长沙理工大学综合英语翻译 unit1 笛卡尔错了：“他人在，故我在” According to Ubuntu philosophy, which has its origins in ancient Africa, a newborn baby is not a person. People are born without ‘ena’, or selfhood, and instead must acquire it through interactions and experiences over time. So the ‘self’/‘other’ distinction that’s axiomatic in Western philosophy is much blurrier in Ubuntu thought. As the Kenyan-born philosopher John Mbiti put it in African Religions and Philosophy (1975): ‘I am because we are, and since we are, therefore I am.’ 乌班图哲学起源于古代非洲。按照它的说法，新生儿尚不能称为“人”。初生时，人没有自我。随着时间的推移，在互动和经验中才能习得它。因此，西方哲学中自我／他者之间清晰的分野在乌班图哲学中变得模糊起来。出生于肯尼亚的哲学家约翰·姆比蒂（John Mbiti）在著作《非洲的宗教与哲学》（African Religions and Philosophy）中如是说：我在，因为我们在；
因为我们在，所以我在。

We know from everyday experience that a person is partly forged in the crucible of community. Relationships inform self-understanding. Who I am depends on many ‘others’: my family, my friends, my culture, my work colleagues. The self I take grocery shopping, say, differs in her actions and behaviours from the self that talks to my PhD supervisor. Even my most private and personal reflections are entangled with the perspectives and voices of different people, be it those who agree with me, those who criticise, or those who praise me. 日常经验告诉我们，一个人一部分从社会的历练中锻造出来。社会关系赋予我们自我认知。我是谁，这个问题的答案依赖于众多他者：家庭、朋友、文化背景、同事等等。在杂货店购物的我和与博士导师交谈的我不是同一个自我。即便是私密、最个人的思绪也不同人的观点和声音纠缠在一起，无论是那些赞同我的人，还是那些批评我的人，抑或是那些赞美我的人。

Yet the notion of a fluctuating and ambiguous self can be disconcerting. We can chalk up this discomfort, in large part, to René Descartes. The 17th-century French philosopher believed that a human being was essentially self-contained and self-sufficient; an inherently rational, mind-bound subject, who ought to encounter the world outside her head with skepticism. While Descartes didn’t single-handedly create the modern mind, he went a long way towards defining its contours. 但是，自我的摇摆不定和充满歧义让人不安。很大程度上，我们可以把这份不安归因于笛卡尔。这位17世纪的法国哲学家认为，人类本质上是自给自足的；
省而理性、受其思想约束的个体，应该以怀疑的态度面对他头脑之外的世界。尽管笛卡尔没有单独创造出现代思维，但他在定义其框架上起到了很大的推动作用。

Descartes had set himself a very particular puzzle to solve. He wanted to find a stable point of view from which to look on the world without relying on God-decreed wisdoms; a place from which he could discern the permanent structures beneath the changeable phenomena of nature. But Descartes believed that there was a trade-off between certainty and a kind of social, worldly richness. The only thing you can be certain of is your own cogito – the fact that you are thinking. Other people and other things are inherently fickle and erratic. So they must have nothing to do with the basic constitution of the knowing self, which is a necessarily detached, coherent and contemplative whole. 笛卡尔给自己提出了一个特别的谜团。他想要找到一种稳定的观点，而非依靠上帝赐予的智慧，来观察这个世界；
由此，他可以透过自然界中变幻莫测的现象分辨出永久性的结构。但笛卡尔认为，稳定性和来自社会的、世俗的多样性之间存在权衡关系。你唯一能确定的，就是“我思故我在”——即，你思考的状态。其他人和其他事物是不稳定且难以预测的存在。因此，它们和认识自己的基本律条毫无关系。认识自我从来都是独自进行的，需要不断的深思。

Few respected philosophers and psychologists would identify as strict Cartesian dualists, in the sense of believing that mind and matter are completely separate. But the Cartesian cogito is still everywhere you look. The experimental design of memory testing, for example, tends to proceed from the assumption that it’s possible to draw a sharp distinction between the self and the world. If memory simply lives inside the skull, then it’s perfectly acceptable to remove a person from her everyday environment and relationships, and to test her recall using flashcards or screens in the artificial confines of a lab. A person is considered a standalone entity, irrespective of her surroundings, inscribed in the brain as a series of cognitive processes. Memory must be simply something you have, not something you do within a certain context. 在认识到精神和身体是完全独立存在的基础上，很少有备受尊敬的哲学家和心理学家被认为是个彻底的笛卡尔式的二元论者。但笛卡尔式的我思故我在目之所及，已遍布每一个角落。记忆测试的实验设计趋于从一个假说出发，即自我和世界之间是可能存在明确界限的。如果记忆仅仅存在于我们的头颅中，那么，将一个人从他的日常生活的环境和社会关系中剥离出来，并在人造的封闭实验室中使用卡片或荧幕来检测他的记忆是百分百可行的。人被视作独立的个体，区别于环绕他的一切，是在大脑中被篆刻为一系列认知过程的存在。记忆一定是你拥有的事实，而不是你在特定环境下的行为产物。

Social psychology purports to examine the relationship between cognition and society. But even then, the investigation often presumes that a collective of Cartesian subjects are the real focus of the enquiry, not selves that co-evolve with others over time. In the 1960s, the American psychologists John Darley and Bibb Latané became interested in the murder of Kitty Genovese, a young white woman who had been stabbed and assaulted on her way home one night in New York. Multiple people had witnessed the crime but none stepped in to prevent it. Darley and Latané designed a series of experiments in which they simulated a crisis, such as an epileptic fit, or smoke billowing in from the next room, to observe what people did. They were the first to identify the so-called ‘bystander effect’, in which people seem to respond more slowly to someone in distress if others are around. 社会心理学标榜自己致力于检验认知和社会间的关系。但即便如此，其研究常常假定如下主张：“询问”这一行为，其真正焦点在于一系列笛卡尔式议题的集合，而不是始终与他人共同演化的自我。在二十世纪六十年代，美国心理学家约翰·达利(John Darley)和比布·拉塔内(Bibb Latané)对吉诺维斯案产生兴趣。吉诺维斯是一位年轻的白人女性，在回家的路上遭到袭击，被歹徒刺伤。很多人看到了这起罪行，却无人挺身而出。达利和拉塔内设计了一系列实验，模拟日常中的危机情况，比如癫痫发作、隔壁房间冒烟等，以此来观察人们的反应。他们首次发现了所谓的“旁观者效应”，即周围有他人存在的时候，人们对处于紧急情况中的个体的响应会变慢。

Darley and Latané suggested that this might come from a ‘diffusion of responsibility’, in which the obligation to react is diluted across a bigger group of people. But as the American psychologist Frances Cherry argued in The Stubborn Particulars of Social Psychology: Essays on the Research Process (1995), this numerical approach wipes away vital contextual information that might help to understand people’s real motives. Genovese’s murder had to be seen against a backdrop in which violence against women was not taken seriously, Cherry said, and in which people were reluctant to step into what might have been a domestic dispute. Moreover, the murder of a poor black woman would have attracted far less subsequent media interest. But Darley and Latané’s focus make structural factors much harder to see. 达利和拉塔内认为，这种现象归因于“责任分散”。在这个过程中，提供帮助的义务在人数众多的群体中被稀释了。但美国心理学家弗朗西斯·切利（Frances Cherry）对此有不同意见。在《社会心理学中的偏执细节：论研究进程》（The Stubborn Particulars of Social Psychology: Essays on the Research Process）中提到，这种通过数字解释行为的方法剔除了重要的语境，使得人们难以理解当事人的真正动机。谢里认为，吉诺维斯杀案反映了当时的社会并不关注女性遭受的暴力困扰，人们也不愿介入一桩可能是家庭纠纷的暴力袭击中。她进一步说，一个贫穷的黑人女性被谋杀也很难吸引媒体的关注。但是，达利和拉塔内关注的焦点让这些结构性的因素变得更加难以察觉。

