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The Independent Culture
I TAKE back some of what I said in this column about the Paddington to Heathrow Express. On my return from California there were just four carriages, necessitating my dragging my luggage half way down the platform. Trolleys are barred from the platform by those idiotic barriers.

Contrast this with arriving at the airport at Geneva, where you can take your trolley up and down escalators between train and plane without any problem. But then the Swiss take travel for granted, while we still see it as a privilege.

The crush in the carriage made it clear to me how much the pleasure of rail travel depends on personal space. I don't want to be jammed up close to people I haven't chosen freely. Especially if they do want to be jammed up close against people they haven't chosen freely.

This principle was exploited by Lord Berners, who used to bag a compartment and then leer and beckon sinisterly at anyone who made as if to enter it. As a result he generally travelled in comfort. By contrast, the car is an extension of personal space which you can hog, control or share with whomever you want. A crowded train affords no such choice.

But then if I had driven, instead, up to the York Maths Funfair last Saturday I would have missed booking a train seat next to the student on his way back up to uni. His dotingly subservient girlfriend queued on his behalf at the buffet, periodically returning with propitiatory beers and pasties to which he grunted acquiescence.

He consumed these messily, pausing only to dislodge cake adhering to the roof of his mouth. She gazed into his eyes with adoration, and when the passengers thinned out they repaired to a nearby seat and began to kiss inexpertly.

More horrifying than this was the fare: pounds 61.10. And I had to drive to London first to take advantage of it. A fellow passenger put it well: "Yesterday I went to Ipswich for pounds 39. For 50 pence more I could have flown to Nice. That's only one way. But then one way to Nice is probab- ly better than two ways to Ipswich."

The Second Maths Funfair in York, organised by John Bibby and the York Maths Teaching Group, was a pure delight. What I have preached about theoretically for the last 20 years was played out in reality before my eyes: children were totally absorbed by mathematical activities: programming turtles, assembling tangrams and playing board games.

Children are naturally attracted to mathematics. This interest does not have to be engendered in them. It does, however, have to be carefully fostered, as imagination can easily be killed off in the daily grind of the national curriculum.

Points to ponder

1. Six commuters A, B, C, D, E & F travel daily in a six-seated train compartment. In how many different ways can they take up their seats?

2. One day F misses the train (it leaves on time). How many more ways have the remaining five of taking up their seats as a result of his absence?

3. What happened to Erich Weiss on Hallowe'en 1926?

Last week's solution

The stick is packed along the diagonal of a cubical parcel of side 1 metre. The length of this is about 1.44 metres.