温伯格《解释世界》第一章 物质和诗意

首先让我们介绍一下背景。在公元前6世纪今天土耳其的西海岸已经被希腊人所占据，他们主要说爱奥尼亚方言。爱奥尼亚最富裕和强大的城市是米利都市。米利都城始建于一个天然海港，迈安德河从附近流过汇入爱琴海。在米利都，希腊人在早于苏格拉底一个世纪前就开始思考构成世界的最基本物质。 我本科在康奈尔大学科学哲学史课上最早接触到米利都学派。在课上我听到米利都人称呼“物理学家”。那时我也在上物理课，包括现代的物质原子理论。在我看来米利都学派与现代物理没有一点相近之处。并不是说米利都学派关于物质特性的理解有多么错误，而是我不能理解他们是如何得出他们的结论的。有关柏拉图之前希腊学派的历史记载支离破碎，但是我能确定在古风时期和古典希腊时期（大约分别是公元前600年到公元前450年和公元前450年到公元前300年）无论米利都或其他任何希腊自然学派都不会像现代科学家一样思索问题。 第一位知名的米利都人是泰勒斯，大约生活在早于柏拉图2个世纪时期。据说他曾预测过一次日食。我们现在确实知道在公元前585年发生过日食，而且该日食在米利都可见。即使受益于巴比伦的日食记录，泰勒斯也不太可能作出这个预测，因为任何日食只能在非常有限的区域内观察到，但是人们把这次预测归功于泰勒斯的事实说明他可能在公元前500年已经享有盛名了。我们不知道泰勒斯是否记载了他的观点。无论如何，泰勒斯没有任何文字流传下来。即使在后世作家的引用中也没有出现过。他是一位传奇人物，在柏拉图时代被列为希腊“七贤”之一（另外还有他的同代人梭伦，传说雅典宪法由他制定）。比如传说泰勒斯证明或从埃及引入了一个著名的几何理论（参见技术说明1）。这里我们感兴趣的是传说泰勒斯认为所有物质都是由一种基本物质构成。亚里士多德著作”形而上学”写道“最早期的哲学家大都认为物质性的东西为万物唯一本原。---- 这派学说的创始者泰勒斯说水是本原”。希腊哲学家传记作者戴奥真尼斯·拉尔修后来写道“他的基本教义是水是宇宙基本物质，世界生机勃勃，充满神灵。” 泰勒斯所谓的“宇宙基本物质”是指所有物质都是由水组成的吗？如果是这样的话，我们无法知道他是如何得出这个结论的。但是如果一个人确信所有物质都是由某一基本物质构成的，那么水是一个不错的选择。水不仅可以以液相存在，而且可以通过冷冻或煮沸转化为固相或气相。很明显生命也离不开水。但是我们不知道泰勒斯是否想过比如说岩石是否真的是由普通的水组成，或许他认为在深层意义上岩石和其他所有固体物质与冰有共性。 泰勒斯有个学生（或是伙伴）阿那克西曼德得出不同的结论。他也认为存在一个单一基本物质，但他并没有将这个物质与任何常见物质相联系。反而他认为这是一种他称之为无限或无穷的神秘物质。关于这点，我们可以从大约生活在1千年后的新柏拉图主义者辛普里丘那里找到对他的观点的描述。辛普里丘文章里有对阿那克西曼德原话的直接引用，见下文中的斜体字： 那些认为本原是单一，变化和无限的众人中，泰勒斯的继任者和学生，帕西亚德斯之子，米利都人阿那克西曼德说无限既是本原又是万物的元素。他说既不是水也不是任何所谓的元素，而是其他无限之物构成天国和世界，万物由之产生的东西，万物又消灭而复归于它，这是命中注定的。因为万物在时间的秩序中不公正，所以受到惩罚，并且彼此互相补充--这是他以颇带诗意的语言说出的话。很明显他看到四元素之间的这种相互变化，他并不认为有必要把任何一个作为基本元素，而是提出了与此不同的构想。 之后不久另一位米利都人阿那克西米尼重新回到了世界万物是由同一物质构成的观点，但是对阿那克西米尼而言这一物质不是水，而是气。他写了一本书，但其中只有一整句话流传了下来：“气即灵魂，主导大众，呼吸和气构成整个世界”。 米利都人的贡献到阿那克西米尼为止就到了尽头。在大约公元前550年米利都和其他小亚细亚爱奥尼亚都城臣服于日渐强大的波斯帝国。公元前499年米利都人发动了一次起义，但被波斯人镇压了。后来虽然复兴成为希腊的一个重镇，但从来没有再次成为希腊科学中心。 米利都以外的爱奥尼亚人继续着对物质特性的探索。色诺芬尼大约公元前570年出生于爱奥尼亚科洛封，后来移居到意大利南部，有资料表明他将土作为基本物质。在他的一首诗中有这样一句话：“万物皆来源于土，复终于土”。但是或许这不过是他对悼辞“尘归尘，土归土”采用的不同表述。在第五章介绍宗教时我们还会讲到色诺芬尼。 大约公元前500年左右在离米利都不远的爱菲斯，赫拉克利特传授火是基本物质的理论。他写了一本书，其中只有部分片段保留下来。其中的一个片段告诉我们，“这个有序的宇宙对于一切都是同一的，非由任何一个神或人所创造，它过去，现在或将来都是永生之火，适时燃烧，适时熄灭。”赫拉克利特强调自然的永恒变化，因而对他来说很自然会把闪耀之火--变化的动因，作为基本元素，而不是更加稳定的土，气和水。 万物不是由一种而是由四种基本元素—水，气，土和火所构成的经典观点可能是恩培多克勒提出来的。恩培多克勒生活在公元前五世纪中叶西西里阿克拉噶斯（今阿格里琴托城），他是本故事早期第一位，几乎也是唯一一位多里安族，而非爱奥尼亚族希腊人。他著有两篇六步格诗，其中许多片段都流传下来。在《论自然》里，我们看到“如何由水，土，气和太阳（火）之混合形成凡物之形之色”以及“火与水与土与无限高之气，由争斗分离，完全平衡，由爱结合，各方相等。” 恩培多克勒和阿那克西曼德使用“爱”和“争斗”或者“正义”和“非正义”可能只是用来比喻有序和无序，类似爱因斯坦有时使用“上帝”来比喻自然界未知的基本定律。但是我们不应该将现代解释强加到前苏格拉底时代的词汇上。在我看来，恩培多克勒将爱和争斗这样的人类情感，或阿那克西曼德将正义和补偿价值观引入到对物质特性的探索突出了前苏格拉底时代与现代物理精神的巨大差距。 这些前苏格拉底时代学者，从泰勒斯到恩培多克勒，似乎认为基本元素都是均匀且不可区分的物质。稍后不久在阿布德拉有人推出了一个不同观点，一个与现代认识比较接近的观点。阿布德拉位于色雷斯海岸，是由公元前499年爱奥尼亚反抗波斯导致的难民创建的。最早知名的阿布德拉哲学家是留基波。他的观点只有一句话流传下来，表明了一个确定性世界观，“没有什么是无端发生的，万物都是有理由和必然的”。现在对留基波的继承人德谟克里特知之甚多。他出生于米利都，于公元前五世纪晚期定居于阿布德拉之前曾在巴比伦，埃及和雅典旅居。德谟克里特的著作涉及道德，自然科学，数学和音乐。他的著作许多片段都保存了下来。其中一个片段表述了世上万物皆由微小且不可分的原子（ 希腊语指“不可切割”）构成，原子在虚空中运动。“甜由约定俗成而存在，苦由约定俗成而存在，只有原子与虚空真实存在。” 与现代科学家一样，这些早期希腊学者致力于透过世界表面现象寻求更深层次的知识。世界万物初看起来并不像是由水，或气，土，火，或由这四个一起，或只由原子构成。 深受柏拉图敬佩的巴门尼德将神秘主义推到了极端。巴门尼德是意大利南部爱利亚（现代韦利亚）地方的人。在公元前5世纪前期巴门尼德讲授大自然表面上的变化和多样性只是一种幻觉，这与赫拉克利特观点完全相反。他的学生爱利亚人芝诺（不要与其他芝诺混淆，比如斯多葛派芝诺）极力维护他的观点。在他的著作“攻击”一书中芝诺提出了一系列关于运动不可能存在的悖论。比如，若要走完全程跑道，首先需要完成一半的距离，然后完成剩余距离的一半，一直下去，无穷无尽，因而完成全程跑道是不可能的。基于同样的道理，只要剩余距离仍然可分，对芝诺来说就不可能走完任何确定距离，所以运动是不可能的。 当然芝诺的理由是站不住脚的。正如亚里士多德后来指出的一样，只要每一步行进时间递减的足够快，没有任何理由可以证实为什么不能在有限的时间内完成无限步数。无限序列比如 ½ + 1/3 + ¼ + 。。。之和确实为无穷大，但是无限序列 ½ + ¼ + 1/8 之和为有限值，结果为1。 最令人惊奇的不是巴门尼德和芝诺错的如此离谱，而是他们根本不去尝试解释如果运动不可能，那么为什么物体看起来在运动。事实上从泰勒斯到柏拉图，无论是在米利都，阿布德拉，爱利亚还是在雅典，没有一个早期希腊人致力于应用他们有关实体的理论来解释表象。 这不单单是智力上的懒惰。早期希腊人的恃才傲物使他们不屑于认识事物的表象。这只是思想方法妨碍科学进步的一例。在历史不同时期人们曾经认为圆形轨道比椭圆形轨道更加完美，金子比铅更加尊贵，人比类人猿更加高级。 我们现在是否还在重复同样的错误，由于忽略了看起来不值一视的现象而错过了赢得科学进展的机会？虽然对此我不能肯定，但我存疑。当然我们不可能探索一切，我们会选取研究我们认为（或对或错）会给科学认知带来最佳前景的问题。从事染色体或神经细胞研究的生物学家研究果蝇和墨鱼，而不是更华丽的鹰和雄狮。基本粒子物理学家有时会被指责只全神贯注于那些最高能量下的现象，但是只有在如此高能下我们才可能去产生和研究假想的高质量粒子，比如暗物质粒子，天文学家告诉我们其占有宇宙所有物质的六分之五。再者我们也足够关注低能下的现象，比如令人迷惑的中微子质量，其只有电子质量的百万分之一。 我这里评价前苏格拉底时代的偏见并不意味着说科学不需要先验知识。例如今天我们期望发现最基本的物理定律符合对称原理，即当我们以某种确定方式改变我们的视角时物理定律不变。类似于巴门尼德的不变性原理。一些对称性原理在物理现象里并不是显而易见的--这被称为自发破缺，也就是说我们的理论方程具有某种简化，比如会以同样方式处理某类粒子，但是支配实际现象的方程的解并不具有同样的简化。尽管如此，与巴门尼德坚守不变性原理不同，支持对称性原理的先验猜想是从多年物理实验中发展起来的，这些物理实验试图找寻描述真实世界的物理原理，对称性破缺和非破缺都由实验验证来确认他们的结果。