地理科学进展 ›› 2009, Vol. 28 ›› Issue (2): 312-320.doi: 10.11820/dlkxjz.2009.02.022

• 理论探索 • 上一篇    

对称性与人文地理系统的规律性

陈彦光   

  1. 北京大学城市与环境学院城市与经济地理系,北京100871
  • 收稿日期:2008-12-01 修回日期:2009-01-01 出版日期:2009-03-25 发布日期:2009-03-25
  • 作者简介:陈彦光(1965-),男,副教授,理学博士,中国地理学会会员.主要研究方向:城市和理论地理学. E-mail:chenyg@pku.edu.cn
  • 基金资助:

    国家自然科学基金项目(40771061).

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

摘要:

长期以来,人文地理学一直未能找到像物理学定律那样严格的规律。究其根源,在于人文地理系统不满足 时空平移对称性。大自然在宇宙尺度和粒子尺度都遵循某种对称法则,但在人类活动的地理尺度上,各种对称规则 似乎都被破坏。因此,严格的普适性不能作为人文地理模型的选择依据。然而,近年的研究表明,人文地理系统在表 面的不对称背后,却隐含着另外一种对称规则。人文地理系统演化的一个隐含的目标似乎就是重建大自然的对称 律。寻找这类隐含的对称法则及其演化机理有助于地理学的理论建设和应用发展。借助典型的实例说明地理对称 问题对人文地理学规律探讨的学术意义,着重论证地理对称性与变换中的不变性的逻辑关系,以及人文地理学对 称性研究的一些相关问题,目的是为人文地理学的理论建设启发新的研究思路。

关键词: 不可观测量, 地理规律, 对称, 对称破缺, 普适性, 人文地理系统, 守恒律

Abstract:

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