Is there a way of reconciling these two accounts of the self – the relational, world-embracing version, and the autonomous, inward one? The 20th-century Russian philosopher Mikhail Bakhtin believed that the answer lay in dialogue. We need others in order to evaluate our own existence and construct a coherent self-image. Think of that luminous moment when a poet captures something you’d felt but had never articulated; or when you’d struggled to summarise your thoughts, but they crystallised in conversation with a friend. Bakhtin believed that it was only through an encounter with another person that you could come to appreciate your own unique perspective and see yourself as a whole entity. By ‘looking through the screen of the other’s soul,’ he wrote, ‘I vivify my exterior.’ Selfhood and knowledge are evolving and dynamic; the self is never finished – it is an open book. 自我有两种面孔，一种是关系化的、与世界紧密相拥的；
另一种是自主内向的——有没有一种方法，可以消除它俩之间的分歧？二十世纪，俄罗斯的哲学家米哈伊尔·巴赫金（Mikhail Bakhtin）认为，答案在于对话。我们需要他人来对自己的存在进行评估，并借此构建完整连贯的自我印象。想一想那些醍醐灌顶的时刻：诗人捕捉到你所感受到的却从未表达出来的东西；
或者在与朋友交谈时你灵光一现，信口而出你曾难以总结、难以表达的一些想法。巴赫金相信，只有在与他人的交往中，你才能欣赏自己独一无二的观点，才能将自己视作一个实体存在。他这样写道：“透过他人的灵魂之窗，我看到了自己的外在”。自我和认识不断演进，永远处于动态；
自我也永不消亡——这点一目了然。

So reality is not simply out there, waiting to be uncovered. ‘Truth is not born nor is it to be found inside the head of an individual person, it is born between people collectively searching for truth, in the process of their dialogic interaction,’ Bakhtin wrote in Problems of Dostoyevsky’s Poetics (1929). Nothing simply is itself, outside the matrix of relationships in which it appears. Instead, being is an act or event that must happen in the space between the self and the world. 因此，现实并不是就在那儿等着我们去发现。“真理不会诞生于或被发现于一个人的头脑中，它诞生于人类集体对真理的追寻之中，诞生于人们之间对话形式的互动中”。这句话出自巴赫金写的《陀思妥耶夫问题》（Problems of Dostoevsky’s Poetics）这本书。“没有任何东西单纯地是它本身，完全脱离它所处的关系网络”。“存在”这个动作或事件一定发生在自我和世界之间的空间。

Accepting that others are vital to our self-perception is a corrective to the limitations of the Cartesian view. Consider two different models of child psychology. Jean Piaget’s theory of cognitive development conceives of individual growth in a Cartesian fashion, as the reorganisation of mental processes. The developing child is depicted as a lone learner – an inventive scientist, struggling independently to make sense of the world. By contrast, ‘dialogical’ theories, brought to life in experiments such as Lisa Freund’s ‘doll house study’ from 1990, emphasise interactions between the child and the adult who can provide ‘scaffolding’ for how she understands the world. 想要纠正笛卡尔式观点的局限性，就要承认，他人对于我们的自我认知有着重要意义。来思考两个不同的儿童心理学模型。简·皮亚杰（Jean Piaget）的认知发展理论提出，笛卡尔式的潮流下个体的成长伴随精神进程方面的重组。不断成长的儿童被描述成一个孤独的学习者，一个富有创新的科学家，孤身一人，奋力要搞清世间的真相。另一个理论——对话理论则不相同。相比之下，从1990年开始，对话理论才在莉萨·弗罗因德的“玩偶屋研究”等一系列实验中得以呈现。该理论强调孩子和成年人之间的互动，认为成年人可以为孩子们了解世界提供“脚手架”。

A grimmer example might be solitary confinement in prisons. The punishment was originally designed to encourage introspection: to turn the prisoner’s thoughts inward, to prompt her to reflect on her crimes, and to eventually help her return to society as a morally cleansed citizen. A perfect policy for the reform of Cartesian individuals. But, in fact, studies of such prisoners suggest that their sense of self dissolves if they are punished this way for long enough. Prisoners tend to suffer profound physical and psychological difficulties, such as confusion, anxiety, insomnia, feelings of inadequacy, and a distorted sense of time. Deprived of contact and interaction – the external perspective needed to consummate and sustain a coherent self-image – a person risks disappearing into non-existence. 这里举一个略残酷的例子：监狱中的单人囚室。这项惩罚最初被用于促进犯人自省，改变囚徒的内心想法，促使他们反思罪行，最终帮助犯人在重返社会时变成一个良好公民。但是，事实上，对这些囚犯的研究表明，如果接受此类惩罚太久，其自我意识就会消融。囚徒们更容易遭受生理和心理上的折磨：焦虑、紧张、失眠、无能感，以及扭曲的时间观念都是困扰他们的问题。如果失去联系与交流这种完善和维持清晰自我形象的外部因素，人会面临失去自我的危险。

The emerging fields of embodied and enactive cognition have started to take dialogic models of the self more seriously. But for the most part, scientific psychology is only too willing to adopt individualistic Cartesian assumptions that cut away the webbing that ties the self to others. There is a Zulu phrase, ‘Umuntu ngumuntu ngabantu’, which means ‘A person is a person through other persons.’ This is a richer and better account, I think, than ‘I think, therefore I am.’ 具身认知和生成认知的领域开始严肃对待自我的对话模式。但是在大多数情况下，科学意义上的心理学非常乐意采纳个人色彩浓厚的、切断了自我与他人相互联系的笛卡尔式假说。有句祖鲁族谚语，Umuntu ngumuntu ngabantu，意思是“他人在，故我在”，在我看来，这句话比“我思故我在”更完满贴切。

Unit2 我们准备好应对下一次火山灾难了吗？ In April 1815, the biggest known eruption of the historical period blew apart the Tambora volcano, on the Indonesian island of Sumbawa, 12,000km from the UK. What happened next testifies to the enormous reach of the biggest volcanic blasts. 1815年4月，历史上最著名的喷发使距印度尼西亚12,000公里的印度尼西亚苏姆巴瓦岛上的坦波拉火山炸毁。接下来发生的事情证明了最大的火山爆炸的巨大影响力。

The Tambora volcano had shown no signs of life for 1,000 years; a single eruption in the previous five millennia provided the only indication that magma was still churning far beneat.It was.On 5 April 1815, a titanic explosion hurled a cloud of ash to a height of more than 30km. Violent, but short-lived, the blast lasted just two hours, after which the volcano returned to a state of brooding menace.According to the lieutenant governor, Thomas Stamford (later Sir Stamford) Bingley Raffles, to whom volcanologists are indebted for his accounts of the eruption, the detonation was so loud that it was mistaken across Java for cannon fire, causing consternation among the British troops, which had ousted the Dutch and French forces just a few years earlier. 坦波拉火山（Tambora）的火山已经有1000年没有生命迹象了。在过去的五千年中，一次喷发提供了唯一的迹象，表明岩浆仍在搅拌之下。1815年4月5日，发生了巨大的爆炸，将一团灰烬推向30公里以上的高度。剧烈，但是爆炸是短暂的，爆炸只持续了两个小时，之后火山又恢复了沉重的威胁状态。因记录了火山喷发事件而令火山学家们感激不已的副州长托马斯·斯坦福德·宾利·莱佛士（后来的斯坦福德爵士）表示，此次火山爆发声音之巨大，以至被误认为是爪哇岛爆发战争时的加农大炮声，令几年前曾驱赶荷兰和法国军队的英国士兵们惊慌失措。