这里不涉及我们应用到人世间的那种价值判断。 随着公元前五世纪晚期苏格拉底，以及其后40年柏拉图的兴起，希腊文明中心舞台转移到了雅典—一座位于希腊大陆上的个别爱奥尼亚都城。我们对苏格拉底的了解完全源自于他在柏拉图对话中的形象以及在阿里斯托芬剧本《云》中的喜剧角色。苏格拉底似乎从来没有将他的观点记录下来，就我们所知他对自然科学并不十分感兴趣。在柏拉图对话录《裴多篇》里苏格拉底回忆他在阅读阿那克萨戈拉（在第七章中将有更多介绍）的作品时是多么失望，因为阿那克萨戈拉纯粹从物理角度描述地球，太阳，月亮和恒星，而不关心好坏。 柏拉图是雅典贵族，这点与他心目中的英雄苏格拉底完全不同。他是第一个诸多著作皆得以完整保存下来的希腊哲学家。与苏格拉底一样，柏拉图更关注人世间事物，而不是物质的自然特性。他希望从政以便有机会付诸实施他的乌托邦和反民主观点。公元前367年柏拉图接受了戴奥尼夏二世的邀请去叙拉古帮助改革他的政府，但是对叙拉古幸运的是改革计划没有任何结果。 在他的对话录《蒂迈欧篇》里柏拉图综合了四种基本元素观点和阿布德拉的原子概念。柏拉图认为恩培多克勒的四元素由微粒组成，微粒形状类似五种数学上称为正多面体实体中的四种。正多面体各个面都是全等的多边形，所有边都相等，相交成相等顶角 （参见技术说明2）。比如立方体是正多面体之一，所有面都是相等的正方形，三个正方形在每个顶角相交。柏拉图设想土的原子是立方形。其他正多面体有正四面体（由四个正三角形面组成的金字塔形），8个边的正八面体，20个边的正二十面体以及12个边的正十二面体。柏拉图认为火原子，气原子和水原子分别具有正四面体形，正八面体形和正二十面体形。这样还剩下一个正十二面体没有算进去。柏拉图设想其代表宇宙。后来亚里士多德引入了第五元素，即以太或精质，他认为以太充满了月亮以外的太空。 许多作品在描述这些早期关于物质本质的猜想时特别强调其如何预示出现代科学的特证。这其中德谟克里特尤其受到推崇。现代希腊一所名牌大学就被命名为德谟克里特大学。确实，人类对组成物质最基本单位的探索持续了上千年，在历史的不同阶段提出过不同的基本元素。在现代早期炼金术士已经识别出三种假定元素：汞，盐和硫。现代化学元素的观点始于十八世纪末期由普利斯特里，拉瓦锡，道尔顿等引发的化学革命，包括自然界存在的92种元素，从氢到铀（有汞和硫，但没有盐），以及越来越多的由人工生成的重于铀的元素。在正常条件下，一种纯化学元素由同样类型的原子组成，元素可以由组成他们的原子不同来区分。今天我们更超越化学元素，研究组成原子的基本粒子。但是不管怎样，我们延续着从米利都开始的对自然基本构成的探索。 但是我认为我们不应过分强调古风或古典希腊时期科学具有的现代一面。现代科学拥有一个非常重要的特征，但前面提到的所有思想家（从泰勒斯到柏拉图）完全没有具备，他们中没有一个尝试去验证或深入解释（可能芝诺例外）他们的假想。在阅读他们的作品时人们不禁要问：“你是怎么知道的？”这点无论对德谟克里特或其他人都一样，在他流传下来的作品片段里一点也看不到他如何呈现物质为什么由原子组成。 柏拉图在他的五元素论中充分体现了他对做出合理解释的不以为然。在《蒂迈欧篇》里，他不是从正多面体开始，而是从三角形开始，三角形相连形成多面体的面。是什么样的三角形哪？柏拉图设想应该是角度分别为45度，45度和90度的等腰直角三角形，以及角度为30度，60度和90度的直角三角形。立方形土原子的正方形平面可以由两个等腰直角三角形构成，火，气和水的正四面体，正八面体和正二十面体的三角平面每个都可以由两个直角三角形构成（神秘地代表宇宙的正十二面体不能这样构成）。为了对此作出解释，柏拉图在《蒂迈欧篇》里说：”如果有人可以告诉我们更好地构成这四实体的三角形选项，那么我会欢迎他们提出的批评。至于我们这部分，我们将跳过余下内容 …, 做出解释将需要太长的篇幅，但是如果有人能够证明事实并非如此，我们将非常欢迎。” 试想在当今社会如果我在一篇物理文章中提出一个有关物质的新设想，而却说需要太长篇幅去解释我的理由，因而挑战我的同行去反证我的设想，会得到什么样的回应。 亚里士多德称早期希腊思想家为physiologi, 有时这被翻译为“物理学家”，但这是误解。Physiologi这个词是指学习自然的学生。早期希腊学者与现代物理学家没有共性。他们的理论没有实效。恩培多克勒猜想元素，德谟克里特猜想原子，但是他们的猜想没能带来对自然界新的认识--而且他们的理论完全无法测试。 在我看来要理解这些早期希腊学者，最好不要把他们当作物理学家，科学家或哲学家，而是当作诗人。 我需要澄清我这样说是什么意思。狭义的诗是指应用韵律，韵脚或头韵的语言。即使从狭义角度来说色诺芬尼，巴门尼德和恩培多克勒也都在作诗。公元前12世纪多里安人的入侵以及青铜器时代迈锡尼文明的没落，希腊人几乎成为文盲。由于没有文字记录，诗几乎成为当代文明流传给后代的唯一途径，因为诗很容易被记住，而散文确很难。公元前700年左右希腊得以文化复兴，但是从腓尼基引入的新字母首先被荷马和赫西奥德用来写希腊黑暗岁月长久口头流传的诗，散文是后来的事。 即使以散文形式写作的希腊早期思想家也采用诗的风格，比如阿那克西曼德，赫拉克利特和德谟克里特。西塞罗说德谟克里特比大多数诗人更像诗人。柏拉图年轻时想成为诗人，虽然他写散文而且在“理想国”里表明对诗的反感，他的写作风格一直受到大众追捧。 我这里说的诗是指广义上的诗：泛指具有美学效果的语言，而不是为了叙述事实。在读迪伦·托马斯的诗“穿过绿色根茎之力让花凋谢，催人老去”时，我们不会认为这是在严肃地描述植物学与动物学中力的统一，我们也不会去寻求证实。我们（至少是我）会认为这只是表达对衰老和死亡的哀伤。 有时很显然柏拉图并不希望人们只从文字上理解。前面提到的例子说明他选择两个三角形作为所有物质基础的论证有多么不足。一个更明显的例子是在《蒂迈欧篇》里柏拉图介绍了历史上早于他数千年曾经繁荣的亚特兰蒂斯王国的故事，柏拉图不可能认真思考过他对几千年前发生的故事真正知道多少。 我并不是说早期希腊学者采用诗意写作是为了回避验证他们的观点。事实上他们认为这根本没有必要。今天我们首先运用我们所提出的理论得出可用实验验证的近似精确结果，然后用实验去测试我们的设想。早期希腊学者以及他们的许多继承者却不是这样，道理很简单：他们从来没有见到别人这样做过。 即使这些早期希腊学者希望被认真对待，但有时他们自己也会怀疑他们的理论。他们会认为不可能获得可靠的知识。在我1977年有关广义相对论的论文中我介绍了一个例子。在有关宇宙假想章节段首，我引用了色诺芬尼的话 “至于哲理，没有人见过，也不会有人知晓众神灵和我提到的事情。如果他坚定地说什么是真理，他自己却没有意识到，对所有事情的意见都由命运决定。” 在《论形式》中德谟克里特做了同样的论述 “我们无法确知任何事” 以及 “许多方面都表明事实上我们不知道每件事具体是怎么样的。” 现代物理仍存诗意元素。我们不用诗的风格写作，大多数物理学家的文章也很难达到散文的水平。但是我们寻求理论之美，而且也用审美来指导我们的科研。我们中的一些人认为这样可行，因为我们历经几个世纪在物理研究中不断的成功和失败的锤炼，会有期待得到自然法则的某一方面，通过这个经验我们会体会到这些自然定律特有的美感。但是我们不会把理论之美作为其真实与否的依据。 比如将不同基本粒子作为弦上不同振动模式的弦理论，极其优美。看上去仅仅是数学上的自恰而已，所以其结构不是随意的，而是很大程度上由数学自恰性这一要求所限定。因而其具有严格的艺术之美—像十四行诗或奏鸣曲。遗憾的是弦理论还没有带来任何可用实验验证的预测，结果理论物理学家（至少我们中的大多数）对该理论是否可以真正应用到现实世界抱有开放态度。所有那些自然界诗意的学生，从泰勒斯到柏拉图正缺乏这种对验证的坚定追求。

First, to set the scene. By the sixth century BC the western coast of what is now Turkey had for some time been settled by Greeks, chiefly speaking the Ionian dialect. The richest and most powerful of the Ionian cities was Miletus, founded at a natural harbor near where the river Meander flows into the Aegean Sea. In Miletus, over a century before the time of Socrates, Greeks began to speculate about the fundamental substance of which the world is made. I first learned about the Milesians as an undergraduate at Cornell, taking courses on the history and philosophy of science. In lectures I heard the Milesians called “physicists.” At the same time, I was also attending classes on physics, including the modern atomic theory of matter. There seemed to me to be