爱英采 | 数学之旅:心怀诗意的探索

文摘   2024-11-22 17:26   上海  


数学之旅

心怀诗意的探索

引言





在人类文明的璀璨星河中,数学以其不可撼动的地位,成为科学与工程的坚实基石,更是我们洞察宇宙奥秘的一把钥匙。尽管其重要性昭然若揭,数学却常被一层恐惧的迷雾所笼罩——这种被称为“数学恐惧症”的现象,其历史源远流长,早在一个世纪前,德国物理学家费利克斯·奥尔巴赫便已着手探究并试图破解这一谜题。






Anxiety about maths has been around for at least a century. It boils down to a misunderstanding about what maths is, says Sarah Hart.MATHS phobia is older than you might think. A hundred years ago, German physicist Felix Auerbach, lamenting the phenomenon and hoping to find ways to address it, wrote a little book called The Fear of Mathematics and How to Overcome It. Maths, he said, has so much to contribute to society that addressing this fear is a challenge of the highest importance. Auerbach was a fascinating character– a scientist but also a patron of the arts. Edvard Munch painted his portrait and Bauhaus School founder Walter Gropius designed his house. For a mathematician like myself, the pleasure of reading his book, now published in English for the irst time, is accompanied by a sigh of regret that the topic is as relevant today as it was a century ago.


对数学的焦虑至少已经存在了一个世纪。萨拉-哈特(Sarah Hart)说,这归根结底是对数学的误解。数学恐惧症的历史比你想象的还要悠久。一百年前,德国物理学家费利克斯-奥尔巴赫(Felix Auerbach)对这一现象深表遗憾,并希望找到解决这一问题的方法,他写了一本名为《数学恐惧症及其克服方法》的小书。他说,数学对社会的贡献如此之大,因此消除这种恐惧是一项极其重要的挑战。奥尔巴赫是一个令人着迷的人物--既是科学家,又是艺术赞助人。爱德华-蒙克为他画像,包豪斯学派创始人沃尔特-格罗皮乌斯为他设计房子。对于像我这样的数学家来说,在阅读他的著作(这是该书首次以英文出版)的同时,也不禁感叹,这个话题在今天和一个世纪前一样具有现实意义。



be around存在的(existing or available)

例句:

This issue/problem has been around for more than a decade.

这个问题已经存在了十多年。


boil down to 归纳为

例句:

He had boiled down a lengthy report to just a few paragraphs.

他把一份冗长的报告浓缩成几段。


phobia / ˈfoʊbiə / n. 恐惧症(a type of anxiety disorder that involves an extreme fear of sth)

词组:

social phobia 社恐

have a phobia of/about…


lament / ləˈment /v. 对… 感到悲痛、失望(to express sadness and feeling sorry about sth)

例句:

The poem opens by lamenting (over) the death of a young man.

这首诗的开篇表达了对一位青年之死的惋惜之情。


address v. 解决(to deal with a matter or problem)

例句:

This issue has yet to be addressed.

此问题尚未得到解决。


patron / ˈpeɪtrən / n. 赞助人&老主顾(a person or group that supports an activity or organization, especially by giving money)

例句:

The Princess Royal is a well-known patron of several charities.

众所周知长公主是数家慈善机构的赞助人。


accompany /əˈkʌmpəni/v. 陪伴,伴随(to go with sb or to be provided or exist at the same time as sth)

例句:

Depression is almost always accompanied by insomnia.

抑郁症几乎总是伴有失眠。



Why do we fear mathematics?  At heart, says Auerbach, it comes down to a fundamental misunderstanding of what math is. The fear of messing up a calculation may be real, but the fact that there are many excellent mathematicians who are terrible at arithmetic proves that numeracy and mathematics aren’t the same thing. We understand this about writing literature. The art of creating a compelling narrative in beautiful prose is different from the technical skill of getting the spelling and punctuation right. The same is true with maths. It isn’t mere calculation.


我们为什么害怕数学?奥尔巴赫说,从根本上说,这是对数学的误解。害怕计算出错可能是真实的,但事实上有很多优秀的数学家算术却很糟糕,这证明计算能力和数学并不是一回事。对于文学创作,我们深有体会。用优美的散文创作引人入胜的叙事艺术,不同于正确拼写和标点符号的文法技巧。数学也是如此。它不仅仅是计算。



mathematics /ˌmæθˈmæt.ɪks/数学

例句:

When it comes to mathematics, he's in a different class to his peers.

在数学方面,他与同龄人处于不同的级别。


mess up 搞砸,搞错(to spoil or damage sth, or to do sth wrong or badly)

例句:

I really messed up the chance.

我真的搞砸了这个机会。


numeracy / ˈnuːmərəsi / n. 数学计算能力(ability to do basic mathematics)

例句:

Statistics on the literacy and numeracy of twelve-year-olds

关于12岁孩子读写和计算能力的统计数据。


compelling adj. 引人入胜的,扣人心弦的&有说服力的(very exciting and interesting and making you want to watch or listen)

例句:

I found the whole film very compelling.

我觉得整部影片都很扣人心弦。

It's a fairly compelling argument for going.

去的理由很有说服力。



What, then, is mathematics Auerbach says it is three things: a science, a language and an art. For me, part of the issue is that we are stuck in the first box. The incredible utility of maths in the sciences and engineering has meant that it is possible, though undesirable, to teach it only with this utility in mind. A focus exclusively on technical skills misses the joy and excitement that can come from finding patterns and understanding them, from seeing the true beauty of mathematics. That beauty lies in wonderfully elegant thinking that allows us to understand the infinite, explore the sublime symmetries of art and nature, and delight in the perfection of an abstract world of ideas.