But the blast was small beer in comparison with what followed. After five days of relative calm, the climactic phase of the eruption began with a colossal explosion that launched a towering column of ash to the edge of space. For four or five days, utter blackness reigned across the island as the hurricane blasts of hot ash and scalding gas – known as pyroclastic flows – scoured the flanks of the volcano of everything and everyone, and drifts of ash metres thick entombed what few signs of life remained. When the explosions ceased and the darkness finally lifted, the view revealed was a vision of Tolkien’s Mordor; a grey landscape within which nothing lived or moved. The top 500m of the volcano was gone, blasted into smithereens, and replaced by a 6km-wide maw from which steam spiralled skywards.Communities on the flanks of the volcano had vanished, along with the lives of around 12,000 men, women and children. These, perhaps, were the lucky ones, as a further 60,000 survivors of the eruption succumbed slowly and agonisingly to famine or disease. 但与随后发生的爆炸相比，这次爆炸就显得微不足道。经过相对平静的五天后，一声巨响宣告了火山爆发的高潮，喷发的火山灰烬柱高耸入云，直逼天际。整个岛屿都笼罩在一片漆黑之中，炙热的火山灰和滚烫的气体——即火山碎屑流，像飓风一样吞噬了火山翼侧的一切事物，几米厚的火山灰掩盖之处死寂沉沉，几乎没有任何生命迹象。当爆炸停止并且黑暗终于消除时，所见的景象就是托尔金的魔都的景象。一种灰色的景观，其中没有人居住或活动。火山的最高500m消失了，被炸成碎片，然后被6公里宽的取代，从中蒸腾出蒸汽。火山两侧的社区以及约12,000名男女儿童的生活都消失了。这些也许是幸运的，因为另外60,000名喷发幸存者缓慢而痛苦地死于饥荒或疾病。

But the consequences were not confined to this Indonesian backwater. The explosion was heard 2,600km away in Sumatra, while giant rafts of floating pumice – some kilometres in length – clogged shipping routes for years. The 50 cubic kilometres or so of ash ejected over the course of the eruption returned to earth in the following days and weeks, leaving a thick covering as far away as Borneo, 500km to the north.In addition to the ash, an estimated 200 million tonnes of microscopic sulphur particles pumped into the stratosphere, spread outwards from Sumbawa to form a giant aerosol veil that enclosed the planet and acted as a block to incoming sunlight. 但是后果不仅仅限于印尼的死水。爆炸发生在苏门答腊岛2600公里以外，而数公里长的漂浮浮石筏阻塞了数年的运输路线。在喷发过程中喷出的约50立方公里的灰烬在接下来的几天和几周内返回地面，厚厚的一层火山灰一直延伸至距北500公里的婆罗洲。除火山灰外，估计有2亿吨微小的硫颗粒被注入平流层，从松巴哇岛向外扩散，形成一个巨大的气溶胶幕，将整个地球包裹起来，成为阻挡阳光照射的屏障。

The consequences for the developed societies of the northern hemisphere were dire. A dry, sulphurous, fog draped itself across the landscape of eastern North America, causing temperatures to plunge and bringing unprecedented summer cold. In New York State, snow fell in June, while the bitter cold and killing frosts wiped out crops and halved the length of the growing season across much of the region. On the other side of the Atlantic, Europe saw summer temperatures down by 2C compared to the average for the decade; the unseasonal cold accompanied by incessant rains and – into the following winter – by unusually powerful storms. Analysis of climate records reveals that 1816, the so-called “year without a summer”, was the second coldest in the northern hemisphere of the past six centuries. 对北半球发达社会的后果是可怕的。干燥，硫磺的雾笼罩着整个北美东部，造成温度骤降，并带来前所未有的夏季寒冷。在纽约州，6月降雪，而严酷的寒冷和霜冻消灭了农作物，并使该地区大部分地区的生长期缩短了一半。在大西洋的另一侧，欧洲的夏季气温比十年来的平均水平下降了2摄氏度。异常的寒冷伴随着持续不断的降雨，并在随后的冬季（伴随着接下来的冬天）爆发了异常强烈的风暴。对气候记录的分析表明，1816年，即所谓的“无夏之年”，是过去六个世纪北半球第二冷的一年。

The alleged cultural implications of this “volcano weather” for Europe are somewhat whimsical. The brilliant, gas-charged, sunsets have been declared by some to have provided the inspiration for some of JMW Turner’s more flamboyant skies. In a similar vein, the damp and gloom of the 1816 summer has been charged with setting the scene for both Lord Byron’s grim vision Darkness, and Mary Shelley’s gothic novel Frankenstein.For the less well-to-do of Europe, however, the Tambora eruption brought nothing less than hunger, disease and death. Widespread harvest failure resulted in the most serious famine for more than a hundred years, doubling the price of grain and spawning bread riots and widespread civil unrest.Such was the degree of breakdown of food supply that economic historian John Post has called the episode “the last, great subsistence crisis in the western world”. Malnourished and weakened, the starving succumbed rapidly to disease, with typhus in particular rife. Many tens of thousands are thought to have died across the continent, including more than 40,000 in Ireland alone. 这种“火山天气”对欧洲的所谓文化影响有些古怪。一些人宣称，明亮，充满气体的日落为约瑟夫·马洛德·威廉·透纳的一些更加绚丽的天空提供了灵感。同样，1816年夏季的潮湿和阴郁被认为是为拜伦勋爵的冷酷视觉《黑暗》和玛丽·雪莱的哥特式小说《科学怪人》设定背景的场景。然而，对于欧洲欠富裕的国家来说，坦波拉火山喷发带来的却只有饥饿，疾病和死亡。广泛的庄稼歉收导致一百多年来最严重的饥荒，使谷物价格翻了一番，并导致面包暴动和普遍的内乱。（因火山爆发而引起的）食物短缺问题十分严重，经济历史学家约翰·波斯特称这时期是“西方世界最近一次严重的生存危机”。营养不良和虚弱，挨饿的人很快死于疾病，尤其是斑疹伤寒。据认为，整个欧洲大陆有成千上万的人死亡，其中仅爱尔兰就有40,000多人死亡。

How would we fare if faced with a Tambora-sized eruption today? Is it even something we could feasibly prepare for? Received wisdom has it that globalisation would make it easier to cope. Should the European harvest fail, so the thinking goes, we can always buy our food from elsewhere. The very interconnectedness of world markets may, however, make things worse – the collapse of food production across Europe, parts of North America and perhaps elsewhere, could result in global shortages which in turn would drive a dramatic rise in the cost of food commodities. At the same time, the intense worldwide competition for food supplies, scarce as a consequence of the harvest failures, could drastically reduce the range of products available in the UK, interfere with supply and distribution, and bring about a collapse of the supermarkets’ ultra-sensitive, time-critical, stock-control systems, leaving their shelves increasingly depleted. While the less well-off could be priced out of purchasing even staple foodstuffs, panic buying by those who can afford it could quickly empty the stores. 如果今天面对坦波拉规模的火山喷发，我们应该怎么办？我们是否可以做一些可行的准备？众所周知，全球化将使这个事情处理起来变得更加容易。如果欧洲的农业歉收，一般想法，我们可以从其他地方购买食物。然而，世界市场间的这一切密切联系可能会令事态恶化——欧洲，北美部分地区以及其他地区的产量危机可能带来全球粮食短缺，进而可能导致食品的成本大幅上涨。与此同时，由荒年而致的粮食短缺问题也会造成激烈的全球食品竞争，可能会大大减少英国可用农产品，干扰供应和分销，导致很多超市异常灵敏的，时间要求严格的库存管理系统全面崩塌，超市食品货架也会变得越来越空旷。不富裕的人由于食品价格定价太高而放弃购买甚至是主食，但那些有能力负担的人的恐慌购买可能会很快买空商店。