very little in common between Milesian and modern physics. It was not so much that the Milesians were wrong about the nature of matter, but rather that I could not understand how they could have reached their conclusions. The historical record concerning Greek thought before the time of Plato is fragmentary, but I was pretty sure that during the Archaic and Classical eras (roughly from 600 to 450 BC and from 450 to 300 BC, respectively) neither the Milesians nor any of the other Greek students of nature were reasoning in anything like the way scientists reason today. The first Milesian of whom anything is known was Thales, who lived about two centuries before the time of Plato. He was supposed to have predicted a solar eclipse, one that we know did occur in 585 BC and was visible from Miletus. Even with the benefit of Babylonian eclipse records it’s unlikely that Thales could have made this prediction, because any solar eclipse is visible from only a limited geographic region, but the fact that Thales was credited with this prediction shows that he probably flourished in the early 500s BC. We don’t know if Thales put any of his ideas into writing. In any case, nothing written by Thales has survived, even as a quotation by later authors. He is a legendary figure, one of those (like his contemporary Solon, who was supposed to have founded the Athenian constitution) who were conventionally listed in Plato’s time as the “seven sages” of Greece. For instance, Thales was reputed to have proved or brought from Egypt a famous theorem of geometry (see Technical Note 1). What matters to us here is that Thales was said to hold the view that all matter is composed of a single fundamental substance. According to Aristotle’s Metaphysics, “Of the first philosophers, most thought the principles which were of the nature of matter were the only principles of all things. . . . Thales, the founder of this school of philosophy, says the principle is water.”1 Much later, Diogenes Laertius (fl. AD 230), a biographer of the Greek philosophers, wrote, “His doctrine was that water is the universal primary substance, and that the world is animate and full of divinities.”2 By “universal primary substance” did Thales mean that all matter is composed of water? If so, we have no way of telling how he came to this conclusion, but if someone is convinced that all matter is composed of a single common substance, then water is not a bad candidate. Water not only occurs as a liquid but can be easily converted into a solid by freezing or into a vapor by boiling. Water evidently also is essential to life. But we don’t know if Thales thought that rocks, for example, are really formed from ordinary water, or only that there is something profound that rock and all other solids have in common with frozen water. Thales had a pupil or associate, Anaximander, who came to a different conclusion. He too thought that there is a single fundamental substance, but he did not associate it with any common material. Rather, he identified it as a mysterious substance he called the unlimited, or infinite. On this, we have a description of his views by Simplicius, a Neoplatonist who lived about a thousand years later. Simplicius includes what seems to be a direct quotation from Anaximander, indicated here in italics:

Of those who say that [the principle] is one and in motion and unlimited, Anaximander, son of Praxiades, a Milesian who became successor and pupil to Thales, said that the unlimited is both principle and element of the things that exist. He says that it is neither water nor any other of the so-called elements, but some other unlimited nature, from which the heavens and the worlds in them come about; and the things from which is the coming into being for the things that exist are also those into which their destruction comes about, in accordance with what must be. For they give justice and reparation to one another for their offence in accordance with the ordinance of time—speaking of them thus in rather poetical terms. And it is clear that, having observed the change of the four elements into one another, he did not think fit to make any one of these an underlying stuff, but something else apart from these.3

