数学家传记
罗伯特·波义耳是一位出生于爱尔兰的科学家,他是皇家学会的创始会员。他在化学方面的工作旨在将其建立为一门基于物质机械论的数学科学。
罗伯特·波义耳 出生于一个新教家庭。他的父亲是 Richard Boyle,科克伯爵,他于 1588 年 22 岁时离开英格兰前往爱尔兰。1600 年被伊丽莎白一世任命为芒斯特议会的书记员,两年后他买下了沃尔特·雷利爵士在科克郡、沃特福德郡和蒂珀雷里郡的庄园。波义耳 的母亲凯瑟琳·芬顿是 Richard Boyle 的第二任妻子,他的第一任妻子在他们的第一个孩子出生后一年内去世。波义耳 是他父母十五个孩子(十五个中有十二个活过童年)中的第七个儿子(第十四个孩子)。波义耳 出生时,Richard Boyle 已 60 多岁,Catherine Boyle 40 多岁。关于他的父亲,波义耳 后来写道 [12]:-
他,凭借上帝对他兴旺勤奋的祝福,从极其微小的起点,建立了如此丰厚而显赫的财富,以至于他的兴旺招来了许多仰慕者,却鲜有匹敌者。
的确,波义耳 很幸运,有大不列颠最富有的人做父亲,尽管不得不说,科克伯爵是以某种可疑的手段获得他的财富的。他曾一度因贪污指控在英格兰被监禁,后来因拥有某些庄园的有缺陷的所有权而被重罚。
科克伯爵和他的妻子认为,年幼的孩子在开始接受教育之前,最好的养育方式可以远离父母提供。波义耳被送到乡下抚养,而他的父亲继续追求越来越高的政治成功。科克伯爵在都柏林的联排别墅里住了四年。他于1629年被任命为高等法院法官,1631年被任命为财政大臣。然而,在都柏林的这段时间里,波义耳的母亲去世了,此后一段时间,波义耳从与他的乡下奶妈的寄养处回来,重新加入他的家庭。
波义耳 于1635年与他的一个兄弟一起被送到英国伊顿公学学习。此时,这所学校正变得时髦,成为重要人物送儿子去的地方。校长是 弗瑞兹·约翰 哈里森,两个年轻的 波义耳 兄弟住在校长家里 [10]:-
除了当时流行的严格古典课程外,男孩们还有法语、舞蹈和音乐的私人教师,为此他们支付额外费用。
波义耳在[12]中向Harrison致敬,他写道Harrison给了他:-
……强烈的求知欲……
在伊顿公学的这个阶段,波义耳的教育显然进展顺利。他受到校长和同学的欢迎。然而,也许Harrison给了他太多特别关注,因为当Harrison退休后,波义耳似乎无法适应新校长给学校带来的教育纪律。意识到他的两个儿子在新校长下学业进展不佳,科克伯爵于1638年11月将儿子们从伊顿公学带走。此后,波义耳由他父亲的一位牧师私下辅导。
12岁时,波义耳被父亲和其中一个兄弟送到欧洲旅行。他们从迪耶普前往巴黎,然后到里昂,最后到达日内瓦。在日内瓦,波义耳与一位私人教师学习法语、拉丁语、修辞学和宗教。他还在下午花时间打网球和击剑。也许最重要的是,他开始学习数学,并很快[12]:-
……他对算术、几何中最有用的部分,以及其从属内容——球体学说、地球学说和筑城术——变得非常熟悉。
1641年,波义耳学习意大利语,为前往那里做准备。那年9月,波义耳和他的导师在威尼斯,然后到1642年初,他们到了佛罗伦萨。伽利略在佛罗伦萨附近的阿尔切特里别墅去世,当时波义耳正住在这座城市。他深受此事影响,仔细研读了伽利略的著作。如果有哪一件事塑造了波义耳的人生并引导他走向科学,那就是这件事。当然,他的新教背景,以及对耶稣会士根深蒂固的恐惧,促成了他对伽利略及其受罗马天主教会对待的同情。波义耳成为伽利略哲学的坚定支持者,并从此时起坚信通过数学和力学研究世界的新方法。
到1642年5月,波义耳和他的导师在马赛等待波义耳的父亲寄钱来,以便他能完成回家的旅程。钱没有到,只收到他父亲的一封信,解释说芒斯特的叛乱完全占据了他的时间和金钱。他确实寄了250英镑支付波义耳的返程费用,但这笔钱从未到达他手中。波义耳回到日内瓦,他似乎主要靠导师的收入生活,而他的父亲继续在利斯莫尔城堡与爱尔兰人作战。国王查理一世与与科克伯爵作战的天主教叛军谈判达成停火,以便他能将部队带回英格兰,帮助他进行已经爆发的内战。科克伯爵始终无法释怀查理将爱尔兰人视为平等,不久后于1643年9月去世。波义耳在父亲去世时仍住在日内瓦。1644年夏天,他卖掉一些珠宝,并用所得的钱资助他返回英格兰的旅费。
回到英格兰后,波义耳有一段时间与他的姐姐凯瑟琳住在一起。她比他大十三岁,是一位有一定地位的女士,嫁给了拉内拉子爵。英格兰处于混乱状态,1642年开始的内战正在国王查理和议会之间进行。查理已迁往牛津,而议会则与苏格兰人订立了条约。作为苏格兰军事支持的回报,他们被许诺建立长老会教会。1644年的几场战役使国王和议会都多少有些混乱。波义耳在英格兰有财产,即斯特尔布里奇庄园,是他父亲留给他的,但国内的局势使事情变得困难。他在一封信中写道(例如见[3]):-
[我]在1644年中期安全进入英格兰,在那里我们发现事情如此混乱,尽管斯特尔布里奇庄园因我父亲去世而传给了我,但我花了将近四个月才到达那里。
事实上,尽管波义耳在四个月后查看了他的新家,但过了更久他才能够搬进去。这发生在1646年3月,此前他与姐姐度过了更多时间,并再次前往法国偿还他欠仍住在那里的导师的债务。尽管波义耳不打算在斯特尔布里奇久留,但他在那里待了大约六年。他可能比他在1646年10月写给法国旧导师的一封信中所承认的更加用功(例如见[3]):-
至于我的学习,我有机会进行,但只是断断续续,视我的闲暇和事务允许而定。我费力涂写了几篇关于各种主题的小文章,有韵文也有散文。……我致力于的其他人文研究,是按照我们新哲学院的原则进行的自然哲学、力学和农学……