On top of this, harvest disruption in response to volcano weather might extend far beyond Europe, and might – in ensuing decades – be exacerbated by the consequence of rampant climate change. In spite of our modern farming methods and distribution systems, the ramifications could be far more severe than we expect. It is also worth considering that while the Tambora blast was approximately 1,000 times bigger than the 2010 Icelandic eruption, it was a minor hiccup in comparison with the greatest volcanic explosions of history. The Toba eruption that excavated the world’s largest volcanic crater in Sumatra, around 74,000 years ago, for example, injected hundreds of times more sulphur gases into the stratosphere than Tambora. The severe “volcanic winter” that followed probably lasted for several years and saw a third or more of the Earth covered with snow and ice and the wholesale dieback of vegetation. 此外，火山天气而造成的庄稼歉收状况可能会远远超出欧洲范围，并且可能在随后的几十年中由于剧烈的气候变化而加剧。尽管我们采用现代农业方法和分配系统，但后果可能比我们预期的要严重得多。还值得考虑的是，尽管坦波拉爆炸案比2010年冰岛喷发大约1,000倍，但与历史上最大的火山爆发相比，这只是个小小的问题。例如，大约在74,000年前，在苏门答腊挖掘出世界上最大的火山口的鸟羽火山喷发，向平流层注入的硫气比坦波拉高出数百倍。

So, if a Tambora-scale scenario would be bad news, far worse could be lying in wait. While we can’t stop the next Tambora, nor handle its potential impacts on the climate and the harvest, we can ensure that contingency plans are in place to keep everyone adequately fed until the sulphur veil dissipates and temperatures return to normal. In the UK at present, contingency food supplies probably amount to little more than a few weeks’ worth. Some serious policy changes are needed if a future volcanic blast is not to bring about another subsistence crisis. 因此，如果坦波拉规模的情景是个坏消息，那就更糟了。虽然我们不能阻止下一次坦博拉，也不能控制应它对其对气候和庄稼的潜在影响，但我们可以实施计划，确保每个人都能吃饱，直到硫磺消散，温度恢复正常。目前在英国，应急食品的供应量可能仅相当于几周的时间。如果未来的火山爆炸不会引起另一次生计危机，则需要进行一些重大的政策调整。

Hazarding a guess about when and where the next Tambora will explode is far from an exact science. Eruptions on such a scale seem to happen, on average, a few times every millennium and one estimate holds that there is a 1 in 10 chance of a comparable event in the next 50 years. The Earth does not, however, operate to a timetable so such an eruption is equally likely to occur in any single year. There is even a chance that climate change may have a hand to play. Looking back at previous episodes of dramatic climate warming provides us with plenty of robust evidence for a vigorous volcanic response, most notably as our world heated up rapidly at the end of the last Ice Age. The reaction is most pronounced at ice-covered volcanoes, where melting reduces the weight acting on the volcanoes beneath, facilitating eruptions and even promoting the production of more magma. Coastal volcanoes may also be brought to eruption as the increased load of water, due to climbing sea levels, bends the crust around the margins of the oceans, squeezing magma upwards like toothpaste out of a tube. 关于下一个坦波拉何时何地爆炸的猜测，远非一门确切的科学。如此大规模的喷发似乎平均每千年发生几次，并且据估计，在未来的50年中，发生类似事件的几率为十分之一。但是，地球没有按时间表运行，因此在任何一年中都可能发生这种喷发。气候变化甚至有可能发挥作用。以往气候急剧变暖的历史时期，最为显著的是在地球气温迅速上升的上个冰河世纪末期，为我们提供了大量有力的证据，证明在该时期发生过剧烈的火山。该反应在冰雪覆盖的火山中最为明显，其融化降低了作用在下方火山上的重量，促进喷发，甚至促进更多岩浆的产生。沿海火山也可能喷发，原因是由于海平面上升，水量增加，使地壳在海洋边缘弯曲，将岩浆像牙膏一样从管中挤出。

No volcano erupts without warning signs, caused by rising magma triggering earthquake swarms and inflating the ground surface. The problem is that out of our world’s 1,300 or more active and potentially active volcanoes, we monitor only a few hundred. The Tambora eruption reinforces the unofficial volcanological axiom: the longer the wait, the bigger the bang. That rule of thumb is borne out by the fact that fully half of the biggest eruptions since 1800 originated at volcanoes that had previously been dormant throughout history. What we should be keeping a special watch on then, in order to prepare ourselves for the next arrival of Vulcan’s shock troops, are those seemingly innocuous volcanoes that have kept their heads down for centuries or even millennia. While there are too many candidates to keep a serious eye on, the numbers can be narrowed down by focusing on those that have been recently “restless”; perhaps best regarded as the volcanologists’ term for “bubbling under”. Beyond that, though, it’s anyone’s guess. 没有岩浆上升，引发地震群和使地面膨胀的现象，没有警告标志的火山就不会爆发。问题在于，在世界上1,300或更多的活跃和潜在活跃的火山中，我们仅监视数百座。坦波拉火山喷发强化了非官方的火山公理：等待时间越长，爆炸声越大。自1800年以来，半数最为猛烈的火山喷发发源自于历史上一直处于休眠状态的火山。这一事实证实了该经验法则。为了让沃尔坎的突击部队下次到来做好准备，我们应该特别注意那些看似无害的火山，它们压低了数百年甚至数千年。尽管有太多候选人无法认真关注，通过关注那些最近“不安”的数字，可以缩小数字；
也许最被认为是火山学家“冒泡”的术语。除此之外，这是任何人的猜测。

Unit3 理论家，实验家和大众物理学的偏见 Most people with more than a passing interest in physics will tell you who came up with the idea of quarks - Murray Gell-Mann. 大多数对物理学仅有一时兴趣的人都会告诉你谁提出了夸克的想法——默里·盖尔曼。

Now gather around the same crowd which knows about Gell-Mann and ask them who Henry Kendall, Jerome Friedman and Richard Taylor are. It’s very likely that you will draw mostly blank stares. 现在，在认识盖尔曼的人群中聚集一堂，问他们亨利·肯德尔，杰罗姆·弗里德曼和理查德·泰勒是谁。你很有可能茫然地看着他们。

Yet “coming up with the idea” was as far as Gell-Mann went in 1964 when he and George Zweig independently developed the concept. Without the 1968 experiments of Kendall, Friedman and Taylor at the Stanford Linear Accelerator Center (SLAC), quarks would have remained a mere theory, a will-o-wisp whose existence was confidently postulated but never proven. 然而，直到1964年盖尔·曼（Gell-Mann）和乔治·茨威格（George Zweig）独立提出这个概念时，他才提出“提出这个想法”。如果没有1968年肯德尔，弗里德曼和泰勒在斯坦福直线加速器中心（SLAC）所进行的的实验，夸克将仅仅是一种理论，一个未经证实的、缥缈的大胆假设。

