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and all the other necessary pieces of coloured cardboard in a derangement of eagerness. So many, the man needed an extra hand to deal with it all: the outward from Cambridge to Wimbledon via Clapham Junction and Willesden Junction covered by one set of reduced-fare permits; a continued discount outward from Wimbledon to Woking, with ‘appropriate alternative documentation’. As the conductor sifted through these triumphs of cunning, Simon’s face was suffused with expectation. The man adopted a bored expression and punched whatever suited him with a machine that pinched the paper hard and left behind purple bumps. Simon snatched the pile back and studied the undulations with satisfaction.

      Another cousin I’d noticed on the family tree was called ‘Bonewit’. This woman appears on the fecund side of the family. It’s difficult to count the tiny layers of type on that half of the poster: seven children to Joseph and Regina; eight to Isaac Shellim and Ammam; ten – no, twelve – wait, my finger’s too fat for the tiny letters, eleven – to Shima and Manasseh: Aaron, Hababah, Ezekiel, Benjamin, David, Hannah, Esther … a rat-a-tat from the Pentateuch. Fifteen kids! to Sarah and Moses David. By the time they got to Gretha Bonewit, their seed was worn out.

      ‘Bonewit?’ said Simon, interrupting. ‘“Wit” is Dutch for “white”. I’ve got a Dutch dictionary in here.’

      As the train passed Addenbrooke’s Hospital, Simon’s attention swerved, to gout. Jolting his hand out of the foreign-dictionary sector of his holdall, he sank it back in six inches further along and two inches to the right, and extracted a scrunched-up Tesco bag containing tablets. Allopurinol, for gout; Voltarol, for swelling (though it’s bad for his kidneys); Atenolol for blood thinning. He washed a selection down with more passionfruit juice and returned to dictionary-hunting.

      ‘Simon, why have you got a Dutch dictionary?’

      ‘Why shouldn’t I have a Dutch dictionary?’

      ‘Do you have a Mongolian dictionary?’

      ‘No.’

      ‘Do you have a dictionary for roast chickens?’

      ‘No.’

      ‘Well, then, why a Dutch one?’

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      Simon’s mother, grandfather Aslan (far right) and Battleaxe.

      ‘Because,’ he honked, triumphant that the answer had got such assiduous courting, ‘I …’ But at this point he found the book in question and pulled it out. ‘Let’s see, aaaah, hnnnn, bonewit, bone, bon … ooh …’ – his eyes lit up – ‘… it means “ticket voucher”.’

      Simon will rot his floorboards with bathwater, immure his kitchen surfaces in Mr Patak’s mixed pickle and hack his hair off with a kitchen knife, but he is never unkind to maps. Returning the dictionary, Simon burrowed a foot and a half to the left and cosseted out an Ordnance Survey ‘Landranger’. He shook it into a sail-sized billow of paper, then pressed it gently into manageable shape.

      Outside, the rain was frenzied. It clattered against the roof and ran in urgent, buffeted streaks along the glass. The flat lands of Cambridgeshire swelled up into a wave of hills.

      When I looked back at Simon, a banana had appeared in his hand.

      ‘Right, your granny. Why did she live in Woking, but your grandfather stayed in Calcutta?’

      ‘I have no idea.’ Simon looked up from his map and considered the point. ‘Isn’t that the sort of thing married couples do?’

      ‘Was there a huge argument?’

      ‘No, oh dear, I don’t know.’

      ‘Did he have a harem?’

      ‘Huuunh. Should he have?’

      Ordinarily, I like to record all interviews, because it’s not just the words that count, but the hesitations and silences. But this opportunity had occurred without notice, and I didn’t have my voice recorder.

      I decided ‘Hnnn’, ‘Uuugh’ and ‘Aaah’ should be noted as ‘Himg’, ‘Uimg’ and ‘Aimg’. Stage directions ‘pained’, ‘dead-eyed’ and ‘yawning’ to be added as appropriate.

      ‘OK. How about this: why did your ancestors leave Iraq for Calcutta in the first place?’

      ‘Oh, dear, no. No, no,’ Simon replied. ‘I can’t possibly remember that. Aimg. How can I be expected to remember what happened before my birth?’

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      Letter to grandparents, from Simon (signing himself by number 5) aged 5.

      In all of Simon’s recollections Kitty hobbles. After emigrating in the year he-doesn’t-know-when, leaving behind he-doesn’t-know-why her husband Aslan, she bought a he-doesn’t-know-what-type-of-house in Woking with a bamboo plantation.

      ‘Bamboo?’

      Simon doesn’t-know-how – I mean, doesn’t know how – it got there. Every day, until her nineties, she dragged herself round, at first flicking gravel off the petunia bed with her walking stick; then, in her final stages of life, pruning the box-hedge parterre from her wheelchair, pushed by a daughter or a friendly guest.

      ‘One of her legs was broken,’ is Simon’s explanation for the hobble.

      ‘Permanently?’ I asked, and paused. ‘Which one?’

      Simon thought carefully. ‘Himg (pained), the left.’ Then he considered the problem a moment longer: ‘A img (aggravated), the right.’

      Another bout of concentration.

      ‘They alternated. Would you like some Bombay mix?’

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      Letter to his mother, aged 5.

      When she wasn’t in the garden, Kitty sat in the front room overlooking the croquet lawn and played bridge. Her entire last thirty years seem to have been wasted on hobbling and cards.

      Grandfather Aslan was ‘fairy-like’. Once every few years he appeared in London for a week, then disappeared. ‘Feeew-ff, just like that.’ The rest of the time he remained in Calcutta, the very successful dealer in … Simon still-doesn’t-know-what.

      That’s it. There’s no point in prolonging this ancestral agony.

      *11

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      Introducing

      Just as a square can be rotated through four turns to get it back to where it was to begin with, and the results laid out in a Group Table, the same approach can be applied to every regular shape. The size of the table you need to draw depends on how many operations have to be performed before you’ve exhausted all the possibilities and ended up back where you started. An equal-sided triangle can be manhandled three times before it’s back on its feet:

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      As before, these represent the act of turning Triangle. The trick of the game is to find all the ways you can fiddle with Triangle and yet leave it looking just the same afterwards

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