,’ including justice, righteousness and long life, so that he may defend the poor, deliver the needy and crush the oppressor and that righteousness may flourish and peace abound.

Psalm 72 is traditionally seen as being written by King Solomon, but some commentators suggest it was written by David to express his hope for Solomon.

Some commentators say the psalm contains memories of the Queen of Sheba visiting Solomon and the Temple in Jerusalem, and associate it with the anointing of Solomon as king while David was still living (see I Kings 1: 39-43).

Some commentators see David’s prayers fulfilled in some sense in the reign of Solomon: a temple will be built and there will be great peace and prosperity; yet the language is larger than Solomon: ‘May his glory fill the whole earth’ (verse 19).

This psalm is also recommended in many lectionaries for Sundays in this time of Epiphany. The psalmist mentions the kings of three areas: Tarshish, thought to be present-day Spain; the Isles, which may refer Crete and Cyprus; and Sheba and Saba, present-day Yemen, with its capital at Saba.

They bring together the trade routes across the breadth of the whole Mediterranean, and from Jerusalem to the tip of the Arabian Peninsula at the entrance to the Indian Ocean and the African coast. In this way, they symbolise poetically all earthly rulers.

The psalmist prays these three kings may bring gifts to the one true king, who delivers the needy, hears the cry of the poor, has pity on the week, saves the needy, delivers them from oppression and violence, redeems their lives and saves them from bloodshed.

‘May he judge your people with righteousness, and your poor with justice’ (Psalm 72: 2) … 72 on a front door in St Albans (Photograph: Patrick Comerford, 2024)

Psalm 72 (NRSVA):

Of Solomon.

1 Give the king your justice, O God,
and your righteousness to a king’s son.
2 May he judge your people with righteousness,
and your poor with justice.
3 May the mountains yield prosperity for the people,
and the hills, in righteousness.
4 May he defend the cause of the poor of the people,
give deliverance to the needy,
and crush the oppressor.

5 May he live while the sun endures,
and as long as the moon, throughout all generations.
6 May he be like rain that falls on the mown grass,
like showers that water the earth.
7 In his days may righteousness flourish
and peace abound, until the moon is no more.

8 May he have dominion from sea to sea,
and from the River to the ends of the earth.
9 May his foes bow down before him,
and his enemies lick the dust.
10 May the kings of Tarshish and of the isles
render him tribute,
may the kings of Sheba and Seba
bring gifts.
11 May all kings fall down before him,
all nations give him service.

12 For he delivers the needy when they call,
the poor and those who have no helper.
13 He has pity on the weak and the needy,
and saves the lives of the needy.
14 From oppression and violence he redeems their life;
and precious is their blood in his sight.

15 Long may he live!
May gold of Sheba be given to him.
May prayer be made for him continually,
and blessings invoked for him all day long.
16 May there be abundance of grain in the land;
may it wave on the tops of the mountains;
may its fruit be like Lebanon;
and may people blossom in the cities
like the grass of the field.
17 May his name endure for ever,
his fame continue as long as the sun.
May all nations be blessed in him;
may they pronounce him happy.

18 Blessed be the Lord, the God of Israel,
who alone does wondrous things.
19 Blessed be his glorious name for ever;
may his glory fill the whole earth. Amen and Amen.

20 The prayers of David son of Jesse are ended.

The Cock Hotel at 72 High Street, Stony Stratford … where the choir of Saint Mary and Saint Giles Church regularly adjourns after Wednesday rehearsals (Photograph: Patrick Comerford, 2024)

01 November 2023

Making sense of 144,000
in the Book of Revelation
and world population figures
on All Saints’ Day, 2023

Part of Fra Angelico’s altarpiece for the convent of San Domenico in Fiesole, near Florence

Patrick Comerford

Today (1 November) is All Saints’ Day, a celebration in the Church Calendar that dates back to Pope Gregory III (731-741). He dedicated a chapel to All Saints in Saint Peter’s in Rome on 1 November to honour ‘the holy apostles and … all saints, martyrs, and confessors, … all the just made perfect who are at rest throughout the world.’

One of the outstanding depictions of All Saints is a five-panel altarpiece made by Fra Angelico’s workshop for the convent of San Domenico in Fiesole, near Florence.

