Soane's Dulwich Picture Gallery, despite being 180 years old, is a comparatively recent example of the trend. For really serious high-tech building failures, you have to go back to medieval times. Not long after the Normans had brought over their solid, Romanesque architecture - itself an impossibly futuristic concept for the benighted Old English - things started to develop rapidly. Gothic, when it arrived around Paris in the 1130s, was not so much a style as a new technology: its strength and grace allowed you to build higher, span wider, and put in more glass, than ever before. Instead of carving holes out of solid walls, you put up a skeletal framework and let the light flood in. The search for a transparent, ethereal, architecture had begun. As had some catastrophic mistakes.

All connoisseurs of the over-ambitious in architecture must visit Beauvais Cathedral, north of Paris, at least once in their lives, as a Muslim must visit Mecca. At Beauvais, begun in 1225, the aim was to build the tallest vaults in the world - outshining Notre Dame, Chartres, and the rest. They built high, all right - at over 150 feet from floor to ceiling, Beauvais is still awe-inspiring. How does it stay up? Well, a big chunk of it didn't. The choir collapsed in 1284. Rebuilding it - this time with better foundations - cost so much that the cathedral was never finished. To this day, it has no nave.

How long can an ambitious building go slowly wrong before its very defect becomes a perceived virtue? Around half a millennium, in the case of the belfry at Pisa Cathedral, better known as the Leaning Tower. As with Beauvais, the problem at Pisa is to do with foundations. But whereas Beauvais lasted nearly 60 years before its collapse and subsequent rebuild, Pisa - completed in 1271, though it started to lean even during as it was built - is still anticipating collapse after more than 600 years. If today's engineers finally work out how to restrain it, the tower may never fall at all: a design defect frozen in the act of self-destruction, a glorious monument to people who tried just a little too hard. Remember: without that famous tilting platform to drop metal balls from, Galileo would have had some difficulty conducting his wonderfully appropriate experiments in gravitation.

There is an assonance between the most ambitious man-made objects and the works of nature. As Ruskin wrote: "There are few rocks, even among the Alps, that have a clear vertical fall as high as the choir at Beauvais." It is, so to speak, a hollow mountain of a building. And the point is that they fixed it: they found a way in the end of making it stand up. In William Golding's 1964 novel The Spire, the building of the eponymous object is seen as an act of faith, taken against all technical advice. It should be impossible, and very nearly is, but somehow the spire, though badly damaged, stands. It is significant that Golding lived in the shadow of Salisbury Cathedral: the spire of Salisbury, finished in 1380 with few of the problems that afflicted its fictional counterpart, in its way the answer to Beauvais. It too was an attempt to go higher than ever before, and it worked. Plenty of other spires on plenty of other cathedrals fell down, but by the 14th century some vital lessons had been learned.

Today, the American architect Frank Lloyd Wright's houses are jealously preserved and restored and protected. So high has his stock risen that people choose to build designs of his that never saw the light of day during his lifetime. He is spoken of as perhaps the greatest architect of the 20th century, eclipsing possibly even Le Corbusier. And Wright's houses notoriously leaked and sagged. Once an enraged client rang him up to complain that water was leaking onto his dining table. "I advise you to move the table," Wright replied, and rang off.