Similar themes proliferate throughout the popular view of physics. Everyone knows Paul Dirac who conjectured the existence of the positron, but how many know Carl Anderson and his collaborator Seth Neddermeyer who actually found it? People similarly know about Wolfgang Pauli and Enrico Fermi stating the requirement for a ghostly particle called the neutrino in the 30s, but ask popular science enthusiasts if they are aware of the dogged pursuit of the neutrino by Raymond Davis for over 30 years and you will likely see knitted brows. Finally, even today, a schoolchild would likely know Einstein’s prediction of the bending of starlight by the gravitational field of a star, but Arthur Eddington’s verification of this fact would be little known. 在整个流行的物理学观点中，相似的主题激增。每个人都知道保罗·狄拉克（Paul Dirac）猜出了正电子的存在，但是有多少人知道卡尔·安德森（Carl Anderson）和他的合作者塞思·内德迈耶（Seth Neddermeyer）真正发现了正电子？类似地，人们也熟悉在30年代提出了幽灵粒子（即中微子）条件的泡利和费米，但如果你询问科普爱好者是否了解雷戴维斯在30余年间，一直不懈地捕捉中微子的踪迹，你很可能发现会他们眉头紧锁。最终，即使在今天，一个小学生仍可能知道爱因斯坦通过恒星的引力场对星光弯曲的预测，但是亚瑟·爱丁顿对这一事实的验证却鲜为人知。

I started mulling over this vivid gap between the public’s appreciation of theorists vs experimentalists on reading a post by physics professor Chad Orzel who, taking a cue from my post about famous American physicists, makes the cogent point that while American theorists lagged behind their European counterparts until the post-war years, they were almost equal to the Europeans even in the 1920s. His point is that we often tend to overemphasize the role of theory over experiment. 我开始思考公众对理论家与实验家的欣赏之间有如此大的差距，在开始阅读物理学教授查德·奥泽尔（Chad Orzel）的文章时，他从我的文章中得出了有关美国著名物理学家的线索，提出了令人信服的观点，即美国理论家落后于欧洲同行直到战后年代，即使在1920年代，才与欧洲相等。他的观点是，我们往往倾向于过分强调理论的作用而不是实验。

Now there’s no doubt that physicists themselves would be the first ones to recognize the value of experimentalists; for instance Anderson, Davis and the Kendall-Friedman-Taylor trio were all recognized by Nobel Prizes. But their recognition in the public mind ranges from vague to non-existent. This gap in perception is especially startling given the singular importance of experiment in physics and all of science, a central paradigm that has been the centerpiece of the scientific method since Galileo (apocryphally) dropped iron balls from the leaning tower of Pisa. Richard Feynman paid a sparkling tribute to the supremacy of experiment when he said: 现在，毫无疑问，物理学家本身是第一个认识到实验价值的人。例如安德森（Anderson），戴维斯（Davis）和肯德尔·弗里德曼·泰勒（Kendall-Friedman-Taylor）三人都获得了诺贝尔奖。但是，它们在公众心中的认可程度从模糊到不存在。考虑到在物理学和所有科学领域中实验都是非常重要的一种范式，这种感知上的差距尤其令人吃惊。自伽利略（据传言）从比萨斜塔上扔下铁球以来，实验就成为核心的科学方法。理查德·费曼（Richard Feynman）向实验物理表达了至高无上的敬意这一做法是引人注目的，他说：
“In general we look for a new law by the following process. First we guess it. Then we compute the consequences of the guess to see what would be implied if this law that we guessed is right. Then we compare the result of the computation to nature, with experiment or experience, compare it directly with observation, to see if it works. If it disagrees with experiment it is wrong. In that simple statement is the key to science. It does not make any difference how beautiful your guess is. It does not make any difference how smart you are, who made the guess, or what his name is – if it disagrees with experiment it is wrong.” “总的来说，我们通过以下过程寻找新法律。首先我们猜测一下。然后，我们计算猜测的结果，以了解我们猜测的定律是如果正确的，那将意味着什么。然后，我们将估算结果与自然，实验或经验进行比较，将其与观察结果直接进行比较，来了解这个假设是否正确。如果假设与实验不一致，那就是错误的。这就是科学的关键就存在于这个简单的说法。你的猜测无论说得天花乱坠，无论你有多聪明，谁做出的猜测，或他叫什么名字，都没有任何差别。如果假设与实验不一致，那就错了。” An even more pointed and roaring tribute to experiment came from the utterly self-assured king of experimental physics, Ernest Rutherford. His opinion of theoreticians was that “they play games with their symbols, but we turn out the real facts of Nature”. And he is said to have admonished the capable students working under his tutelage - nine of whom won Nobel Prizes - to not “let me catch anyone talking about the Universe”. 更加自负的对实验的敬意来自完全的实验物理学之王欧内斯特·卢瑟福。他对理论物理学家的看法是“他们玩带有符号的游戏，但我们揭示自然的真实面目”。据说他警告那些在他指导下有能力的学生——其中有九人获得了诺贝尔奖——不要“让我抓住任何谈论宇宙的人”。

Rutherford was the ultimate experimentalist and Feynman was the ultimate theorist but Feynman was well aware of how a well-conceived experiment is really the only thing that can make or break a theory. Ironically, the public devaluing of experimentalists applies to Feynman’s own work. The theory of quantum electrodynamics which he developed is perhaps the most accurate theory in physics. As one example, it can calculate the magnetic moment of the electron correctly to an unprecedented 15 decimal places. But we would never have known this if it weren’t for the experimentalists who devised increasingly ingenious experiments to measure the parameter. Yet everyone has heard of Feynman, but who has heard of Lamb, Kusch or Foley? 卢瑟福是最终的实验主义者，费恩曼是极端的的理论物理学家，但费恩曼清楚地意识到，构思良好的实验的确是是唯一可以使理论成立或打破的方法。具有讽刺意味的是，公众对实验家的贬低适用于费曼自己的工作。他研究的量子电动力学理论也许是最准确的物理学理论。举一个例子，它可以将电子的磁矩正确地计算到空前的15个小数位。但是，如果不是实验物理学家发明了越来越精巧的实验来测量参数，我们将永远不会知道这一点。然而，每个人都听说过费曼，但是谁听说过Lamb，库许或弗利呢？ It seems to me that there are at least two important reasons why the public, in spite of tacitly appreciating the all-important role of experiment in physics, fails to give experimentalists their due. First is the sheer success of theoretical physics in uncovering the deepest mysteries of the universe through armchair speculation. Nobody can fail to gasp in awe at an Einstein or Bohr who, working with a few facts and pencil and paper, divine grand operating principles for the cosmos in short order. 在我看来，至少有两个重要的原因可以解释为什么公众尽管默认了实验在物理学中至高无上的重要作用，却没有给实验物理学家应有的地位。首先是理论物理学家在椅子上推测揭示宇宙的奥秘是成功的。无人不深深崇敬爱因斯坦或玻尔等敬科学家，他们仅依据一些事实，靠着纸笔，便在短时间内推测出宇宙宏伟的运行规律。

Compared to their efforts based on pure thought, the corresponding efforts of experimentalists who get down on their knees, liberally coat their hands with grease and spend most of their time soldering electronic circuits and fashioning precision machine parts on a lathe sounds humdrum and boring. Yet this mundane work is an essential step toward the grand finale of hard factual discovery. Even the rare combination of theorist and experimentalist appreciates this; for instance, in spite of his pioneering contributions to theory, Fermi always said that his first love was experiment and he could often be found performing the most mundane of tasks. 与他们与理论物理学家的努力相比，实验物理学家做出的相应努力是卑躬屈膝的，他们的手上抹上油脂，并花费大量时间在车床上焊接电子电路和制造精密机械零件，这听起来很乏味和无趣。然而，这项平凡的工作是朝着艰辛的事实发现大结局迈出的重要一步。即使是身兼理论和实验的物理学家也对此表示赞同。例如，尽管费米（Fermi）在理论上做出了开创性的贡献，但他始终说，他最初的爱是实验，人们经常可以发现他在实验室进行的是最平凡的工作。

