22 February 2019
Whilst studying an old
stone tablet containing a mathematics lesson for some Iraqi children around
1500BC, Ernst Weidner alerted the world of mathematics to the possibility that
the Pythagorean Theorem was well known a millennium before Pythagoras.
Unfortunately, when he was
studying the tablet in 1916, part of it was missing. It wasn’t discovered until
the 1980s. At that time, Christopher Walker was looking through the vast supply
of stone fragments in the British Museum.
Quite by chance, he
discovered the piece of stone which was missing from Weidner’s mathematics
lesson. On it was direct evidence that the Pythagorean Theorem was known to the
people of Iraq around 1500BC! But it took 3,500 years to declare it to the
21 February 2019
Pythagoras was a Greek mathematician living around 500BC. He is credited with what has become known as ‘The Pythagorean Theorem’. This gives us a fundamental property of a right-angled triangle.
Essentially, when we square
the length of the hypotenuse, we discover that it is the sum of the squares of
the lengths of the two other sides. In this, Pythagoras effectively transformed
space into numbers!
Not so long ago, it was
revealed that Pythagoras was not the first to discover this. It was known by
the Babylonians a thousand years before!
Having said that, the Iraqis may have forgotten it by the time of Pythagoras.
I hope not because it made
me wonder whether Jesus knew about the Pythagorean Theorem? Remember his
forebears were exiled in Babylon in the sixth century. If the mathematics of
right angled triangles was still taught, did the exiles carry it back to
20 February 2019
Seneca, a Roman philosopher living at the time of Christ, wrote an essay entitled, ‘On the Shortness of Life’. Length of days does not matter. What does matter is the wisdom with which we fill our days. In this extract, Seneca counsels us to value our time because it is in limited supply.
‘You live as if you were destined to live forever, no thought of your frailty ever enters your head, of how much time has already gone by you take no heed. You squander time as if you drew from a full and abundant supply, though all the while that day which you bestow on some person or thing is perhaps your last.’
19 February 2019
‘Having good thoughts really does improve your health’ said the headline in my daily newspaper. I was keen to read more. The
research comes from a study undertaken by the universities of Oxford and
The crucial aspect of their
study focuses on the body’s threat response
which can damage the immune system. Being compassionate towards
ourselves switches off the threat response which places the body in a state of
‘By switching off our threat response, we boost our immune system and
give us the best chance of healing.’ said one of
the researchers. And this can only be good for a person’s physical and mental
Thinking good thoughts is a
constituent part of the Gospel, beautifully articulated by St. Paul when he
wrote his Epistle of Joy whilst imprisoned in Rome for his allegiance to
Christ. The letter was written to the church at Philippi.
‘Whatsoever things are true, whatsoever things are honest, whatsoever
things are just, whatsoever things are lovely, whatsoever things are of good report; if there be any virtue
and if there be any praise, think on these things.’
Think on these things! It’s
the wisdom of two millennia which is now being affirmed by a more scientific
enquiry. But it stands to reason that filling our minds with kind and beautiful
thoughts can only do us good. It is the Word of God!
18 February 2019
Last month, a volunteer working for the Scottish
Stained Glass Trust asked to visit
Prestonkirk and Stenton to take photographs of the stained glass. Whilst he was
there, he took over 800 raw images!
He wrote to tell me that he had taken 230 images of
the large five light window in the chancel at Stenton. He likes to take images
at different exposure settings so that he can choose the best for the record.
This magnificent window was by CE Kempe. Apparently,
it is a fine example of his early work. The photographer could tell me this
because it contains his three wheatsheaf shield in the bottom left hand corner.
This means that the window was made before 1895.
Thereafter, the stained-glass artist used the more common single wheatsheaf as
his logo. He is going to send us some examples of the sixty or so images he
In passing, he wrote, ‘It was a pleasure to visit and make photo-records of such well-
maintained and obviously well-supported churches, with polished brasses, not a
speck of dust to be seen, even leaflets lined up like guardsmen on parade ….’
