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Abstract：
Of the four interrelated concepts in the title, only symmetry has an exact mathematical definition. In mathematical development, symmetry is a graded variable-in marked contrast with the popular binary conception of symmetry in and out of the laboratory (i.e. an object is either symmetrical or nonsymmetrical). Because the notion does not have a direct graded perceptual counterpart (experimental participants are not asked about the amount of symmetry of an object), students of symmetry have taken various detours to characterize the perceptual effects of symmetry. Current approaches have been informed by information theory, mathematical group theory, randomness research, and complexity. Apart from reviewing the development of the main approaches, for the first time we calculated associations between figural goodness as measured in the Garner tradition and measures of algorithmic complexity and randomness developed in recent research. We offer novel ideas and analyses by way of integrating the various approaches.
摘要：
在标题中四个相互关联的概念中，只有对称性有精确的数学定义。在数学发展中,对称性是一个分级变量，与实验室内外流行的二元对称性概念形成鲜明对比（即对象是对称的或非对称的）。因为这个概念没有直接分级的感知对应物（实验参与者没有被问及物体的对称量），对称学生采取了各种弯路来表征对称的感知效果。目前的方法已经被信息论所告知，数学群论，随机性研究，和复杂性。除了审查主要方法的发展外，我们首次计算了Garner传统中测量的形象善与最近研究中开发的算法复杂性和随机性之间的关联。我们通过整合各种方法提供新颖的想法和分析。
