温伯格《解释世界》第九章 阿拉伯人

公元5世纪西罗马帝国灭亡后，讲希腊语的东罗马继续以拜占庭帝国存在，其领土面积甚至仍在扩张。东罗马帝国在赫拉克利乌斯皇帝统治期间军事上取得辉煌胜利。其军队在公元627年尼尼微战役中击败罗马的宿敌-波斯帝国军队。但是十年内拜占庭却不得不迎战更为强大的对手。 古代阿拉伯人被认为是蛮族，他们居住在罗马帝国与波斯帝国的边境，“刚好在沙漠与沃土的分界线”。他们是异教徒，他们信奉的宗教以位于西阿拉伯居住地汉志一带的麦加为中心。公元六世纪末期麦加人穆罕默德开始着手号召阿拉伯人昄依一神教。遭遇抵抗后，他与随从于公元622年逃往麦地那，后来他们以麦地那为军事基地占领了麦加和大部分阿拉伯半岛。 穆罕默德公元632年去世后，大部分穆斯林接受定都于麦地那的四位继任者的统治：他们是穆罕默德的弟子及亲属阿布·伯克尔，欧麦尔，奥斯曼和阿里。今天的逊尼派穆斯林把他们尊称为“四大正统哈里发。” 尼尼微战役仅仅九年之后，穆斯林就于公元636年占领了拜占庭属地叙利亚，接着吞并了波斯，美索不达米亚和埃及。 他们的扩张将阿拉伯人带入全球舞台。比如阿拉伯将军阿穆占领亚历山大里亚后向哈里发欧麦尔汇报：“我占领了一座城池，关于这座城，我只能说它有6000个宫殿，4000个公共浴池，400个剧院，12000菜贩，和40000犹太人。” 少数阿拉伯人只接受穆罕默德女婿—第四位哈里发阿里的统领，这些人是现代什叶派穆斯林的先驱。在一场针对阿里的叛乱中阿里与他的儿子侯赛因被杀害，从此伊斯兰世界完全分裂。公元661年一个新的王朝—逊尼倭马亚哈里发王朝在大马士革建立。 在倭马亚时代阿拉伯领土扩展到现代的阿富汗，巴基斯坦，利比亚，突尼斯，阿尔及利亚，以及摩洛哥，大部分西班牙，包括阿姆河在内的大部分中亚地区。从他们占有的拜占庭领地他们开始吸纳希腊科学。其中一些希腊知识来自于波斯，查士丁尼关闭新柏拉图学院后波斯统治者在伊斯兰教兴起之前非常欢迎希腊学者的到来（其中包括辛普里丘）。 阿拉伯科学在下一个逊尼王朝—阿巴斯哈里发王朝进入了黄金时代。公元754到775年统治阿巴斯王朝的哈里发曼苏尔在美索不达米亚底格里斯河两岸建立了阿巴斯王朝首府—巴格达，它成为当时世界最大的城市，或者说至少是除中国以外的最大城市。巴格达最著名的统治者是公元786到809年的哈里发哈伦·拉希德，他因《一千零一夜》而闻名。在拉希德和他的儿子阿尔·马蒙（公元813到833哈里发）统治期间，对希腊，波斯和印度作品的翻译达到顶峰。阿尔·马蒙派了一个使团到君士坦丁堡带回希腊手稿。使团中可能就有伟大的译者—医学家侯奈因·伊本·伊斯哈格，他创建了翻译王国，培训他的儿子和外甥从事翻译。侯奈因翻译了柏拉图和亚里士多德的著作，他也翻译了底奥斯可里底斯，盖伦和希波克拉底的医学文稿。欧几里德，托勒密以及其他一些人的数学成果也在巴格达被翻译为阿拉伯文，有些是先译为古叙利亚文再转译。历史学家菲利普·希提极好地对比了这阶段巴格达的好学与中世纪早期欧洲的无知：“东方的拉希德和阿尔·马蒙探索希腊和波斯哲学的时候，西方的查理大帝和他的大臣们只在学习如何书写自己的名字。” 阿巴斯哈里发对科学最大的贡献是建立翻译与研究中心—智慧宫。人们认为这个中心对阿拉伯人的作用类似于亚历山大博物馆对希腊人的作用。但阿拉伯语言和文学家迪米特里·古塔斯并不这样认为。他指出智慧宫只是翻译前伊斯兰时期波斯书本，其中大部分是波斯历史和诗歌，而不是希腊科学。人们只知道阿尔·马蒙时代少量在智慧宫翻译的作品，而那是译自波斯文，而非希腊文。我们后面会介绍在智慧宫所开展的天文研究，但我们对其规模一无所知。不过可以确定的是无论是否在智慧宫，拉希德和阿尔·马蒙时代的巴格达已经成为一个集翻译与研究为一体的伟大中心。 阿拉伯科学不只局囿于巴格达，而是向西扩展到埃及，西班牙和摩洛哥，向东扩展到波斯和中亚。从事科学研究的不只是阿拉伯人，还包括波斯人，犹太人和土耳其人。他们都是阿拉伯文明的一部分，并以阿拉伯文写作（或至少是阿拉伯文字体系）。那时阿拉伯文的地位类似于今天的英文。有时很难区分这些人的族裔，我把他们统称为“阿拉伯人”。 大体上我们可以将这些阿拉伯智者分为两类：一类是真正的数学家和天文学家，他们对我们今天所说的哲学不太关心。另一类是哲学家和医学家，他们深受亚里士多德的影响，对数学不热衷。他们对天文学的兴趣只限于占星术。在有关行星运行理论方面，哲学家/医学家倾向于亚里士多德以地球为中心的同心圆理论，而天文学家/数学家一般遵循第八章介绍的托勒密本轮和均轮理论。我们后面会看到，这种分歧在欧洲一直持续到哥白尼时代。 阿拉伯科学成就是众多学者共同努力的结果，这其中并没有哪位像科学革命时代的伽利略或牛顿那样突出。下面对中世纪阿拉伯学者做一些简介，我希望这可以体现出他们成就的深度以及广度。 巴格达第一位重要的天文学家/数学家是阿尔·花剌子模--公元780年出生于现代乌兹别克斯坦的波斯人。（注：他的全名是穆罕默德·本·穆萨·阿尔·花剌子模，阿拉伯人全名很长，我一般只给出此人被人所知的简名。我也会省去一些不重要的标符，比如元音上的横标。对不懂阿拉伯文的读者（比如我）这些不重要。）阿尔·花剌子模在智慧宫工作，他制作的天文表（部分基于印度人的观察）受到广泛应用。其最著名的数学专著是《移项及集项的科学》，该书献给阿尔·马蒙哈里发（他有一半波斯血统）。我们现代“代数”一词就源于此书名。但该书并不真正是现代意义代数方面的书。比如书中关于二次方程的解是用文字描述的，而不是用代数方面非常重要的符号（在这方面阿尔·花剌子模的数学逊于丢番图）。我们现在求解问题的规则—“算法”一词也是源自阿尔·花剌子模。《移项及集项的科学》一书中包含罗马数字，60进位的巴比伦数字以及从印度学来的一种新的10进位数字，这常常令人困惑。可以说阿尔·花剌子模对数学最大的贡献是他将印度的10进位数字引入到阿拉伯，后来在欧洲把这些数称为阿拉伯数字。 除了阿尔·花剌子模这种精英人才之外，在巴格达还有一批在九世纪极富创造力的天文学家，包括阿尔·法甘尼（阿法甘纳斯）（注：阿法甘纳斯是中世纪欧洲知晓的拉丁化名字。后面其他阿拉伯人我也给出拉丁化名字），他创作了深受欢迎的对托勒密《天文学大成》一书的总结，而且拓展了托勒密《行星假说》中描述的行星运行设想。 这批巴格达学者的主要工作是改善埃拉托色尼对地球大小的测量。尤其是阿尔·法甘尼计算出的地球周长要更小，这在几个世纪之后大大激励哥伦布坚信他完全可以从西班牙向西安全航行到日本（见前面第七章中的注释），这也许是历史上最幸运的误算。 对欧洲天文学家最富影响力的阿拉伯人是公元858年出生于美索不达米亚北部的阿尔·巴塔尼（阿巴塔尼阿斯）。他应用并修正了托勒密的《天文学大成》，精确测量了黄道与天赤道的231/2度夹角，年和季节长度，岁差以及恒星位置。他从印度引入了三角函数正弦，替代了喜帕恰斯使用和计算的弦。（见技术说明15）。哥白尼和第谷·布拉赫后来常常引用到他的工作。 波斯天文学家阿尔·苏菲（阿左飞）也做出了一个重要发现，但其对天文学的意义直到20世纪才被人所知。公元964年在著作《恒星》中，阿尔·苏菲描述了在仙女座一直存在的“一朵云”。这是人们对我们现在所说的星系的最早观察。他提到的是旋涡星系M31。阿尔·苏菲在伊斯法罕工作期间也参与了将希腊天文学翻译为阿拉伯语的工作。 阿巴斯时代最杰出的天文学家可能是阿尔·比鲁尼。中世纪的欧洲对他并不了解，所以他的名字没有拉丁文。阿尔·比鲁尼生活于中亚地区，他1017年访问了印度，在那里教授希腊哲学。他研究了地球自转的可能性，给出了各个城市精确的经纬度，计算了正切函数表，而且测量了多种固体和液体的比重。他对虚假的占星术嗤之以鼻。阿尔·比鲁尼在印度发明了测量地球周长的新方法。他这样描述： 在我生活在印度南达纳城堡时，我注意到从城堡西边高山上观察，一大片平原呈现在高山南部。