Wednesday, 19 November 2008

Descartes's cracked ceiling

I’ve always found the story of how Cartesian coordinates were discovered deeply dissatisfying.

The tradition is that Descartes was sick in bed and looking at the ceiling when he saw some cracks in it. He wondered ‘how would I tell somebody the exact position of any one of those cracks?’ It came to him a flash of inspiration: ‘I know: I’d tell them the distance to the crack from one wall and the distance to the crack from another wall perpendicular to the first. That will determine the position uniquely.’ And so Cartesian coordinates were invented.

All very well and fine, you’d think. It’s another Newton-and-the-apple moment. Great as far as it goes.


But look at all the things it leaves untold.

Why was he looking at the ceiling instead of reading a book like anyone sensible would do? Surely a book would have been more fun. He’d have enjoyed himself and centuries of school kids wouldn’t have been put through the agony of studying his discovery ever since.

And anyway why would he want to identify the position of a crack exactly to someone else? Couldn’t they just look and see it for themselves? In any case, the issue isn’t to determine its position, but to repair it or at least paint over it.

And then there’s the most worrying aspect of all. How did the cracks get to be there in the first place? Subsidence? Seismic activity? Did he check whether the house was still structurally sound? The cracks might have been symptoms of serious risk to members of his household. What steps did he take to minimise it?

But that’s the problem. The story’s been told and retold by mathematicians. These are people who spend for ever establishing things like with the number 1 and a successor function you can derive the whole of arithmetic, as if not knowing that ever stopped anyone counting. Really important things just pass them by.


Tuesday, 18 November 2008

Rockin', rollin nostalgia many miles away

I’ve just tracked down a recording on You Tube of the Seekers singing Morningtown.

Do you know the song? In the right mood you could describe it as sweet. In another mood, you’d just think ‘what is this cloying drivel?’ Not something to say too loud: I like Australians and they like to think that whatever they do, they do better than anyone else. They’re often right, though perhaps not as often as they believe. We need to humour them, so it would be wrong to suggest that this Australian group from the sixties was anything but extraordinary. Let’s just say that the song can seem extraordinarily cloying.

Strangely, it’s precisely that cloying quality that gave the song its importance to me.

The British army stages an annual endurance event called Ten Tors, in which young people walk 35, 45 or 55 miles, depending on age, in teams of six across tough terrain on Dartmoor, in Devon, south west England. Dartmoor is one of the few wild areas left in the country and has the magic of anywhere that has not been tamed, that you have to treat with respect – it can kill you if you don’t – while enjoying its flashes of sudden beauty.




Typical Dartmoor terrain, with the Devonport Leat that takes water to Plymouth

Ten Tors takes place over a weekend and an essential part of it is the Saturday night spent out on the moor, sleeping if you’re lucky, shivering in the cold and wet if you’ve sacrificed protection against the elements to a desire to keep your pack light. Your aim is to visit ten of the granite outcrops called tors, getting a card stamped at each one.

Haytor

The first time I did Ten Tors was in 1967. I hadn’t trained hard enough. Within the first few miles, with thirty still to go, I realised that I was already in far more pain than I should have been. By the evening, I was exhausted. We slept, using the term loosely, wrapped in space blankets, under polythene sheets, with rivulets of moisture trickling down necks, shoulders, thighs, and calves, while gusts of wind regularly blew under the polythene. The following day, I found a team-mate in front of me and another behind, and they forced me to keep up a decent pace for five or six miles, until their own energy flagged and they couldn’t push me along any more.

Well, we made it in the end, and later I was delighted that we had. At the time, though, I had no sense of elation. I felt lousy physically, and humiliated morally: I had performed weakly, delayed my team and made their own expedition more painful.

There had only been one moment of comfort and Morningtown had been central to it.

It happened at about the second Tor. I was already in trouble. As we reached the Tor, I heard a team of girls resting on the rocks and singing Morningtown – sweetly, of course. These weren’t sirens displaying their charms on the rocks, singing sailors to their destruction. They were fourteen year olds like me, shapeless in their oilskins, and they weren’t even great singers: their voices were pretty but slight, only just audible where the Tor gave shelter from the wind. Even so, the song conjured up a world a long way from where I was. It represented kindness and gentleness. Everything that was different from the cold, the wet, the brutality I was going through and which was, as my gut told me, going to get worse.

What I particularly liked about the moment was that I knew it was transitory. I’d never see them again. We were only in the same place for a few minutes. I didn’t know who they were, and though I remember them, I’m sure they don’t remember me. I was given a brief respite and it left a memory that stayed all the longer because the moment had been so fleeting.

That’s why Morningtown means far more to me than the song itself deserves.

