数学家传记
约翰·维尔金斯是英国数学家,是皇家学会的创始人之一。他撰写了关于天文学和机械机器的著作。
约翰·维尔金斯的父亲是Walter Wilkins,一位来自牛津的金匠。在[6]中,Aubrey这样描述Walter Wilkins:——
……一个非常机敏的人,头脑极具机械天赋。他非常热衷于做实验,满脑子想的都是永动机。
维尔金斯娶了清教徒牧师弗瑞兹·约翰 Dod的女儿Jane Dod,约翰是他们的四个孩子之一。维尔金斯于1625年去世,当时约翰还是个男孩,Jane再婚。约翰的继父随后成为Francis Pope,这段婚姻所生的一个儿子Walter Pope,终生都是维尔金斯的密友。
约翰的早期教育在[4]中是这样描述的:-
他的拉丁语和希腊语是由Edward Sylvester教的,那是一位著名的希腊学者,在牛津诸圣堂区开办了一所私立学校:他的进步如此之大,以至于十三岁时就在1627年复活节学期进入新学堂成为一名学生。他在那里没有待很久,就转到了莫德林学堂,……并在1631年10月在那里取得了人文学科学位。他后来领受了圣职。
毕业后,他在牛津担任导师,随后被任命为Fawsley的牧师。之后他先后担任过若干著名人物的 chaplain,包括William Fiennes、George the Eighth Lord Berkeley和Charles Louis。Fiennes是上议院中詹姆斯一世和查理一世的主要反对者,也是英国内战中议会的支持者,而Louis则是国王查理一世的侄子、Frederick V之子、普法尔茨选帝侯。据说维尔金斯之所以被任命担任后一个职位,是因为他在数学方面的专长,“他把全部闲暇都献给了数学”。
1648年4月13日,维尔金斯被任命为牛津瓦德汉学院院长。此时他仍是选帝侯王子Charles Louis的 chaplain,因此没有条件取得院长所要求的神学博士学位。由于这一点,他获准有时间攻读该学位,并于1648年12月19日获得学位。他之所以能够如此迅速地抽出时间取得学位,是1648年10月24日签署《威斯特伐利亚和约》的结果。这结束了三十年战争的德国阶段,莱茵普法尔茨归还给Charles Louis,他返回了海德堡。维尔金斯似乎在这一时期前后游历了多个欧洲目的地,很可能是从海德堡返回时,他曾陪同Charles Louis前往那里。
维尔金斯在牛津的履职无疑极为出色。他参加了多个力图恢复大学及其各学院自治权的委员会。当时大学正受到各个宗教派别的攻击,这些派别既攻击大学的管理方式,也攻击其课程设置。维尔金斯在捍卫大学抵御这些宗教攻击方面尤为有力。他之所以能有力地这样做,是因为他推动了教育改革,使大学转向有益于人类的实用学问。他的目标是[1]:-
……为新科学赢得承认,把尼古拉·哥白尼、约翰内斯·开普勒、伽利略、Gilbert、马兰·梅森等人的工作提请他的同胞注意。
维尔金斯在A discourse concerning a new planet(1640)中大力主张一种新的科学方法。他的话今天在我们听来相当“显而易见”,这恰恰标志着他在其中起了重要作用的17世纪思想革命的成功。他写道,我们不应当:
……如此迷信地崇敬古代,以至于把从某位教父笔下流出、或经古人一致认可的一切都当作正典接受。……每一个寻求真理的人,都应当始终保持哲学上的自由;不要沦为任何人意见的奴隶,以至于认为他所说的一切都绝无谬误。我们必须努力凭我们自己的经验去弄清事物本身是什么……而不是别人对它们说了什么。如果在这样不偏不倚的探究中,我们偶然发现一条新路,而且是一条偏离常轨的路,这既不是我们的过错,也不是我们的不幸。
在同一部著作中,维尔金斯还主张反对用《圣经》来判定关于物理世界的事实:
如果我们能使《圣经》免于哲学争论,那对我们来说是幸运的。如果我们能安于让它在其被赋予的目的上保持完美,即作为我们信仰与顺从的准则,而不把它延伸为判断那些要靠我们自己的勤勉和经验去发现的自然真理的法官,那就好了。
所用的论据与伽利略的论据相似,但没有证据表明维尔金斯实际上见过伽利略所著的、包含这些论据的Letter to Castelli。情况倒可能相反,我们不得不说,几乎可以肯定维尔金斯是完全独立于伽利略提出他的论据的。