这个“新的哲学学院”在信的后文中也被波义耳称为“无形学院”。它正是不久后将成为“Royal Society of London”的那个学会,并且在波义耳于Stalbridge过着多少有些孤独的生活时,为他提供了与科学世界的唯一联系。他盼望着去伦敦,在那里学院的成员们[3]:-
……不时地赏光与我为伴。
正是在无形学院中的讨论,促使波义耳阅读了威廉·欧垂的Clavis Mathematica以及马兰·梅森和皮埃尔·伽桑狄的著作。波义耳自访问意大利时起就赞同尼古拉·哥白尼的观念,如今他更坚定地持有这些观点,并深信物质的原子论。在无形学院中,这些观点被认为是新自然哲学的观点。
这一时期对波义耳 来说是困难的,因为他努力避免在内战中被强迫选边站。他的忠诚有些分裂,他的父亲是坚定的保皇党人,他的姐姐凯瑟琳是坚定的议会派。基本上他对双方都缺乏同情,但内战的最终结果对他有利。查理一世被击败并处决,但在1650年,查理二世在苏格兰登陆并试图重新掌权。克伦威尔领导议会军队,在1650年击败了苏格兰人,1651年再次击败他们,1652年爱尔兰人也被克伦威尔击败。波义耳 在1652年前往爱尔兰照看那里的地产。当克伦威尔将爱尔兰土地分配给英国殖民者时,他最终成了一个非常富有的人。从那时起,他能够完全致力于科学,而无需赚钱。然而,应该指出的是,波义耳 在花钱方面非常慷慨,他周围的许多人都从这种慷慨中受益。
波义耳 在1653年访问伦敦时会见了约翰 约翰·维尔金斯,即无形学会的领导人。此时约翰·维尔金斯 刚被任命为牛津瓦德汉学院的院长,他计划从那里管理无形学会。他强烈鼓励波义耳 加入他们在牛津,并邀请他住在学院里。波义耳 决定去牛津,但不愿接受约翰·维尔金斯 提供的住宿,而是选择安排自己的房间,以便进行科学实验。在牛津,他加入了一群有远见的科学家,包括约翰 约翰·维尔金斯、约翰 约翰·沃利斯(他是萨维尔几何学教授)、Seth Ward(他是萨维尔天文学教授),以及克里斯托弗·克里斯托弗·雷恩,后者将在1661年接替沃德成为萨维尔天文学教授。从1654年起,波义耳 住在牛津,尽管他从未担任任何大学职位。
他在物理学和化学方面做出了重要贡献,最为人所知的是波义耳定律(有时称为马里奥特定律),描述了理想气体。波义耳定律出现在1662年为他1660年的著作New Experiments Physio-Mechanicall, Touching the Spring of the Air and its Effects所写的附录中。1660年的文本是他与罗伯特·胡克一起用空气泵进行了三年实验的结果,他雇佣罗伯特·胡克作为助手。该装置是由罗伯特·胡克设计的,使用它波义耳发现了一系列重要事实。他表明,除其他事项外,声音不会在真空中传播,他证明了火焰需要空气,生命也是如此,并且他研究了空气的弹性特性。
1662年的附录不仅包含波义耳关于气体体积与压力关系的定律,还包含了对波义耳正文中关于真空工作的辩护。许多科学家,尤其是托马斯·霍布斯,曾主张真空不可能存在,并声称波义耳用真空泵得到的结果必定是某种尚未发现的力的结果。波义耳在1666年的另一本书名为Hydrostatic paradoxes。它[1]:-
……既是对布莱兹·帕斯卡流体静力学工作的深刻批判,充满了对布莱兹·帕斯卡实验方法的敏锐观察,也是对流体压力一系列重要而巧妙实验的呈现。
在The Sceptical Chemist(1661)中,波义耳反对亚里士多德关于土、气、火、水四元素的观点。他主张物质由微粒构成,而这些微粒本身又由基本粒子的不同构型以不同方式组合而成。尽管这部著作中的许多观念取自勒内·笛卡儿,但他在某一点上与他根本分歧。波义耳关于基本粒子在流体中自由运动、在固体中较不自由的观点,遵循了勒内·笛卡儿。然而,勒内·笛卡儿不相信真空,而是相信一种无处不在的以太。波义耳进行了许多实验,使他相信真空,并且在未发现以太的实验证据后,否定了以太的观念。他确实在总体信念上遵循勒内·笛卡儿,即世界基本上是一个由少数简单数学定律支配的复杂系统。
在考虑光学,特别是颜色时,波义耳并不那么成功。他在1664年出版了Experiments and considerations touching colours,但很愿意承认罗伯特·胡克1665年的工作更优越,并且他完全承认艾萨克·牛顿1672年发表的想法应该取代他自己的。
波义耳是皇家学会的创始会士。他通过这个学会发表了他关于空气物理性质的结果。他在化学方面的工作旨在将其建立为一门基于物质机械论的数学科学。正是因为这个原因,我们决定将波义耳纳入这个数学家档案中,因为尽管他自己没有发展任何数学思想,但他是最早主张所有科学都应作为数学的应用来发展的人之一。尽管在他之前其他人已将数学应用于物理学,但波义耳是最早将数学应用扩展到化学的人之一,他试图将其发展为一门科学,其复杂外观仅仅是简单数学定律应用于简单基本粒子的结果。
1668年,波义耳离开牛津,前往伦敦与他的姐姐拉内拉夫人同住。在那里,他成了伊萨克·巴罗的邻居,但似乎与另一位邻居、医生托马斯·西德纳姆有更多共同的科学兴趣。1669年,他姐姐的丈夫去世。然而,有些人却热衷于为波义耳找一位妻子。约翰·沃利斯找到了一位他认为特别适合做波义耳妻子的人,并写信给他说:-
如果我能成为使两位如此优秀的人在彼此身上获得幸福的幸运工具……我不知道我还能以什么其他方式更令自己满意。