我想到我应该尝试我新的方法（前面介绍过的方法），这样我从山顶凭经验测量了蓝天与大地间的夹角。我发现（到地平线）视线比（地平面方向）参考线低34弧秒。然后我测量了山的垂向（即其高度）为652.055腕尺，腕尺是当地测量布匹使用的标准长度单位。 （注：阿尔·比鲁尼这里混合使用了十进制和六十进制。他给出的山高为652；3；18，即652加3/60加18/3600，现代十进制为652.055） 基于这组参数阿尔·比鲁尼计算出地球半径为12803337.0358腕尺。他的计算有些错误，由他的数据得出的结果应该是1千3百3拾万腕尺（见技术说明16）。当然他不可能把山的高度测量到他所说的数值精度, 这样1千2百8拾万与1千3百3拾万没有什么区别。阿尔·比鲁尼把地球半径的数值给到12位精度，他与我们前面看到的阿里斯塔克斯犯了同样的错误：即计算结果精度高于计算所依据测量值的精度。 我也曾这样闯过祸。多年前我的一个暑期打工工作是计算原子在原子束装置中穿过一系列磁体后的轨迹。这是在台式计算机或电子计算器之前，我那时用的是电动计算器，可以进行加减乘除计算到8位数。我那时过于懒惰，在报告中直接写上了这台设备输出的8位数计算结果。我的老板抱怨说我计算基于的磁场测量精度只有百分之几，超过这个精度的数据都没有意义。 另外我们无法判断阿尔·比鲁尼得出的地球半径为1千3百万的是否准确，因为我们不知道他的腕尺有多长。他说1英里有4000腕尺，但他所说的1英里又是什么意思哪？ 欧玛尔·海亚姆是位诗人，天文学家，他公元1048年出生于波斯纳霞堡，公元1131年去世于此地。他在伊斯法罕掌管天文台，编纂天文表，设计日历改革。在中亚撒马尔罕他从事代数方面研究，比如三次方程解法。英文世界对他的认识源自于他的诗人身份。十九世纪爱德华·菲兹杰拉德从他在波斯创作的大量四行诗体中翻译了75首诗，称为《鲁拜集》。作为一位坚定的现实主义者，他强烈反对占星术。 阿拉伯人对物理最大的贡献是在光学方面，首先是十世纪末期的伊本·扎尔可能解决了折射光方向问题（第13章有详细介绍），然后是伟大的阿尔·海什木(阿尔哈森)。阿尔·海什木约公元965年出生于美索不达米亚南部的巴士拉，在埃及工作。他的现存作品包括《光学》，《月光》，《月晕和彩虹》，《抛物面镜》，《影子的形成》，《星光》，《论光》，《燃烧的球体》，以及《日月食形成》。他正确地认识到光从一种介质到另一介质产生的折射现象是由于光速的变化，他通过实验发现只有小角度情况下反射角才与入射角成正比。但是他并没有给出正确的通式。在天文学方面，他延续阿德拉斯托斯和西昂的努力，致力于给托勒密的均轮和本轮做出物理解释。 人们现在认为早期化学家贾比尔·伊本·哈杨在八世纪晚期或九世纪早期已经大放异彩。我们对他的一生了解不多，我们也不清楚众多归功于他的成就是否真是他一人所为。在十三世纪和十四世纪的欧洲出现众多拉丁文作品，人们认为这些作品出自于一位叫“格柏”的作者，但是现在人们认为这些作品的作者与人们归之于贾比尔·伊本·哈杨的阿拉伯作品作者不是同一个人。贾比尔开发了蒸发，提纯，熔化，以及结晶技术。他也曾专注于将廉价金属转化为黄金，因而常被人称为炼金术师。但那时化学家和炼金术师并无明确区别，也不存在任何基础科学理论告诉人们这种转化根本不可行。在我看来，对科学的未来尤为重要的是下面两类研究的差别：一类是那些遵循德谟克里特思路的化学家或炼金术师，无论他们的理论是否正确，但他们确以纯自然方式探索物质世界；另一类是那些类似于柏拉图（以及阿那克西曼德, 恩培多克勒，除非他们在用比喻）那样的学者，他们把人类或宗教价值观赋予他们所研究的物质。贾比尔可能属于后者。例如他把数字28赋予化学意义，因为《古兰经》所采用的阿拉伯语有28个字母。28也是7与4的乘积，7代表金属个数，4代表其属性：冷，热，湿，干。 阿拉伯医学/哲学方面最早期的重要人物是阿尔·金迪(阿肯德斯)，他出生于巴士拉的一个贵族家庭，公元九世纪在巴格达工作。他追随亚里士多德，曾致力于融合亚里士多德与柏拉图以及伊斯兰的学说。阿尔·金迪博学多才，对数学非常感兴趣，但是与贾比尔一样，他仿效毕达哥拉斯学派把数学作为一种数字法术。他创作了有关光学和医学方面作品，攻击炼金术，但他又为占星术辩护。阿尔·金迪也参与了将希腊文翻译为阿拉伯文的指导工作。 令人印象更加深刻的是阿尔·拉奇（拉奇斯），他比阿尔·金迪晚一代，是说阿拉伯语的波斯人。他的作品包括《论天花与麻疹》。在《盖伦医学质疑》中他挑战这位罗马医学家的权威，质疑从希波克拉底以来所提倡的健康是四种体液平衡的理论（见第四章）。他解释说：“医学是种哲学，不能不容许对那些显赫作者的质疑）。与一般阿拉伯医学家的观点不同，阿尔·拉奇也同样挑战亚里士多德的教义，比如空间必须有限的教条。 最著名的伊斯兰医学家是伊本·西纳（阿维森纳）--另一位说阿拉伯语的波斯人。他公元980年出生于中亚布哈拉附近，后来成为布哈拉苏丹宫廷御医，还被任命为一个省的主管。伊本·西纳属于亚里士多德学派，与阿尔·金迪一样，他也试图融合亚里士多德与伊斯兰学说。他的《医典》是中世纪最富影响力的医学著作。 同时医学在伊斯兰的西班牙也开始蓬勃发展。阿尔-扎哈拉维（阿尔布卡西斯）公元936年出生于安达卢西亚都市科尔多瓦附近，他在那里一直工作到1013年去世为止。他是中世纪最伟大的外科医生，对基督教欧洲有巨大影响。也许是由于外科手术比其他医术受那些错误理论影响较小，阿尔-扎哈拉维寻求将医学与哲学和神学分开。 但医学与哲学的分离并没有持续下去。一世纪之后医学家伊本·巴哲(阿芬帕斯)出生于萨拉戈萨，先后在萨拉戈萨，非斯，塞维勒和格拉纳达等地从事学术活动。他属于亚里士多德学派，反对托勒密及其天文学，但是他并不认可亚里士多德的运动理论。 伊本·巴哲的继任者是他的学生伊本·图菲利（亚勒巴瑟），他也出生于穆斯林西班牙。他先后在格拉纳达，休达和丹吉尔行医，后来在穆瓦希德王朝任御医兼大臣。他认为亚里士多德与伊斯兰间不存在分歧，像他的老师一样，他也反对托勒密天文学的本轮和偏心理论。 伊本·图菲利也有一个杰出的学生—阿尔·比特拉几。他是一位天文学家，他继承了他的老师对亚里士多德的评述，反对托勒密。阿尔·比特拉几曾试图用同心圆来重新解释行星在本轮上的运行，但没有成功。 一位穆斯林西班牙的医学家后来更以哲学家而闻名。伊本·路西德（阿威罗伊）1126年出生于科尔多瓦，该市阿匍的孙子。他1169年在塞维利亚，1171年在科尔多瓦做法官，在伊本·图菲利的推荐下于1182年开始做宫廷御医。作为一名医学家，伊本·路西德最著名的成就是认识眼睛视网膜的作用，但他的名望主要出于他作为亚里士多德评述者的成就。他对亚里士多德的赞美达到令人尴尬的程度： （亚里士多德）创建和完善了逻辑学，物理学，以及形而上学。我之所以说他创建了这些学科是因为在他之前关于这些学科的著作不值一提，远不及他的著作。我说他完善了这些学科是因为在他之后一直到我们现代，将近1千5百年，没人能对他的著作有所增减，也没人能从他的著作中找到任何关键错误。 现代作家萨曼·拉什迪的父亲选择拉什迪为姓来向伊本·路西德的世俗理性主义表达敬意。 伊本·路西德自然也反对托勒密天文学，认为其违背物理学--即亚里士多德的物理学。他也知道亚里士多德的同心圆理论不能“保持视运动”，他致力于修正亚里士多德理论以使其与观测更加相符，但最终他认为这只能留给后代： 年轻时的我希望我可以获得这项（天文）研究的成功。现在到了晚年，我已经失去希望，一些障碍挡在我的面前。但是我这里所言可能会引发后世研究者的关注。我们当今的天文学还不能描述现实。我们提出的模型只有计算意义，与现实不符。 当然伊本·路西德对后世研究人员的期望只能落空。没有人能让亚里士多德的行星理论成功。 穆斯林西班牙同样在进行认真的天文研究。十一世纪托莱多的阿尔·查尔卡利（阿尔扎切尔）是第一个测量太阳环绕地球视轨道的进动（实际上当然是地球环绕太阳轨道的进动）的天文学家，现在人们知道这主要是由于地球与其他行星间的引力造成的。