奥尔巴赫说,数学是三样东西:科学、语言和艺术。对我来说,问题的一部分在于我们被困在了第一个框框里。数学在科学和工程学中令人难以置信的实用性意味着,只考虑数学的实用性是可能的,尽管这并不可取。如果只关注技术技能,就会错过从发现规律和理解规律中,从看到数学真正的美中获得的快乐和兴奋。这种美在于奇妙而优雅的思维,它能让我们理解无限,探索艺术和自然中崇高的对称性,并为抽象概念世界的完美而欣喜。



utility /juːˈtɪl.ə.ti/ n. 作用,实用(the usefulness of sth)

例句:

The utility of this substance has been proven in a series of tests.

这种物质的用途已在一系列测试中得到证明。


exclusively  /ɪksˈkluː.sɪv.li/ adv. 仅仅,专门地

例句:

This offer is available exclusively to our established customers.

只有本店老客户才能享受这一优惠价。


sublime / səˈblaɪm / v. adj. 崇高的,非凡的(extremely good, beautiful or enjoyable)

例句:

The book has sublime descriptive passages.

这本书中有一些非常优美的描写段落。


symmetry / ˈsɪmətri/n.对称(性)

例句:

The design of the house had a pleasing symmetry, its oblong shape being picked up in its elongated windows.

房子的设计透着一种赏心悦目的对称美,狭长的窗户使长方形的结构显得更加和谐。





As a language, what sets math apart is the universality of its truths– you can become fluent wherever you are from. As Auerbach memorably puts it, you cannot do “German mathematics with a Japanese accent”. But it is the case for maths as an art that is closest to my heart.In researching my book Once Upon a Prime, about the beautiful connections between mathematics and literature, I have found many examples of mathematicians and poets praising each other’s disciplines.This is no surprise, as mathematics is, says Auerbach, “without exception, a poetic art”. If we can be shown the beauty of mathematics, we will forget to be afraid of the technical details underpinning it. Today’s self-help gurus like to point out that, physiologically, we experience anxiety the same way we experience excitement. So, if your heart is racing and your palms are sweating before a big event, you simply have to tell yourself that you are excited.


作为一门语言,数学的与众不同之处在于其真理的普遍性--无论你来自哪里,你都可以流利地使用数学。正如奥尔巴赫(Auerbach)令人难忘的说法,你不可能 “用日本口音做德国数学”。但是,数学作为一门艺术,才是最贴近我内心的东西。研究我的著作《Once Upon a Prime》(关于数学与文学之间的美丽联系)时,我发现了许多数学家和诗人互相赞美对方学科的例子。这并不奇怪,因为数学,奥尔巴赫说,“无一例外,它是一门诗意的艺术”。如果可以向我们展示数学之美,我们就会忘记害怕支撑数学的技术细节。当今的自学大师们喜欢指出,从生理学角度讲,我们体验焦虑的方式与体验兴奋的方式相同。因此,如果你在重大活动前心跳加速、手心出汗,你只需告诉自己你很兴奋。


 

set sth/sb apart 使突出、显眼

例句:

What set her apart from the other candidates for the job was that she has a lot of original ideas.


universality/ ˌjuːnɪvɜːrˈsæləti / n. 普遍性,广泛性

例句:

The universality of his dilemma is one to which we can all relate.

他的困境的普遍性是我们都能体会到的。


as sb put it正如某人所说


underpin v. 支持,构成基础(to give support, strength, or a basic structure to sth)

例句:

He presented data to underpin his argument.

他提供了数据来支持他的论点。


guru  /ˈɡʊr.uː/ n. 某些宗教中的导师、领袖

a lifestyle guru生活专家



In the same way, fear can be negative (dread) or positive (awe). Our goal should be to try to move people along a continuum from a view of mathematics as a collection of calculations whose impenetrability engenders dread to an appreciation of a profoundly beautiful language whose complexity inspires awe.A hundred years on, Auerbach’s writing is as pertinent as ever. It is a timely reminder that “maths anxiety”, as it is now called, remains as much a challenge in 21st century as it was in the 20th.



同样,恐惧可以是消极的(畏惧),也可以是积极的(敬畏)。我们的目标应该是努力让人们沿着一个连续统一体的方向前进,从把数学看成是一种计算的集合,其不可捉摸性会让人产生恐惧,到欣赏一种深奥美丽的语言,其复杂性会让人产生敬畏。一百年过去了,奥尔巴赫的写作一如既往地中肯。这及时地提醒了我们,现在所谓的“数学焦虑”,在21世纪和20世纪一样,仍然是一个挑战。



dread v.&n. 害怕,畏惧(a strong feeling or fear or worry)

例句:

He's dreading the exam - he's sure he's going to fail.

他很担心考试——他觉得自己肯定过不了。


awe /ɔː/ n. 敬畏(a feeling of great respect sometimes mixed with fear or surprise)

例句:

You can't help but stand in awe of (= respect greatly and fear slightly) powerful people.

在权势人物面前,你不由自主会毕恭毕敬。


impenetrability / ɪmˌpenɪtrəˈbɪləti / n. 不可理解(the quality of being impossible to understand)

例句:

A key channel of investor communications is still the annual report, famous for its impenetrability.

投资者沟通的一个主要渠道仍然是年报,它以其难以理解而闻名。


engender  /ɪnˈdʒen.dər/ v. 产生,引起

例句:

Her latest book has engendered a lot of controversy.

她的最新著作引起了很多争议。


pertinent / ˈpɜːrt(ə)nənt / adj. 切题的,相关的(relating directly to the subject )

例句:

Chapter One is pertinent to the post-war period.

第一章与战后时期有关。




文案 | 耿浩洋

排版 | 濮弈宁

审核 | 兰璐 王年畅 桂文杰

文章出处 | New Scientist

图片出处 | 百度&New Scientist

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