波义耳似乎成功地避开了这类为他安排婚姻的企图。1670年6月,他中风导致瘫痪,但慢慢恢复了健康。他继续工作,并在伦敦的家中招待客人。来访者如此频繁,以至于他不得不限制访问,以便有时间继续他的科学研究,他在许多优秀助手的帮助下进行这些研究。
1680年,他拒绝了担任皇家学会主席的邀请。他解释说,他的理由是宗教方面的,因为他无法宣誓必要的誓言。波义耳的宗教一面在这本传记中我们尚未提及,然而它是他生活中的一股重要力量。也许不必更早提及他强烈的基督教信仰的原因是,对波义耳来说,宗教与机械论世界[1]之间没有冲突:-
……对他来说,一个能够创造机械宇宙——能够创造运动中的物质,遵循某些定律,我们所知的宇宙能够以有序的方式从中产生——的上帝,远比一个创造没有科学定律的宇宙的上帝更值得钦佩和崇拜。
Robert Boyle was born into a Protestant family. His father was Richard Boyle, Earl of Cork, who had left England in 1588 at the age of 22 and gone to Ireland. Appointed clerk of the council of Munster by Elizabeth I in 1600, he bought Sir Walter Raleigh's estates in the counties of Cork, Waterford, and Tipperary two years later. Robert's mother, Catherine Fenton, was Richard Boyle's second wife, his first having died within a year of the birth of their first child. Robert was the seventh son (and fourteenth child) of his parents fifteen children (twelve of the fifteen survived childhood). Richard Boyle was in his 60s and Catherine Boyle in her 40s when Robert was born. Of his father Robert would later write [12]:-
He, by God's blessing on his prosperous industry, from very inconsiderable beginnings, built so plentiful and so eminent a fortune, that his prosperity has found many admirers, but few parallels.
Indeed, Robert was fortunate to have the richest man in Great Britain for a father although, one would have to say, the Earl of Cork had acquired his fortune by somewhat dubious means. He was imprisoned in England on charges of embezzlement at one stage and later was fined heavily for possessing defective titles to some of his estates.
The Earl of Cork and his wife believed that the best upbringing for young children, up to the time they began their education, could be provided away from their parents. Robert was sent away to be brought up in the country while his father continued to aim for higher and higher political success. The Earl of Cork lived for four years in his town house in Dublin. He was appointed a lord high justice in 1629 and lord high treasurer in 1631. However, during this time in Dublin Robert's mother died and some time after this Robert returned from his stay with his country nurse to rejoin his family.
Robert was sent, together with one of his brothers, to study at Eton College in England in 1635. At this time the school was becoming fashionable as a place where important people sent their sons. The headmaster was John Harrison and the two young Boyle brothers lived in the headmaster's house [10]:-