17 February 2019
How many hymns do you know which employ scientific imagery. We may think initially of Psalm 8 which was written three thousand years ago, ‘When I consider thy heavens, the work of thy fingers, the moon and the stars, which thou hast ordained; what is man, that thou art mindful of him? and the son of man, that thou visitest him?
there’s Joseph Addison’s famous, ‘The
spacious firmament on high, with all the blue ethereal sky’. But what
others come to mind? There is one from the twentieth century in our
hymnary. It was written Albert Bayly and
begins, ‘Great God of every shining
constellation’. It talks about ‘the atom’s hidden forces’ and describes
God as ‘True Life, awaking life in cell
and tissue’. There aren’t many like it. Why not?
reasons. The first is that the scientific and poetic minds are considered to be
different. People say that different
sides of the brain are being exercised
in these two spheres of thinking. The result is unchallenged
The second is that scientific language is not so readily embraced either in poetic forms nor in devotional metaphors. Sometimes it appears to alienate us from God, our traditions and our comfortable symbolism. ‘God of concrete, God of steel’ etc.
But the paucity of hymns celebrating the scientific age and, more particularly, the work of God within scientific discoveries only emphasises the foolish division between faith and science and reinforces the view that the Church is out of touch with our contemporary world.
16 February 2019
For the past four years, the Wood Foundation has been sponsoring an initiative in the Primary Schools across eight local authorities ‘to improve the confidence, skills and science support networks for primary teachers.’
researchers evaluating this Raise Project discovered that the children
thoroughly enjoyed the classroom experiments. There was a strong indication
that the children would enjoy being involved in science when they left school.
there were three inhibiting factors. The first was the negative attitude
towards science at home. The second was the lack of confidence amongst
teachers. The third was the invisibility of people working in scientific jobs.
other words, if the children never see nor know a scientist within their own
community and therefore have no role model, how will they be able to see
themselves working in such an alien sphere of employment?
seems very odd that in a century which has seen so much scientific advancement, the teaching of science and the
opportunities which it affords should not be encouraging more science and more
scientists within our society.
15 February 2019
In his book, ‘Levels of
Life’, Julian Barnes introduces us to Felix Tournachon, one of the first
balloonists. He was affectionately known by the nickname, Nadar. ‘His gusts of energy and flames of hair
seemed enough to lift a balloon into the air by themselves.’ he says of the
Interestingly, he was also
interested in photography and gained a reputation as a very skilled maker
of photographic portraits. But Barnes
informs us that Nadar brought these two disparate interests together.
He was the first person to
take his camera into the balloon, build a dark room in its basket, prepare the
plates whilst the balloon was in the sky and take a photograph of the earth
from the air. No one had ever thought of it before!
It’s common place for us.
We take our i-phones everywhere and photograph everything and anything, the
mundane as well as the unexpected, the boring details of our eating and
drinking and the fantastic sights we see on our travels.
But Nadar was the first –
and initially he had little success. He persevered and managed to reproduce a
faint image – two pigeons on a farm
roof, a stationary cart, a man looking
up at the balloon!
No one else had ever been
able to capture a view of the earth from this perspective. Barnes sees in it a
coming together of two things – truth as in the photographic picture and magic
as in the adventure of ballooning high above the earth. For him ‘Love is the meeting point of truth and
14 February 2019
Recently, I was on holiday
for the weekend and found myself browsing in a delightful bookshop in the
Borders. I hadn’t intended to buy anything but I couldn’t resist what was
described as a book of ‘Scottish poems
for growing older’.
It was edited by Lizzie
McGregor and had a forward by Sally Magnusson. For the rest of the day,
Mary-Catherine’s peace was regularly interrupted with quotations from this rich
and illuminating text. One was simply called, ‘Watching the Telly with You’.
It surprised me that what
Roald Dahl and the Oompah Loompahs considered to be a means of rotting the
brain, should confirm the value of a companionship enriched by the years and
the pleasure of simply being together.
It was written by Diana Hendry.
We could go to Paris of
but not so often. And it
might not be quite
as cosy as the sofa, the
fire, our slippers,
the zapper. Sometimes
I think about it, hankering
a little like
the lovelorn do, for that
front door locked, feet up,
loved up and watching the telly with you.
Happy Valentine’s Day!
13 February 2019
In his essay on King James
1, Thomas Cogswell emphasises the king’s theological prowess and his enjoyment
of theological debate. As King of Scotland, he listened to two sermons every
Sunday and was well able to understand, criticise and interrupt!