1656年,维尔金斯与奥利弗·克伦威尔的妹妹罗比娜结婚,由于瓦德汉学院的章程禁止院长结婚,他获得了特别豁免。尽管奥利弗·克伦威尔于1658年去世,但与他的妹妹结婚对他的职业生涯毫无损害!1659年,奥利弗·克伦威尔的儿子、英格兰护国公理查德·克伦威尔任命维尔金斯为剑桥大学三一学院院长。然而,理查德·克伦威尔于1659年5月25日被迫退位,1660年君主制复辟,查理二世成为国王。当亨利·费恩声称查理一世曾承诺给他院长职位时,维尔金斯被剥夺了职位。维尔金斯已婚的事实被用作罢免他的手段。
剑桥许多人对维尔金斯的离去感到惋惜,尤其是Isaac 伊萨克·巴罗。然而,从许多方面看,离开剑桥反而使维尔金斯得以以一种他若留在那里便不会发生的方式影响皇家学会的创立,而这被证明是他职业生涯中最杰出的成就之一。
1645年,维尔金斯住在伦敦时,第一次与一群人有了交往,这些人最终会组成皇家学会。约翰·沃利斯写道,那个学会的开端是:-
……大约在1645年(如果不是更早的话),当时维尔金斯博士(那时是伦敦的帕拉丁选帝侯王子的随行牧师)[以及包括沃利斯本人在内的其他一些人]在某个特定的日子和时辰每周聚会,违反者要受一定的处罚,每周缴纳用于实验费用的捐款,并共同商定了一些规则,来讨论和谈论这类事务……
About the year 1648-49, some of our company being removed to Oxford (first Dr Wilkins, then I, and soon after Dr Goddard) our company divided. Those in London continued to meet there as before (and we with them, when we had occasion to be there, and those of us at Oxford ... and divers others, continued such meetings in Oxford, and brought those Studies into fashion there...
事实上,当维尔金斯在沃德姆时,他聚集了一群:-
……对自然哲学和人类学问的其他部分充满好奇的值得尊敬的人。
这个牛津小组在维尔金斯担任沃德姆学院院长期间在沃德姆学院聚会,但在维尔金斯搬到剑桥后,他们在波义耳的住所聚会。在维尔金斯离开剑桥回到伦敦后,他加入了每周在格雷沙姆学院聚会的小组。Royal Society成立的那次会议的报告如下:-
备忘录 1660年11月28日。以下这些人按照他们中大多数人的通常习惯,在格雷沙姆学院聚会,听克里斯托弗·雷恩先生的讲座,即:威廉·布朗克勋爵、罗伯特·波义耳先生、布鲁斯先生、罗伯特·莫里爵士、保罗·尼尔爵士、维尔金斯博士、戈达德博士、佩蒂博士、鲍尔先生、鲁克先生、克里斯托弗·雷恩先生、希尔先生。讲座结束后,他们按照通常的方式退席进行相互交谈。
在此期间,维尔金斯博士和戈达德博士历经所有这些变迁,从最初开始直到他们去世,一直坚持这些会议(并对其产生了很大影响)……
尽管在君主制复辟后他被剑桥解职,维尔金斯很快便得到查理二世的青睐。1662年4月11日,国王任命他为伦敦圣劳伦斯犹太教堂的牧师。1668年11月14日,他被祝圣为切斯特主教。此后他频繁往返于切斯特和伦敦之间,尽管大部分时间都在切斯特度过。然而到1672年,他健康状况不佳,于11月去世后,于12月12日安葬于圣劳伦斯犹太教堂。
1638年,维尔金斯出版了他的第一本书The Discovery of a World in the Moon,实际上是以匿名方式出版的。1640年,他也以匿名方式出版了A Discourse concerning a New Planet,从那时起,Discourse和Discovery就作为一部单一著作一起出版。这部著作面向普通读者而非该领域的专家,其目的是普及由尼古拉·哥白尼、约翰内斯·开普勒和伽利略提出的宇宙观。主要论点是月球不是一个发光的圆盘,而是一个拥有类似地球景观的世界。当然,维尔金斯并不是第一个提出这种理论的人;例如伽利略也曾以类似方式论证过。也许更令人惊讶的是,他相信月球是一个可居住的行星,并预测有一天前往月球的旅行将成为可能。同样,维尔金斯也不是第一个提出这一设想的人,但这正是他思考方式的典型特征,任由自己的思想驰骋于那些别人会觉得过于非传统而不予考虑的想法之中。
