There is a feeling in highly developed societies with centralized systems of government that an orderly society and geometrical town planning go hand in hand. This association is not exclusive to Western societies: Inca, Indian and Chinese civic planning has exhibited similar tendencies. Nor is it exclusive to totalitarian regimes, as it has featured prominently in socialist notions of ‘new towns’.

The most beguiling images of a community governed by mathematical order are the surviving Renaissance representations of ‘ideal cities’. None is more serenely beautiful than a painting from Urbino that is currently on show in Florence in the exhibition L'uomo del Rinascimento (The Renaissance Man), which can be seen at at the Palazzo Strozzi in Florence until 23 July. The exhibition centres on the architecture and writing of Leon Battista Alberti, author in 1435 of On Painting, the first book to expound the theory of linear perspective.

Many aspects of the ideal city from Urbino remain elusive. The artist and date are uncertain, and its original purpose is unclear. The most closely dated parallels are some doors, decorated with inlaid wooden panels of ideal cities, in the Ducal Palace at Urbino, which were installed between 1474 and 1482. The ruler of Urbino, Federico da Montefeltro, was shaping Urbino itself into as much of an ideal city as the existing buildings would allow.

The painting in question was also part of a decorative ensemble, as its edges show that it was built into a piece of furniture, perhaps a chest, couch or bed. Infrared reflectography has revealed the huge effort that went into drafting the carefully conceived buildings in absolutely meticulous perspective, by disclosing part of the intricate carbon-based underdrawing. One surprise is that the central ‘temple’ was originally conceived as a structure with a flat façade and loggia below a triangular pediment. It might have been a governmental building, like those found at the centre of squares in Tuscan new towns from the late thirteenth century onwards. It was then transformed into a centralized building, almost certainly religious in function.

Everything speaks of an orderly society. The temple refers to the majesty of God's order, and the ‘parish church’ behind and to the right serves for daily devotions. The palaces, with their gracious arcades, shelter pedestrians and their owners in comfort and style. Rooftop loggias provide retreats for well-ventilated relaxation, and the tiled piazza is clean and hygienic. And the beneficent rulers have provided two octagonal wells from which the citizens can draw clear water.

The whole is an essay in the geometry of perfect proportions and the good life. Only the people are missing: the ideal city is awaiting its ideal citizens. Will the city form them, shaping their values? Or have the people formed the city as their utopia?

Alberti himself, as the author of a treatise on the family, believed there was a natural order in the created world, and that we should adopt it in our lives. But he was realist enough, as was Federico, to know that human society needs the central imposition of rules.

Whether a city for contented dwellers can be planned scientifically, or whether it emerges organically from the free-market jungle, remains a mighty issue for town planners. When the Renaissance actually constructed planned cities, as they did at Urbino and Pienza, they somehow achieved a precarious balance between imposition and individuality. It is a difficult balance to contrive.