Aside from normative ideas and methods for obtaining "goodness" in the form of cities, there is a body of systematic work since the nineteenth century in urban social science that attempts to explain what cities "are" rather than what they "ought to be." This class is a summary of the major categories of this work.
In the first instance, the city is regarded as a unique historic process. There is a rich literature of urban histories positioning cities as derivative from their own, specific culture. Emphasis is placed on observation, "reading" as Ruskin conceived of it, and the "reading" of Venice (Ruskin) is compared to that of Manchester (Engels), as well as to those of Benjamin, Norberg-Schulz and Rasmussen.
In the second, the city is regarded as an ecology of people such that each social group occupies space according to economic position and class. Derivative from general propositions of the sociology of the city (Weber, Simmel and Spengler), the work of the Chicago School, Park and Burgess in particular, suggest that the competition and accommodation of social groups produces a city of dynamic concentric rings from a center to a zone of commuters. Hoyt, however, assumed the forces of such ecological patterning would result in sectoral shapes. But both propositions regarded space as a neutral medium through which social groups interact. The third category regards the city as an economic engine in which space, unlike in the previous category, is both an additional cost imposed on the economy but also a resource for production or consumption. At a regional scale, the location of the settlement in the case of heavy industrial production would be an optimized function of raw materials, labor and product markets (Isard). In the case of agricultural distribution, systematic distributional patterns also emerge (Von Thunen), as they do in the creation of regularly spaced central places based on hexagonal market areas (Christaller). Within the city itself, the form of the city is argued around the willingness or ability of different groups to pay rent for land either close to or at a distance from the center, this expressed in curves for each class of activity (Alonso).
The fourth set of propositions regards the city as a field of forces, a communications network of particles which attract and repel each other much as they do in physics. Subsets of these ideas include population potential maps, gravity models, communications flows, and various topological models. Another category suggests that the most appropriate description of the city's functional form lies in understanding it as a system of linked decisions. One version focuses on the decisions taken by the powerful in the community (Forrester), others on the participation of citizens in a democratic city, and yet others on the game, in which people interact together according to fixed rules and produce agreed-upon outcomes. There is a last category, more explicitly ideological, which rejects previous theories of competition and posits the city as an arena of conflict, in which the city's form is the residue and sign of struggle, and also something that is shaped and used to wage it (Castells, Harvey, Lefebvre and Gordon).
Lehrer, Jonah. "A Physicist Solves the City," The New York Times, December 17, 2010.
Plans of metropolitan cores in Atlanta region and predominant metropolitan growth pattern, 1995 (Robert Charles Lesser & Co.)