GEOGRAPHY AND THE PROPERTIES OF SURFACES. ENERGY FLOW AND SPATIAL ORDER, WITH SPECIAL REFERENCE TO MIXED HEXAGONAL CENTRAL PLACE HIERARCHIES.
Abstract
This paper is a major revision of Harvard Theoretical Geography Paper No. 5. The number of market areas (cumulated number of towns) for each order in a central place hierarchy is predicted. Given an array of numbers corresponding to geometric series to the bases 3, 4, and 7, the number of market areas depends on both the cut off point in the array, and the number of orders required. Given these constraints, the geometric means of the groupings required to create orders should approximate a geometric progression. The expected number of market areas is the convergence of the arithmetic and geometric means of the groups. This equilibrium balances opposing tendencies for minimum overland work and maximum work savings on economies of scale. In addition, the entropy of the system approaches the maximum possible. Six empirical studies show correspondence to this model, even though the investigators were operating without knowledge of the model, and used different methods to detect hierarchy. Further applications of this model in geomorphology, ecology, physiology, and botany are suggested. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Jan 03, 1968
- Accession Number
- AD0663910
Entities
People
- Michael J. Woldenberg
Organizations
- Harvard University