## Essay: The new science of cities – Michael Batty

The author of this book The new science of cities Michael Batty is Bartlett Professor of Planning at University College London, where he is Chairman of the Center for Advanced Spatial Analysis (CASA), and Visiting Distinguished Professor at Arizona State University. He is the coauthor of ‘ Fractal Cities: A Geometry of Form and Function ‘, and he also write another book ‘ Cities and Complexity: Understanding Cities with Cellular Automata, Agent-Based Models, and Fractals ‘. The next few paragraphs in this article makes summarizes and reviews for several chapters of the famous book ‘ The new science of cities ‘.

In Chapter V of this book, for some hierarchies in city, such as population hierarchies, it meets proportionate random growth Eq.(5.1) in this book, which leads to lognormal size distributions. But when introducing a minimum threshold, the hierarchies distribution is no longer lognormal, becoming a power law distribution, which is generally called Gibrat process. Gibrat process can converge to a pure scaling law’Zipf’s law. It is a very important law, and is similar to ‘Twenty-Eighty law’ or Pareto principle, namely only a small portion plays a decisive role, about 20%, and the remaining 80% in spite of the majority, but it is secondary. For example, 80% of the results come from 20% of your pay. Zipf’s law can also be applied in urban hierarchies, such as the hierarchies of roads connecting in the city, a few roads are at a higher hierarchy and most roads belong to a lower hierarchy.

The hierarchy generated by the proportionate random growth process Eq. (5.1) is the simplest pattern, and it cannot be a good model because it does not consider any kind of competition and interaction between different regions. But in real life there are some interaction between different cities or regions, for example the people in small towns, they move to the big cities in order to acquire the better lives and more jobs, thus affecting the population of the two regions’hierarchy distribution. Therefore, using proportionate random growth to analyze the growth process of a city is totally inadequate. Eq.(5.3) is superior to Eq.(5.1), because it considers an additional term’the diffusion term, considering the effect of the mutual diffusion between different regions. However, its shortcoming is that the distributions generated from Eq.(5.3) with diffusion are somewhat flat, and the hierarchical structure is not obvious, and as the level of diffusion is increased, the hierarchical structure begins to disappear. Compared to the previous two formulas, Eq.(5.4) is the best to represent the city size, because it not only considers the diffusion, but also adds the agglomeration economies, making the hierarchical structure relatively apparent.

In Chapter VI, using a unifying framework to represent the relations between points and lines (namely junctions and streets): bipartite graphs. This bipartite graphs measurement simply count the number of points per line and lines per point, which is the simple count of the in-degrees and out-degrees. Its advantage is that the measurement does not require any complicated digital computing, but the more usual approach is to examine the number of common points for any pair of lines or the number of common lines for any pair of points, thus forming the primal and dual characterizations of the problem. This measurement is called direct measurement, it belongs to connectivity and direct measures between elements, but more appropriate measures is to calculate the routes between the elements based on the indirect links, ensuring the shortest routes. This measure is called indirect measurement based on step length, its disadvantage is ignoring the relative importance and the strengths, and each step is given equal weight, whereas in fact as the step length gets greater, the relative importance of the step gets smaller. So compared to the former three measurements, the weighed distance measures is better. Eq.(6.24) represents the index of similarity between each pair of distance, and it is chi-square-like. Based on the Eq.(6.24), the similarity index between weighed distance measurement with bipartite graphs measurement and direct measurement is higher, more than 80%, whereas the similarity index between the indirect measurement based on step length with other three distance measures is smaller, lying in 60%’70%.

Based on Chapter VI, Chapter VII introduces six distance measurements in complex networks: bipartite graphs measurement, direct measurement, indirect measurement (based on step length), weighed distance measurement, Euclidean distance measures and proximity measures. Among them, the strengths and weaknesses of the first four measurements have been analyzed in the preceding paragraph. For the fifth one, spatial networks are composed of axial lines and straight line segments, Euclidean distance measurement only computes straight line distances, and extends to computing curved lines from straight lines. The fifth measurement’s advantage is to avoid calculating the topological distance of the curved lines directly, and calculating the geometry distance of straight lines is relatively simple, yet its disadvantage is that the calculation of the curved lines is not precise in the spatial networks. The sixth one’proximity measures’is the extending of the third one’step length distance measures, and it focuses on the adjacency of the elements rather than the geometric distance. Proximity measures have low correlations with Euclidean measures and high correlation with other four measures with respect to both the dual and primal problems, since Euclidean measures aim to calculating the geometric distance, while proximity measures focus on the adjacency.

Chapter 11 introduces Markovian design machines. Here it uses the term ‘machine’ rather than ‘model’, making that the designers can have more imagination, and it will not cause too much restraint and limit for the designer. The term ‘model’ is too strict, while the term ‘machine’ allows that Markovian design has greater flexibility, so using the term ‘machine’ instead of ‘model’. The classification of design machines: completely connected, strongly connected chains, unilaterally connected chains, weakly connected and disconnected chains. The former two kinds belong to irreducible chains, and the last three types belong to reducible chains. Each element has equal weights for completely connected chains, different weights for strongly connected chains, the larger weights represent the relative importance is larger. There are only one factor to dominate in unilaterally connected chains, whose weight is one and other factors’ weight are zero. Among them the strongly connected design type has more applications in the life, such as housing construction process, it should belong to strongly connected chains, because each process (namely each element) has different weights, and the weight of housing foundations should be the maximum, thus this process is irreducible chain.

The above content is the summarizes and reviews for several chapters of this book ‘ The new science of cities ‘, including Chapter 5, 6, 7, and Chapter 11. Nigel Thrift, the Vice Chancellor of Warwick University, once said ‘Michael Batty’s remarkable work has become the foundation of a new science of urban flows and networks that uses big data and sharp theory as tools to dig deep into how and what cities are, and how they can be designed in better ways. This is the book that sets the benchmark that all others will have to follow’. Thus this book is of great value and very comprehensive in spite of some mistakes. It is a powerful tool and is worthy of further study for the readers.