But though the book omits this, it gradually makes clear what the thing is about creating ideal societies: they have to be designed as precision objects, they cannot just (pace Morris) be left to happen by themselves. To design and rule a utopia, you must be a serious control freak. You must know exactly where everyone is, how many there are, what they are doing, where they are going, and how. The city therefore becomes a machine for life, work, and surveillance. That is why they take the forms they do - usually grid-pattern, circular, polygonal, or, very rarely, linear. They tend to remain on paper because real life leads to compromise. Brasilia (a built Utopia of original shape that is another surprising omission from this book) quickly became engulfed in messy shanty-towns as the normal order reasserted itself.

The book starts, as it must, with Thomas More’s island of Utopia of 1516. More devised a deliberately ambiguous word from ancient Greek which can mean either “No Place” or “Place of well-being”. In the Italian Renaissance, painters liked to depict ideal cities, usually in the form of great public buildings around squares. Thereafter, serious planning began. Eaton correctly summarises Utopias as “the intellectual dreams of would-be reformers” and notes that such people must then enter into virtual marriage contracts with people in power in order to try to implement them (again, one cannot help thinking of Rogers’ increasingly frustrating relationship with New Labour).

There are fictional Utopias and dystopias to be found here -movie examples include Fritz Lang’s scary 1925 Metropolis, or Vincent Korda and H.G. Wells’s diametrically opposed Everytown in “Things to Come” of 1936. Another omission from this period is Jean de Brunhoff’s Celesteville, the Utopian city of Babar the elephant which, with its grid-pattern of identical buildings and twin Palaces of Work and Pleasure, very much reflects an older generation of paternalistic ideal-city planning. But Eaton, who is nothing if not relentlessly serious, does give us lots on that older generation, most notably the work of the inspired but megalomaniac late 18th century architect Claude-Nicholas Ledoux. Being French but without child readers to consider like de Brunhoff, Ledoux tended to add a large legalized brothel to his grandiose plans, whether for rebuilding Paris or making new industrial towns. Later he rationalized this: his “Oikema” or House of Passion, he said, would lead the young onto the path of virtue via that of depravity.