A little later another Milesian, Anaximenes, returned to the idea that everything is made of some one common substance, but for Anaximenes it was not water but air. He wrote one book, of which just one whole sentence has survived: “The soul, being our air, controls us, and breath and air encompass the whole world.”4 With Anaximenes the contributions of the Milesians came to an end. Miletus and the other Ionian cities of Asia Minor became subject to the growing Persian Empire in about 550 BC. Miletus started a revolt in 499 BC and was devastated by the Persians. It revived later as an important Greek city, but it never again became a center of Greek science. Concern with the nature of matter continued outside Miletus among the Ionian Greeks. There is a hint that earth was nominated as the fundamental substance by Xenophanes, who was born around 570 BC at Colophon in Ionia and migrated to southern Italy. In one of his poems, there is the line “For all things come from earth, and in earth all things end.”5 But perhaps this was just his version of the familiar funerary sentiment, “Ashes to ashes, dust to dust.” We will meet Xenophanes again in another connection, when we come to religion in Chapter 5. At Ephesus, not far from Miletus, around 500 BC Heraclitus taught that the fundamental substance is fire. He wrote a book, of which only fragments survive. One of these fragments tells us, “This ordered kosmos,* which is the same for all, was not created by any one of the gods or of mankind, but it was ever and is and shall be ever-living Fire, kindled in measure and quenched in measure.”6 Heraclitus elsewhere emphasized the endless changes in nature, so for him it was more natural to take flickering fire, an agent of change, as the fundamental element than the more stable earth, air, or water. The classic view that all matter is composed not of one but of four elements—water, air, earth, and fire—is probably due to Empedocles. He lived in Acragas, in Sicily (the modern Agrigento), in the mid- 400s BC, and he is the first and nearly the only Greek in this early part of the story to have been of Dorian rather than of Ionian stock. He wrote two hexameter poems, of which many fragments have survived. In On Nature, we find “how from the mixture of Water, Earth, Aether, and Sun [fire] there came into being the forms and colours of mortal things”7 and also “fire and water and earth and the endless height of air, and cursed Strife apart from them, balanced in every way, and Love among them, equal in height and breadth.”8 It is possible that Empedocles and Anaximander used terms like “love” and “strife” or “justice” and “injustice” only as metaphors for order and disorder, in something like the way Einstein occasionally used “God” as a metaphor for the unknown fundamental laws of nature. But we should not force a modern interpretation onto the pre-Socratics’ words. As I see it, the intrusion of human emotions like Empedocles’ love and strife, or of values like Anaximander’s justice and reparation, into speculations about the nature of matter is more likely to be a sign of the great distance of the thought of the pre- Socratics from the spirit of modern physics. These pre-Socratics, from Thales to Empedocles, seem to have thought of the elements as smooth undifferentiated substances. A different view that is closer to modern understanding was introduced a little later at Abdera, a town on the seacoast of Thrace founded by refugees from the revolt of the Ionian cities against Persia started in 499 BC. The first known Abderite philosopher is Leucippus, from whom just one sentence survives, suggesting a deterministic worldview: “No thing happens in vain, but everything for a reason and by necessity.”9 Much more is known of Leucippus’ successor Democritus. He was born at Miletus, and