Sunday, 16 November 2008

The envy of the world

Change, many in Britain feel, is synonymous with decline. So our rightwing press – which is most of it – resounds with denunciations of deplorable initiatives, usually by government, to undermine some cherished, once grand institution. We might read:

‘The British judicial system is the envy of the world. And yet the government has struck a blow at the very roots of that system more damaging than anything even Hitler’s blitz could throw at us.’

On looking into it more closely, you’ll probably find that what government has done is to issue a timid consultation paper into whether top lawyers’ fees are a little excessive, or whether a few more women or even – don’t say it too loud – one or two more blacks among our judges might improve the balance of the courts.

What I really like is the idea that Britain is the envy of the world. I picture the little boy in his village on the Limpopo who has been caught stealing rice from his neighbour. He’s facing the council of elders with his guts churning in trepidation. ‘Oh, woe is me,’ he’s saying (sorry for the old fashioned turn of phrase: I couldn’t afford a better translator), ‘if only I was up in front of a beak in London. Then I’d be sure of a proper hearing, because the British judicial system is the envy of us all.’

And it isn’t just the judges. The world loves our army too. US forces breathe a sigh of relief when they hear that British units are on the way. ‘Oh, thank God,’ they all say, ‘we can go home at last. The Brits will have this insurgency sorted in no time. Our work is done.’

Emotions run high on the other side too. In Afghanistan, the British have been using snatch land rovers, vehicles whose armour plating might best be described as discreetly understated. So there’s consternation among the Taliban on seeing a British patrol approach. ‘Hold the bomb, boys,’ they call to each other, ‘we’ll keep it for a tank. Just throw a can of lighter fluid at this lot.’

The National Health Service is another beacon to the world. Our NHS dentists are like precious stones, which is presumably why finding one these days is like drawing teeth. As for our General Practitioners, no other country can rival their talent. Where else do doctors reach a diagnosis with so little evidence? A visit to a GP goes something like this:

‘Ah, hello doctor. I’m afraid I’m a little worried about the pain/ache/twitching/smell of putrefaction [delete as applicable] from my arm/leg/head/lungs.’

‘Ah yes. How long have you had the problem?’

‘Since yesterday. I thought I’d better see you about it quickly.’

‘Good.’ He scribbles on a pad, tears off a sheet and offers it to you. ‘Take this four times a day for two weeks. That should clear it up.’

‘Really? Shouldn’t you examine me or get some tests done or something?’

‘Oh, no need to bother with all that just yet. Let’s wait until you’re ill.’

The only British organisation that isn’t regarded as the envy of the world is our favourite whipping boy, the BBC. David Cameron, leader of the Conservative Party, recently joined in the fun. Two BBC comedians had overstepped the mark in their pursuit of bold and iconoclastic humour, and broadcast some pretty ugly, pretty tasteless material. One of them resigned, another has been suspended. Lesley Thomas, the controller of the channel that broadcast the material has also gone, which is a pity since she was good at the work and will be missed. You’d think that would close the chapter. But when the BBC is down, you can trust Cameron to put the boot in. So he issued what for want of a better word we have to call a ‘thought piece’ about the corporation, in particular castigating the high salaries of the top executives.

After all, what have BBC executives done to win our admiration or loyalty? OK, they may have produced outstanding nature programmes, brilliant adaptations of the classics, fine new drama, informative and balanced news broadcasting, fascinating historical series, excellent radio. Even, with a few exceptions, some pretty impressive comedy.

But apart from that? What have they achieved? Compared to our judges, our generals and our doctors, what claim do they have to be the envy of the world?


Postscript with little relevance to any of the above

Lord Salisbury, prime minister at the turn of the twentieth century, pointed out ‘If you believe the doctors, nothing is wholesome; if you believe the theologians, nothing is innocent; if you believe the military, nothing is safe.’

Don’t know why that appeals to me. It just does.

Wednesday, 12 November 2008

Dovedale: who needs Switzerland?

In Pride and Prejudice, though Elizabeth Bennett’s visit to Derbyshire ultimately leads to far more, her initial aim is to see some of the beauty spots, such as Dovedale. And having just been there myself, I can vouch for its being worth the trip.

England doesn’t really do deep gorges encased in cliffs, but if you’re happy with gentle green slopes, woodland alternating with grassy banks and a river dancing down the middle, then Dovedale’s charm is for you.


The rich green that is the hallmark of the English countryside comes at a price, and we paid that price during our visit: it didn’t rain constantly but it did rain repeatedly. And when we got up on to the tops of the hills, it wasn’t just the view that was breathtaking but also the gale.

Still, the place is worth a little physical discomfort, and it’s easy enough to dress for the weather.



Janka wrapped up warm like the rest of us

A plaque at the entrance to the valley points out that Byron claimed, ‘I can assure you there are things in Derbyshire as noble as Greece or Switzerland’. As it happens, the river Dove is the border of Derbyshire, so half of Dovedale is in Staffordshire. But, as we were told in the nearby pub where we had lunch, the best bits of Derbyshire are in Staffordshire.