At the Union of the Crowns,
the king moved south and befriended the bishops. He debated with them and sometimes
sent for them to comfort him in some personal agony. Preferment was bestowed by
the king on good preachers.
Sometimes he would meet
with preachers prior to the delivery of their sermon to discuss what they were
going to say. He had a phrase for this activity. It was called ‘tuning the
pulpit’. Whilst preachers may not be happy about this kind of interference, it is a happy image.
For it looks at the pulpit
and the preacher within as a musical instrument. Like all musical instruments,
sometimes it needs tuning. Some tune the pulpit through study and prayer and
much reflection on the pastoral care of the people within their charge.
The Lutherans regularly
tune their pulpits with a crucifix hung on a pillar opposite the preacher lest
he forget his purpose. But whether it’s tuned by study, prayer, a king’s theological mind or a crucifix, it should
always be tuned for love and the love song which has its origin in God.
12 February 2019
At J-Team the children were
thinking about worry. In discussion, they worried about the dark, the future,
being alone and so on. This led into an animation about Jesus and his teaching
about worry. Before that, the children made four paper dolls holding hands.
It’s an old paper craft
which was almost second nature to us at Primary School – fold the paper in
half, fold each side into the centre, fold into a quarter, draw a picture of a
person and cut it out! Not so easy for them!
On each of the four people,
they had to draw a different expression – happy, sad, surprised and worried.
Never was such a simple activity enjoyed so much! The facial expressions and
the colour schemes are all different. The figures are all unique.
Sometimes we are wont to
think that children do not worry or should not worry or have no reason to worry. The truth is that we
all worry. It’s a natural emotion. Having said that, we need to learn
strategies to cope with it.
Jesus provides that. Just
look at the birds and the flowers. They don’t worry about food or clothing and
yet God provides all that they need. The splendour of the king could never
match them! If God cares for them, will he not care for us too? Simple, really?
11 February 2019
When my dad died in 2010,
he had been in a Nursing Home for eleven months. His personal effects had
diminished enormously. What remained from the family home was stored in our
attic waiting for my brother to decide what he wanted.
He died before a decision
was made and I have had little reason to consider what was left of his life and
our family home. Recently, I began to sort it all out. It was a fascinating
experience reliving my childhood.
There is an old tape
recorder with a box of spools. I am singing treble in one of them. Three
violins which my dad played all his life enlivening many a kirk soiree and
Gaelic Choir ceilidh with his generous fiddle music.
And what’s this? A bag of
cutlery and table linen – beautifully embroidered napkins and bone-handled
knives and forks. The cutlery for fish are very distinctive and the old spoon
which was used in the sugar bowl now looks like a miniature shovel.
An inconspicuous cardboard
box yields an unexpected secret. The contents belonged to my mother. One who
had a habit of giving her possessions away has carefully preserved a boxful of
Two white dresses – the one
for her engagement and the other for her wedding day. There is a silver handbag
and matching shoes, a veil carefully wrapped up in tissue paper and a silver
cardboard horseshoe wrapped in a sachet of moth powder.
Her wedding day was clearly a very important event in her life for memories have been lovingly treasured in this box of clothes. She always used to say to us, ‘You were born in love’. What better gift can we give a child than this thoughtful affirmation of love?
10 February 2019
In Isaiah, we see that the God of Israel has entered our humanity
and likened his love for his own people as a love of Bridegroom for Bride. ‘As the bridegroom rejoices over the
bride, so shall your God rejoice over you.’
The bride is described as ‘a crown of beauty in the hand of the Lord’
– something rare and beautiful,
something to be treasured and admired, something which adds sparkle to life and
living and the world around.
God gives his bride a new name. ‘You shall be called, ‘My Delight is in Her’’. What a fancy name but this is how God looks upon his bride and understands her whole being. She is delightful. Despite her wayward ways, she is a delight to him.
This is love’s power. It does not focus on human frailty and characteristic foibles, it loves for no other reason than love’s sake. He cannot help loving his bride for despite everything that happens, she is and always will be a delight to him.
9 February 2019
So much of our world and
our experience is inexplicable. Although we live in a world where science is
the predominant intellectual force and commands so much respect, it does not
hold the answers to so many important questions.
