Cities are obvious metaphors for life. We call roads 'arteries' and so forth.

We form cities in order to enhance interaction, to facilitate growth, wealth creation, ideas, innovation, but in so doing, we create, from a physicist's viewpoint, entropy.

Knowing and being cognizant of the underlying principles and dynamics, seeing the problem in a broad systemic context, thinking quantitatively and analytically, all need to be integrated with the necessarily dominant focus on detail relevant to the specific problem in order to optimize design and minimize unintended consequences.

So in marked contrast to infrastructure, which scales sublinearly with population size, socioeconomic quantities – the very essence of a city – scale superlinearly, thereby manifesting systematic increasing returns to scale.

A major intent is to show that underlying the extraordinary complexity, diversity, and apparent messiness of the world we live in lies a surprising unity and simplicity when viewed through the lens of scale.

Many of the most interesting phenomena that we have touched upon fall into this category, including the occurrence of disasters such as earthquakes, financial market crashes, and forest fires. All of these have fat-tail distributions with many more rare events, such as enormous earthquakes, large market crashes, and raging forest fires, than would have been predicted by assuming that they were random events following a classic Gaussian distribution.

But like all excellent, fulfilling and meaningful relationships, it has also occasionally been frustrating and challenging.

The two dominant components that constitute a city, its physical infrastructure and its socioeconomic activity, can both be conceptualized as approximately self-similar fractal-like network structures.

Thus, to avoid collapse a new innovation must be initiated that resets the clock, allowing growth to continue and the impending singularity to be avoided.

It is all too often forgotten that the whole point of a city is to bring people together, to facilitate interaction, and thereby to create ideas and wealth, to enhance innovative thinking and encourage entrepreneurship and cultural activity by taking advantage of the extraordinary opportunities that the diversity of a great city offers.