文章基本信息

标题：Spatial Analysis through the Looking Glass
本地全文：下载
作者：Peter Martin
期刊名称：Solstice
印刷版ISSN：1059-5325
出版年度：2007
卷号：XVIII
期号：1
出版社：Institute of Mathematical Geography
摘要：One of the delightful attractions that mathematics and geography have in common is that they offer fresh views of the world. Both fields of inquiry are circumspect almost by definition, and as soon as one looks around without prejudice, one discovers alternatives to one’s provincial world view. In mathematics, formalism and generalization are the seemingly sterile keys that open the gates to fertile fields of invention that, for its unexpected—even unexpectable—consequences, is indistinguishable from discovery. Formalism engenders the “what if” assumptions that lead to strange constructions, with their uncanny applicability to physics—non-Euclidean geometry, complex numbers, the Mandelbrot set. Generalization is the building of broader and broader analogies—the essence of cognition that Hofstadter has called ‘chunking” (Hofstadter 2002). The joy of mathematics is that one gets more than what one bargained for; one discovers connections that one did not anticipate. The net effect is that the familiar is seen anew, as a “special case”.