In a special edition of
‘Scientific American’, I read an article about the spectral gap. This is the
amount of energy required to move a material from one state into another e.g.
ice into water and so on.
recently proved that it will never be possible to determine whether all
materials have a spectral gap or not. What this implies is that there may be
other big scientific questions which will
be proved to be undecidable.
In other words, whilst our
scientific understanding of the Universe will continue to grow so will our
acknowledgement that certain scientific questions will never ever be answered.
And, what’s more, we can prove that we will never discover the answers!
This fascinating result has
a bearing on the miracles of Jesus not least the resurrection! How did this happen? Is it like
the spectral gap question? Can it ever be proved? Is it something which one day
will be proved to be undecidable?
8 February 2019
I am very careful with my backdoor key. I keep it my
pocket and at night I carefully lay it on the table beside the bed. So it was a
surprise to me to lose my key. I searched everywhere and couldn’t find it
despite the finitude of space!
I got another and was even more careful about this
one. Strangely enough, it vanished too. Whilst there has been no other evidence
to suggest that I may be dementing, I thought it very odd that my careful
routines had been breached so easily.
I began to think there was a pattern to these losses.
It had never happened before – and now it had happened twice. An alternative
routine had somehow been developed which had circumvented my awareness. I
When Colin broke his ankle, I visited him in Leeds.
Sitting on a comfortable chair in his living-room, I felt my key sliding out of
my pocket! A near miss – but it set me thinking. What if this had been
happening at home? Perhaps my key had fallen out of my pocket and down the side
of the chair.
When I followed up this detective work, not only did I
find three backdoor keys but also a pen, a comb and a fifty-pence piece! They
had all slipped out of my pocket, fallen down the side of the chair and into the
wooden structure which was sealed off with sacking.
Although it took time, I was thrilled. I had found my
lost keys. The loss did not imply the onset of dementia. A pattern of loss had
been created and made worse by my recent loss of weight and loosely fitting
7 February 2019
John Burningham died last month. We knew him through
his work as a children’s author and illustrator. His work was widely acclaimed
and he was awarded many glittering prizes not only here but in many parts of
There was an unattributed obituary in the Herald. I
discovered that he had been married to Helen Oxenbury with whom he
collaborated. She described her husband as ‘a gargantuan character’ and paid
tribute to his skill and insight.
She concluded, ‘I don’t know what I would have done if I hadn’t met John. He’s guided me, influenced me and inspired me my entire life.’ Is there a finer tribute than this? O that we could inspire others and literally fill them with the spirit to enjoy life in all its fullness.
6 February 2019
Last week, a minister called
Classic FM with a request. He was phoning from a Nursing Home in the south of
England. He had just taken a midwinter service. However, the falling snow
prevented him from travelling thirty miles south to take another.
He knew that the residents would
be waiting for his arrival. Interestingly,
the service was always prefaced by some music from Classic FM. A member
of staff ensured that it was broadcast through the television.
Because he couldn’t get there,
the minister thoughtfully told the presenter about the residents waiting in the
Nursing Home and asked for a piece of Mozart to be dedicated to them.
And so he remembered them. In his
wintry absence, he had connected with them through the music of Classic FM.
They were not forgotten but remembered by a nation and that special communion
facilitated by minister and people was restored.
5 February 2019
Standing on the metal bridge at
7-30 in the morning, I saw a little dipper dancing on a stone. He was singing.
But to whom? I looked up and around at the trees and the dawning sky but saw
I walked on but stopped short. I
should take a photograph of the little bird. When I went back I could see that
the sing song dipper had been joined by
his mate, charmed no doubt by his early morning singing! Now they were dancing
And I saw that autumn’s windfall of apples which had
lain on the grass by the Knowes field all through December had now vanished.
And there were no red berries on the hawthorn bushes. Jessie struck eight and
she was crystal clear.
The hare was running across the
frosted field under the fading crescent moon
and there was much crackling at the side of the road as the frosted
leaves magnified the sound of birds and other creatures moving in the
undergrowth, hidden from view. Magical moments, confirming the value of life
and living even in the winter!