Besides the strictly classical course of study then in vogue, the boys had private tutors in French, dancing, and music, for whom they paid extra fees.
Boyle paid tribute to Harrison in [12] where he writes that Harrison gave him a:-
... strong passion to acquire knowledge ...
At this stage of his time at Eton, Boyle's education was clearly going well. He was popular with both his headmaster and his fellow pupils. However, perhaps he had been given too much special attention by Harrison for, when Harrison retired, Boyle seemed unable to fit in with the educational discipline the new headmaster brought to the school. Realising that neither of his sons were progressing well at school under the new headmaster, the Earl of Cork took his sons away from the Eton in November 1638. After this Boyle was tutored privately by one of his father's chaplains.
At the age of 12 Boyle was sent by his father, with one of his brothers, on a European tour. From Dieppe they travelled to Paris, then on to Lyon before reaching Geneva. In Geneva Boyle studied with a private tutor French, Latin, rhetoric and religion. He also spent time in the afternoons playing tennis and fencing. Perhaps most importantly of all he began to study mathematics and soon [12]:-
... he grew very well acquainted with the most useful part of arithmetic, geometry, with its subordinates, the doctrine of the sphere, that of the globe, and fortification.
In 1641 Boyle learnt Italian in preparation for visiting there. In September of that year Boyle and his tutor were in Venice, then by the beginning of 1642 they were in Florence. Galileo died in his villa in Arcetri, near Florence, while Boyle was living in the city. He was much influenced by this event and he carefully studied Galileo's works. If any one event shaped Boyle's life and directed him towards science, then it was this. Of course his Protestant background, with an ingrained fear of Jesuits, contributed to his sympathy for Galileo and his treatment by the Roman Catholic Church. Boyle became a strong supporter of Galileo's philosophy and believed strongly from this time in the new approach to studying the world through mathematics and mechanics.