他提出进动值为每年12.9弧秒，与现代的每年11.6弧秒非常接近。包括阿尔·查尔卡利在内的天文学家使用早期阿尔·花刺子模和阿尔·巴塔尼的工作构建了《托莱多星表》，这是对托勒密《实用天文表》的继承。这些天文表以及后续的一些星表详细描述了太阳，月亮以及行星在黄道的视运行，这是天文学史上里程碑式的成就。 在倭马亚王朝及后来柏柏尔人建立的阿尔摩拉维德王朝，西班牙是国际化的求学中心，那里对犹太人与对穆斯林同样友善。摩西·本·马里蒙 (迈蒙尼德) 就是出生于这段幸福时光的犹太人，他1135年出生于科尔多瓦。在伊斯兰地区犹太人和基督徒传来都没有好过二等公民，但在中世纪犹太人在阿拉伯的生活条件比在基督教欧洲要好很多。不幸的是本·马里蒙年轻时西班牙受狂热的伊斯兰教徒穆瓦希德哈里发管制，他不得不逃跑，曾试图在阿买拉，马拉喀什，凯撒里亚和开罗寻找安身之处，最后在开罗郊区塔城安居下来，一直生活到1204年去世。他既是犹太教祭司--在中世纪犹太人中间拥有巨大影响，也是一位颇受赞赏的医生—为阿拉伯人也为犹太人看病。他最著名的作品是《困惑者指南》，采用书信方式写给一位困惑的年轻人。在书中他表达了否定托勒密天文学的观点，因为其与亚里士多德观点不符： 你通过从我这里以及从《天文学大成》那里学到了天文学；我们没有时间涉猎更多。你已经知晓天体规则运行理论，以及恒星运行轨迹与观察相符取决于两个假设前提：我们必须假定均轮，或偏心，或两者组合。现在我会说明这两个假设是不规则的，完全不符合自然科学。 后面他又承认托勒密的模型与观测相符，而亚里士多德的模型并不相符，就像之前普罗克鲁斯做的一样，本·马里蒙认识到理解天体运行的难度，他倍感绝望 ： 除了一些数学计算，人类对天体一无所知，你知道这样会走多远。我可以用诗来描写：“天空属于上帝，他将地球授予其子人类”。也就是说，上帝对天空，对其特性，本质，构成及本原有完全和真实认识；但是他只给人类赋予认识天空之下事物的能力。 事实上正好相反，现代科学早期首先是认识了天体的运行。 阿拉伯科学对欧洲的影响可以从一系列源于阿拉伯语的单词中得以证实：不只是代数和算法，还有恒星名如毕宿五，大陵五，贯索四，牛郎星，参宿四，北斗六，参宿七，织女星等等（这里把英文名译为中文星名，译者注），以及化学术语如碱，蒸馏器，酒精，茜素，当然还有炼金术。 上面简短的概述让我们疑惑：为什么反而是医学家坚信亚里士多德教义，比如伊本·巴哲，伊本·图菲利，伊本·路西德，以及本·马里蒙。我认为有三种可能。其一，医学家们大多对亚里士多德生物学方面的作品甚感兴趣，正好亚里士多德这方面作品最为出色。另外，阿拉伯医学家受盖伦作品影响极深，盖伦本人非常推崇亚里士多德。最后，医学领域理论与实践间的冲突不易发生（现在仍然一样），亚里士多德的物理和天文理论与实际观察不完全相符对医学家来说并不重要。相反，天文学家的工作对结果精度要求极高，比如编制日历；测量大地距离；每天准确的祈祷时间；确定朝拜方向（祈祷者需要面向麦加方向）；即使天文学家将他们的科学应用到占星术，他们也需要精确确定任何一天太阳和行星在黄道的位置；他们不会容忍会导致错误结果的理论，比如亚里士多德理论。 阿巴斯王朝1258年灭亡，那年旭烈兀率领的蒙古大军摧毁了巴格达，杀死了哈里发。其实在这之前阿巴斯王朝管制已然解体。政治和军事大权从哈里发落到土耳其苏丹手上，甚至哈里发的宗教权威也由于独立伊斯兰政权的出现而衰落：包括在西班牙的后倭马亚王朝，在埃及的法蒂玛王朝，在摩洛哥与西班牙的阿尔摩拉维德王朝，以及后来在北非和西班牙的阿尔摩哈德王朝。部分叙利亚和巴勒斯坦地区被基督教徒临时占据，先是被拜占庭人，接着被法兰克十字军。 阿拉伯科学在阿巴斯王朝灭亡之前已经开始衰落，这种衰落可能始于公元1100年。其后再没有出现像阿尔·巴塔尼，阿尔·比鲁尼，伊本·西纳和阿尔·海什木这样出色的科学家。这是一个颇有争议的观点，其争议的尖锐程度可以从今天的政治中体现出来。但一些学者否认有任何衰落。 当然即使在阿巴斯时代结束后一些科学仍然在波斯和印度的蒙古人以及奥斯曼土耳其人中延续。比如1259年旭烈兀下令在波斯修建马拉盖天文台，他刚刚攻克巴格达才一年，这是为了向那些帮助过他的星相学家致谢。天文台创始主管，天文学家阿尔·图西在这里创作了球面几何著作（球面上大圆遵循的几何，比如恒星的概念球面），编制天文表，修正托勒密本轮。阿尔·图西创建了一个科学王国，他的学生阿尔·斯瑞兹是天文学家和数学家，阿尔·斯瑞兹的学生阿尔·法里斯在光学方面做出了开拓性工作，他对彩虹及其色彩做出了解释，这是由于阳光在雨滴中的折射造成的。 在我看来更为耀眼的是十四世纪大马士革天文学家伊本·阿尔·沙提尔。他在早期马拉盖天文学家的基础上发展出一种行星运行理论。他用一对本轮替代了托勒密的匀速点，这样他的模型满足了柏拉图的行星的运行由匀速圆周运动组成的要求。伊本·阿尔·沙提尔同样基于本轮概念提出了月球运行理论,该理论解决了托勒密理论中地月距离变化过大问题。哥白尼著作《小注解》中记载了他早期研究中一个与伊本·阿尔·沙提尔完全一样的月球理论，以及一个与伊本·阿尔·沙提尔视运行一致的行星运行理论。现在一般认为哥白尼年轻时在意大利求学时知晓这些结果（可能也知道这些结果的来源）。 一些学者认为哥白尼后来使用了阿尔·图西在研究行星运行时发明的几何结构—“图西双圆”（数学上将两个相接触的圆的转动转换为在直线上的振动的方法）。但人们不确认哥白尼究竟是自己发明了这个几何结构还是从阿拉伯那里学到的图西双圆。哥白尼不吝于将之归功于阿拉伯人，他引用了五个名字，包括阿尔·巴塔尼，阿耳·比特拉几，以及伊本·路西德，但他没有提及阿尔·图西。 发人深省的是无论阿尔·图西或伊本·阿尔·沙提尔对哥白尼有多少影响，他们的工作在伊斯兰天文学家中并没有被继承下去。图西双圆和伊本·阿·沙提尔行星本轮理论都是为了解决由于行星的椭圆运行轨迹以及太阳不在运转中心而带来的复杂性。（阿尔·图西，伊本·阿尔·沙提尔以及哥白尼那时都不了解这些）。这种复杂性对托勒密理论与对哥白尼理论有同样的影响，与地心说和日心说无关。阿拉伯天文学家在现代之前从来没有认真思考过日心说。 伊斯兰国家仍然在不断建立新的天文台。其中最伟大的天文台可能是十四世纪二十年代帖木儿帝国(由帖木儿（泰姆勃兰）所创建) 的统帅兀鲁伯在撒马尔罕城建立的天文台。该天文台精确计算了恒星年（365天，5小时，49分钟，15秒）以及二分点进动（70年每度，而不是75年每度。现代值是71.46年每度）。 医学方面在阿巴斯王朝灭亡之际有了一个重要发现。阿拉伯医学家伊本·阿尔·纳菲斯提出肺部血液循环理论，血液从右心室流过肺部，与空气混合，然后又流回左心室。伊本·阿尔·纳菲斯在大马士革和埃及行医，他还写过有关眼科方面的论文。 尽管有这些成就，但总体上伊斯兰世界科学在阿巴斯时代结束之际开始失去发展动力，从此一直衰落下去。后来的科学革命只是发生在欧洲，不在伊斯兰。伊斯兰科学家没有涉足科学革命。即使17世纪后已经有了天文望远镜，伊斯兰世界天文观测仍然限于肉眼天文观测（虽然借助一些仪器）。这些天文观测也只是用于日历和宗教目的，而不是为了科学。 人们不可避免地会产生与罗马帝国灭亡时科学的衰落同样的疑问：科学衰落是否与宗教扩张有关？科学与宗教的冲突在伊斯兰与在基督教世界一样复杂，我没有明确的答案。不过这里至少有两个问题，其一，伊斯兰世界科学家普遍对宗教持什么态度？也就是说是不是只有那些排除宗教影响的科学家才会成为有创造力的科学家？其二，穆斯林社会对科学持什么态度？ 阿巴斯时代科学家对宗教普遍存有怀疑态度。最明显的例子是天文学家欧玛尔·海亚姆，人们普遍认为他是无神论者。他在《鲁拜集》的几首四行诗中表达了对宗教的怀疑： 三生事业尽朦胧 一世浮华总落空 今日有钱须买醉 鼓声山外任隆隆

