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Symmetry and Contextuality
European Review ( IF 0.8 ) Pub Date : 2020-06-25 , DOI: 10.1017/s1062798720000411
Hartmann Römer

The general concept of symmetry is realized in manifold ways in different realms of reality, such as plants, animals, minerals, mathematical objects or human artefacts in literature, fine arts and society. In order to arrive at a common ground for this variedness a very general conceptualization of symmetry is proposed: Existence of substitutions, which, in the given context, do not lead to an essential change. This simple definition has multiple consequences: -The context dependence of the notion of symmetry is evident in the humanities but by no means irrelevant yet often neglected in science. The subtle problematic of concept formation and the ontological status of similarities opens up. -In general, the substitutions underlying the concept of symmetry are not really performed but remain in a state of virtuality. Counterfactuality, freedom and creativity come into focus. The detection of previously hidden symmetries may provide deep and surprising insights. -Related to this, due attention is devoted to the aesthetic dimension of symmetry and the breaking of it. -Finally, we point out to what extent life is based on the interplay between order and freedom, between full and broken symmetry.

中文翻译:

对称性和情境性

对称的一般概念在现实的不同领域以多种方式实现,例如植物、动物、矿物、数学对象或文学、美术和社会中的人类人工制品。为了达到这种多样性的共同点,提出了一个非常普遍的对称概念:存在替换,在给定的上下文中,不会导致本质变化。这个简单的定义有多重后果: -对称概念的上下文相关性在人文学科中很明显,但在科学中绝非无关紧要但经常被忽视。概念形成的微妙问题和相似性的本体论地位展开了。- 一般而言,对称概念背后的替换并未真正执行,而是保持在虚拟状态。反事实,自由和创造力成为焦点。检测先前隐藏的对称性可能会提供深刻而令人惊讶的见解。- 与此相关,适当注意对称的美学维度及其破坏。- 最后,我们指出生活在多大程度上是基于秩序与自由之间、完全对称与破碎对称之间的相互作用。
更新日期:2020-06-25
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