By May 1642 Boyle and his tutor were in Marseilles waiting for money from Boyle's father so that he could complete the journey home. This did not arrive, merely a letter from his father explaining that a rebellion in Munster was fully occupying his time and money. He did send £250 to pay for Boyle's return, but the money never reached him. Boyle returned to Geneva where he seems to have lived mainly on his tutor's earnings, while his father continued to fight the Irish at Lismore Castle. King Charles I negotiated a cease-fire with the Catholic rebels fighting the Earl of Cork so that he might bring his troops back to England to help him in the civil war which had broken out. The Earl of Cork never got over Charles treating the Irish as equals and he died shortly after in September 1643. Robert Boyle was still living in Geneva when his father died. In the summer of 1644 he sold some jewellery and used the money that he was paid to finance his return trip to England.
Back in England, Boyle lived for a while with his sister Katherine. She was thirteen years older than him and was a lady of some importance, married to Viscount Ranelagh. England was in a chaotic state, the civil war which had began in 1642 was being fought between King Charles and the parliament. Charles had moved to Oxford while the parliament had formed a treaty with the Scots. In return for Scots military support they were promised the establishment of a Presbyterian church. Several battles in 1644 left both King and parliament somewhat in disarray. Boyle had property in England, the manor of Stalbridge, left to him by his father but the situation in the country made things difficult. He wrote in a letter (see for example [3]):-
[I] got safe into England towards the middle of the year 1644, where we found things in such a confusion, that although the manor of Stalbridge were by my father's decease descended unto me, yet it was near four months before I could get thither.
In fact although Boyle inspected his new home after four months, it was much longer before he was able to move in. This happened in March 1646 after he had spent more time with his sister and made a return trip to France to repay his debts to his tutor who continued to live there. Although Boyle did not intend to spend long at Stalbridge, he remained there for around six years. He probably studied harder than he admits in a letter sent to his old tutor in France in October 1646 (see for example [3]):-
As for my studies, I have had the opportunity to prosecute them but by fits and snatches, as my leisure and my occasions would give me leave. Divers little essays, both in verse and prose, I have taken pains to scribble upon several subjects. ... The other humane studies I apply myself to, are natural philosophy, the mechanics and husbandry, according to the principles of our new philosophical college ...
This "new philosophical college" is also called by Boyle the "Invisible College" later in the letter. It is the society which would soon became the "Royal Society of London" and it provided Boyle's only contact with the world of science while he lived a somewhat lonely life at Stalbridge. He would look forward to his visits to London where members of the College [3]:-
.. do now and then honour me with their company.
It was discussions in the Invisible College which led to Boyle reading Oughtred's Clavis Mathematica as well as the works of Mersenne and Gassendi. Boyle had from the time of his visit to Italy favoured the ideas of Copernicus and he now held these views deeply, together with a deep belief in the atomic theory of matter. In the Invisible College these views were considered to be those of the new natural philosophy.
This period was a difficult one for Boyle for he tried hard not to be forced to take sides in the civil war. His loyalties were somewhat divided, his father having been a staunch Royalist, his sister Katherine a staunch Parliamentarian. Basically he had little sympathy with either side, but the final outcome of the civil war turned out to his advantage. Charles I was defeated and executed but, in 1650, Charles II landed in Scotland and tried to regain power. Cromwell, leading the parliamentary forces, defeated the Scots in 1650, again in 1651, and the Irish were also defeated by Cromwell in 1652. Boyle went to Ireland in 1652 to look after his estates there. He ended up a very rich man when Cromwell apportioned Irish lands to the English colonists. From that time on he was able to devote himself entirely to science without the need to earn money. It should be noted, however, that Boyle was a very generous man with his money, and many around him benefited from this generosity.
Boyle met John Wilkins, the leader of the Invisible College, in London when he visited there in 1653. At this time Wilkins had just been appointed as Warden of Wadham College in Oxford and he was planning to run the Invisible College from there. He strongly encouraged Boyle to join them in Oxford and invited him to live in the College. Boyle decided to go to Oxford but preferred not to accept Wilkins' offer of accommodation, choosing instead to arrange his own rooms where he could carry out his scientific experiments. At Oxford he joined a group of forward looking scientists, including John Wilkins, John Wallis who was the Savilian Professor of Geometry, Seth Ward who was the Savilian Professor of Astronomy, and Christopher Wren who would succeed Ward as Savilian Professor of Astronomy in 1661. From 1654 Boyle lived in Oxford, although he never held any university post.