地狱天堂说未真 恒恒贤哲几多人 玲珑妙口今安在 三尺泥中不复开

少年执尘好谈玄 邹子雕龙衍子天 犹是野狐心未语 金函不学学逃禅

（译者注：爱德华·菲兹杰拉德将这些诗译文英文，上面中文译文为黄克孙英译版本） （英文翻译当然失去了部分诗意，但是原意还在）。海亚姆去世后被人称为“吞噬教义的毒蛇”，这其实不无道理。今天伊朗政府审查制度要求海亚姆诗集出版时必须进行编辑，删除或修改掉其中的无神论观点。 亚里士多德学派学者伊本·路西德1195年因异端倾向而遭放逐。另一位医学家阿尔·拉奇是位直言不讳的怀疑论者。在他的著作《先知的骗局》中他提出所谓奇迹只不过是些骗术。人们并不需要宗教领袖，欧几里德和希波克拉底比宗教领袖重要的多。他的同代人天文学家阿尔·比鲁尼对这些观点极为赞赏，他特意写了一本阿尔·拉奇传记。 相反，医学家伊本·西纳在与阿尔·比鲁尼的通信中恶毒攻击阿尔·拉奇，说他应该多关注他了解的东西，比如脓肿和粪便。天文学家阿尔·图西是虔诚的什叶派教徒，他创作过神学作品。从天文学家阿尔·苏菲的名字就可以看出来他是位苏菲派穆斯林。 我们很难去平衡这些个例。大多数阿拉伯科学家都没有留下他们的宗教观。我猜想沉默更可能是怀疑或害怕的体现，而不是虔诚。 接下来是穆斯林大众对待科学的态度。创建智慧宫的阿尔·马蒙哈里发肯定是位重要的科学支持者，也许是由于他属于穆尔台齐来派，他们寻求更加理性的解释古兰经，后来他们因此而受到攻击。但是不要以为穆尔台齐来派是宗教怀疑论者，他们对《古兰经》为上帝之言毫不怀疑，只不过他们认为《古兰经》为上帝所创造，而不是自古有之。也不要将他们与现代自由派混淆，他们迫害那些认为不需要上帝来创造永恒的《古兰经》的穆斯林。 到公元十一世纪，伊斯兰世界出现对科学的公然敌视态度。天文学家阿尔·比鲁尼这样控诉伊斯兰极端分子的反科学态度： 他们中的极端分子将科学盖上无神论的印章，称科学使人迷失方向。他们这样做的目的是为了使更多像他们这样无知的人憎恶科学，从而掩盖他们的无知，以便完全摧毁科学和科学家。 有一件趣闻广为人知。一位宗教法学家谴责阿尔·比鲁尼，因为天文学家使用的仪器上用的是基督教拜占庭人说的希腊语标示月份。阿尔·比鲁尼回答说：“拜占庭人也吃饭”。 人们普遍认为是阿尔·安萨里（阿尔加惹尔）加剧了科学与宗教间的紧张局面。阿尔·安萨里1058年出生于波斯，后来移居到叙利亚和巴格达。他的思想体系也不断发生变化，从正统伊斯兰到怀疑论者，然后又回到正统伊斯兰，但是结合了苏菲神秘主义。他吸收亚里士多德成就，在他的著作《哲学家的目标》中将之做了总结。后来在他最著名的著作《哲学家的矛盾》一书中他攻击理性主义。（亚里士多德学派学者伊本·路西德创作了《哲学家矛盾的矛盾》予以反击。）阿尔·安萨里这样阐述他的希腊哲学观： 我们时代的异端分子听说过苏格拉底，喜帕恰斯，柏拉图，亚历山大等等的大名。他们被这些哲学家的追随者所蒙蔽，这些追随者夸大了哲学家的贡献—这些古代大师被夸大到拥有无与伦比的智力，他们所发展出来的数学，逻辑，物理和形而上学最为深刻，他们杰出的智力使人们深信他们有能力通过推演方法揭示隐藏在事物背后的真相。依仗他们超群的智力以及杰出的成就，他们拒绝接受宗教的权威，否认宗教历史上的合理性成分，他们认为这些都只是假装圣洁，微不足道。 阿尔·安萨里用“机缘论”形式—一种认为事情的发生是单一事件，不受任何自然定律的制约，完全是上帝意志的体现的教条—来攻击科学。（这个教条在伊斯兰并不新鲜，一世纪之前阿尔·阿萨里就发展了该教条，他是穆尔台齐来派的反对者）。在他的问题十七—“对坚信不可能违背事件自然过程的反驳”，阿尔·安萨里这样写道： 在我们看来，人们所相信的原由与实际结果间的联系并不重要 ……(上帝)具有无穷能力，可以让人不需要进食即可免于饥饿，也可以让人不被砍头而死亡，甚至可以让那些被砍掉头颅的人存活，或者任何其他相关的事情（不管人们认为是什么原由），哲学家否认这种可能性，事实上他们坚信这完全不可能。对这些事（不可胜数）的探究可能需要无尽的篇幅，让我们之考虑其中一例—用火点燃一块棉布。我们认为火与棉布的接触可能不会导致棉布的点燃，我们也认为棉布不需要与火接触也可能变为灰烬。他们不相信这些……我们说是上帝--上帝自己或通过天使--让棉布变黑，破碎，化为灰烬。火无生命，不起作用。 基督教和犹太教也相信奇迹的存在，不遵循自然规则，但是这里我们看到阿尔·安萨里否定所有的自然法则。 这很难理解，因为我们在自然界确实观察到了一些规律。阿尔·安萨里不会没有意识到把手放到火里是件危险的事。他应该至少给科学在伊斯兰世界留下一个位置，就像十七世纪尼古拉·马勒伯朗士对上帝意志的认识一样。但是阿尔·安萨里没有这么做。阿尔·安萨里在他的另一部作品《科学的源头》中阐明了他的理由，他把科学与酒相提并论。酒助于健体，但伊斯兰世界禁酒。同样天文学和数学强化心灵，但是“我们然而担心有人会被之吸引，把这些当作信条，这很危险。” 不只是阿尔·安萨里的作品让我们看到中世纪伊斯兰世界对科学日益明显的敌对。在1194年穆瓦希德王朝的科尔多瓦—伊斯兰世界巴格达的另一端--乌里玛（当地宗教学者）焚烧了所有医学和科学方面书籍。1449年宗教狂热分子摧毁了位于撒马尔罕的兀鲁伯·别克的天文台。 在今天的伊斯兰世界我们可以看到当年困扰阿尔·安萨里的同样担忧。我已故的朋友阿卜杜斯·萨拉姆（巴基斯坦物理学家，由于他在英国和意大利的成就而成为第一位获得诺贝尔科学奖的穆斯林）曾经告诉我，他试图劝说富有的波斯湾产油国统治者在科学研究上进行投入。他发现他们热心于支持技术，但是他们害怕纯科学会腐蚀文化。（萨拉姆自己是为虔诚的穆斯林。他属于艾哈迈迪耶教派，在巴基斯坦该派被认为是异端邪说，他多年不能返回他的祖国。） 具有讽刺意味的是二十世纪的赛义德·库特布—一位现代极端伊斯兰分子的精神领袖—要求用普世纯粹的伊斯兰教来替代基督教，犹太教，以及当时的伊斯兰教，部分是基于他希望这样可以创建一种伊斯兰科学来弥合科学与宗教间的罅隙。但是阿拉伯科学家在他们的黄金时代并没有在从事阿拉伯科学。他们在从事科学。

