The Joy of Algebra - At Last!

Cartoon from:-   domintelthegmat.com

The above cartoon says it all really.

When I was at school, all those decades ago,

 I managed to get a pass in all the branches of mathematics we were taught,

 but it was merely for the purpose of passing the relevant exams.

I never understood the why, what, or wherefore of any of it,
or it's relevance to real life.

What I did do was live in constant terror of the subject and the teachers.

I scraped by, trying to solve the problems we were set in uncomprehending panic.

I was perfectly able to get many different answers to those same problems, 

 never properly knowing how I arrived at any of them

My "workings out" were guess work and luck,

of which the latter must have been in plentiful supply,

as I managed to keep afloat.

Needless to say, once the need to perform at school was over

 an iron curtain descended over my struggles with maths,

as, like an extinct language,

 the very subject became a distant memory.

The only vibrant memory in connection with the subject

was the picture of our maths teacher in grammar school,

beating his head against the blackboard,

 whilst his faced turned a deep puce whenever one of us
so much as hesitated when called upon to stand and solve an example,

or answer a question put to us.

I was terrified enough at presenting my ignorance to the whole class,

let alone the added fear that he would succumb to apoplexy because of me.

Ever since, I have shied away from anything containing figures, declaring,

as my mind went blank,

"I don't do maths."

Then about a week ago I watched this video, culled from the glorious posts on

.Ennis Blue

Do yourself a favour and check it out.

Well I hope you check out both the tumblr.com site I'm recommending,

and the video below.

The video is a little long but well worth it as it moves into the unexpected.

Now the mathematics Frenkl finally talks about is one I thoroughly understand;

holding no terrors for me.

What did challenge me was in his introduction he says

 how exciting, elegant, and beautiful, the world of mathematics is.

It reminded me I had been envious of a friend 

who said the same kind of thing to me years before.

They both obviously saw maths like this,

image :-  www.cs.ox.ac.uk

whilst to me that book was definitely closed.

I hated the thought of what I was missing,

so I set about finding a basic maths site to cater for my depth of incomprehension, 

and made a start.

At first my brain rebelled.

I stared at the work sheets in panic.

Even the explanations and examples

 left me baffled.

Perhaps I was past it,

 and the ancient grey cells would refuse to play ball.

Then, just like that moment

 the optician drops the final lens into your prescription frames,

and the symbols on the wall chart pop into clarity,

I saw!

In the great scheme of things nothing huge has happened.

 The algebra I have revised is the most basic.

Absolute beginners steps.

Nevertheless what truly thrilled me was,

for the first time I understood what I was doing!

I saw the symmetry and reciprocity of the numbers,

in their trueness to themselves within the motif unfolding

 as I added, subtracted, multiplied, and divided.

This was me, understanding equations!

Unbelievably,  I began actually enjoying the problems to the extent

I was skipping through the worksheets,

checking my answers, and with one eye on the clock,

wondering how many more I could fit in

 before I had to begin to prepare the evening meal.

Then, once things had been set to cook, sneaking back for a few more.

Of course one swallow doesn't make a summer,

the leopard hasn't changed it's spots,

and the mouse hasn't got all the cheese!

In other words

I know I haven't turned into a mathematician in one fell swoop,

 and never will.

I will doubtless be just as baffled by new problems again very soon, 

and my achievement threshold might well turn out to be quite low.

Heck!  Even in my euphoric state of discovery I was still making careless mistakes,

and my multiplication tables were decidedly rusty.

I know it will take work.

That's why I persevered

 until I had three worksheets in a row with no mistakes.

The wonder is,

the place in my brain I had shut down in fear and incomprehension

has been re-opened to new understanding.

Embryonic, life giving, delightful, understanding.

Seventy three isn't too old to learn after all!

Be Blessed

P.S. If there is something you have struggled with, maybe for a long time, 

why don't you give it a go again? 

 If you have already done so, or when you do,

 why don't you let me know in the comment box below?

  I would so love to share your joy, and mutual encouragement.

A Bonfire Night Sunset

We had a horribly wet day last Saturday.

Guy Fawkes Day had fallen in the week,

 so many of the celebratory bonfire parties and firework displays

 were planned for that weekend evening.

It looked as though they were going to be washed out before they got started.

For wont of something to do in the rain we decided to pay a visit to a local retail centre, 

and as we drove there they rain gradually stopped.

By  the time we got there the sun had come from behind the leaden curtain of clouds

just in time to set.

We don't get the spectacularly technicoloured sunsets here 

that you do in other parts of the world,

but they are still beautiful;

especially coming so unexpectedly, out of a dark day.

It brought to mind a radio programme I'd heard the day before.

I had only caught the last fifteen minutes

 so hadn't got the name of the American serviceman it was about.

I heard enough to know during WW11 he had spent forty odd days adrift in an open boat 

with some of his comrades in arms;

and that in the strafing they endured at least one life was lost.

Then they were picked up by the Japanese.

Believing they were in possession of important information,

 the Japanese interned them in a camp 

where our protagonist was brutally, and repeatedly tortured

 until he lost consciousness, then revived in order for the process to be continued.

His outstanding bravery boosted the morale of his fellow prisoners,

 most of whom died before he was at last liberated.