Although the altarpiece was made in his workshop, it is not sure whether Fra Angelico (1395-1455) painted the work himself as he regularly had others do the actual painting. Gold leaves were used in altarpieces like this, and he paint is tempera, a mix of colour pigments with egg yolk that is long lasting. The blue colour was made with the expensive lapis lazuli.

Part of Fra Angelico’s altarpiece for the convent of San Domenico in Fiesole, near Florence

The first of the three lectionary readings for All Saints Day today is:

9 After this I looked, and there was a great multitude that no one could count, from every nation, from all tribes and peoples and languages, standing before the throne and before the Lamb, robed in white, with palm branches in their hands. 10 They cried out in a loud voice, saying,

‘Salvation belongs to our God who is seated on the throne, and to the Lamb!’

11 And all the angels stood around the throne and around the elders and the four living creatures, and they fell on their faces before the throne and worshipped God, 12 singing,

‘Amen! Blessing and glory and wisdom
and thanksgiving and honour
and power and might
be to our God for ever and ever! Amen.’

13 Then one of the elders addressed me, saying, ‘Who are these, robed in white, and where have they come from?’ 14 I said to him, ‘Sir, you are the one that knows.’ Then he said to me, ‘These are they who have come out of the great ordeal; they have washed their robes and made them white in the blood of the Lamb.

15 For this reason they are before the throne of God,
and worship him day and night within his temple,
and the one who is seated on the throne will shelter them.
16 They will hunger no more, and thirst no more;
the sun will not strike them,
nor any scorching heat;
17 for the Lamb at the centre of the throne will be their shepherd,
and he will guide them to springs of the water of life,
and God will wipe away every tear from their eyes.’ (Revelation 7: 9-17)

In the verses immediately before this reading, we are told:

‘Do not damage the earth or the sea or the trees, until we have marked the servants of our God with a seal on their foreheads.’

4 And I heard the number of those who were sealed, one hundred and forty-four thousand, sealed out of every tribe of the people of Israel:

5 From the tribe of Judah twelve thousand sealed,
from the tribe of Reuben twelve thousand,
from the tribe of Gad twelve thousand,
6 from the tribe of Asher twelve thousand,
from the tribe of Naphtali twelve thousand,
from the tribe of Manasseh twelve thousand,
7 from the tribe of Simeon twelve thousand,
from the tribe of Levi twelve thousand,
from the tribe of Issachar twelve thousand,
8 from the tribe of Zebulun twelve thousand,
from the tribe of Joseph twelve thousand,
from the tribe of Benjamin twelve thousand sealed. (Revelation 7: 3-8)

I love the clear implication that the salvation of humanity is directly and intricately intertwined with the command, ‘Do not damage the earth or the sea or the trees.’

The number 144,000 is a natural number. It is significant in many religious traditions and belief systems. The number 144,000 appears three times in the Book of Revelation, in this passage (Revelation 7: 3-8), and in two other places:

Then I looked, and there was the Lamb, standing on Mount Zion! And with him were one hundred and forty-four thousand who had his name and his Father’s name written on their foreheads (Revelation 14: 1).

3 and they sing a new song before the throne and before the four living creatures and before the elders. No one could learn that song except the one hundred forty-four thousand who have been redeemed from the earth. 4 It is these who have not defiled themselves with women, for they are virgins; these follow the Lamb wherever he goes. They have been redeemed from humankind as first fruits for God and the Lamb, 5 and in their mouth no lie was found; they are blameless. (Revelation 14: 3-5)

The number 12 is used throughout the Bible to symbolise completeness, perfection, and God’s power. Think for a moment of the 12 tribes of Israel or 12 disciples of Christ. There are also 12 patriarchs from Seth to Noah; 12 patriarchs from Shem to Jacob; 12 spies led the way into the Promised Land; there were 12 judges from Othniel to Samuel; and King David appointed 24 groups of 12 (a total of 288) to lead music of praise in the temple (I Chronicles 25).

Exodus 39: 14 recalls there Aaron’s breastplate had 12 precious stones, ‘corresponding to the names of the sons of Israel; they were like signets, each engraved with its name, for the twelve tribe.’

All Saints’ Day is the Patronal Festival in All Saints’ Church, Margaret Street, London

The figure 12 also has symbolic significance in the New Testament. Christ promises the disciples, ‘Truly I tell you, at the renewal of all things, when the Son of Man is seated on the throne of his glory, you who have followed me will also sit on twelve thrones, judging the twelve tribes of Israel’ (Matthew 19: 28).