After the collapse in the fifth century of the western Roman Empire, the Greek-speaking eastern half continued as the Byzantine Empire, and even increased in extent. The Byzantine Empire achieved a climactic military success during the reign of the emperor Heraclius, whose army in AD 627 in the battle of Nineveh destroyed the army of the Persian Empire, the ancient enemy of Rome. But within a decade the Byzantines had to confront a more formidable adversary. The Arabs were known in antiquity as a barbarian people, living in the borderland of the Roman and Persian empires, “that just divides the desert and the sown.” They were pagans, with a religion centered at the city of Mecca, in the settled portion of western Arabia known as the Hejaz. Starting at the end of the 500s, Muhammad, an inhabitant of Mecca, set out to convert his fellow citizens to monotheism. Meeting opposition, he and his acolytes fled in 622 to Medina, which they then used as a military base for the conquest of Mecca and of most of the Arabian Peninsula. After Muhammad’s death in 632, a majority of Muslims followed the authority of four successive leaders headquartered at first at Medina: his companions and relatives Abu Bakr, Omar, Othman, and Ali. They are recognized today by Sunni Muslims as the “four rightly guided caliphs.” The Muslims conquered the Byzantine province of Syria in 636, just nine years after the battle of Nineveh, and then went on to seize Persia, Mesopotamia, and Egypt. Their conquests introduced the Arabs to a more cosmopolitan world. For instance, the Arab general Amrou, who conquered Alexandria, reported to the caliph Omar, “I have taken a city, of which I can only say that it contains 6000 palaces, 4000 baths, 400 theatres, 12,000 greengrocers, and 40,000 Jews.”1 A minority, the forerunners of today’s Shiites, accepted only the authority of Ali, the fourth caliph and the husband of Muhammad’s daughter Fatima. The split in the world of Islam became permanent after a revolt against Ali, in which Ali as well as his son Hussein was killed. A new dynasty, the Sunni Ummayad caliphate, was established at Damascus in 661. Under the Ummayads Arab conquests expanded to include the territories of modern Afghanistan, Pakistan, Libya, Tunisia, Algeria, and Morocco, most of Spain, and much of central Asia beyond the Oxus River. From the formerly Byzantine lands that they now ruled they began to absorb Greek science. Some Greek learning also came from Persia, whose rulers had welcomed Greek scholars (including Simplicius) before the rise of Islam, when the Neoplatonic Academy was closed by the emperor Justinian. Christendom’s loss became Islam’s gain. It was in the time of the next Sunni dynasty, the caliphate of the Abbasids, that Arab science entered its golden age. Baghdad, the capital city of the Abbasids, was built on both sides of the Tigris River in Mesopotamia by al-Mansur, caliph from 754 to 775. It became the largest city in the world, or at least the largest outside China. Its best-known ruler was Harun al-Rashid, caliph from 786 to 809, famous from A Thousand and One Nights. It was under al-Rashid and his son al-Mamun, caliph from 813 to 833, that translation from Greece, Persia, and India reached its greatest scope. Al-Mamun sent a mission to Constantinople that brought back manuscripts in Greek. The delegation probably included the physician Hunayn ibn Ishaq, the greatest of the ninth-century translators, who founded a dynasty of translators, training his son and nephew to carry on the work. Hunayn translated works of Plato and Aristotle, as well as medical texts of Dioscorides, Galen, and Hippocrates. Mathematical works of Euclid, Ptolemy, and others were also translated into Arabic at Baghdad, some through Syriac intermediaries. The historian Philip Hitti has nicely contrasted the state of learning at this time at Baghdad with the illiteracy of Europe in the early Middle Ages: “For while in the East al-Rashid and al- Mamun were delving into Greek and Persian philosophy, their contemporaries in the West, Charlemagne and his lords, were dabbling in the art of writing their names.”2 It is sometimes said that the greatest contribution to science of the Abbasid caliphs was the foundation of an institute for translation and original research, the Bayt al-Hikmah, or House of Wisdom. This institute is supposed to have served for the Arabs somewhat the same function that the Museum and Library of Alexandria served for the Greeks. This view has been challenged by a scholar of Arabic language and literature, Dimitri Gutas.3 He points out that Bayt al-Hikmah is a translation of a Persian term that had long been used in pre-Islamic Persia for storehouses of books, mostly of Persian history and poetry rather than of Greek science. There are only a few known examples of works that were translated at the Bayt al-Hikmah in the time of al-Mamun, and those are from Persian rather than Greek. Some astronomical research, as we shall see, was going on at the Bayt al-Hikmah, but little is known of its scope. What is not in dispute is that, whether or not at the Bayt al-Hikmah, the city of Baghdad itself in the time of al-Mamun and al-Rashid was a great center of translation and research. Arab science was not limited to Baghdad, but spread west to Egypt, Spain, and Morocco, and east to Persia and central Asia. Participating in this work were not only Arabs but also Persians, Jews, and Turks. They were very much a part of Arab civilization and wrote in Arabic (or at least in Arabic script). Arabic then had something like the status in science that English has today. In some cases it is difficult to decide on the ethnic background of these figures. I will consider them all together, under the heading “Arabs.” As a rough approximation, we can identify two different scientific traditions that divided the Arab savants. On one hand, there were real mathematicians and astronomers who were not much concerned with what today we would call philosophy. Then there were philosophers and physicians, not very active in mathematics, and strongly influenced by Aristotle. Their interest in astronomy was chiefly astrological. Where they were concerned at all with the theory of the planets, the philosopher/physicians favored the Aristotelian theory of spheres centered on the Earth, while the astronomer/mathematicians generally followed the Ptolemaic theory of epicycles and deferents discussed in Chapter 8. This was an intellectual schism that, as we shall see, would persist in Europe until the time of Copernicus. The achievements of Arab science were the work of many individuals, none of them clearly standing out from the rest as, say, Galileo and Newton stand out in the scientific revolution. What follows is a brief gallery of medieval Arab scientists that I hope may give some idea of their accomplishments and variety. The first of the important astronomer/mathematicians at Baghdad was al-Khwarizmi,* a Persian born around 780 in what is now Uzbekistan. Al-Khwarizmi worked at the Bayt al-Hikmah and prepared widely used astronomical tables based in part on Hindu observations. His famous book on mathematics was Hisah-al-Jabr w-al-Muqabalah, dedicated to the caliph al-Mamun (who was half Persian himself). From its title we derive the word “algebra.” But this was not really a book on what is today called algebra. Formulas like the one for the solution of quadratic equations were given in words, not in the symbols that are an essential element of algebra. (In this respect, al-Khwarizmi’s mathematics was less advanced than that of Diophantus.) From al-Khwarizmi we also get our name for a rule for solving problems, “algorithm.” The text of Hisah al-Jabr w-al-Muqabalah contains a confusing mixture of Roman numerals; Babylonian numbers based on powers of 60; and a new system of numbers learned from India, based on powers of 10. Perhaps the most important mathematical contribution of al- Khwarizmi was his explanation to the Arabs of these Hindu numbers, which in turn became known in Europe as Arabic numbers. In addition to the senior figure of al-Khwarizmi, there were collected in Baghdad a productive group of other ninth-century astronomers, including al-Farghani (Alfraganus),* who wrote a popular summary of Ptolemy’s Almagest and developed his own version of the planetary scheme described in Ptolemy’s Planetary Hypotheses. It was a major occupation of this Baghdad group to improve on Eratosthenes’ measurement of the size of the Earth. Al-Farghani in particular reported a smaller circumference, which centuries later encouraged Columbus (as mentioned in an earlier footnote) to think that he could survive an ocean voyage westward from Spain to Japan, perhaps the luckiest miscalculation in history. The Arab who was most influential among European astronomers was al-Battani (Albatenius), born around 858 BC in northern Mesopotamia. He used and corrected Ptolemy’s Almagest, making more accurate measurements of the ~23½° angle between the Sun’s path through the zodiac and the celestial equator, of the lengths of the year and the seasons, of the precession of the equinoxes, and of the positions of stars. He introduced a trigonometric quantity, the sine, from India, in place of the closely related chord used and calculated by Hipparchus. (See Technical Note 15.) His work was frequently quoted by Copernicus and Tycho Brahe. The Persian astronomer al-Sufi (Azophi) made a discovery whose cosmological significance was not recognized until the twentieth century. In 964, in his Book of the Fixed Stars, he described a “little cloud” always present in the constellation Andromeda. This was the earliest known observation of what are now called galaxies, in this case the large spiral galaxy M31. Working at Isfahan, al-Sufi also participated in translating works of Greek astronomy into Arabic. Perhaps the most impressive astronomer of the Abbasid era was al-Biruni. His work was unknown in medieval Europe, so there is no latinized version of his name. Al-Biruni lived in central Asia, and in 1017 visited India, where he lectured on Greek philosophy. He considered the possibility that the Earth rotates, gave accurate values for the latitude and longitude of various cities, prepared a table of the trigonometric quantity known as the tangent, and measured specific gravities of various solids and liquids. He scoffed at the pretensions of astrology. In India, al-Biruni invented a new method for measuring the circumference of the Earth. As he described it:4

