主观几何学初步探讨

Primary Research on Subjectivity Geometry

此处的所谓“主观几何学”是指使用数学的语言和方法,研究抽象了的客观形体和其观察记录之间的关系的学科.当观察记录的过程中考虑主观因素(如观察器的位置,人体视觉系统的功能等)的影响时,便带来了许多不同于通常几何学的特点.本文给出基本假设;建议球面观察记录;研究了抽象的客观形体及其观察记录之间的基本对应关系以及给出应用上述理论的例子.我们期望主观几何学的研究将影响或连系于视觉系统生理学,应用光学等研究,并在测量、导航和仿生学等中得到应用.

The so-called 'Subjectivity Geometry' herein is a course for studying the relationship between the abstracted object configuration and its observed record by means of mathematical methods and described by mathematical language. There are many features differing from the common geometry when the effects of the subjectivity (such as the position of the observer, the functions of the visual system of human) are taken into account during the observing-recording process. In this paper, some basic assumptions are made; spherical observing record is suggested; the fundamental relationship between the abstracted object configuration and its corresponding observed record is studied; and an example of application of the above theory is presented. We anticipate that the study of subjectivity geometry will influence, or will be associated with the study of physiology of the visual system, applied optics etc., and will be useful in surveying, pilotage and imitative biology, etc.