Original Articles

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

  • College of Urban and Environmental Sciences, Peking University, Beijing 100871, China

Received date: 2008-12-01

  Revised date: 2009-01-01

  Online 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.

Cite this article

CHEN Yanguang . New Way of Looking at Human Geographical Laws Using the Idea from Symmetry[J]. PROGRESS IN GEOGRAPHY, 2009 , 28(2) : 312 -320 . DOI: 10.11820/dlkxjz.2009.02.022


[1] Von Neumann J. Collected Works (Vol.6).New York/Oxford: Pergamon Press, 1961. 492.

[2] Martin G J. All Possible Worlds: A History of Geographical Ideas (4th Rev. edn). New York, NY: Oxford University Press, 2005. 416~427.

[3] Hurst MEE. Geography has neither existence nor future. In: Johnston R J (ed.). The Future of Geography. London: Methuen, 1985. 59~91.

[4] 张祖林.当代西方地理学中的地理虚无主义.华中师范大 学学报(自然科学版),1994,28(2):269~276.

[5] 白光润.地理学的哲学贫困.地理学报,1995,50(3):279~ 287.

[6] Carroll C. National city -size distributions: What do we know after 67 years of research? Progress in Human Geography, 1982,6(1): 1~43.

[7] Gabaix X, Ioannides Y M. The evolution of city size distributions. In: Henderson J V, Thisse J F. Handbook of Urban and Regional Economics, Vol. 4 (Chapter 53). Amsterdam: North-Holland Publishing Company, 2004. 2341~ 2378.

[8] Cadwallader M T. Urban Geography: An Analytical Approach. Upper Saddle River, NJ: Prentice Hall, 1996. 114~117.

[9] Batty M, Longley P A. Fractal Cities: A Geometry of Form and Function. London: Academic Press, Harcourt Brace & Company, Publishers, 1994. 234~320.

[10] Harvey D 著,高泳源,刘立华,蔡运龙译.地理学中的解 释.北京:商务印书馆,1996.136~ 157.

[11] 叶大年. 地理与对称. 上海: 上海科技教育出版社, 2000,3.

[12] 叶大年,赫伟,徐文东,李哲.中国城市的对称分布.中国 科学(D 辑),2001,31(7):608~616.

[13] 陈彦光,刘继生.中心地体系与水系分形结构的相似性 分析.地理科学进展,2001,20(1):81~88.

[14] 刘继生, 陈彦光.Davis 规律与Beckmann 模型的数理等 价性———城市体系等级结构的宏观-微观对称性分析. 经济地理,2001,21(2),231~234.

[15] Lee TD. Symmetries, Asymmetries, and the World of Particles. Seattle and London: University of Washington Press, 1988.3~29.

[16] Mandelbrot B B. The Fractal Geometry of Nature. New York: W. H. Freeman and Company, 1983. 19.

[17] Frankhauser P. La Fractalité des Structures Urbaines (Fractality of Urban Structure). Paris: Economica, 1994.

[18] 陈彦光. 分形城市系统:标度、对称和空间复杂性.北京: 科学出版社,2008.

[19] Arlinghaus S. Fractals take a central place. Geografiska Annaler B, 1985,67(2): 83~88.

[20] 陈彦光. 城市体系Koch 雪花模型的实证研究———中心 地K3 体系中的分形与分维. 经济地理,1998,18(4):33~ 37.

[21] Frankhouser P. Aspects fractals des structures urbaines. L'Espace Geographique, 1990, 19(1): 45~69.

[22] Wong D, Fotheringham A S. Urban systems as examples of bounded chaos: Exploring the relationship between fractal dimension, rank-size, and rural to urban migration. Geografiska Annaler B, 1990,72: 89~99.

[23] 陆大道. 区域发展及其空间结构. 北京: 科学出版社, 1995, 137~141.

[24] 刘继生,陈彦光. 点-轴系统的分形结构及其空间复杂性 探讨. 地理研究,2003,22(4):447~454.

[25] 周一星. 主要经济联系方向论. 城市规划,1998,(2):22~ 25.

[26] Weyl H. Symmetry. Princeton, N J: Princeton University Press, 1989, 10.

[27] Feynman R. The Character of Physical Law. Cambridge, MA: The MIT Press, 1970, 84~107.

[28] Clark C. Urban population densities. Journal of Royal Statistical Society, 1951,114: 490~496.

[29] Zipf GK. Human Behavior and the Principle of Least Effort. Reading, MA: Addison-Wesley, 1949. 417~441.

[30] 陈勇,陈嵘,艾南山,李后强. 城市规模分布的分形研究. 经济地理,1993,13(3):48~-53.

[31] Kline M. Mathematics in Western Culture. London: George Allen and Unwin, 1954.410~431.

[32] 小川直树著,李毓昭译. 给讨厌数学的人.哈尔滨:哈尔 滨出版社,2006. 46~58.

[33] Stewart I 著,周仲良,周斌成,钟笑译. 第二重奥秘—生 命王国的新数学. 上海:上海科学技术出版社,2002,50.

[34] 陈彦光. 中心地体系空间结构的标度定律与分形模型— 对Christarller 中心地模型的数学抽象与理论推广. 北京 大学学报(自然科学版),2004,40(4):626~634.

[35] Holloway S L, Rice S P, Valentine G (eds.). Key Concepts in Geography. London: SAGE Publications, 209~229.

[36] 艾南山,陈嵘,李后强. 走向分形地貌学. 地理学与国土 研究,1999,15(2):92~96.

[37] Philo C, Mitchell R, More A. Reconsidering quantitative geography: Things that count (Guest editorial). Environment and Planning A, 1998, 30(2): 191~201.

[38] 顾朝林,陈璐. 人文地理学的发展历程及新趋势. 地理学 报,2004,59(增刊):11~20.

[39] Schaefer F K. Exceptionalism in geography: A methodological examination. Annals of the Association of Ameri-can Geographers, 1953, 43: 226~249.

[40] Fotheringham A S, O'Kelly M E. Spatial Interaction Models: Formulations and Applications. Boston: Kluwer Academic Publishers, 1989, 2.

[41] Waldrop M. Complexity: The Emerging of Science at the Edge of Order and Chaos. NY: Simon and Schuster, 1992, 136~143.

[42] Zanette D, Manrubia S. Role of intermittency in urban development: a model of large-scale city formation. Physical Review Letters, 1997, 79(3): 523~526.

[43] Buchanan M. Ubiquity: The Science of History or Why The World is Simpler Than We Think. London: Weidenfeld & Nicolson, 2000. 157~160.

[44] 陈彦光. 地理学的模型建设及其选择标准. 亚热带资源 与环境学报,2008,3(4):1~7.