When I happened to be living in the fort of Nandana in the land of India, I observed from a high mountain standing to the west of the fort, a large plain lying south of the mountain. It occurred to me that I should examine this method [a method described previously] there. So, from the top of the mountain, I made an empirical measurement of the contact between the Earth and the blue sky. I found that the line of sight [to the horizon] had dipped below the reference line [that is, the horizontal direction] by the amount 34 minutes of arc. Then I measured the perpendicular of the mountain [that is, its height] and found it to be 652.055 cubits, where the cubit is a standard of length used in that region for measuring cloth.*

From these data, al-Biruni concluded that the radius of the Earth is 12,803,337.0358 cubits. Something went wrong with his calculation; from the data he quoted, he should have calculated the radius as about 13.3 million cubits. (See Technical Note 16.) Of course, he could not possibly have known the height of the mountain to the accuracy he stated, so there was no practical difference between 12.8 million cubits and 13.3 million cubits. In giving the radius of the Earth to 12 significant figures, al-Biruni was guilty of misplaced precision, the same error that we saw in Aristarchus: carrying out calculations and quoting results to a much greater degree of precision than is warranted by the accuracy of the measurements on which the calculation is based. I once got into trouble in this way. I had a summer job long ago, calculating the path of atoms through a series of magnets in an atomic beam apparatus. This was before desktop computers or pocket electronic calculators, but I had an electromechanical calculating machine that could add, subtract, multiply, and divide to eight significant figures. Out of laziness, in my report I gave the results of the calculations to eight significant figures just as they came from the calculating machine, without bothering to round them off to a realistic precision. My boss complained to me that the magnetic field measurements on which my calculation was based were accurate to only a few percent, and that any precision beyond this was meaningless. In any case, we can’t now judge the accuracy of al-Biruni’s result that the Earth’s radius is about 13 million cubits, because no one now knows the length of his cubit. Al-Biruni said there are 4,000 cubits in a mile, but what did he mean by a mile? Omar Khayyam, the poet and astronomer, was born in 1048 in Nishapur, in Persia, and died there around 1131. He headed the observatory at Isfahan, where he compiled astronomical tables and planned calendar reform. In Samarkand in central Asia he wrote about topics in algebra, such as the solution of cubic equations. He is best known to English-speaking readers as a poet, through the magnificent nineteenth-century translation by Edward Fitzgerald of 75 out of a larger number of quatrains written by Omar Khayyam in Persian, and known as The Rubaiyat. Unsurprisingly for the hardheaded realist who wrote these verses, he strongly opposed astrology. The greatest Arab contributions to physics were made in optics, first at the end of the tenth century by Ibn Sahl, who may have worked out the rule giving the direction of refracted rays of light (about which more in Chapter 13), and then by the great al-Haitam (Alhazen). Al-Haitam was born in Basra, in southern Mesopotamia, around 965, but worked in Cairo. His extant books include Optics, The Light of the Moon, The Halo and the Rainbow, On Paraboloidal Burning Mirrors, The Formation of Shadows, The Light of the Stars, Discourse on Light, The Burning Sphere, and The Shape of the Eclipse. He correctly attributed the bending of light in refraction to the change in the speed of light when it passes from one medium to another, and found experimentally that the angle of refraction is proportional to the angle of incidence only for small angles. But he did not give the correct general formula. In astronomy, he followed Adrastus and Theon in attempting to give a physical explanation to the epicycles and deferents of Ptolemy. An early chemist, Jabir ibn Hayyan, is now believed to have flourished in the late eighth or early ninth century. His life is obscure, and it is not clear whether the many Arabic works attributed to him are really the work of a single person. There is also a large body of Latin works that appeared in Europe in the thirteenth and fourteenth centuries attributed to a “Geber,” but it is now thought that the author of these works is not the same as the author of the Arabic works attributed to Jabir ibn Hayyan. Jabir developed techniques of evaporation, sublimation, melting, and crystallization. He was concerned with transmuting base metals into gold, and hence is often called an alchemist, but the distinction between chemistry and alchemy as practiced in his time is artificial, for there was then no fundamental scientific theory to tell anyone that such transmutations are impossible. To my mind, a distinction more important for the future of science is between those chemists or alchemists who followed Democritus in viewing the workings of matter in a purely naturalistic way, whether their theories were right or wrong, and those like Plato (and, unless they were speaking metaphorically, Anaximander and Empedocles), who brought human or religious values into the study of matter. Jabir probably belongs to the latter class. For instance, he made much of the chemical significance of 28, the number of letters in the alphabet of Arabic, the language of the Koran. Somehow it was important that 28 is the product of 7, supposed to be the number of metals, and 4, the number of qualities: cold, warm, wet, and dry. The earliest major figure in the Arab medical/philosophical tradition was al-Kindi (Alkindus), who was born in Basra of a noble family but worked in Baghdad in the ninth century. He was a follower of Aristotle, and tried to reconcile Aristotle’s doctrines with those of Plato and of Islam. Al-Kindi was a polymath, very interested in mathematics, but like Jabir he followed the Pythagoreans in using it as a sort of number magic. He wrote about optics and medicine, and attacked alchemy, though he defended astrology. Al-Kindi also supervised some of the work of translation from Greek to Arabic. More impressive was al-Razi (Rhazes), an Arabic-speaking Persian of the generation following al- Kindi. His works include A Treatise on the Small Pox and Measles. In Doubts Concerning Galen, he challenged the authority of the influential Roman physician and disputed the theory, going back to Hippocrates, that health is a matter of balance of the four humors (described in Chapter 4). He explained, “Medicine is a philosophy, and this is not compatible with renouncement of criticism with regard to the leading authors.” In an exception to the typical views of Arab physicians, al-Razi also challenged Aristotle’s teaching, such as the doctrine that space must be finite. The most famous of the Islamic physicians was Ibn Sina (Avicenna), another Arabic-speaking Persian. He was born in 980 near Bokhara in central Asia, became court physician to the sultan of Bokhara, and was appointed governor of a province. Ibn Sina was an Aristotelian, who like al-Kindi tried to reconcile with Islam. His Al Qanum was the most influential medical text of the Middle Ages. At the same time, medicine began to flourish in Islamic Spain. Al-Zahrawi (Abulcasis) was born in 936 near Córdoba, the metropolis of Andalusia, and worked there until his death in 1013. He was the greatest surgeon of the Middle Ages, and highly influential in Christian Europe. Perhaps because surgery was less burdened than other branches of medicine by ill-founded theory, al-Zahrawi sought to keep medicine separate from philosophy and theology. The divorce of medicine from philosophy did not last. In the following century the physician Ibn Bajjah (Avempace) was born in Saragossa, and worked there and in Fez, Seville, and Granada. He was an Aristotelian who criticized Ptolemy and rejected Ptolemaic astronomy, but he took exception to Aristotle’s theory of motion. Ibn Bajjah was succeeded by his student Ibn Tufayl (Abubacer), also born in Muslim Spain. He practiced medicine in Granada, Ceuta, and Tangier, and he became vizier and physician to the sultan of the Almohad dynasty. He argued that there is no contradiction between Aristotle and Islam, and like his teacher rejected the epicycles and eccentrics of Ptolemaic astronomy. In turn, Ibn Tufayl had a distinguished student, al-Bitruji. He was an astronomer but inherited his teacher’s commitment to Aristotle and rejection of Ptolemy. Al-Bitruji unsuccessfully attempted to reinterpret the motion of planets on epicycles in terms of homocentric spheres. One physician of Muslim Spain became more famous as a philosopher. Ibn Rushd (Averroes) was born in 1126 at Córdoba, the grandson of the city’s imam. He became cadi (judge) of Seville in 1169 and of Córdoba in 1171, and then on the recommendation of Ibn Tufayl became court physician in 1182. As a medical scientist, Ibn Rushd is best known for recognizing the function of the retina of the eye, but his fame rests chiefly on his work as a commentator on Aristotle. His praise of Aristotle is almost embarrassing to read:

[Aristotle] founded and completed logic, physics, and metaphysics. I say that he founded them because the works written before him on these sciences are not worth talking about and are quite eclipsed by his own writings. And I say that he completed them because no one who has come after him up to our own time, that is, for nearly fifteen hundred years, has been able to add anything to his writings or to find any error of any importance in them.5