had traveled in Babylon, Egypt, and Athens before settling in Abdera in the late 400s BC. Democritus wrote books on ethics, natural science, mathematics, and music, of which many fragments survive. One of these fragments expresses the view that all matter consists of tiny indivisible particles called atoms (from the Greek for “uncuttable”), moving in empty space: “Sweet exists by convention, bitter by convention; atoms and Void [alone] exist in reality.”10 Like modern scientists, these early Greeks were willing to look beneath the surface appearance of the world, pursuing knowledge about a deeper level of reality. The matter of the world does not appear at first glance as if it is all made of water, or air, or earth, or fire, or all four together, or even of atoms. Acceptance of the esoteric was taken to an extreme by Parmenides of Elea (the modern Velia) in southern Italy, who was greatly admired by Plato. In the early 400s BC Parmenides taught, contra Heraclitus, that the apparent change and variety in nature are an illusion. His ideas were defended by his pupil Zeno of Elea (not to be confused with other Zenos, such as Zeno the Stoic). In his book Attacks, Zeno offered a number of paradoxes to show the impossibility of motion. For instance, to traverse the whole course of a racetrack, it is necessary first to cover half the distance, and then half the remaining distance, and so on indefinitely, so that it is impossible ever to traverse the whole track. By the same reasoning, as far as we can tell from surviving fragments, it appeared to Zeno to be impossible ever to travel any given distance, so that all motion is impossible. Of course, Zeno’s reasoning was wrong. As pointed out later by Aristotle,11 there is no reason why we cannot accomplish an infinite number of steps in a finite time, as long as the time needed for each successive step decreases sufficiently rapidly. It is true that an infinite series like ½ + ⅓ + ¼ + . . . has an infinite sum, but the infinite series ½ + ¼ + ⅛ + . . . has a finite sum, in this case equal to 1. What is most striking is not so much that Parmenides and Zeno were wrong as that they did not bother to explain why, if motion is impossible, things appear to move. Indeed, none of the early Greeks from Thales to Plato, in either Miletus or Abdera or Elea or Athens, ever took it on themselves to explain in detail how their theories about ultimate reality accounted for the appearances of things. This was not just intellectual laziness. There was a strain of intellectual snobbery among the early Greeks that led them to regard an understanding of appearances as not worth having. This is just one example of an attitude that has blighted much of the history of science. At various times it has been thought that circular orbits are more perfect than elliptical orbits, that gold is more noble than lead, and that man is a higher being than his fellow simians. Are we now making similar mistakes, passing up opportunities for scientific progress because we ignore phenomena that seem unworthy of our attention? One can’t be sure, but I doubt it. Of course, we cannot explore everything, but we choose problems that we think, rightly or wrongly, offer the best prospect for scientific understanding. Biologists who are interested in chromosomes or nerve cells study animals like fruit flies and squid, not noble eagles and lions. Elementary particle physicists are sometimes accused of a snobbish and expensive preoccupation with phenomena at the highest attainable energies, but it is only at high energies that we can create and study hypothetical particles of high mass, like the dark matter particles that astronomers tell us make up five-sixths of the matter of the universe. In any case, we give plenty of attention to phenomena at low energies, like the intriguing mass of neutrinos, about a millionth the mass of the electron. In commenting on the prejudices of the pre-Socratics, I don’t mean to say that a priori reasoning has no place in science. Today, for