Saint Mark’s Gospels recalls how in one hour, Jesus heals a woman who had been bleeding for 12 years and then goes immediately to restore to life a girl who is 12 years old. The first woman is older, with a continual flow of blood, losing hr life blood; the young girl is given back her life blood and comes to life. Both touch Christ and after 12 years are restored to new life (Mark 5: 25-42).

In the Book of Revelation, Christ makes a similar promise to some who will come out of the last age of the church, known as Laodicea (which means ‘judging the people’): ‘To the one who conquers I will give a place with me on my throne, just as I myself conquered and sat down with my Father on his throne’ (Revelation 3: 21).

Revelation describes two groups of 12 (a total of 24) elders who sit around the throne of God, representing the 12 tribes in the Hebrew Bible and the 12 apostles in the New Testament (Revelation 4: 4). One vision in Revelation tells how a ‘great portent appeared in heaven: a woman clothed with the sun, with the moon under her feet, and on her head a crown of twelve stars’ (Revelation 12: 1). The 12 stars above the woman’s head are a symbol of the leadership of the church (I Corinthians 11: 10).

That great city, the holy Jerusalem … had a wall great and high, and had twelve gates, and at the gates twelve angels, and names written thereon, which are the names of the twelve tribes of the children of Israel … the holy city Jerusalem coming down out of heaven from God … has a great, high wall with twelve gates, and at the gates twelve angels, and on the gates are inscribed the names of the twelve tribes of the Israelites … And the wall of the city has twelve foundations, and on them are the twelve names of the twelve apostles of the Lamb (see Revelation 21: 10-14).

The foundation stones of the New Jerusalem (see Revelation 21: 19, 20) appear to be identical to the 12 precious stones on Aaron’s breastplate (Exodus 39: 14).

The figurative use of the whole number 1,000 is also found throughout the Bible. For example, God increases the number of the Israelites 1,000 times (Deuteronomy 1: 11); God keeps the covenant to 1,000 generations (Deuteronomy 7: 9); and God owns the cattle on 1,000 hills (Psalm 50: 10). Other examples are found in Exodus 20: 6; and II Samuel 18: 12; Psalm 84: 10; and Isaiah 60: 22.

The number 12 becomes a symbol of totality, and when it is squared and multiplied by 1,000 it acquires more emphasis. With 1,000 as a multiplier of 12, the numbers 12,000 and 144,000 are imbued with a particular significance that is interpreted variously in Christianity. Some take the numbers in the Book of Revelation to be symbolic, representing all God's people throughout history in the heavenly Church.

All Souls’ Day is being celebrated in Saint Editha’s Church, Tamworth, tomorrow

Even in conversation, I often find any discussion of the number 144,000 is met by references to the belief among Jehovah’s Witnesses that exactly 144,000 faithful Christians from the year 33 AD until the present day will be resurrected to heaven as immortal spirit beings to spend eternity with God and Christ, serving as king-priests for 1,000 years. They believe all other people accepted by God will have an opportunity to live forever in a restored paradise on earth.

Popular interpretations of the number 144,00, from Jehovah’s Witnesses to literalist evangelicals and fundamentalists, miss out on the interesting poetical and mathematical richness and significance of the number 144,000.

I try to imagine how many people are needed to make up 144,000 people in any one place at any one time. When I was working as a journalist, there were conflicting claims from the police and organisers about the number of people on the streets at any protest or march. To arrive at an impartial estimate, you would count how many people passed one point in a minute, and then multiply that figure by the number of minutes it took the marchers to pass that particular place.

Of course, adjustments had to be made. There are always bottlenecks that hold up a protest for minutes on end, and marches always have gaps and trail off at the end. But, with those allowances, it was a fairly accurate way of making an impartial count.

Inside All Saints’ Church, Margaret Street, London (Photograph: Patrick Comerford, 2023)

If the Book of Revelation is finding a poetic way of describing 144,000 passing through one particular point over one 24-hour period, that is a vast number: 6,000 people every hour, 100 people every minute, 2 or 3 people every second.

If the Book of Revelation is describing two lots of 144,000 people – one group of 144,000 standing on Mount Zion, and a second group of 144,000 before the throne – then we are talking about 288,000 people. In a 24-hour day, that would involve 12,000 people passing by every hour, or 200 every minute in a day.