The father of the modern author Salman Rushdie chose the surname Rushdie to honor the secular rationalism of Ibn Rushd. Naturally Ibn Rushd rejected Ptolemaic astronomy, as contrary to physics, meaning Aristotle’s physics. He was aware that Aristotle’s homocentric spheres did not “save the appearances,” and he tried to reconcile Aristotle with observation but concluded that this was a task for the future: In my youth I hoped it would be possible for me to bring this research [in astronomy] to a successful conclusion. Now, in my old age, I have lost hope, for several obstacles have stood in my way. But what I say about it will perhaps attract the attention of future researchers. The astronomical science of our days surely offers nothing from which one can derive an existing reality. The model that has been developed in the times in which we live accords with the computations, not with existence.6

Of course, Ibn Rushd’s hopes for future researchers were unfulfilled; no one ever was able to make the Aristotelian theory of the planets work. There was also serious astronomy done in Muslim Spain. In Toledo al-Zarqali (Arzachel) in the eleventh century was the first to measure the precession of the apparent orbit of the Sun around the Earth (actually of course the precession of the orbit of the Earth around the Sun), which is now known to be mostly due to the gravitational attraction between the Earth and other planets. He gave a value for this precession of 12.9" (seconds of arc) per year, in fair agreement with the modern value, 11.6" per year.7 A group of astronomers including al-Zarqali used the earlier work of al-Khwarizmi and al-Battani to construct the Tables of Toledo, a successor to the Handy Tables of Ptolemy. These astronomical tables and their successors described in detail the apparent motions of the Sun, Moon, and planets through the zodiac and were landmarks in the history of astronomy. Under the Ummayad caliphate and its successor, the Berber Almoravid dynasty, Spain was a cosmopolitan center of learning, hospitable to Jews as well as Muslims. Moses ben Maimon (Maimonides), a Jew, was born in 1135 at Córdoba during this happy time. Jews and Christians were never more than second-class citizens under Islam, but during the Middle Ages the condition of Jews was generally far better under the Arabs than in Christian Europe. Unfortunately for ben Maimon, during his youth Spain came under the rule of the fanatical Islamist Almohad caliphate, and he had to flee, trying to find refuge in Almeira, Marrakesh, Caesarea, and Cairo, finally coming to rest in Fustat, a suburb of Cairo. There until his death in 1204 he worked both as a rabbi, with influence throughout the world of medieval Jewry, and as a highly prized physician to both Arabs and Jews. His best-known work is the Guide to the Perplexed, which takes the form of letters to a perplexed young man. In it he expressed his rejection of Ptolemaic astronomy as contrary to Aristotle:8

You know of Astronomy as much as you have studied with me, and learned from the book Almagest; we had not sufficient time to go beyond this. The theory that the spheres move regularly, and that the assumed courses of the stars are in harmony with observation, depends, as you are aware, on two hypotheses: we must assume either epicycles, or eccentric spheres, or a combination of both. Now I will show that each of these two hypotheses is irregular, and totally contrary to the results of Natural Science.

He then went on to acknowledge that Ptolemy’s scheme agrees with observation, while Aristotle’s does not, and as Proclus did before him, ben Maimon despaired at the difficulty of understanding the heavens:

But of the things in the heavens man knows nothing except a few mathematical calculations, and you see how far these go. I say in the words of the poet9 “The heavens are the Lord’s, but the Earth he has given to the sons of man”; that is to say, God alone has a perfect and true knowledge of the heavens, their nature, their essence, their form, their motion, and their causes; but He gave man power to know the things which are under the heavens. Just the opposite turned out to be true; it was the motion of heavenly bodies that was first understood in the early days of modern science. There is testimony to the influence of Arab science on Europe in a long list of words derived from Arabic originals: not only algebra and algorithm, but also names of stars like Aldebaran, Algol, Alphecca, Altair, Betelgeuse, Mizar, Rigel, Vega, and so on, and chemical terms like alkali, alembic, alcohol, alizarin, and of course alchemy. This brief survey leaves us with a question: why was it specifically those who practiced medicine, such as Ibn Bajjah, Ibn Tufayl, Ibn Rushd, and ben Maimon, who held on so firmly to the teachings of Aristotle? I can think of three possible reasons. First, physicians would naturally be most interested in Aristotle’s writings on biology, and in these Aristotle was at his best. Also, Arab physicians were powerfully influenced by the writings of Galen, who greatly admired Aristotle. Finally, medicine is a field in which the precise confrontation of theory and observation was very difficult (and still is), so that the failings of Aristotelian physics and astronomy to agree in detail with observation may not have seemed so important to physicians. In contrast, the work of astronomers was used for purposes where correct precise results are essential, such as constructing calendars; measuring distances on Earth; telling the correct times for daily prayers; and determining the qibla, the direction to Mecca, which should be faced during prayer. Even astronomers who applied their science to astrology had to be able to tell precisely in what sign of the zodiac the Sun and planets were on any given date; and they were not likely to tolerate a theory like Aristotle’s that gave the wrong answers. The Abbasid caliphate came to an end in 1258, when the Mongols under Hulegu Khan sacked Baghdad and killed the caliph. Abbasid rule had disintegrated well before that. Political and military power had passed from the caliphs to Turkish sultans, and even the caliph’s religious authority was weakened by the founding of independent Islamic governments: a translated Ummayad caliphate in Spain, the Fatimid caliphate in Egypt, the Almoravid dynasty in Morocco and Spain, succeeded by the Almohad caliphate in North Africa and Spain. Parts of Syria and Palestine were temporarily reconquered by Christians, first by Byzantines and then by Frankish crusaders. Arab science had already begun to decline before the end of the Abbasid caliphate, perhaps beginning about AD 1100. After that, there were no more scientists with the stature of al-Battani, al-Biruni, Ibn Sina, and al-Haitam. This is a controversial point, and the bitterness of the controversy is heightened by today’s politics. Some scholars deny that there was any decline.10 It is certainly true that some science continued even after the end of the Abbasid era, under the Mongols in Persia and then in India, and later under the Ottoman Turks. For instance, the building of the Maragha observatory in Persia was ordered by Hulegu in 1259, just a year after his sacking of Baghdad, in gratitude for the help that he thought that astrologers had given him in his conquests. Its founding director, the astronomer al-Tusi, wrote about spherical geometry (the geometry obeyed by great circles on a spherical surface, like the notional sphere of the fixed stars), compiled astronomical tables, and suggested modifications to Ptolemy’s epicycles. Al-Tusi founded a scientific dynasty: his student al-Shirazi was an astronomer and mathematician, and al-Shirazi’s student al-Farisi did groundbreaking work on optics, explaining the rainbow and its colors as the result of the refraction of sunlight in raindrops. More impressive, it seems to me, is Ibn al-Shatir, a fourteenth-century astronomer of Damascus. Following earlier work of the Maragha astronomers, he developed a theory of planetary motions in which Ptolemy’s equant was replaced with a pair of epicycles, thus satisfying Plato’s demand that the motion of planets must be compounded of motions at constant speed around circles. Ibn al-Shatir also gave a theory of the Moon’s motion based on epicycles: it avoided the excessive variation in the distance of the Moon from the Earth that had afflicted Ptolemy’s lunar theory. The early work of Copernicus reported in his Commentariolus presents a lunar theory that is identical to Ibn al-Shatir’s, and a planetary theory that gives the same apparent motions as the theory of al-Shatir.11 It is now thought that Copernicus learned of these results (if not of their source) as a young student in Italy. Some authors have made much of the fact that a geometric construction, the “Tusi couple,” which had been invented by al-Tusi in his work on planetary motion, was later used by Copernicus. (This was a way of mathematically converting rotary motion of two touching spheres into oscillation in a straight line.) It is a matter of some controversy whether Copernicus learned of the Tusi couple from Arab sources, or invented it himself.12 He was not unwilling to give credit to Arabs, and quoted five of them, including al-Battani, al-Bitruji, and Ibn Rushd, but made no mention of al-Tusi. It is revealing that, whatever the influence of al-Tusi and Ibn al-Shatir on Copernicus, their work was not followed up among Islamic astronomers. In any case, the Tusi couple and the planetary epicycles of Ibn al-Shatir were means of dealing with the complications that (though neither al-Tusi nor al-Shatir nor Copernicus knew it) are actually due to the elliptical orbits of planets and the off-center location of the Sun. These are complications that (as discussed in Chapters 8 and 11) equally affected Ptolemaic and Copernican theories, and had nothing to do with whether the Sun goes around the Earth or the Earth around the Sun. No Arab astronomer before modern times seriously proposed a heliocentric theory. Observatories continued to be built in Islamic countries. The greatest may have been an observatory in Samarkand, built in the 1420s by the ruler Ulugh Beg of the Timurid dynasty founded by Timur Lenk (Tamburlaine). There more accurate values were calculated for the sidereal year (365 days, 5 hours, 49 minutes, and 15 seconds) and the precession of the equinoxes (70 rather than 75 years per degree of precession, as compared with the modern value of 71.46 years per degree). An important advance in medicine was made just after the end of the Abbasid period. This was the discovery by the Arab physician Ibn al-Nafis of the pulmonary circulation, the circulation of blood from the right side of the heart through the lungs, where it mixes with air, and then flows back to the heart’s left side. Ibn al-Nafis worked at hospitals in Damascus and Cairo, and also wrote on ophthalmology. These examples notwithstanding, it is hard to avoid the impression that science in the Islamic world began to lose momentum toward the end of the Abbasid era, and then continued to decline. When the scientific revolution came, it took place only in Europe, not in the lands of Islam, and it was not joined by Islamic scientists. Even after telescopes became available in the seventeenth century, astronomical observatories in Islamic countries continued to be limited to naked-eye astronomy13 (though aided by elaborate instruments), undertaken largely for calendrical and religious rather than scientific purposes. This picture of decline inevitably raises the same question that was raised by the decline of science toward the end of the Roman Empire—do these declines have anything to do with the advance of religion? For Islam, as for Christianity, the case for a conflict between science and religion is complicated, and I won’t attempt a definite answer. There are at least two questions here. First, what was the general attitude of Islamic scientists toward religion? That is, was it only those who set aside the influence of their religion who were creative scientists? And second, what was the attitude toward science of Muslim society? Religious skepticism was widespread among scientists of the Abbasid era. The clearest example is provided by the astronomer Omar Khayyam, generally regarded as an atheist. He reveals his skepticism in several verses of the Rubaiyat:14