维尔金斯研究密码和暗号,于1641年出版了他的著作Mercury, or the Secret and Swift Messenger。这本书讨论了与交流和语言相关的广泛思想。他研究了世界不同地区不同语言的问题,并寻找解决这一阻碍学习的祸害的办法。他触及了通用语言的想法,这是他在最后一部著作中再次讨论的主题。
维尔金斯还撰写了关于机械装置的著作,于1648年出版了Mathematical Magick, or the wonders that may be performed by mechanical geometry。该书阐述了机械的基本原理,第一部分描述了天平、杠杆、轮子、滑轮、楔子和螺旋。维尔金斯随后解释了如何组合这些装置:-
……用一根头发将任何橡树连根拔起,用一根稻草将其举起,或一口气将其吹倒。
这一切相当耸人听闻,尤其是插图,但维尔金斯的想象建立在良好的数学原理之上。他描述的一种装置是烟转烤肉架,最早由列奥纳多·达·芬奇绘制草图。这种机器由安装在垂直轴上的水平风帆组成,由烟囱中上升的热空气驱动。使用了一套齿轮系统,使得烟转烤肉架能够转动烤肉叉。
维尔金斯和罗伯特·胡克多年来共同研制机器,据记载:-
...在欧洲其他地方找不到在零件和 ingenuity 方面能与之相比的人。
有两部著作对维尔金斯关于机器的思考产生了特别重要的影响。它们是Guidobaldo del Monte的Liber mechanicorum(1577年)和马兰·梅森的Cogitata Physico-Mathematica(1644年)。事实上,可以公允地指出,维尔金斯在众多领域都大大受惠于马兰·梅森,因为两人观点极为相近。在许多方面,人们可以把维尔金斯的工作看作是对马兰·梅森那些更为技术性的著作的普及。
维尔金斯的最后一部著作论述一种通用语言,由于原稿在1666年伦敦大火中被毁,这部著作不得不重写。它在[1]中被描述如下:-
第一部分描述语言和字母表的起源……。第二部分是对所有思想领域中的概念所作的详尽分类,P M Roget显然是以维尔金斯的这部著作为基础撰写他的《英语单词宝库》的。第三部分涉及语法、句法、正字法、元音和辅音。第四部分给出所提出的新文字和语言的符号,并给出使用示例和说明。
让我们通过维尔金斯自己对符号插图:Wilkins_ever.gif ↗的解释来说明他的通用语言。
通性字符插图:Wilkins_space.gif ↗表示空间的属。左侧的锐角表示第一差,即时间。另一个附标表示差下的第九种,即永恒。此附标末端的环表示该词须作副词用;因此其意义必与我们用短语“永永远远”所表达者相同。
这也许很巧妙,但从这一个例子可以清楚看出,学习这种语言总会带来重大困难。使用维尔金斯的新语言的困难,被与他同时代的一位人士很好地概括如下:——
一位被认为极有能力的博士
设计出全人类将用以交谈的方案,
不顾巴别塔的混乱,
凭借一种称为普遍字符的东西。
那字符要学多久,
实在超出我的判断。
至于维尔金斯的字符,Aarsleff在[1]中写道:——
他一生中赢得并保持了政治和宗教派别最为各异的人们的友谊与尊敬。无疑,魅力、谈吐敏捷和精力等个人品质在他的成功中起了作用,但更深层的原因似乎在于他信奉超越任何特定派别排他利益的信念。从头到尾,他所有著作所倡导的科学和宗教观点,到他去世时已证明代表了时代的精神。新科学已经胜利……
曾与维尔金斯密切合作的罗伯特·胡克,在Micrographia(1665)的序言中对他作了如下美好的赞颂:——
几乎没有一项发明,是这个国家在我们这个时代产生的,而不是以某种方式由他的帮助推进的。……他确实是一个为人类福祉而生、为国家荣誉而生的人。在他举止的温和中,在他心灵的平静中,在他心灵的无限善良中,我们有一个明显的例子,说明真正的、原始的、不偏不倚的宗教是什么样子,在它被特定的派系所败坏之前。
John Wilkins's father was Walter Wilkins, a goldsmith from Oxford. In [6] Aubrey describes Walter Wilkins as:-
... a very ingenious man with a very mechanical head. He was much for trying of experiments, and his head ran much upon the perpetual motion.