The pub, by the way, was just as impressive as the dale. It served outstandingly good home cooking, nothing out of a packet or a tin, nothing out of a microwave. Delicate, sophisticated. Far better that most pubs. And a great place to take our French visitors, demonstrating that you can, despite the increasingly discredited myth, eat well in England.

So who needs Swizterland? Dovedale has it all. Except perhaps the Alps. And the skiing. And Lakes Geneva, Thun, Zurich or Lucerne. Or the cities of Geneva, Zurich, Thun, Lucerne, to say nothing of Basel. Or the compliant banking system. Or the pharmaceutical industry. Or fondue or Rösti or perch fillets. Or the decent weather.

Postscript that’s only vaguely related: Misty’s misfortune

Before we set out for Dovedale, I let Misty out and then forgot to get him back in, so he spent the whole day outside. That wouldn’t have been so bad except for the fireworks. There’ve been a lot of them recently.

Sensible countries have their firework days in the summer: the US on the fourth of July, the French on the fourteenth, the Swiss on the first of August. In England, our fireworks celebrate the moment when we tortured to death Guy Fawkes for having tried to blow up the Houses of Parliament, an offence for which most people today would probably have let him off with a caution. As he was arrested on the fifth of November, we have the party when it’s cold, generally wet and miserable.

Because they’re so close, there’s a tendency to conflate Guy Fawkes day with Halloween, so we have fireworks on the 31st of October too. What’s more, people buy their fireworks early and, having bought them, can’t resist the temptation of letting some of them off immediately. So we get firework explosions pretty well every night for two weeks from late October.

I don’t mind, but the cat and the dog hate it. They cower in a corner behind the furniture when they’re indoors. But poor old Misty wasn’t even able to do that. He was out there in the dark, the cold, the rain with no protection from the bangs.

My wife Danielle looked at me as though I was something that Misty might have dragged in, had he been in at all.

We periodically went outside, calling ‘Misty! Pss, pss, pss. Come on Misty!’ He does come when called, usually – all of Danielle’s cats have responded to their names, but with Misty it’s more hit and miss than with the others. He didn’t show up.

By about ten at night, with a crescendo in the firework noise, Danielle decided to head out looking for him. Her demeanour towards me was that of someone who is very deliberately not saying what is on her mind about people who leave cats outside when they should be indoors. She took Janka to help with the search, although when you say ‘Where’s Misty?’ to Janka all she really does is rush around barking, without actually finding him, unless he’s right under her nose.

Danielle had been gone only a few minutes when there was a mew at the back door. When we opened it, Misty shot in and immediately demanded food. Once fed, he headed upstairs to find a bed that met his demanding standards of a place to rest from the day’s exertions. Cool as cucumber. Bold as brass.


Misty relaxes

Meanwhile Danielle was out there frantically searching. However, I had no more success standing on the doorstep and calling ‘Danielle! Pss, pss, pss. Come on Danielle!’ than when I tried it with Misty.

But of course there was a happy ending. Danielle and Janka came back eventually and anxiety was replaced by relief, frowns by smiles. And I stored away a valuable lesson: make sure the cat’s indoors before setting off for the joys of England’s answer to Switzerland.

Tuesday, 11 November 2008

Obama: not a black politician

I’m struggling to train myself not to think of Barack Obama as a black politician, but as a politician who happens to be black.

Jesse Jackson is a black politician. Throughout his career he’s been an outspoken champion of the rights of his underprivileged black fellow citizens. It's made him a powerful voice against injustice but, as he demonstrated when he ran for president, it's also made him unelectable. Unlike Obama.

It’s not surprising that Jackson hasn’t always been Obama’s greatest fan, whatever he may say now. Back in July, he accused Obama of ‘talking down to black people’ and said he wanted ‘to cut his nuts off’. It would be hard to view this as an enthusiastic endorsement, except for someone nursing ambitions of a singing career as a castrato.

Obama didn’t just win overwhelming black support. His support among all groups, white as well as black, Asian as well as Hispanic, has given him the right to be considered president elect of the whole of the US. His problem isn’t about who voted for him, but about dealing with the 59 million who voted against him and managing the inevitable disappointment of his supporters, whatever their racial background.

That’s the kind of problem of success that Jesse Jackson never ran the slightest risk of having to face.

No wonder his initial view of the Obama candidacy had a bit of a surgical edge.

Saturday, 8 November 2008

Terror of the schools

It was intriguing to learn that in the most recent year for which figures are available, 1540 children under five were excluded from English schools for physical or verbal violence.

Where do they get the capacity to be that threatening at that age?