Some for the Glories of the World, and some Sigh for the Prophet’s Paradise to come; Ah, take the Cash, and let the Credit go, Nor heed the rumble of a distant Drum!

Why all the Saints and Sages who discuss’d Of the two Worlds so learnedly, are thrust Like foolish Prophets forth; their Words to Scorn Are scatter’d, and their mouths are stopt with Dust.

Myself when young did eagerly frequent Doctor and Saint, and heard great argument About it, and about: but evermore Came out by the same door as in I went.

(The literal translation into English is of course less poetic, but expresses essentially the same attitude.) Not for nothing was Khayyam after his death called “a stinging serpent to the Shari’ah.” Today in Iran, government censorship requires that published versions of the poetry of Khayyam must be edited to remove or revise his atheistic sentiments. The Aristotelian Ibn Rushd was banished around 1195 on suspicion of heresy. Another physician, al- Razi, was an outspoken skeptic. In his Tricks of the Prophets he argued that miracles are mere tricks, that people do not need religious leaders, and that Euclid and Hippocrates are more useful to humanity than religious teachers. His contemporary, the astronomer al-Biruni, was sufficiently sympathetic to these views to write an admiring biography of al-Razi. On the other hand, the physician Ibn Sina had a nasty correspondence with al-Biruni, and said that al- Razi should have stuck to things he understood, like boils and excrement. The astronomer al-Tusi was a devout Shiite, and wrote about theology. The name of the astronomer al-Sufi suggests that he was a Sufi mystic. It is hard to balance these individual examples. Most Arab scientists have left no record of their religious leanings. My own guess is that silence is more likely an indication of skepticism and perhaps fear than of devotion. Then there is the question of the attitude of Muslims in general toward science. The caliph al-Mamun who founded the House of Wisdom was certainly an important supporter of science, and it may be significant that he belonged to a Muslim sect, the Mutazalites, which sought a more rational interpretation of the Koran, and later came under attack for this. But the Mutazalites should not be regarded as religious skeptics. They had no doubt that the Koran is the word of God; they argued only that it was created by God, and had not always existed. Nor should they be confused with modern civil libertarians; they persecuted Muslims who thought that there was no need for God to have created the eternal Koran. By the eleventh century, there were signs in Islam of outright hostility to science. The astronomer al- Biruni complained about antiscientific attitudes among Islamic extremists:15

The extremist among them would stamp the sciences as atheistic, and would proclaim that they lead people astray in order to make ignoramuses, like him, hate the sciences. For this will help him to conceal his ignorance, and to open the door to the complete destruction of science and scientists.

There is a well-known anecdote, according to which al-Biruni was criticized by a religious legalist, because the astronomer was using an instrument that listed the months according to their names in Greek, the language of the Christian Byzantines. Al-Biruni replied, “The Byzantines also eat food.” The key figure in the growth of tension between science and Islam is often said to be al-Ghazali (Algazel). Born in 1058 in Persia, he moved to Syria and then to Baghdad. He also moved about a good deal intellectually, from orthodox Islam to skepticism and then back to orthodoxy, but combined with Sufi mysticism. After absorbing the works of Aristotle, and summarizing them in Inventions of the Philosophers, he later attacked rationalism in his best-known work, The Incoherence of the Philosophers.16 (Ibn Rushd, the partisan of Aristotle, wrote a riposte, The Incoherence of the Incoherence.) Here is how al-Ghazali expressed his view of Greek philosophy:

The heretics in our times have heard the awe-inspiring names of people like Socrates, Hippocrates, Plato, Aristotle, etc. They have been deceived by the exaggerations made by the followers of these philosophers—exaggerations to the effect that the ancient masters possessed extraordinary intellectual powers; that the mathematical, logical, physical and metaphysical sciences developed by them are the most profound; that their excellent intelligence justifies their bold attempts to discover the Hidden Things by deductive methods; and that with all the subtlety of their intelligence and the originality of their accomplishments they repudiated the authority of religious laws: denied the validity of the positive contents of historical religions, and believe that all such things are only sanctimonious lies and trivialities.

Al-Ghazali’s attack on science took the form of “occasionalism”—the doctrine that whatever happens is a singular occasion, governed not by any laws of nature but directly by the will of God. (This doctrine was not new in Islam—it had been advanced a century earlier by al-Ashari, an opponent of the Mutazalites.) In al-Ghazali’s Problem XVII, “Refutation of Their Belief in the Impossibility of a Departure from the Natural Course of Events,” one reads:

In our view, the connection between what are believed to be the cause and the effect [is] not necessary. . . . [God] has the power to create the satisfaction of hunger without eating, or death without the severance of the head, or even the survival of life when the head has been cut off, or any other thing from among the connected things (independently of what is supposed to be its cause). The philosophers deny this possibility; indeed, they assert its impossibility. Since the inquiry concerning these things (which are innumerable) may go to an indefinite length, let us consider only one example—viz., the burning of a piece of cotton at the time of its contact with fire. We admit the possibility of a contact between the two which will not result in burning, as also we admit the possibility of a transformation of cotton into ashes without coming into contact with fire. And they reject this possibility. . . . We say that it is God who—through the intermediacy of angels, or directly—is the agent of the creation of blackness in cotton; or of the disintegration of its parts, and their transformation into a smouldering heap or ashes. Fire, which is an inanimate thing, has no action.

Other religions, such as Christianity and Judaism, also admit the possibility of miracles, departures from the natural order, but here we see that al-Ghazali denied the significance of any natural order whatsoever. This is hard to understand, because we certainly observe some regularities in nature. I doubt that al- Ghazali was unaware that it was not safe to put one’s hand into fire. He could have saved a place for science in the world of Islam, as a study of what God usually wills to happen, a position taken in the seventeenth century by Nicolas Malebranche. But al-Ghazali did not take this path. His reason is spelled out in another work, The Beginning of Sciences,17 in which he compared science to wine. Wine strengthens the body, but is nevertheless forbidden to Muslims. In the same way, astronomy and mathematics strengthen the mind, but “we nevertheless fear that one might be attracted through them to doctrines that are dangerous.” It is not only the writings of al-Ghazali that bear witness to a growing Islamic hostility to science in the Middle Ages. In 1194 in Almohad Córdoba, at the other end of the Islamic world from Baghdad, the Ulama (the local religious scholars) burned all medical and scientific books. And in 1449 religious fanatics destroyed Ulugh Beg’s observatory in Samarkand. We see in Islam today signs of the same concerns that troubled al-Ghazali. My friend the late Abdus Salam, a Pakistani physicist who won the first Nobel Prize in science awarded to a Muslim (for work done in England and Italy), once told me that he had tried to persuade the rulers of the oil-rich Persian Gulf states to invest in scientific research. He found that they were enthusiastic about supporting technology, but they feared that pure science would be culturally corrosive. (Salam was himself a devout Muslim. He was loyal to a Muslim sect, the Ahmadiyya, which has been regarded as heretical in Pakistan, and for years he could not return to his home country.) It is ironic that in the twentieth century Sayyid Qutb, a guiding spirit of modern radical Islamism, called for the replacement of Christianity, Judaism, and the Islam of his own day with a universal purified Islam, in part because he hoped in this way to create an Islamic science that would close the gap between science and religion. But Arab scientists in their golden age were not doing Islamic science. They were doing science.