To be fair though, it’s hard not to admire theorists when many experimentalists, as ingenious as their contraptions are, “simply” validate things which the theorists have already said. Anderson might have discovered the positron, but Dirac invented it first. Eddington might have observed deflected starlight, but Einstein simply plucked it out of thin air based on what seemed like magical speculation. 不过，公平地说，我们很难不崇拜理论物理学家，因为虽然很多实验物理学家像他们的实验装置一样富有创意，但也“仅仅”是验证了理论物理学家早已说过的东西。安德森可能发现了正电子，但狄拉克首先了提出了它。爱因斯坦具有魔力般的推测，但是爱丁顿只是发现了这些星光的折射。

Firstly however, it’s very important to realize that all the awe for Einstein which we rightly feel comes only after the fact, after a thousand increasingly demanding tests of general relativity have established the veracity of the theory beyond any doubt. As Feynman said, no matter how pretty the theory looks and no matter how brilliant its creator sounds, it is no more than a hypothesis until it’s verified. Einstein unverified would have been a mystic. Fortunately the public seems to have gradually woken up to the straitjacket that ugly, grease-and-solder experiment imposes on elegant theory. This is most apparent in the decline of popular versions of string theory; after a period of breathless ascendancy by its proponents, the public seems to increasingly realize the gaping chasm between theory and experiment which the string theoretical framework constantly displays. String theory in fact is the perfect test of the ability of an informed public to distinguish between fact and speculation, and so far the signs seem promising. 但重要的是，我们首先认识到，我们对爱因斯坦的所有崇敬之情都是来自于广义相对论在经过数千次的日益严苛的测试才被证实这一事实之后。正如费曼所说的那样，无论理论看起来多么漂亮，其创造者听起来多么出色，在经过验证之前，它不过是一种假设。爱因斯坦未经验证将是一个神秘主义者。幸运的是，公众似乎已经逐渐意识到，丑陋的油脂润滑实验将优雅的理论强加于紧身衣上。显然大众对弦论流行版本的逐渐衰落。在弦理论其支持者经过一阵鼓吹之后，公众似乎已经意识到理论和实验的分歧。实际上，弦论是对知识渊博的公众区分事实和推测的能力的完美测试，到目前为止，迹象似乎越来越有希望的。

Secondly, there are also outstanding example of discoveries made by experimenters which really had no theoretical precedent. That is what makes Rutherford and Faraday the two greatest experimental physicists in history. Rutherford discovered the atomic nucleus in 1908, but it took thirty years for physicists to develop a concrete theory of the nucleus. Similarly Faraday discovered the seamless relationship between electricity and magnetism - one of the very few examples of unification by experiment - but it took until after his death for Maxwell to come up with his pioneering theory of electromagnetism. Experimentalists often follow in the steps of theorists, but the instances in which they lead the way are as full of creativity and achievement as the work of an Einstein, Bohr or Feynman. And even when they follow, they are the ones who bridge the gap between idea and hard fact. 其次，还有一个杰出的例子，表明实验者的发现确实没有理论先例。这就是使卢瑟福和法拉第成为历史上最伟大的两个实验物理学家的原因。卢瑟福于1908年发现了原子核，但是物理学家花了三十年的时间才发展出具体的原子核理论。同样地，法拉第发现了电与磁之间紧密的关系，这是通过实验进行统一的极少数例子之一，但是直到麦克斯韦死后，麦克斯韦才提出了开拓性电磁学理论。实验物理学家经常跟随理论物理学家的脚步，而有时他们也会引领理论物理学家，其过程就像爱因斯坦、波尔或费曼等科学家的工作一样充满了创造力，成就非凡。即便是他们在跟随理论物理学家，他们的工作就是在想法和铁一般的事实中架起一道桥梁。

The other big reason why for the public seems to downplay the key role of experiments is the bias in physics popularization toward theory. And here at least part of the blame must be laid at the feet of experimentalists themselves. For instance if we ponder over who the leading physics popularizers in the last twenty years are, the names that come to our minds include Brian Greene, Lisa Randall, Leonard Susskind, Brian Cox and Sean Carroll. Almost no experimenter makes the list; Anil Ananthaswamy is one of those rare writers who has shined a light on the heroic efforts of experimenters in validating cutting-edge theories. In a previous post I mentioned how the public has been fed increasingly exotic and speculative physics fare that tends to influence their opinion about what they consider are the most important fields in physics. Cosmology and quantum theory rank high on their list, condensed matter physics and biophysics rank low. But condensed matter theory still ranks higher than condensed matter experiment. Observational cosmology still takes a backseat to speculations about the Big Bang. This has to change. 公众看轻实验物理学的关键作用的另一个重要原因是在宣传时会偏向理论物理学。在这里，至少部分的责任必须由实验物理学家自己承担。例如，如果我们仔细考虑一下过去20年中领先的物理学普及者是谁，我们想到的名字包括Brian Greene，Lisa Randall，Leonard Susskind，Brian Cox和Sean Carroll。几乎没有实验物理学家列出清单。阿尼尔·安纳塔斯瓦米（Anil Ananthaswamy）是罕见的作家之一，他揭示了实验物理学家在验证前沿理论方面的英勇努力。在上一篇文章中我提到了向公众提供越来越多的异国情调和推测的的物理学的东西，这往往会影响他们对他们认为是什么是物理学中最重要领域的看法。宇宙论和量子理论在他们的榜单上排名靠前，而凝聚态物理学和生物物理学则排名在后。但是，凝聚态理论的排名仍然高于凝聚态实验。观察宇宙学与有关“大爆炸”的理论相比仍然处于后座。这种现象必须改变。

If we want to improve the public visibility of experimentalists and place experimentalists in their rightful place in the pantheon of popular physics, the main initiative would have to come from experimentalists themselves. There is no doubt that experimental physics has seen some amazing advances in the last two decades, so there＇s certainly no dearth of stories to tell. For instance just last year the Nobel Prize in physics went to Serge Haroche and David Weinland who have achieved amazing feats in trapping ions and atoms and verifying some of the most bizarre predictions of quantum mechanics. Yet where are the books which elaborate on these successes? Three years ago the physics Nobel again went to experimenters who used the simplest and most ingenious methods to create graphene. Still there are no vividly written books about these experiments. There are plenty of other motifs, from the observation of supernovae and x-ray astronomy to the manipulation of single DNA molecules using lasers, which can be productively captured in popular physics books. In addition the manipulation of these tools to plumb the depths of nature’s secrets is every bit as exciting to its practitioners as calculating the curvature of spacetime is to its own. It’s up to those who deftly wield this machinery to convey their personal pleasure of finding things out to the public. 如果我们想提高实验物理学家的公众知名度，并将实验物理学置于科普物理学殿堂的合适位置，主要还是靠实验物理学家自己。毫无疑问，在过去的二十年中，实验物理学取得了惊人的进步，肯定有许多故事可讲。例如，仅在去年，诺贝尔物理学奖就颁发给塞尔吉·哈罗什（Serge Haroche）和戴维·温兰德（David Weinland），他们在捕获离子和原子并验证量子力学的一些最离奇的预测方面取得了惊人的成就。但是，详细描述他们取得这些成就的书在哪里呢？三年前诺贝尔物理学再次颁给了介绍了使用最简单，最巧妙的方法创建石墨烯的实验物理学家。仍然没有关于这些实验的生动著作。从超新星和X射线天文学的观察到使用激光操作单个DNA分子，还有许多其他图案，可以在流行的物理书籍中有效地介绍捕捉到的这些图案。此外，巧用这些工具探究自然界的奥秘，对实验物理学家来说，就与计算时空的曲率对理论物理学家一样令人兴奋。那些熟练地使用此工具的人可以将自己发现事物的乐趣传递给公众。