Walter Wilkins married Jane Dod, the daughter of the Puritan minister John Dod, and John was one of their four children. Walter Wilkins died in 1625 while John was still a boy and Jane remarried. John's stepfather then became Francis Pope and a son of this marriage, Walter Pope, remained a close friend of John Wilkins throughout his life.
John's early education is described in [4] in the following way:-
He was taught his Latin and Greek by Edward Sylvester, a noted Grecian, who kept a Private School in the Parish of All Saints in Oxford: His Proficiency was such, that at Thirteen Years of Age he entered a Student in New-Inn, in Easter-Term 1627. He made no long stay there, but was removed to Magdalen Hall, ... and there he took his Degree in Arts in October 1631. He afterwards entered into Orders.
After graduating, he tutored in Oxford, then was appointed Vicar at Fawsley. He was then chaplain to a number of famous men, including William Fiennes, George the Eighth Lord Berkeley, and Charles Louis. Fiennes was a leading opponent of James I and Charles I in the House of Lords and a supporter of Parliament in the English Civil Wars while Louis was the nephew of King Charles I, the son of Frederick V, and the prince elector Palatine. Wilkins is said to have been appointed to this latter post because of his expertise in mathematics "to which he devoted all his leisure".
On 13 April 1648 Wilkins was appointed Warden of Wadham College, Oxford. At this time he was still chaplain to the prince elector Charles Louis and was not, therefore, in a position to take the degree of doctor of divinity which was required of a Warden. Because of this he was allowed time to study for the degree which he obtained on 19 December 1648. That he was able to devote time to take his degree so soon was a consequence of the Peace of Westphalia having been signed on 24 October 1648. This ended the German phase of the Thirty Years' War and the Rhenish Palatinate was restored to Charles Louis who returned to Heidelberg. Wilkins seems to have travelled to a number of European destinations around this time, probably on returning from Heidelberg where he accompanied Charles Louis.
Wilkins certainly carried out his duties at Oxford with great skill. He sat on various committees which sought to restore the autonomy of the university and its colleges. The university was under attack at this time from various religious factions who attacked both the way it was governed and the curriculum. Wilkins was particularly vigorous in defending the university against these religious attacks. He was in a strong position to do so for he had promoted changes in education moving the university towards practical learning which would benefit mankind. He aimed to [1]:-
... gain acceptance for the new science, to bring the work of Copernicus, Kepler, Galileo, Gilbert, Mersenne, and others, to the attention of his countrymen.
Wilkins, in A discourse concerning a new planet (1640), argued strongly for a new approach to science. That his words sound rather "obvious" to us today is a mark of the success of the revolution in seventeenth century thought in which he played a major role. He wrote that we should not be:-
... so superstitiously devoted to Antiquity as for to take up everything as canonical which drops from the pen of a Father, or was approved by the consent of the Ancients. ... It behoves everyone in search of Truth, always to preserve a philosophical liberty; not to be enslaved to the opinion of any man, as to think whatever he says to be infallible. We must labour to find out what things are in themselves by our own experiences ... not what another says of them. And if in such an impartial enquiry, we chance to light upon a new way, and that which is besides the common road, this is neither our fault, nor our unhappiness.
