Beauty is in the blind spot of the beholder

IF 0.3 Q4 MATHEMATICS

Mathematics Enthusiast Pub Date : 2021-01-01 DOI:10.54870/1551-3440.1522

Ron Aharoni

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引用次数: 0

Abstract

: The paper addresses the time-old question of what is beauty. A rather ambitious, if not to say presumptuous, endeavour. But I do not aim high – I do not claim to get anywhere near unearthing the secret. Rather, I will use examples from mathematics, poetry, music and chess to substantiate one thesis: that the elusory character of beauty is not incidental. Its defiance of definition is part of its essence. The aesthetic sensation requires unawareness of its precise origin. Beauty is felt when some order is perceived, that is not fully comprehended. The order is too complex, or well hidden, or too novel, to surface in its entirety. This is the reason for our ability to enjoy a piece of art for the hundredth time – we never fully fathom its inner order. This is also the reason for the feeling of awe that the beauty inspires: mystery and magic are at its heart. I will compare mathematical techniques and features with those of poetry - like compression, summoning patterns from one field to solve problems in another, or self-reference, and show how beauty is generated in the two domains in a similar way. I will also comment on the beauty-generating effect of unexpectedness in both domains. That novelty generates beauty is a trite observation (“the most expected feature of a poem is its unexpectedness”, as somebody put it), but the question why this is so is not often addressed – I will connect it with the “blind spot” idea. In a final section I try to answer the question that is at least as difficult as “what is beauty” – “why beauty?”. The fact that it pervades our lives indicates that it has an important role – what is it? To arouse the reader’s curiosity, let me summarize the attempted answer in one word – ‘change’. That aim that is so coveted and so hard to achieve – a change in the pattern of our actions, aims and perceptions. The style of the paper is non-scientific, and non-erudite, reflecting my belief that scientific pretensions in the humanities deflect from “softer”, more genuine, understanding.

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情人眼里出西施

：这篇论文探讨了什么是美这个由来已久的问题。这是一项相当雄心勃勃的努力，如果不是说是冒昧的话。但我的目标并不高——我并不声称能在任何地方揭开这个秘密。相反，我将用数学、诗歌、音乐和国际象棋的例子来证实一个论点：美的难以捉摸的特征不是偶然的。它对定义的蔑视是其本质的一部分。美感需要不知道它的确切来源。当一些秩序被感知，但却没有被完全理解时，美就会被感受到。秩序过于复杂，或者隐藏得很好，或者过于新颖，无法完整地展现出来。这就是我们能够第一百次欣赏一件艺术品的原因——我们从未完全理解它的内在秩序。这也是这种美所激发的敬畏感的原因：神秘和神奇是它的核心。我将把数学技术和特征与诗歌的技术和特征进行比较——比如压缩，从一个领域调用模式来解决另一个领域的问题，或者自我参考，并展示美是如何以相似的方式在这两个领域产生的。我还将评论意想不到在这两个领域中的美丽生成效果。新奇产生美是一种老生常谈的观察（正如有人所说，“一首诗最令人期待的特点是它的出乎意料”），但为什么会这样的问题并不经常被解决——我会把它与“盲点”的想法联系起来。在最后一节中，我试图回答一个至少和“什么是美”一样难的问题——“为什么是美？”。它弥漫在我们的生活中，这表明它有着重要的作用——它是什么？为了引起读者的好奇心，让我用一个词来概括尝试的答案——“改变”。这个令人垂涎而又难以实现的目标——改变了我们的行动模式、目标和观念。这篇论文的风格是非科学的、非博学的，反映了我的信念，即人文学科中的科学伪装偏离了“更温和”、更真诚的理解。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Mathematics Enthusiast MATHEMATICS-

CiteScore

1.40

自引率

0.00%

发文量

期刊介绍： The Mathematics Enthusiast (TME) is an eclectic internationally circulated peer reviewed journal which focuses on mathematics content, mathematics education research, innovation, interdisciplinary issues and pedagogy. The journal exists as an independent entity. The electronic version is hosted by the Department of Mathematical Sciences- University of Montana. The journal is NOT affiliated to nor subsidized by any professional organizations but supports PMENA [Psychology of Mathematics Education- North America] through special issues on various research topics. TME strives to promote equity internationally by adopting an open access policy, as well as allowing authors to retain full copyright of their scholarship contingent on the journals’ publication ethics guidelines. Authors do not need to be affiliated with the University of Montana in order to publish in this journal. Journal articles cover a wide spectrum of topics such as mathematics content (including advanced mathematics), educational studies related to mathematics, and reports of innovative pedagogical practices with the hope of stimulating dialogue between pre-service and practicing teachers, university educators and mathematicians. The journal is interested in research based articles as well as historical, philosophical, political, cross-cultural and systems perspectives on mathematics content, its teaching and learning. The journal also includes a monograph series on special topics of interest to the community of readers.