Experiment is the ultimate arbiter of science and it’s a pity that the current popular physics literature does not reflect this all-important fact. Experimenters and their journalist friends need to now pick up the baton and run with it. They need to communicate to the public why ion traps are as engrossing as Lie groups, why even the most elegant mathematical edifice can crumble in the face of confounding experimental evidence, why, in Rutherford’s words, “the theorists play games with their symbols while they are the ones who turn out the real facts of nature”. 实验是科学的终极仲裁者，可惜的是，当前流行的物理学文献并未反映出这一至关重要的事实。实验人员及其记者朋友一起对实验物理学进行宣传。他们需要对公众宣传，为什么离子陷像李群一样引人入胜；
这就是为什么即使是最宏伟的数学大厦也可能在令人困惑的实验证据面前崩塌；
用卢瑟福的话说：“理论物理学家在只不过在玩符号游戏，而实验物理学家是揭示自然的真实真相的人”。

unit4 神奇数字：数学方程式可以美丽吗？ Paul Dirac had an eye for beauty. In one essay, from May 1963, the British Nobel laureate referred to beauty nine times. It makes four appearances in four consecutive sentences. In the article he painted a picture of how physicists saw nature. But the word beauty never defined a sunset, nor a flower, or nature in any traditional sense. Dirac was talking quantum theory and gravity. The beauty lay in the mathematics. 保罗·狄拉克对美有眼光。在1963年5月的一篇文章中，这位英国诺贝尔奖获得者九次提到美。它连续四个句子出现。在这篇文章中，他描绘了物理学家如何看待自然。但“美“这个词从来不是夕阳，也不是花，也不是任何传统意义上的自然。狄拉克在谈论量子理论和引力。美在于数学。

What does it mean for maths to be beautiful? It is not about the appearance of the symbols on the page. That, at best, is secondary. Maths becomes beautiful through the power and elegance of its arguments and formulae; through the bridges it builds between previously unconnected worlds. When it surprises. For those who learn the language, maths has the same capacity for beauty as art, music, a full blanket of stars on the darkest night. 数学美意味着什么？它不是关于页面上符号的外观。这充其量是次要的。数学之美，在于其论证和公式的力量和优雅，在于它贯通了原本互不相干的世界。当它惊喜。对于学习数学这门语言的人而言，数学和艺术、音乐以及在漆黑夜空中的满天斗星一样，可以美轮美奂。

“The slow movement of the Mozart clarinet concerto is a really beautiful piece of music, but I don’t print off a page of the score and put that on my wall. It’s not about that. It’s about the music and the ideas and the emotional response,” says Vicky Neale, a mathematician at Oxford University. “It’s the same with a piece of mathematics. It’s not how it looks, it‘s about the underlying thought processes.” “莫扎特单簧管协奏曲的缓慢移动是一首非常美妙的音乐，但我不打印出乐谱的一页，而是把它写在墙上。不是这个这是关于音乐、思想和情感反应，“牛津大学数学家维琪·尼尔说。“这与一块数学相同。它不是它看起来的样子，它是关于底层的思维过程。

Brain scans of mathematicians show that gazing at formulae considered beautiful by the beholder elicits activity in the same emotional region as great art and music. The more beautiful the formula, the greater the activity in the medial orbito-frontal cortex. “So far as the brain is concerned, maths has beauty just like art. There is common neurophysiological ground,” says Sir Michael Atiyah, an honorary professor of mathematics at Edinburgh University. 对数学家的大脑扫描显示，当他们凝视其认为美丽的公式时，所激发的大脑情感区域与欣赏伟大的艺术和音乐时所激发的区域相同。公式越漂亮，中皮层前皮层的活动就越大。“就大脑而言，数学就像艺术一样有美。有共同的神经生理学基础，“爱丁堡大学数学名誉教授迈克尔·阿提亚爵士说。

Ask mathematicians about the most beautiful equation and one crops up time and again. Written in the 18th century by the Swiss mathematician, Leonhard Euler, the relation is short and simple: eiπ+1 = 0. It is neat and compact even to the naive eye. But the beauty comes from a deeper understanding: here the five most important mathematical constants are brought together. Euler’s formula marries the world of circles, imaginary numbers and exponentials. 向数学家们询问最美丽的方程，一个反复出现。由瑞士数学家莱昂哈德·欧拉于18世纪写成，这种关系简短而简单：eiπ+1 = 0。它整洁紧凑，甚至用肉眼看也是美的。但美来自于一个更深刻的理解：这个公式，汇集了数学上最重要的5个常数。欧拉的公式结合了圆圈、虚数和指数的世界。

The beauty of other formulae may be more obvious. With E=mc2, Albert Einstein built a bridge between energy and mass, two concepts that had previously seemed worlds apart. Maggie Aderin-Pocock, the space scientist, declared it the most beautiful equation and she is in good company. “Why is it so beautiful? Because it comes to life. Now energy will have mass and mass can be put into energy. These four symbols capture a complete world. It’s difficult to imagine a shorter formula with more power,” says Robbert Dijkgraaf, director of the Institute for Advanced Study in Princeton, where Einstein was one of the first faculty members. 其他公式的美可能更明显。在E_mc2中，阿尔伯特·爱因斯坦在能量和质量之间架起了一座桥梁，这两个概念以前是毫不相关。空间科学家玛吉·阿德林-波科克宣称这是最美丽的方程式，而且她很认同这个观点。“为什么它这么漂亮？因为它有生命。现在能量将有质量，质量可以放入能两种。这四个符号抓住了整个的世界。很难想象有一个更短的公式，能比这个公式有更强大的力量。“普林斯顿高级研究所所长罗伯特·迪克格拉夫说，爱因斯坦是这个研究所第一批的教职员工之一。

“One of the reasons there’s almost an objective beauty in mathematics is that we use the word beautiful also to indicate the raw power in an idea. The equations or results in mathematics that are seen to be beautiful are almost like poems.The power per variable is something that is part of the experience. Just seeing a huge part of mathematics or nature being described with just a few symbols gives a great sense of elegance or beauty,” Dijkgraaf adds. “A second element is you feel its beauty is reflecting reality. It’s reflecting a sense of order that’s out there as part of the laws of nature.” “数学中几乎客观美的原因之一是，我们使用“美丽“这个词来表示一个想法中的原始力量。数学结果几乎和诗歌一样美。每个变量的功率是体验的一部分。纷繁复杂的大自然就数学只用几个符号就体现了，给人一种极大的优雅或美感，“Dijkgraaf补充道。“第二个因素是，你觉得它的美丽正在反映现实。它反映了一种秩序感，这种秩序是自然法则的一部分。

The power of an equation to connect what seem like completely unrelated realms of mathematics comes up often. Marcus du Sautoy, a maths professor at Oxford, has more than a soft spot for Riemann’s formula. Published by Bernhard Riemann in 1859 (the same year Charles Darwin stunned the world with On the Origin of Species), the formula reveals how many primes exist below a given number, where primes are whole numbers divisible only by themselves and one, such as 2, 3, 5, 7 and 11. While one side of the equation describes the primes, the other is controlled by zeros. 一个等式常常具有将看似完全无关的数学领域联系起来的力量。牛津大学的数学教授马库斯·杜·索托伊对里曼的公式有着更多的支持。该公式由伯恩哈德·里曼于1859年出版（同年查尔斯·达尔文用《物种起源》震惊了世界），该公式揭示了在给定数字以下存在多少素数，其中质数仅能由自身整数整，一个，如2，3，5，7 和 11。方程的一侧描述质数，另一侧由零控制。