In the same work Wilkins argued against the Holy Scriptures being used to determine facts about the physical world:-
It were happy for us if we could exempt Scripture from philosophical controversies. If we could be content to let it be perfect for that end unto which it was intended, for a Rule of our Faith and Obedience, and not to stretch it to be a Judge of such natural truths as are to be found out by our own industry and experience.
The arguments used are similar to those of Galileo but there is no evidence to suggest that in fact Wilkins had seen the Letter to Castelli by Galileo which contains these arguments. Rather the reverse, and we have to say that it is almost certain that Wilkins put forward his arguments entirely independently of Galileo.
In 1656 Wilkins married Robina, a sister of Oliver Cromwell, obtaining special dispensation since the statutes of Wadham College prohibited the Warden from marrying. Although Oliver Cromwell died in 1658, being married to his sister did his career no harm at all! In 1659 Richard Cromwell, Oliver Cromwell's son and the Lord Protector of England, appointed Wilkins as Master of Trinity College Cambridge. However Richard Cromwell was forced to abdicate on 25 May 1659 and in 1660 the monarchy was restored when Charles II became King. Wilkins was deprived of his post when Henry Ferne claimed that he had been promised the position of Master by Charles I. The fact that Wilkins was married was used as a device to remove him.
Many at Cambridge regretted Wilkins' departure, particularly Isaac Barrow. However, in many ways leaving Cambridge allowed Wilkins to influence the foundation of the Royal Society it a way that would not have happened had he remained there, and this proved to be one of the finest achievements of his career.
In 1645, while living in London, Wilkins had first become associated with a group of men who would eventually form the Royal Society. Wallis writes that the beginnings of that Society were:-
... about the year 1645 (if not sooner) when Dr Wilkins (then Chaplain to the Prince Elector Palatine in London) [and a number of other men including Wallis himself] met weekly on a certain day and hour, under a certain penalty, and a weekly contribution for the charge of experiments, with certain rules agreed amongst us, to treat and discourse of such affairs...
About the year 1648-49, some of our company being removed to Oxford (first Dr Wilkins, then I, and soon after Dr Goddard) our company divided. Those in London continued to meet there as before (and we with them, when we had occasion to be there, and those of us at Oxford ... and divers others, continued such meetings in Oxford, and brought those Studies into fashion there...
In fact while Wilkins was at Wadham he gathered round him a group of:-
... worthy persons inquisitive into natural philosophy and other parts of human learning.
This Oxford group met in Wadham College while Wilkins was Warden there but, after Wilkins moved to Cambridge, they met at Boyle's lodgings. After Wilkins left Cambridge and returned to London he joined with the group which were meeting weekly at Gresham College. The report of the meeting at which the Royal Society was founded reads:-
Memorandum November 28 1660. These persons following according to the usual custom of most of them, met together at Gresham College to hear Mr Wren's lecture, viz. The Lord Brouncker, Mr Boyle, Mr Bruce, Sir Robert Moray, Sir Paule Neile, Dr Wilkins, Dr Goddard, Dr Petty, Mr Ball, Mr Rooke, Mr Wren, Mr Hill. And after the lecture was ended they did according to the usual manner, withdraw for mutual converse.
Returning to the account given by Wallis of the founding of the Royal Society:-
All this while, Dr Wilkins and Dr Goddard, through all these changes, continued those meetings, (and had a great influence on them) from the first original, till the days of their death ...
Although he had been dismissed from Cambridge on the restoration of the monarchy, Wilkins was soon in favour with Charles II. On 11 April 1662 the King made him vicar of St Lawrence Jewry in London. He was consecrated Bishop of Chester on 14 November 1668. He then journeyed frequently between Chester and London although he spent most time in Chester. By 1672, however, he was suffering ill health and after his death in November he was burried at St Lawrence Jewry on 12 December.
In 1638 Wilkins published his first book The Discovery of a World in the Moon which was in fact appeared anonymously. In 1640 he published, also anonymously, A Discourse concerning a New Planet and from this time the Discourse and the Discovery have been published together as a single work. The work is addressed to the general reader rather than experts in the subject, and its aim is to popularise the view of the universe due to Copernicus, Kepler and Galileo. The main argument is that the Moon is not a shining disk but rather it is a world with a landscape like that of the Earth. Of course Wilkins was not the first to put forward such a theory; for example Galileo had argued in a similar way. Perhaps more surprisingly, he believed that the Moon is a habitable planet and he predicts that one day travel to the Moon will be possible. Again Wilkins was not the first to come up with this suggestion but it is typical of the way that he thought, allowing his mind to roam through ideas which others would have found too unconventional to consider.