The numbers 12, 60 and 144,000 are part of our cultural heritage dating back to Ancient Near East or Middle East societies. Sumerians looked to the heavens when they Invented the system of time we use to this day. It may seem curious that we divide the hours into 60 minutes and the days into 24 hours.

We use a multiple 12 rather than 10 because when the ancient Sumerians were inventing time, they did not operate on a decimal (base-10) or duodecimal (base-12) system but a sexagesimal (base-60) system.

For those ancient Sumerian innovators, who first divided the movements of the heavens into countable intervals, 60 was the perfect number. The number 60 can be divided by 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, and 30 equal parts. Moreover, ancient astronomers believed there were 360 days in a year, a number that 60 fits neatly into six times.

The Sumerian Empire may not have lasted for long. But, for more than 5,000 years, the world has continued to use its calculations when it comes delineating time.

All Saints’ Church, Calverton, near Stony Stratford, Buckinghamshire, dates from the 12th century and was rebuilt in 1818 and 1824 (Photograph: Patrick Comerford)

In a burst of imagination on this All Saints’ Day, I thought of the figure 144,000 in the Book of Revelation as a poetic adaptation of Ancient Near East mathematical philosophy, and 144,000 are invited into the Kingdom of God, every day since, say the year 1 CE, for the past 2023 years, the total of people involved is 106,401,708,000. And if there two groups of 144,000 people in the Book of Revelation, that number doubles to 212,803,416,000.

And if the work of salvation is retrospective, going back in time as well as forward in time, perhaps that number could be doubled to at least 425,606,832,000, but probably much, much more.

That is more people than the number of people living today.

That is more people than the number of people who have ever lived on earth.
The UN estimates that the world population in mid-2023 is 8.1 billion (8,045,311,447).

In research for the National Library of Medicine some years ago, C Haub asked, ‘How many people have ever lived on earth?’ Assuming a constant growth rate and birth rates of 80 per 1,000 through to 1 AD, 60 per 1,000 from 2 AD to 1750, and the low 30s per 1,000 by modern times, he concluded 105 billion people have lived on earth, of whom 5.5% are alive today.

An earlier date for the appearance of human life on earth would raise the numbers. But any figures we come to are surpassed excessively by any number of people we could ever imagine ever alive on earth.

I am overwhelmed.

God’s love embraces more people than I can ever imagine, or could ever possibly exist in time, past, present or future. God’s love is beyond measure, is beyond limit, and the saints we celebrate and rejoice with today are beyond any number I can imagine or calculation you or I can make.



09 May 2022

Paolozzi’s statue inspired by
Blake and Newtown brings
together belief and reason

Sir Eduardo Paolozzi’s 12-ft bronze sculpture of Sir Isaac Newton outside the British Library (Photograph: Patrick Comerford, 2022)

Patrick Comerford

As two of us walked from Euston station to King’s Cross at the weekend, we stopped at the British Library to admire Sir Eduardo Paolozzi’s magnificent 12-foot bronze sculpture of Sir Isaac Newton.

Paolozzi’s statue in the Piazza was completed in 1995. It depicts Sir Isaac Newton in his search for knowledge, and has become, perhaps, the British Library’s most famous resident.

Paolozzi’s Newton is inspired by William Blake’s 1795 watercolour of Newton (1795) illustrating how Newton’s equations changed our view of the world to being one determined by mathematical laws.

Blake’s original watercolour shows Newton surrounded by the glories of nature but oblivious to it all. Instead, he is focused on reducing the complexity of the universe to mathematical dimensions, bending forward with his compass.

Paolozzi’s six-tonne sculpture was cast by the Morris Singer Foundry, established in 1848 and best known for the Trafalgar Square lions.

Sir Eduardo Luigi Paolozzi (1924-2005) was a Scottish artist, known for his sculpture and graphic works. He is widely considered to be one of the pioneers of pop art. His interpretation of Newton was inspired by both Newton and Blake together – one representing science and the other representing poetry, art and the imagination.

He decided that this synthesis would be perfect for the British Library: ‘While Blake may have been satirising Newton, I see this work as an exciting union of two British geniuses. Together, they present to us nature and science, poetry, art, architecture – all welded, interconnected, interdependent.’

