18 December 2023

Golden Mean: A parable for Christmas

A new short story by Alan Garner.

First love. It matters. It comes once. Never again. It doesn’t repeat. It’s not recurring. There’s no dot over the decimal.

I like numbers. Numbers don’t change.

If you measure the length of your bank card and divide it by its breadth the answer is one point six one eight. Now take a four-bar Kit-Kat. It must be the four. Measure it the same way. Answer: one point six one eight. And so are a lot of matchboxes. But not the Strike Anywhere the Original Cook’s Matches, or Swan Vesta the Smoker’s Match. I don’t smoke. Smoking kills you. It says so on the packet.

You get it with Tarot cards, too. They’re best left alone. They mess your mind up, because they make patterns in your thoughts that you could believe are telling you what’s going to happen to you, and some doctors use them with disturbed patients because they claim that the exploration of the inner self leads to greater freedom within the individual. It doesn’t. A doctor tried it on me once, and all I got was bad dreams.

Now take the planets. If you start with Mercury, nearest the Sun, and call that “One”, then the difference of ratio between its orbit and that of Venus is one point six one eight: approximately. And so on; right the way out to Neptune.

Big hospital doors are the same as bank cards and matchboxes. I mean big doors in hospitals; but it may be when the hospital’s big, too.

The human body fits. Even the head and face.

Speaking of faces: when I was nine years old, my mother told me that I was never to have anything to do with Welsh girls. Their eyes were too close together, she said. I asked her what was wrong with that. She said: “Never you mind.” And I said: “Everyone’s got two eyes, close together.” She said I was cheeking her, and she smacked me on the legs with the sponge sole of my father’s slipper. It hurt a lot. But I didn’t cry.

I like numbers. Numbers don’t change.

One point six one eight. That’s special: what’s known as an Irrational Number. I like them best of all.

An Irrational Number is any Real Number that is not a Rational Number. Almost all Irrational Numbers are Transcendental, and all Transcendental Numbers are Irrational. It can readily be shown that the Irrational Numbers are precisely those numbers whose expansion in any given base, such as decimal or binary, never ends and never enters a periodic pattern. It never ends, never reaches Infinity. It goes on for ever and does not repeat.

My favourite number is Phi. That’s a Greek letter. It’s not the same as others. It’s also called the Golden Mean, aka Golden Ratio, aka Sacred Cut, aka Divine Portion; and it’s the unique ratio such that the ratio of the whole to the larger portion is the same as the ratio of the larger portion to the smaller portion. That’s beautiful. So elegant.

The Golden Mean was discovered by the ancient Greeks. It was a pupil of Pythagoras who proved it: Hippasus of Metapontum. But Pythagoras couldn’t accept that Irrational Numbers existed, so he had Hippasus drowned.

I nearly drowned once. My mother’s brother; that’s my uncle; he said he’d teach me to swim. So he took me to the swimming baths and up to the top of the chute at the deep end and pushed. I hit my head and the lifeguard had to save me and I went to hospital with concussion. I still can’t swim.

Anyway, another time I was in hospital and I was being taken to theatre. Isn’t it funny how one word can make such a difference? If you’re going to “the” theatre, you look forward to it; but if you’re going to theatre – Well.

I was lying on the trolley, in the foyer I suppose you’d call it, with my feet pointing towards the big door. The doctor said: “Just a scratch.” (Now that’s good psychology. When they say: Just a prick, you know it’s going to hurt, because it’s invasive. It also sounds a bit rude. But a scratch isn’t anything.) Then he told me to start counting. I got as far as one point six one eight zero three three nine eight, and the next thing I knew I was back in bed in the ward.

What’s good about Irrational Numbers is they expand on and on for ever, free as a bird, nearer and nearer to the Truth, but never ending, never stopping, never dying. I wish we were like that. I’d like to be Irrational.

She was my uncle’s wife’s niece. She came from Wales for a holiday one summer. And how we quarrelled! She said I didn’t know about music and I said she didn’t know about rocks. We wasted so much time.

Then we went to the Pictures at the Rex Cinema. The tickets were two shillings and three pence each, and the bus fare was tuppence ha’penny, both ways. We sat two rows from the front in a double seat, on the left. It was in the days before wide screens such as VistaVision, which had an aspect of one to one point six six, very close to Phi. The film was The Glass Mountain, starring Michael Denison and Dulcie Gray, with Tito Gobbi, of operatic fame. It was about a composer who crashes on a mountain in Italy in World War Two and is saved by partisans. He falls in love with one of them and turns their story into an opera when the war’s over. I’d never heard music like that. And we fell in love. It was so… innocent. She taught me a Welsh word: cariad. I couldn’t eat; and she couldn’t; and there were two days left before she went home. I saw her off on the 14.12. train, British Summer Time. Of course my mother knew. She said: “Did you kiss her?” I felt sick.

I like numbers. Numbers are real. Numbers don’t change.

And that was that. She was going to come back at Christmas, but she didn’t. I don’t know why; but I can guess. I wrote to her every day, and she wrote too; and then she stopped. Without a word. After a while, I stopped. I was that upset, and couldn’t think what to say. Then, years after, I found all her letters bundled together with an elastic band at the bottom of a drawer where my mother kept her sewing things. The envelopes had been opened, and the elastic was stiff and hard and crumbly. I put them in a box and buried them under a tree. I didn’t read them.

