PROGRESS IN GEOGRAPHY ›› 2009, Vol. 28 ›› Issue (2): 312-320.doi: 10.11820/dlkxjz.2009.02.022

• Original Articles • Previous Articles    

New Way of Looking at Human Geographical Laws Using the Idea from Symmetry

CHEN Yanguang   

  1. College of Urban and Environmental Sciences, Peking University, Beijing 100871, China
  • Received:2008-12-01 Revised:2009-01-01 Online:2009-03-25 Published:2009-03-25


Because of asymmetry of space and time translation, geographers have been trying in vain to find theoretical laws which are like the natural laws in classical physics for a long time. The basic laws at large scale of macro level (cosmos) and small scale of micro level (particles) keep symmetric in both space and time. However, for human scale of medium level (e.g. cities), all symmetry rules seem to be broken. For a geographical phenomenon, mathematical model is not always one and only, and model parameter values are not constant. Consequently, “universality” cannot be taken as a criterion of selecting geographical models or laws. The most difficult problem of theoretical construction in geography just rests with breaking symmetry of human scale. In this instance, we need now judgment standards of geographical models and laws based on new philosophy. Fortunately, a discovery is made by the author these years that a good geographical model, especially, mathematical model, always has some types of invariance through transformation indicative of variance. Invariance suggests symmetry, including translational symmetry, dilation symmetry, lateral symmetry, rotational symmetry, etc. For theoretical models or rules, universality is a kind of ex -symmetry of natural laws, while invariance of transformation is in fact an in - symmetry of models. Geographical laws seem to conform to some in-symmetry rules instead of exsymmetry rules. The evolution aim of geographical systems seems to reconstruct the symmetry rules of nature. It is of significance for us to explore geographical symmetry, in particular in human geography, such as symmetrical distributions in time or in space, and the symmetry between time and space, or between macro-level and micro -level, and so on. In this paper, a preliminary thought is presented to research geographical laws of human systems using the concepts from symmetry. Some conclusions may be revealing for future geographical research at home and abroad.

Key words: conversation, geographical law, human system, immensurable quantity, symmetry, symmetry breaking, universality