instance, we expect to find that our deepest physical laws satisfy principles of symmetry, which state that physical laws do not change when we change our point of view in certain definite ways. Just like Parmenides’ principle of changelessness, some of these symmetry principles are not immediately apparent in physical phenomena—they are said to be spontaneously broken. That is, the equations of our theories have certain simplicities, for instance treating certain species of particles in the same way, but these simplicities are not shared by the solutions of the equations, which govern actual phenomena. Nevertheless, unlike the commitment of Parmenides to changelessness, the a priori presumption in favor of principles of symmetry arose from many years of experience in searching for physical principles that describe the real world, and broken as well as unbroken symmetries are validated by experiments that confirm their consequences. They do not involve value judgments of the sort we apply to human affairs. With Socrates, in the late fifth century BC, and Plato, some forty years later, the center of the stage for Greek intellectual life moved to Athens, one of the few cities of Ionian Greeks on the Greek mainland. Almost all of what we know about Socrates comes from his appearance in the dialogues of Plato, and as a comic character in Aristophanes’ play The Clouds. Socrates does not seem to have put any of his ideas into writing, but as far as we can tell he was not very interested in natural science. In Plato’s dialogue Phaedo Socrates recalls how he was disappointed in reading a book by Anaxagoras (about whom more in Chapter 7) because Anaxagoras described the Earth, Sun, Moon, and stars in purely physical terms, without regard to what is best.12 Plato, unlike his hero Socrates, was an Athenian aristocrat. He was the first Greek philosopher from whom many writings have survived pretty much intact. Plato, like Socrates, was more concerned with human affairs than with the nature of matter. He hoped for a political career that would allow him to put his utopian and antidemocratic ideas into practice. In 367 BC Plato accepted an invitation from Dionysius II to come to Syracuse and help reform its government, but, fortunately for Syracuse, nothing came of the reform project. In one of his dialogues, the Timaeus, Plato brought together the idea of four elements with the Abderite notion of atoms. Plato supposed that the four elements of Empedocles consisted of particles shaped like four of the five solid bodies known in mathematics as regular polyhedrons: bodies with faces that are all identical polygons, with all edges identical, coming together at identical vertices. (See Technical Note 2.) For instance, one of the regular polyhedrons is the cube, whose faces are all identical squares, three squares meeting at each vertex. Plato took atoms of earth to have the shape of cubes. The other regular polyhedrons are the tetrahedron (a pyramid with four triangular faces), the eight-sided octahedron, the twenty-sided icosahedron, and the twelve-sided dodecahedron. Plato supposed that the atoms of fire, air, and water have the shapes respectively of the tetrahedron, octahedron, and icosahedron. This left the dodecahedron unaccounted for. Plato regarded it as representing the kosmos. Later Aristotle introduced a fifth element, the ether or quintessence, which he supposed filled the space above the orbit of the Moon. It has been common in writing about these early speculations regarding the nature of matter to emphasize how they prefigure features of modern science. Democritus is particularly admired; one of the leading universities in modern Greece is named Democritus University. Indeed, the effort to identify the fundamental constituents of matter continued for millennia, though with changes from time to time in the menu of elements. By early modern times alchemists had identified three supposed elements: mercury, salt, and sulfur. The modern idea of chemical elements