A paradox is an incongruity that seems to be contradictory or an outcome that is different from that envisaged. There are seven worth highlighting in the context of cities. The first and overarching paradox is the conflict between risk and creativity that will be elaborated upon below. The other six are:

• Calculating tangibles in a world of intangibles. We live in a 'weightless economy', or an economy of ideas, where 80 per cent of wealth is created through intangibles. We talk too of the importance of people. Yet our systems of measurement and the calculation of value are out of step and lag behind realities. For instance, accountancy systems invented in a mercantilist age and developed under industrialism remain largely focused on measuring assets as material entities. People, who as ideas-generators create most value, are by contrast treated as an accounting cost even though in the sale of a company they are part of its goodwill.

As mentioned earlier, too much of our data gathering is based on nations and static measures when it is cities that are the driving forces of national economies and it is relations and flows that reveal more about urban dynamics than quantities of attributes such as population.

• Accessibility and isolation. Can there be too much access? Being swamped with cascades of uncontrolled information impossible to filter is a well-known problem. Reflection often thrives more on being under-stimulated. Accessibility is deemed an unquestioned good, yet too much accessibility can destroy what it sets out to do. Unfettered access can make things too popular or bring things into reach too easily. The isolated settlement that thrives on being distant can suddenly find the outside world too close for comfort. It can be overwhelmed by popularity fired by a new accessibility and mass mobility. The critical mass tips from being 'just right' to being 'out of control'. A heritage setting can inspire and generate welcome tourism. Yet if too many visitors appear, they can drain the lifeblood of and drown local identity. The result may be that a city's future is determined by the nostalgic past that visitors want to see, but which residents do not need, with knick-knack shops, souvenir outlets and interpretative centres that gel the past into aspic.

• Porousness and identity. People need to be porous to new influences as well as to retain their identities. We need to be both local and global to survive in the current world, selectively open and closed at the same time. We need boundaries and borders to ground and anchor identity as well as bridges to connect us to the outside. Although identity is shaped by a variety of factors, from upbringing and friendship networks to work, crucially it is also rooted in geography and place. In spite of increased mobility, a sense of place remains a core value and often acts as the pivot point around which a person acts. This tends to mean that cities need to balance being parochial and cosmopolitan.

• Space and density. People want space and density at the same time. Some will want both, others one or the other. Space is at a premium and will become the benchmark of luxury. Perceived lack of space will drive location decisions, lifestyle choices, densities and technological development. Systems to optimize space, such as roads, will develop by making journeys more efficient through autonomous vehicle control devices involving smart card technology so that a greater number of cars can travel at far higher speeds in convoys on existing roads or by car sharing. Simultaneously, and in a seemingly contradictory way, densities will increase as the number of households rises and urban vitality is deemed to come from close-knit mixed uses, so shaping the look and feel of cities.

• City and country. The more we move to the country, the less like countryside it will become. According to a recent UK RICS survey, only 4 per cent of people want to live in urban areas, a figure constant since similar surveys were first conducted in the mid-1990s.14 The overwhelming majority want to live in the countryside. This will exacerbate the intense pull out of urban areas, putting pressure on market towns and villages whose formal integrity will be blown apart by in-fill, edge developments and rises in population. It will all merge into a built-up mass. The overall feeling will be of many highways connecting some settlements rather than many settlements connected by some roads. The battle between perceived urban and rural values will surely get worse.

• Age and technology. The capacity to handle technology is a form of power, and the young feel more comfortable with it than older generations. As technological change drives the economy, it could thus transform power relationships between generations. We already know that children teach parents how to use videos, email and the internet: they have become the translators of the modern world. In a global culture where age has engendered respect, what will technology do to social relations when older people feel increasingly disenfranchised? For some older people there is a growing sense of being an immigrant in their own technological country.

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