Every piece of cartography is a fib, but some are more mendacious than others. Simon Calder unravels the secrets of the traveller's most basic tool

The prize for the world's most user-friendly map must surely go to Harry Beck's map of the London Underground ­ until you try it out on the surface. Suppose you are at Shoreditch and wish to get to Bethnal Green. At a glance you see the Tube journey will involve three changes of train. But, on the map, the stations are almost touching each other. Surely a few steps north-west from Shoreditch will take you there? Wrong; try one mile east. But if you employ a map in a way that was never intended, that's your problem. You might as well try to find your way through the capital from the Old Kent Road to Mayfair using only the Monopoly board.

Locals and tourists alike love the Underground map: an elegant solution to presenting the world's most complicated railway network in a form that allows you to plot a subterranean course while knowing nothing else of London. By eliminating almost every element of reality from the map, it becomes a supremely valuable tool. Like any map, though, it is profoundly false.

Imagine a visitor arriving at London Bridge railway station, wishing to get to Borough, one stop down the Northern Line. The apparent distance between the two is large ­ as far as the 10-station trip from Warwick Avenue to South Kensington, and surely worth the £1.50 Tube fare. In fact, a five-minute stroll will cover the distance.

The first casualty of any attempt to represent a messy, three-dimensional world on paper, parchment or computer screen is truth. Every map is a lie, but some are more mendacious than others.

"This is a political document, not a map," declares Neil Taylor, the British tour operator who pioneered travel behind the Iron Curtain. He is peering at a chart of East Berlin, produced in the capital of the German Democratic Republic in 1977. The Wall was a brutal strip of concrete, barbed wire and minefields, designed to seal the East German population in an ideological vacuum. Here, though, the frontier is portrayed as nothing more sinister than an innocuous, dotted-grey line, separating the East German capital from the apparently unpopulated pastures of West Berlin beyond. Odd patches of green and the East German-run S-Bahn railway are all that enliven the emptiness of the western half. "Even this map represents progress on those that were printed just after the Wall went up", says Taylor. "They showed West Berlin as a complete blank."

Politicians could thus test the temperature of the Cold War from the wide open spaces in the West depicted on the Stadtplan von Berlin, Hauptstadt der DDR. From the East German citizen's point of view, this attractive and tourist-friendly map worked just fine, too. It shows in details only those areas where he or she could go: the barrier, where two conflicting political systems crunched up against one another, meant there was no prospect of visiting the shops of the Ku'damm or the sleaze of Neu Kölln.

Maps are much more than devices to get you from Kürfurstendam to Friedrichstrasse or Shoreditch to Bethnal Green. They are imbued with power: of ownership, of attack, of alliance. With such power comes mischief, propaganda and secrecy, which is why cartographers have always been geo-political spin-doctors.

Even the great cartographer Gerhard Mercator produced a map in 1564 that came dangerously close to destabilising Elizabethan England. "It showed a distinctly Catholic country a generation after the dissolution of the monasteries," says Peter Barber, who is deputy map librarian at the British Library. Mercator never visited Britain, yet he published a highly detailed map that, he said, an unidentified stranger had asked him to prepare. Barber describes it as "a passport for any invader".

"In the 16th century most people might have known their locality, but they had really very, very little idea of the world beyond that. A good cartographer carried that knowledge around in his head."

Amid the turbulent politics of 16th-century Europe, such intelligence was greatly sought after. Good map-makers were endowed with a kind of cartographic immunity. Mercator went on to produce his 1569 Projection of the world, the answer to a mariner's prayer. On this chart, you could set a course from Plymouth in Devon to Plymouth Massachusetts, relative to true north, and be confident of reaching the right point on the New England coast. Not the shortest transatlantic voyage, but the surest. A side-effect of Mercator's remarkable Projection is that relative land areas are distorted. Greenland, for example, appears to be as large as South America, while in reality it is one-ninth the size ­ a planet-sized deception, say some.

"The earth in true proportion for the first time," trilled the publicity for a "revolutionary" map in the early 1970s. "The main advantage of the Peters Projection over the 'normal' Mercator Projection is that the size of all surfaces is given correctly."

The projection offered by Arno Peters, a German historian, showed an unfamiliar world. North America, Europe and Siberia appeared to retreat towards the horizon. Australia resembled the twisted frown of a clown, while Africa looked as if it has been hung out to dry. "See how this changes your world view!"

It certainly offered a less Euro-centric representation than traditional projections. Third World charities, radical politicians and well-intentioned undergraduates pinned their colours to Peters' mast and Blu-Tak'd the map to the wall. The plaudits would have dismayed James Gall, a Scots priest, had he not conveniently died around a century earlier. In 1855 he had hatched an identical projection andpublished the map in Scottish Geographical. My attempts to track down Peters proved as unsuccessful as sailing the Atlantic armed with only his map, but his royalties are still rolling in.

Maps mean big money. Ask the AA, which has just agreed to pay £20m to the Ordnance Survey, Britain's official mapping organisation, to settle a long-running dispute over copyright. Or visit Pontypool Place. You can find this small street in Southwark marked on page 53 of the Mini A-Z of London slanting from north-west to south-east. Strange, because it actually runs from south-west to north-east.

The practice of introducing deliberate distortions is known as "fingerprinting". Map-makers use the technique to protect their intellectual property. Injecting falsehoods makes plagiarism much easier to prove. The cartographer wants to minimise inconvenience for users, and so parts company with reality in places that won't mislead readers. Pontypool Place, featuring abandoned industrial premises and a car park, is an obvious candidate for twisting through 90 degrees.

Sometimes a map may omit an entire country for commercial purposes. Often the country that finds itself erased is Israel. "The mapping of the Middle East mirrors the complexity of the region's politics," says Douglas Schatz, managing director of Stanford's map and travel guide shop in London.

"A map of an Arab country will have a sizeable potential market in that country. It must present a view that accords with the political view or else it would not be acceptable." Look to the west of the Sea of Galilee on a map of Syria and you will be hard-pressed to detect much sign of Israel. Even the inflight "Skymaps" aboard some airlines are programmed to avoid any mention of the nation.

Some omissions are the result of cartographic cock-up, not commerce or conspiracy. Seattle, the largest city in the Pacific Northwest, famously vanished from a road map of the US, and this year Dartford was consigned to cartographic oblivion on a new tourist map published by Kent County Council. But slips of the hand that wipe out towns and cities aren't in the same league as the tangle of fibs that continues cartographically to trap the traveller.

Back in East Berlin, the checkpoint guards were made to look Charlies more than a decade ago. On any modern map, the blanks of West Berlin are filled in with urban clutter, and the streets in the east of the capital have reverted to their historic names, rather than those of petty Politburo tyrants.

Satellite technology enables any serious foe easily to map the terrain from Dover to Dounreay. Surely there can be no point in any democratic government falsifying maps? The Ordnance Survey disagrees: "A small number of classified and declassified sites still appear as blank spaces on our maps."

'The Secrets of Maps' presented by Simon Calder and produced by Pam Rutherford, will be repeated on BBC Radio 4 at 3.45pm daily from Monday 4 June to Thursday 7 June