dates from the chemical revolution instigated by Priestley, Lavoisier, Dalton, and others at the end of the eighteenth century, and now incorporates 92 naturally occurring elements, from hydrogen to uranium (including mercury and sulfur but not salt) plus a growing list of artificially created elements heavier than uranium. Under normal conditions, a pure chemical element consists of atoms all of the same type, and the elements are distinguished from one another by the type of atom of which they are composed. Today we look beyond the chemical elements to the elementary particles of which atoms are composed, but one way or another we continue the search, begun at Miletus, for the fundamental constituents of nature. Nevertheless, I think one should not overemphasize the modern aspects of Archaic or Classical Greek science. There is an important feature of modern science that is almost completely missing in all the thinkers I have mentioned, from Thales to Plato: none of them attempted to verify or even (aside perhaps from Zeno) seriously to justify their speculations. In reading their writings, one continually wants to ask, “How do you know?” This is just as true of Democritus as of the others. Nowhere in the fragments of his books that survive do we see any effort to show that matter really is composed of atoms. Plato’s ideas about the five elements give a good example of his insouciant attitude toward justification. In Timaeus, he starts not with regular polyhedrons but with triangles, which he proposes to join together to form the faces of the polyhedrons. What sort of triangles? Plato proposes that these should be the isosceles right triangle, with angles 45°, 45°, and 90°; and the right triangle with angles 30°, 60°, and 90°. The square faces of the cubic atoms of earth can be formed from two isosceles right triangles, and the triangular faces of the tetrahedral, octahedral, and icosahedral atoms of fire, air, and water (respectively) can each be formed from two of the other right triangles. (The dodecahedron, which mysteriously represents the cosmos, cannot be constructed in this way.) To explain this choice, Plato in Timaeus says, “If anyone can tell us of a better choice of triangle for the construction of the four bodies, his criticism will be welcome; but for our part we propose to pass over all the rest. . . . It would be too long a story to give the reason, but if anyone can produce a proof that it is not so we will welcome his achievement.”13 I can imagine the reaction today if I supported a new conjecture about matter in a physics article by saying that it would take too long to explain my reasoning, and challenging my colleagues to prove the conjecture is not true. Aristotle called the earlier Greek philosophers physiologi, and this is sometimes translated as “physicists,”14 but that is misleading. The word physiologi simply means students of nature (physis), and the early Greeks had very little in common with today’s physicists. Their theories had no bite. Empedocles could speculate about the elements, and Democritus about atoms, but their speculations led to no new information about nature—and certainly to nothing that would allow their theories to be tested. It seems to me that to understand these early Greeks, it is better to think of them not as physicists or scientists or even philosophers, but as poets. I should be clear about what I mean by this. There is a narrow sense of poetry, as language that uses verbal devices like meter, rhyme, or alliteration. Even in this narrow sense, Xenophanes, Parmenides, and Empedocles all wrote in poetry. After the Dorian invasions and the breakup of the Bronze Age Mycenaean civilization in the twelfth century BC, the Greeks had become largely illiterate. Without writing, poetry is almost the only way that people can communicate to later generations, because poetry can be remembered in a way that prose cannot. Literacy revived among the Greeks sometime around 700 BC, but the new alphabet borrowed from the Phoenicians