I liked Christmas when I was little. Well, Christmas Eve and Christmas Day, what with the excitement of Santa coming and me trying to stay awake to see him, though I never did, and the empty pillow case at the foot of my bed. Then waking up and seeing it all bulgy and pointy, and taking everything out one at a time, and my Rupert Book and Beano and Dandy Annuals at the bottom, though I didn’t know why Santa gave me football boots and boxing gloves as well. Then sitting on the buffet by the fire and reading all morning until we went to my granddad’s for dinner, and my grandma telling me to be careful when I ate my Christmas pudding in case there was a lucky silver threepenny bit in it and there always was.

But Boxing Day was different. We had to go to my uncle’s for tea, and everybody drank whisky and cherry brandy and talked loudly and laughed and smoked cigarettes which made the air blue. Then we sat by the fire and the grown-ups went on drinking and laughing. I didn’t understand what they were saying or what was so funny, and after a while they stopped laughing and my mother and uncle began yang-yanging over things that had happened a long time ago and blaming each other and my aunty left them to it and washed the pots and my father put his cap on and went to the pub and I wanted to go home and read my Annuals but I couldn’t.

The Golden Mean has been discovered several times. It was described by two Indians called Gopala and Hemachandra in 1150, when they were trying to find the best way of packing bins; and in Europe Leonardo Pisano Bonacci, 1170 to 1250, he studied it. Leonardo’s better known by his nickname, Fibonacci. I don’t know why he used his nickname, but he was one of the cleverest mathematicians of all time. He introduced decimals and Arabic numbers to the West, and what a difference that must have made. Where would we be if we were still stuck with Roman numerals? I mean, imagine, instead of trying to divide ninety-nine by twenty-seven, which is three point six recurring, you had to divide XCIX by XXVII. They must have been a strange lot, the Romans. And they didn’t have zero. It’s a good job the Arabs came along. Anyway, Fibonacci used his Golden Mean to describe the growth of an idealised (although biologically unrealistic) rabbit population; then he did the same for counting bees; but I don’t know why.

Artists and architects had discovered long since that, by using Phi, or the Golden Mean, they could create feelings of order and balance. It’s in the Parthenon at Athens, and lots of other old buildings, like Notre-Dame at Paris and the Cenotaph at London. There’s something about it that makes us happier.

She died young.

Only the other day, I looked out her photograph and measured the bridge of her nose and between her eyes. It was one to one point six one eight. So my mother was wrong. Her eyes weren’t too close together.

That’s why I like numbers. Numbers are real.

I don’t want to fall out with anybody; but if you believe something, there’s no getting round it by rational argument. In my book, faith and proof are oil and water.

Personally, I’d say that I am religious, but I don’t believe. It’s not what I’m against, but what I’m for. And I’m for uncertainty. As soon as you think you know, you’re finished. You’re brain-dead. You don’t listen and you can’t hear. Same as my mother and uncle yang-yanging on Boxing Days. If you’re certain of anything, you shut the door on the possibility of discovery.

[See also: What cells tell us about life]

A story’s the best way of showing what I think. I must have read it in a book somewhere.

One of the gods is sitting on top of the highest mountain in the world, and he’s crying. Another god comes up and asks him what the matter is and what are all those ants down there so excited about. He says, “They’re not ants, they’re people. I was holding the Jewel of Absolute Wisdom; and I dropped it; and it fell into the world and smashed. Everyone down there has got a tiny splinter of it; but they each think they’ve got the whole and they’re all running around and shouting and telling each other, but no one’s listening.”

I can’t put it better than that. I’m not saying it happened. It’s a good metaphor, and it gives us a chance to begin to understand. But once you “know”, you become a wazzock; (that’s what we’d call them, round here); and wazzocks, they won’t be told. They don’t know how to argue, and they don’t want to. They’ve no imaginations. They wouldn’t recognise a metaphor if they trod on it. They’re all the same, and the worst of the lot are the atheists. Atheism’s just as much a faith as any other, except that it’s more ignorant than most.

Irrational Numbers are the closest I know to Truth. You can follow an Irrational Number for eternity (though that’s a dubious word to use) but you’ll never be certain. You’ll never quite get there. Which is as it should be. You’ll be closer than if you didn’t follow; but if you’re a wazzock you can’t even start.

So when I saw her off on the train, and that felt pretty final, without what happened to her later, I was wrong.

Death has no part in the Golden Mean.

I think of my Phi cariad returned to every form she may be in and ever was, flying outwards, free as a bird, free from the damnation of certainty, free in the timelessness, free in the one point six one eight zero three three nine eight eight seven four nine eight nine four eight four eight two zero four five eight six eight three four three six five six three eight one one seven seven two zero three zero…

This short story was originally published in December 2022.

Alan Garner was born in 1934 and is the author of novels including “The Weirdstone of Brisingamen”, “The Owl Service” (both HarperCollins), and, most recently, “Treacle Walker” (Fourth Estate), which was shortlisted for the 2022 Booker Prize

[See also: Day and age]