4 February 2019
O wert thou in the cauld blast,
On yonder lea, on yonder lea,
My plaidie to the angry airt,
I’d shelter thee, I’d shelter thee;
Or did Misfortune’s bitter storms
Around thee blaw, around thee blaw,
Thy bield should be my bosom,
it a’, to share it a’.
Robert Burns has chosen to use
some wintry imagery in this love poem. For the cold wintry weather forms the
perfect foil to illuminate the warmth of love and the contrast between death
and intimations of new life.
And so the poet offers his
sweetheart room under his plaidie and a shelter from the wintry storm not built with wood and stone but simply his bosom where she
may rest her head through the worst of winter’s cauld blasts!
His little poem brings these striking
images together – the barrenness of winter and the fruitfulness of love, the
shelter built with physical materials and the protection which love can afford
in a warm embrace.
3 February 2019
written the blog and transformed the words onto these irregular polygons, I had
to decide how to present this visually in a single piece. A box with thirty-one
polygons inside circles would be a bit boring. A straight line would be worse.
What about a spiral?
appear naturally in the world and can be seen in spiral galaxies, weather
patterns, shells and staircases. The movement of a snail creates a spiral
pattern and the tendrils of plants form spirals too. It is to be found in
mathematics and it is always beautiful to look at.
I decided to create my spiral using coloured card stuck onto a black background. The photograph, which is still a work in progress, shows God in the centre of the spiral and the irregular polygons spiralling outwards ever approximating but never reaching the eternal.
2 February 2019
I was on study leave last October, I was exploring infinity in mathematics and
theology, hoping to find some common ground which would lead to a deeper
understanding of God. One of my starting
points was the circle.
has no beginning and no end and so it shapes the wedding ring which celebrates
a love which is eternal. One way of looking at the circle is to see it as a
polygon with an infinite number of sides.
you look at a circle and draw a hexagon inside and then a septagon and then an
octagon and so on, you can see that the polygon is approximating to the circle
more and more. This was what I needed for my ‘Fun a Day Dundee’.
decided to write my blog inside a polygon with the same number of sides as the
day of the month. So for 3 January, I used a triangle. For 4 January, I used a
square. For 5 January, I used a pentagon and so on. For 31 January, I used an
irregular polygon with 31 sides!
1 January, I used a dot and for 2 January, I used a straight line. The dot was
in the middle of my first word GOD and the straight line connects ‘Thank’ with
‘you’. In this way, I was able to visualise the blogging for the first two days
of the month.
1 February 2019
January, I decided to write my daily blog in a different way. I began in a
minimalist fashion by using one word for the first day of January increasing
this to two words for the second and so on until I had written thirty-one words
for the last day of the month.
did this because I was persuaded to participate in a community arts project
called ‘Fun a Day Dundee’. It encourages
people to do something creative every day in January and gives them a chance to
exhibit their work once the month is over.
challenge was not simply to come up with an idea but to transform the idea into
something artistic which would have a visual impact on the viewer. As one who
was creating in words this was a bigger challenge than writing a smaller blog
Ending is beginning by another name for in conclusion
there is the potential for change like
the ugly chrysalis and the beautiful butterfly and old Simeon standing at February’s
door departing in peace.
Morning has broken like the first morning
Blackbird has spoken like the first bird
Praise for the singing
Praise for the morning
Praise for them springing fresh from the world.
A Periodic Table of Elements was found in a St. Andrews University chemistry cupboard. The chart’s German printer and elements not included made it the oldest Table in the world!
28 January 2019
No one seems to be talking about it but a full page spread in the newspaper details
the plight of twenty-two million dying
of hunger in the Yemen!
A significant birthday draws us into old age and
an adventure where imagination
replaces limbs and we are free to fly
all over the world and beyond ….
26 January 2019
Early morning walk with Jupiter, Holst’s ‘Bringer of
Jollity’! Jovialis, of Jupiter, gives
jovial! It vanished from sight before
reaching home, leaving a plump full moon!
25 January 2019
And brithers be for a’that! – national manifesto from the bard who gave the
world a song where hands are held for auld lang syne.
24 January 2019
Group raised £320 for the Winter Night Shelter at Bethany. It costs £21 per bed
space! Fifteen homeless people will be warmer tonight!