After the war he sort out those who had been his guards and torturers in the camp

in order to meet, and sincerely forgive them,

 and work for reconciliation.

Though his health was broken by his experiences

 he had survived. 

Many of his comrades of similar age and fitness had succumbed in the camps,

yet he went on to live to a ripe old age.

His widow said, when she had asked him how he accounted for his survival 

his explanation was simply that he had never lost hope;.

adding that his faith had given him this strength.

Beyond this he said,

 it was sight of the sky at dawn, or sunset,

 which continually lifted his spirit.

As I listened to the story I marveled that he should name something so ephemeral, 

as being memorable to sustaining his crucial inner strength.

Watching the moments of sunset change over the rain drenched car park

 and remembering that story

 made me realise anew

 we are surely made for beauty.

And if we are made for beauty,
 surely it may be found.

Even in the most unlikely places.


 The heavens declare the glory of God; the skies proclaim the work of his hands.
Ps.19:1

Be Blessed 

By Unexpected Beauty

Remembrance Day - Will We Remember?

Photograph: Massimo Crisafi/GuardianWitness

This is the iconic art installation

 where each ceramic poppy planted at the Tower of London 

honours a life lost by service men and women
 of Britain and the Commonwealth during WW1.

Huge as it is,

 it is a drop in the ocean of all lives lost fighting in conflicts since;

and this only under one flag.

Remember the dead of every nation,

then and now,

and those who had not signed up for war,

too vast to count.

As we left the chutch this morning
 the opening words of the dismissal from the Eucharist

held deeper meaning, hope, and direction, for each of us today
as they tell us,

.

Go in Peace...

It s not yet three in the afternoon,

but it's so dark a day
I am sitting snug in a pool of lamplight.

Rain rattles against the window.

Car tyres hiss through puddling water,

and the wind buffets down the chimney, 

 sending whatever is in it's way banging down the street.

There is always an extra coziness in 

being sheltered, safe, and warm,

 and listening to a storm going on outside

don't you think?

Sometimes the storm isn't just outside of course,

but very much raging around inside us

with a crashing tide of anxiety, 

or a quiet depth of despair that we alone feel we know.

If you know how that feels, this song, based on a verse from Psalm 32
may just speak to you
about a place of peace within the storm.

Weekend Blessings.

Sleeping Like a Dormouse , - Or Not... P.S.

I admit I sometimes click to "publish" too quickly,

and this was one of these times.

A song was going through my mind as I woke to the thoughts I described in the blog

Sleeping Like a Dormouse , - Or Not.

It was the chorus of a simple children's chorus we sing in church sometimes.

After each verse describing the grandeur of creation the chorus goes,

"Your love for me stretches farther than far.

I can't imagine just how great your are.

Just how great you are!"

So the background for this sense of confident relaxing into safe, refreshing sleep.

 was this knowledge of being loved farther than we can ever imagine;

held in, and by a love,

 infinite, and infinitely knowing.

Now, I know sleep, and the dark of night, can hold a seeming infinitey of it's own.

Perhaps sleep will not come,

or we waken again and again.

 Too soon for our busy lives.

Too soon for our fizzing thoughts to settle.

Maybe it is the content of our dreams which disturbs us.

We wake trying to fight ourselvers awake and away from them.

Sometimes we can wrest a meaning out of them.

 Another time they simply leave us baffled and disturbed.

If you are in that place there are many sources on the wonderful world wide web

where meanings to your dreams are offered.

Maybe you can seek them out for help.

There are ancient prayers to settle us for sleep,

or calm us on our waking.

(Tap in night prayers to find prayers of many faith traditions,)

But, goodness you know how to use the net!

I come just to offer you those child- like words,

you are loved "farther than far",

and to pray you the grace to trust in that each night,

in sleep or wakefulness.

Take them to bed with you and roll them round your mind.

Your love For Me Stretches

Farther than far.
I can't imagine just how great you are,
Just how great you are.

Be Blessed


P.p.s.  They aren't bad words for the day time either!

Sleeping Like a Dormouse. - Or Not...

All my life I've slept in the foetal position.

Curled up defensively like a dormouse on it's side,

my body curved around itself,

my arms cuddling me to sleep,

 sealing the package.

This morning I woke to a strange thought forming 

as I swam up out of sleep.

How much better would it be to sleep,

body stretching to it's length in the bed,

recumbent, yet poised.

A diver launching into the mystery of dreams,

there to play like an otter,

twisting and turning with the flow;

Looking, learning, playing,

to emerge at morning's shore line

 refreshed and full of hope. 

Rolling over,

 I skated my pointed toes down along the warm sheets

to curl around an imaginary board's edge.

 and lifted my arms in the classic diver's pose above my head.

Body open, extended, expectant.

 photo;-  www.swimminglessons.com sg

No, of course it didn't work.

The bed too short.

The wall too close.

But something lingered

 to challenge me in my fully wakened state.

Was my dormouse body telling me

 I enter sleep more guardedly than I spend my days.

Perhaps I need to learn to be

vulnerable, and open, and trusting

  in these night hours when

 my consciousness slips,

 free to dream,
 in that deeper stream away from my own direction.

I can't help feeling there is a sweet promise in the waking whisper

strange as it seems.

Be Blessed