“This formula turns these these indivisible prime numbers, into something completely different,” says du Sautoy. “On the one side, you’ve got these indivisible prime numbers and then Riemann takes you on this journey to somewhere completely unexpected, to these things which we now call the Riemann zeros. Each of these zeros gives rise to a note – and it’s the combination of these notes together which tell us how the primes on the other side are distributed across all numbers.” “这个公式把这些不可分割的质数变成完全不同的东西，“杜索托伊说。“一方面，你已经得到了这些不可分割的质数，然后黎曼带你踏上去完全意想不到的地方的旅程，这些东西，我们现在称之为里曼零。每个零都产生一个题解，正是这些题解的组合告诉我们另一侧的质数是如何分布在所有数字上的。

More than 2,000 years ago, the ancient Greek mathematician, Euclid, solved a numerical puzzle so beautifully that it still makes Neale smile every time it comes to mind. “When I think about beauty in mathematics, my first thoughts are not about equations. For me it’s much more about an argument, a line of thinking, or a particular proof,” she says. 2000多年前，古希腊数学家欧几里德完美地解决了一个数字难题，尼尔每念及此便会欣然而笑。“当我想到数学中的美时，我的第一个想法不是方程。对我来说，这更多的是关于争论、思路或特定证据，“她说。

Euclid proved there are infinitely many prime numbers. How did he do it? He began by imagining a universe where the number of primes was not infinite. Given a big enough blackboard, one could chalk them all up. 欧几里德证明有无限多的质数。他是怎么做到的？他首先想象一个素数不是无限的。如果有足够的黑板，他就可以用粉笔把这个黑板写满。

He then asked what happened if all these primes were multiplied together: 2 x 3 x 5 and so on, all the way to the end of the list, and the result added to the number 1. This huge new number provides the answer. Either it is a prime number itself, and so the original list was incomplete, or it is divisible by a smaller prime. But divide Euclid’s number by any prime on the list and always there is a 1 left over. The number is not divisible by any prime on the list. “It turns out you reach an absurdity, a contradiction,” says Neale. The original assumption that the number of primes is finite must be wrong. 然后，他问如果所有这些素数相乘，发生了什么：2 x 3 x 5 等，一直到列表的末尾，结果添加到数字 1。这个巨大的新数字提供了答案。它要么是质数本身，因此原始列表不完整，要么它被较小的质数整除。但是，将欧几里德的数字除以列表中的任何素数，最后的结果就是1 。该数字不能被列表中的任何素数整除。尼尔说：“原始假设素数有限，事实证明，与之相悖，这个假设一定是错误的。

“The proof for me is really beautiful. It takes some thinking to get your head around it, but it doesn’t involve learning lots of difficult concepts. It’s surprising that you can prove something so difficult in such an elegant way,” Neale adds. “对我来说，证据真的很漂亮。它需要一些思考来推算，但它不涉及学习很多困难的概念。令人惊讶的是，你能以如此优雅的方式证明如此困难的事情，“Neale 补充道。

Behind beautiful processes lie beautiful mathematics. Well, some of the time. Hannah Fry, a lecturer in the mathematics of cities at UCL spent years staring at the Navier-Stokes equations. “They’re a single mathematical sentence that is capable of describing the miraculously beautiful and diverse behaviour of almost all of Earth’s fluids,” she says. With a grasp of the formulae, we can understand blood flow in the body, make boats glide through the water, and build awesome chocolate enrobers. 这样美丽的过程，就是数学的美丽。嗯，有一段时间。汉娜·弗莱是大学城市数学的讲师，她花了数年时间盯着纳维耶-斯托克斯方程。“它们是一个单一的数学句子，能够描述几乎所有地球流体的神奇美丽和多样化的运行方式，“她说。掌握了这些公式，我们便能理解血液如何在我们的体内流动，建造飘在水中的船只，以及发明制作美味巧克力的浸挂糖衣机。

In his 1963 essay, Dirac elevated beauty from an aesthetic response to something far more profound: a route to the truth. “It is more important to have beauty in one’s equations than to have them fit experiment,” he wrote, continuing: “It seems that if one is working from the point of view of getting beauty in one’s equations, and if one has really a sound insight, one is on a sure line of progress.” Shocking at first pass, Dirac captured what is now a common sentiment: when a beautiful equation seems at odds with nature, the fault may lie not with the maths, but in applying it to the wrong aspect of nature. 在1963年的论文中，狄拉克将美从审美反应提升到更深刻的高度：通往真理的道路。“在一个人的方程中拥有美比让它们适合实验更重要，“他写道，继续说道：“似乎如果一个人从在方程中获取美的角度工作，如果一个人真的有敏锐的洞察力，那一个人就处于一个肯定的底线上。乍一看，让人惊奇，但狄拉克扑捉到了一种普遍的看法：当一个美丽的方程式看似有悖自然规律时，错误可能不在数学本身，而在于将其用错了领域。

“Truth and beauty are closely related but not the same,” says Atiyah. “You are never sure that you have the truth. All you are doing is striving towards better and better truths and the light that guides you is beauty. Beauty is the torch you hold up and follow in the belief that it will lead you to truth in the end.” “真理和美丽是密切相关的，但不同，“阿提亚说。“你永远不会确定，你有真相。你所做的只是努力追求更好、更好的真理，指引你的光是美。美是你举起并跟随的火炬，相信它最终会引导你走向真理。

Something approaching faith in mathematical beauty has led physicists to draw up two of the most compelling descriptions of reality: supersymmetry and string theory. In a supersymmetric universe, every known type of particle has a heavier, invisible twin. In string theory, reality has 10 dimensions, but six are curled up so tight they are hidden from us. The mathematics behind both theories are often described as beautiful, but it is not at all clear if either is true. 一些认为数学是越来越美的信心促使物理学家们对这个现实进行了两个最引人注目的描述：超对称和弦理论。在超对称宇宙中，每一种已知的粒子都有一个更重的、不可见的孪晶。在弦理论中，现实有10个维度，但6个维度被紧紧卷起来，隐藏起来。这两种理论背后的数学通常被描述为美丽，但还没有完全弄清楚这两种理论是否是真理。

There is a danger here for mathematicians. Beauty is a fallible guide. “You can literally be seduced by something that is not correct. This is a risk,” says Dijkgraaf, whose institute motto, “Truth and Beauty” features one naked and one dressed woman. “Sometimes I feel that physicists, like Odysseus, must tie themselves to the mast of the ship so they are not seduced by the sirens of mathematics.” 对数学家来说，这里有一个危险。美可能是一个错误的引导。“你可能被一些不正确的东西所引诱。这就有风险，“Dijkgraaf说，普林斯顿研究所的院训，“真理和美丽“的特点是一个裸体和一个穿衣服的女人。“有时候我觉得物理学家，像奥德修斯一样，必须把自己绑在船的桅杆上，这样他们就不会被数学的汽笛声所诱惑（不会受到数学的干扰）。

It may be that mathematicians and scientists are the only groups that still use the word “beautiful” without hesitation. It is rarely employed by critics of literature, art or music, who perhaps fear it sounds superficial or kitschy. 也许数学家和科学家是唯一仍然毫不犹豫地使用“美丽“一词的群体。“美丽”这个词很少被文学、艺术或音乐评论家使用，他们也许担心这个词听起来肤浅或古怪。

“I’m very proud that in mathematics and science the concept of beauty is still there. I think it’s an incredibly important concept in our lives,” says Dijkgraaf. “The sense of beauty we experience in maths and science is a multidimensional sense of beauty. We don’t feel it’s in any conflict with being deep, or interesting, or powerful, or meaningful. For the mathematician it’s all captured by that one word.” “我感到非常自豪的是，在数学和科学中，仍然存在美的概念。我认为这是我们生活中一个非常重要的概念，“迪克格拉夫说。“我们在数学和科学中体验的美感是一种多维度的感觉。我们认为它不会与深沉、有趣、强大或有意义产生任何冲突。对于数学家来说，这一切都被“美”那个词所迷惑。