Wilkins worked on codes and ciphers publishing his work Mercury, or the Secret and Swift Messenger in 1641. The book discussed a wide range of ideas associated with communication and language. He looked at the problem of different languages in different parts of the world and looked for a solution to this curse which hindered learning. He touched on the idea of a universal language, a topic that he returned to in his final work.
Wilkins also wrote on mechanical devices, publishing Mathematical Magick, or the wonders that may be performed by mechanical geometry in 1648. It is an account of the fundamental principles of machines and the first part describes the balance, lever, wheel, pulley, wedge and screw. Wilkins then explains how to combine these devices:-
... to pull up any oak by the roots with a hair, lift it up with a straw, or blow it up with one's breath.
It was all rather sensational, particularly the illustrations, but Wilkins imagination was based on good mathematical principles. One device he described was the smokejack, first sketched by Leonardo da Vinci. This machine consisted of horizontal sails mounted on a vertical shaft and driven by the hot air rising up a chimney. A gearing system was used so that the smokejack could turn a roasting spit.
Wilkins and Hooke worked together on machines for many years and it is reported that:-
... persons together were not to be found else where in Europe, for parts and ingenuity.
Two works were particularly important in influencing Wilkins thinking on machines. These were Liber mechanicorum (1577) by Guidobaldo del Monte and Cogitata Physico-Mathematica (1644) by Mersenne. In fact it is fair to note that Wilkins owed quite a debt to Mersenne in a whole variety of areas for the two shared views closely. In many ways one can look at Wilkins work as popularising the more technical writings of Mersenne.
Wilkins' last work, which had to be rewritten since the original was destroyed in the Great Fire of London in 1666, is on a universal language. It is described in [1] in the following way:-
The First Part describes the origin of languages and alphabets... . The Second Part is an exhaustive classification of notions in all spheres of thought, P M Roget clearly based his Thesaurus on this work of Wilkins. The Third Part relates to grammar, syntax, orthography, vowels and consonants. The Fourth Part provides the symbols of the proposed new writing and language, and gives examples and instructions for its use.
Let us illustrate Wilkins' universal language by giving his own explanation of the symbol插图:Wilkins_ever.gif ↗.
The generic character插图:Wilkins_space.gif ↗ doth signify the genus of space. the acute angle on the left side doth denote the first difference, which is Time. The other affix signifies the ninth species under the differences, which is Everness. The Loop at the end of this affix denotes the word is to be used adverbially; so that the sense of it must be the same which we express by the phrase, For Ever and Ever.
It may be clever, but it is clear from this one example that learning the language would always present major problems. The difficulty in using Wilkins' new language is nicely summed up by one of his contemporaries who wrote:-
A Doctor counted very able
Designs that all mankind converse shall,
Spite o' the confusion was at Babell,
By a character called universall.
How long that character will be learning,
That truly passeth my discerning.
As to Wilkins' character, Aarsleff writes in [1]:-
Throughout his life, he gained and retained the friendship and respect of men of the most diverse political and religious persuasions. No doubt such personal qualities as charm, ready conversation, and energy played their part in his success, but a deeper reason would seem to lie in his commitment to beliefs that transcended the exclusive interests of any particular faction. From the first to the last, all his writings advocate scientific and religious views that by the time of his death had proved that they represented the temper of the times. The new science had triumphed ...
Hooke, who had worked closely with Wilkins, wrote the following fine tribute to him in the Preface to Micrographia (1665):-
There is scarce one invention, which this nation has produced in our age, but it has some way or other been set forward by his assistance. ... He is indeed a man born for the good of mankind, and for the honour of his country. in the sweetness of whose behaviour, in the calmness of his mind, in the unbounded goodness of his heart, we have an evident instance, what the true and primitive unpassionate religion was, before it was soured by particular factions.
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