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The sole repository of absolute truth is of course mathematics and the latest issue of Mathematics Today reveals another small step forward.

Barry Doe tells of a country whose rail service has trebled in quantity and halved in journey time since 1949, yet whose ticket prices for non-commuter services have dropped by more than a third. The country? Great Britain. Claims that fares are now extortionate are based on a false comparison - between open return fares in 1949 and 1993. But no one uses the open return nowadays except for business people before 9am.

Doe concludes: "Even forgetting Apex, buy a walk-on fare for standard class travel on any day bar Friday, for travel on virtually any train after the morning peak, and long-distance rail travel has never been cheaper."