He made important contributions to physics and chemistry and is best known for Boyle's law (sometimes called Mariotte's Law) describing an ideal gas. Boyle's law appears in an appendix written in 1662 to his work New Experiments Physio-Mechanicall, Touching the Spring of the Air and its Effects (1660). The 1660 text was the result of three years of experimenting with an air pump with the help of Hooke whom he employed as his assistant. The apparatus had been designed by Hooke and using it Boyle had discovered a whole series of important facts. He had shown, among other things, that sound did not travel in a vacuum, he had proved that flame required air as did life, and he investigated the elastic properties of air.
The 1662 appendix did not only contain Boyle's law which relates volume and pressure in a gas, but it also contained a defence of Boyle's work on the vacuum which appeared in the main text. Many scientists, particularly Hobbes, had argued that a vacuum could not exist and claimed that Boyle's results obtained with the vacuum pump must be the result of some as yet undiscovered force. Another book by Boyle in 1666 was called Hydrostatic paradoxes. It is [1]:-
... both a penetrating critique of Pascal's work on hydrostatics, full of acute observations upon Pascal's experimental method, and a presentation of a series of important and ingenious experiments on fluid pressure.
In The Sceptical Chemist (1661) Boyle argued against Aristotle's view of the four elements of earth, air, fire and water. He argued that matter was composed of corpuscles which themselves were differently built up of different configurations of primary particles. Although many ideas in this work were taken over from Descartes, in one respect he fundamentally disagreed with him. Boyle's ideas that the primary particles move freely in fluids, less freely in solids, followed Descartes. However, Descartes did not believe in a vacuum, rather he believed in an all pervading ether. Boyle had conducted many experiments which led him to believe in a vacuum and, having found no experimental evidence of the ether, to reject that idea. He did follow Descartes in his overall belief that the world was basically a complex system governed by a small number of simple mathematical laws.
In considering optics, in particular colour, Boyle was not so successful. He published Experiments and considerations touching colours in 1664 but was quite prepared to acknowledge that Hooke's work of 1665 was superior and he completely acknowledged that Newton's ideas, published in 1672, should replace his own.
Boyle was a founding fellow of the Royal Society. He published his results on the physical properties of air through this Society. His work in chemistry was aimed at establishing it as a mathematical science based on a mechanistic theory of matter. It is for this reason that we have decided to include Boyle into this archive of mathematicians for, although he did not develop any mathematical ideas himself, he was one of the first to argue that all science should be developed as an application of mathematics. Although others before him had applied mathematics to physics, Boyle was one of the first to extend the application of mathematics to chemistry which he tried to develop as a science whose complex appearance was merely the result on simple mathematical laws applied to simple fundamental particles.
In 1668 Boyle left Oxford and went to live with his sister Lady Ranelagh in London. There he became a neighbour of Barrow but seemed to have more common scientific interests with another neighbour Thomas Sydenham, a physician. In 1669 his sister's husband died. Some however, were keen to find Boyle a wife. Wallis found someone whom he considered particularly suitable to be Boyle's wife and wrote to him saying:-
If I might be the happy instrument in making two so excellent persons happy in each other ... I do not know in what else I could more approve myself.
Boyle seemed to have successfully avoided such attempts to marry him off. In June 1670 he had a stroke which left him paralysed but slowly he recovered his health. He continued to work and to entertain at his London home. Visitors were so frequent that he had to restrict visits so that he had time to continue with his scientific researches, which he did with the help of many excellent assistants.
In 1680 he declined the offer that he serve as President of the Royal Society. He explained his reasons were religious in that he could not swear to necessary oaths. The religious side of Boyle is one which we have not mentioned in this biography, yet it was an important force in his life. Perhaps the reason it has not been necessary to mention his strong Christian faith earlier is that to Boyle there was no conflict with religion and a mechanistic world [1]:-
... for him a God who could create a mechanical universe - who could create matter in motion, obeying certain laws out of which the universe as we know it could come into being in an orderly fashion - was far more to be admired and worshipped than a God who created a universe without scientific law.
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