Andrew Ritchie, inventor of the Brompton folding bicycle, once mused that the perfect portable bike would be "like a magic carpet . . . You could fold it up and put it into your pocket or handbag". Then he paused: "But you'll always be limited by the size of the wheels. And so far no one has invented a folding wheel."
It was a rare - indeed unique - occasion when I was able to put Ritchie right. A 19th-century inventor, William Henry James Grout, did in fact devise a folding wheel. His bike, predictably named the Grout Portable, was a penny farthing with a frame that split into two and a larger wheel that could be dismantled into four pieces. All the bits fitted into Grout's Wonderful Bag, a leather case secured with buckles and straps.
Grout's aim: to get round the problems of carrying a bike on a train. Now doesn't that sound familiar? Grout had an incentive to find a way of making a bike small enough for train travel: the penny farthing was a huge beast. And crucially, the primitive design of early bicycles gave him an advantage: in Grout's day, tyres were solid, which made the business of splitting a wheel into four separate quadrants relatively simple. You couldn't do the same with a wheel fitted with a one-piece pneumatic tyre.
So, in a 21st-century context, is the idea of the folding wheel dead? It is not. A British design engineer, Duncan Fitzsimons, has developed a prototype that can be squashed into something the approximate shape of a slender ellipse. Throughout, the tyre remains inflated. Hard to visualise? Then have a look at www.duncfitz.co.uk .
Will the young Fitzsimons's folding wheel make it into production? I haven't the foggiest idea. But his inventiveness illustrates two things. First, people have been saying for more than a century that bike design has reached its limit, save for incremental advances. It's as silly a notion now as it was 100 years ago: there's plenty still to go for.
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Second, it is in the realm of folding bikes that we are seeing the most interesting innovations. You can buy a folding bike for less than £1,000 that can be knocked down so small that it can be carried on a plane - minus wheels, of course - as hand baggage.
Folding wheels would make all manner of things possible.
Have we yet got the magic carpet of Andrew Ritchie's imagination? No. But it's progress.