was first used by Homer and Hesiod to write poetry, some of it the long-remembered poetry of the Greek dark ages. Prose came later. Even the early Greek philosophers who wrote in prose, like Anaximander, Heraclitus, and Democritus, adopted a poetic style. Cicero said of Democritus that he was more poetic than many poets. Plato when young had wanted to be a poet, and though he wrote prose and was hostile to poetry in the Republic, his literary style has always been widely admired. I have in mind here poetry in a broader sense: language chosen for aesthetic effect, rather than in an attempt to say clearly what one actually believes to be true. When Dylan Thomas writes, “The force that through the green fuse drives the flower drives my green age,” we do not regard this as a serious statement about the unification of the forces of botany and zoology, and we do not seek verification; we (or at least I) take it rather as an expression of sadness about age and death. At times it seems clear that Plato did not intend to be taken literally. One example mentioned above is his extraordinarily weak argument for the choice he made of two triangles as the basis of all matter. As an even clearer example, in the Timaeus Plato introduced the story of Atlantis, which supposedly flourished thousands of years before his own time. Plato could not possibly have seriously thought that he really knew anything about what had happened thousands of years earlier. I don’t at all mean to say that the early Greeks decided to write poetically in order to avoid the need to validate their theories. They felt no such need. Today we test our speculations about nature by using proposed theories to draw more or less precise conclusions that can be tested by observation. This did not occur to the early Greeks, or to many of their successors, for a very simple reason: they had never seen it done. There are signs here and there that even when they did want to be taken seriously, the early Greeks had doubts about their own theories, that they felt reliable knowledge was unattainable. I used one example in my 1972 treatise on general relativity. At the head of a chapter about cosmological speculation, I quoted some lines of Xenophanes: “And as for certain truth, no man has seen it, nor will there ever be a man who knows about the gods and about the things I mention. For if he succeeds to the full in saying what is completely true, he himself is nevertheless unaware of it, and opinion is fixed by fate upon all things.”15 In the same vein, in On the Forms, Democritus remarked, “We in reality know nothing firmly” and “That in reality we do not know how each thing is or is not has been shown in many ways.”16 There remains a poetic element in modern physics. We do not write in poetry; much of the writing of physicists barely reaches the level of prose. But we seek beauty in our theories, and use aesthetic judgments as a guide in our research. Some of us think that this works because we have been trained by centuries of success and failure in physics research to anticipate certain aspects of the laws of nature, and through this experience we have come to feel that these features of nature’s laws are beautiful.17 But we do not take the beauty of a theory as convincing evidence of its truth. For example, string theory, which describes the different species of elementary particles as various modes of vibration of tiny strings, is very beautiful. It appears to be just barely consistent mathematically, so that its structure is not arbitrary, but largely fixed by the requirement of mathematical consistency. Thus it has the beauty of a rigid art form—a sonnet or a sonata. Unfortunately, string theory has not yet led to any predictions that can be tested experimentally, and as a result theorists (at least most of us) are keeping an open mind as to whether the theory actually applies to the real world. It is this insistence on verification that we most miss in all the poetic students of nature, from Thales to Plato.