It took me until I was at least ten before I could become a really sustained irritation to my teachers. From that age, however, I did carve myself something of a niche as the most disruptive pupil in my school. It destroyed my hopes – never bright – of a sporting career, as for two years I missed every Wednesday afternoon sports session in punishment for some misdemeanour or other. The process culminated in the headmaster telling me one Wednesday morning, ‘David, you are the only child on detention this week out of 500 and I’m not going to keep a teacher back just for you. So instead I’m going to cane you.’

I’m as keen an opponent of corporal punishment as the next liberal, but I have to admit that from a purely personal point of view I preferred it to the alternative: six strokes of the cane caused little pain and were over in seconds. Detention took hours and was real punishment. Not sufficiently unpleasant to stop me cheeking my teachers, but desperately tedious all the same.

The only problem with being spared detention is that I didn’t have any sports kit with me, seeing as I hadn’t needed any for such a long time. Or did I actually own any at all? My parents could safely have avoided the expense.

My real fear of teachers came once I was a parent. When my elder son came home from his second week at school, he was looking frightened.

‘What is it? What’s worrying you?’ we asked him.

Tearfully, he explained ‘my teacher says I have to take off all my clothes to have a pee.’

Our blood ran cold. This was in the middle of one of the periodic scares about child sexual abuse. They were making our son take off all his clothes to have a pee? What was going on?

It was Friday evening so there was nothing we could do. We tried to enjoy the weekend but it wasn’t easy with that shadow hovering over us. But eventually Monday morning came and I confronted the teacher. She looked at me as though I was slightly pitiable if not crazy.

‘We told him that he’d have to change for P.E.’

Unspoken but unmistakeable was the reproach ‘just what were you about to accuse me of?’ Given what had been going through my mind over the weekend, that wasn’t a subject I wanted to discuss with her.

Physical Education! She was talking about changing for games. It seems that sports kit was becoming an issue in my life again. A ghost from my past had come to haunt my weekend.

Perhaps it was long-delayed retribution for having caused my own teachers so much pain. Karma, basically.

Monday, 3 November 2008

Ghosts that haunt us yet

It’s impossible to generalise about nations. Every country has its Obamas and its Kennedys, but it also has its Quayles or its Palins, and you take the rough with the smooth. Even so, I have to admit to a particular tenderness for the Irish. I don’t remember ever really disliking an Irishman and most have amazed me with their wit and their warmth.

This is odd. Mutual goodwill is not common between the English and the Irish. An Irish friend, surprised at my supporting Ireland in a rugby match, told me ‘No Irishman would ever support England, you know. If England were playing Zimbabwe he’d support Zimbabwe.’ Seen from Ireland, the gulf between the countries is much wider than the Irish Sea, and it runs with blood not water.

What’s true in general isn’t always true in particular. A few years ago, my mother came across a woman with a soft Irish brogue who seemed familiar. ‘Don’t we know each other?’ she asked, ‘Surely we’ve met before.’ They were close friends from the war years who hadn’t seen each other for half a century. They’ve renewed a friendship that’s been close and cordial ever since.

Soon after the war, the friend took my mother to a meeting addressed by James Larkin, Junior. He was a recently elected member of the DaĂ­l, the Irish parliament, and the son of ‘Big Jim’ Larkin, the trade unionist who had been an ally of James Connolly. Connolly was the outstanding figure among Irish Patriots and was shot after the 1916 Easter Uprising by the British, though he was in a wheelchair as a result of the injuries he’d received during the fighting. Perhaps I should say ‘shot by the English’ rather than ‘by the British’. The Irish don’t have an argument with the Welsh, or even really with the Scots: although it was Scots Presbyterians who expropriated Catholic lands in Ulster to form the ‘plantation’ with consequences that still reverberate today, every Irishman knows that the dastardly hand responsible was actually English.

As the two young women arrived at the younger Larkin’s meeting, my mother's friend whispered ‘now you just watch him: he won’t make it to ten minutes without mentioning Cromwell.’

It’s said that the tragedy of the Irish is that their memories are too long, and the tragedy of the English is that their memories are too short. To most Englishmen, Cromwell is a vague memory from schooldays, of the man who sent Charles I to the scaffold. Most Irish people, on the other hand, feel that without their sustained resistance Cromwell would still be rampaging through their land today, at the head of a British – sorry, English – army. I always tell Irish friends that Cromwell was the man who brought Ireland the gift of peace, but usually only get a mirthless laugh in response.

My mother timed Larkin. He mentioned Cromwell within the first five minutes.

It was a great pleasure to make some new Irish friends eighteen months ago. We met on neutral ground, in the home of a Hungarian in Strasbourg, surely ideal conditions for setting aside historical rivalries. They were charming, warm and witty. Each time we’ve met them since has been as enjoyable as the first. One of my regrets at moving away from Strasbourg is that it makes it more difficult to see them.

But for all that – they’d mentioned Cromwell within ten minutes of our being introduced.

Deep, and wide, that Irish Sea. And it still flows red.