For example, in this sculpture, Newton’s body resembles a mechanical object, joined with bolts at the shoulders, elbows, knees and ankles, demonstrating the relationship between nature and science.

The architect Sir Colin St John Wilson commissioned this sculpture as it embodies the purpose of the British Library as a place serving humanity’s endless search for truth, both in the sciences and the humanities.

The statue is based on an extremely rare colour print and watercolour of Newton by William Blake that is now in the Tate Gallery. It is so rare, in fact, that only two versions of this print exist.

The mathematician, philosopher, physicist, astronomer, alchemist, theologian and author Sir Isaac Newton (1642-1727) is widely recognised as one of the greatest mathematicians and physicists of all time and among the most influential scientists, and he was a key figure in the Enlightenment. His book, Philosophiæ Naturalis Principia Mathematica (1687), established classical mechanics. He formulated the laws of motion and universal gravitation that formed the dominant scientific viewpoint until it was superseded by the theory of relativity.

Newton was a fellow of Trinity College Cambridge and the second Lucasian Professor of Mathematics at the University of Cambridge. He was a devout but unorthodox Christian who privately rejected the doctrine of the Trinity. He refused to take holy orders in the Church of England, unlike most fellows of Cambridge colleges in the day.

He spent the last three decades of his life in London, as Warden (1696-1699) and Master (1699-1727) of the Royal Mint, and was President of the Royal Society in 1703-1727.

The poet, painter, and printmaker William Blake (1757-1827) was largely unrecognised when he died 100 after Newton. as an English. Today, however, Blake is seen as a seminal figure in the history of the poetry and the visual art of the Romantic Age. He lived almost his entire life in London and produced a diverse and symbolically rich collection of works that embrace the imagination as ‘the body of God’ or ‘human existence itself.’

Blake’s great works of art include his ‘Ancient of Days’ (1794), drawing on Daniel 7, while his best-known poem is ‘Jerusalem.’ In that poem, Blake described England over 200 years ago as a ‘green and pleasant land.’ When his poem was slightly altered by the composer Sir Hubert Parry, it became the unofficial anthem of England.

The poem, written as a tribute to John Milton, was inspired by a myth that Christ once travelled to England with Joseph of Arimathea, and that they had visited Glastonbury. This myth is reflected in the original title of Blake’s short poem, ‘And did those feet in ancient time.’

Blake’s ‘green and pleasant land’ is contrasted sharply in his poem with an England that is being overrun by ‘dark Satanic Mills.’

It is not that Blake is yearning for a flight to the countryside from the cities of the Industrial Revolution. But looking at the Albion Flour Mills built in Southwark by John Rennie and Samuel Wyatt, he saw this tall new building as a symbol of the destruction of another era and of the oppression of the workers and their families.

Blake saw the new cotton mills and collieries of his time as a mechanism for the enslavement of the masses and the destruction of culture:
‘And all the Arts of Life they changed into the Arts of Death in Albion ...’

The words of the anthem are, paradoxically, an apocalyptic warning about a future England that is faced with choice between either embracing a more open way of life or of oppressing the masses.

William Blake’s notebook, with drafts of his poems and many drawings, is part of the manuscripts collection at the British Library. In Folio 12 in his notebook (‘The Rossetti Manuscript’), in pen and black ink with pencil, Blake has written part of the poem ‘You don’t believe’ along the left-hand edge.

In this poem Blake refers to Newton:

You don’t believe — I won’t attempt to make ye:
You are asleep — I won’t attempt to wake ye.
Sleep on! sleep on! while in your pleasant dreams
Of Reason you may drink of Life’s clear streams.
Reason and Newton, they are quite two things;
For so the swallow and the sparrow sings.

Reason says ‘Miracle’: Newton says ‘Doubt.’
Aye! That’s the way to make all Nature out.
‘Doubt, doubt, and don’t believe without experiment’:
That is the very thing that Jesus meant,
When He said ‘Only believe! believe and try!
Try, try, and never mind the reason why!’


So, in Paolozzi’s sculpture at the British Library, Blake’s belief in miracles can be seen to provide a contrast to Newton’s self-excluding observational stance.

Sir Eduardo Paolozzi’s sculpture of Sir Isaac Newton was inspired by William Blake’s watercolour (Photograph: Patrick Comerford, 2022)