数学家传记
约翰·迪伊是英国学者,著有三角学、历法改革、航海、地理学和占星术方面的作品。他成为玛丽女王的占星家,但因被指控为魔术师而遭监禁。
约翰·迪伊的父亲是Roland Dee,他有威尔士血统。Roland Dee经营纺织品,此外,还是亨利八世宫廷的绅士缝纫师。在后一个职位上,他为王室制作服装,并为国王购买和供应面料。迪伊的母亲是Jane Wild。Jane十五岁时嫁给了Roland,三年后,弗瑞兹·约翰(他们的第一个也是唯一的孩子)出生了。
约翰 从1535年起在埃塞克斯郡切姆斯福德的一所学校接受教育,然后于1542年11月进入剑桥大学圣约翰学院。在那里他学习了希腊语、拉丁语、哲学、几何学、算术和天文学。Woolley 写道[10]:-
他后来回忆说,他如此渴望学习,如此“热衷于钻研”,以至于每天工作十八个小时,只留四个小时睡觉、两个小时吃饭。数学是他的热情所在……
在1546年,即他作为本科生的最后一年,他开始进行天文观测。他使用一个象限仪和一个十字测天仪进行了观测(正如他后来在Compendious Rehearsal):-中所写)
……对这个世界元素部分中实际存在的天体影响和作用的观测(精确到小时和分钟的观测非常多)。在随后的几年里,我进行了数千次这样的观测。
也许我们在此阶段应该说几句话来解释这段引文。人们不会期望一位现代天文学家说“对天体影响的观测”,但迪伊与他那个时代的一般做法一样,相信占星术。然而,迪伊寻求一种科学解释,说明为什么一个人出生时行星的位置会影响他们的未来。他会论证每个天体都发出力的射线,作用于所有其他天体。人们可以将此视为万有引力定律的一种早期形式,但这可能有些夸大了迪伊的想法。然而,艾萨克·牛顿的力的概念确实源自诸如迪伊的魔力等概念。然而,我们应该强调,迪伊的方法始终是通过数学,他寻求一种科学解释。
迪伊于1546年获得学士学位,并成为圣约翰学院的会士。1546年12月,他成为剑桥大学三一学院的会士。亨利八世于1546年创立了三一学院,这是剑桥大学最大的学院,迪伊成为其创始会士之一。
由于对英格兰的科学氛围不满,迪伊在1548年至1551年间前往欧洲大陆旅行。他首先访问了布鲁塞尔附近的鲁汶,于1548年6月24日抵达,在那里他与海马·弗里修斯和墨卡托一起学习。不久,墨卡托成为迪伊特别亲密的朋友,他们一起讨论了宇宙的新模型。迪伊后来写道:-
我们彼此友谊与亲密关系的习惯是,在整整三年里,我们两人中任何一方都未曾有超过整整三天不见对方。
在鲁汶期间,迪伊写了两篇关于天文学的文本。1550年,他前往布鲁塞尔会见在那里工作的数学家。似乎大约在这个时候,他遇到了佩德罗·努内斯,他们成了亲密的朋友。同年,迪伊前往巴黎,在那里讲授欧几里得的Elements。他一定是一位令人印象深刻的讲师,因为据报道,人们蜂拥而至听他的讲座,讲座教室挤得水泄不通。1551年,迪伊被提供巴黎数学教授的职位,但他拒绝了。三年后,他也拒绝了牛津的数学讲师职位。
回到英格兰后,迪伊于1552年2月进入彭布罗克伯爵的服务,然后在同年年底进入诺森伯兰公爵的服务。在担任后一个职位期间,他写了一部关于潮汐的著作。
国王爱德华六世去世后,天主教徒和新教徒之间在继承问题上出现了巨大分歧。天主教徒玛丽女王违背许多新教徒的意愿登上了王位,这些新教徒担心自身的安全。事实上他们的担心是有道理的,因为玛丽发动了一场针对著名新教徒的运动,其中被捕的一个人就是Roland Dee,即迪伊的父亲,他于1553年8月被囚禁。他获释了,但只是在被剥夺了所有财产之后。约翰原本期望从父亲那里继承可观的财富,从而能够从事科学研究而无需为谋生担忧,此时却陷入了困境。他本可以通过接受1554年牛津大学提供给他的数学职位来解决经济问题,但他对英国大学学术水平的看法使他拒绝了这个职位。
1555年5月28日,迪伊被捕并被指控“计算”。此时,在英格兰,数学被认为等同于拥有魔法力量,22写道(见[22]),当局已经:-
……烧毁数学书籍,因为它们是 conjuring 书籍。
尽管他犯有对他提出的指控,迪伊在被关押三个月后于8月获释。尽管他作为自由人获释,但他的收入来源被切断,使他陷入严重的经济困难。迪伊的父亲于1555年去世,未能收回他的财富。至于迪伊的宗教立场,这似乎更难确定。他似乎有充分理由试图避免在天主教与新教的争论中选边站,但从监狱获释后,他似乎完全适应了曾监禁他的天主教政权。他可能出于政治便利而改变了立场,但我们稍后会看到,有一种理论认为他是在充当间谍。
1556年1月15日,迪伊向玛丽女王提出了建立国家图书馆的计划。这是一个极好的方案,通过找到所有重要书籍的副本并将它们保存在一个皇家图书馆中来保存学问,人们可以查阅以解决:-
……这些疑虑和学问上的难点,可能会困扰和烦扰他们的头脑,[而]学问[将会]得到惊人的推进。
该计划并未获得官方支持,但尽管如此,迪伊不顾其经济困难,仍着手创建自己的图书馆。关于他所建立的图书馆的藏书目录,见[7]。
玛丽女王于1558年去世,新教徒伊丽莎白成为女王。迪伊很快得到了伊丽莎白的青睐,甚至被要求运用他的占星术技能为她选择最适合加冕的日子。他照做了,但人们不禁要问,一个与前天主教政府关系如此密切的人,怎么会这么快就得到青睐。Woolley [10] 认为,迪伊可能在玛丽的政府中为伊丽莎白充当间谍,这肯定与事件相符,也能解释一些否则令人费解的事情。
在接下来的五年里,迪伊在国外度过,为他的图书馆收集书籍,并研究天文学、占星术、数学、编码和魔法——所有这些主题在他努力理解宇宙终极真理的过程中,在他的头脑中都是相互关联的。尽管他与伊丽莎白女王关系密切,并经常向她提供建议,但他从未从她那里获得他所渴望的经济保障,以使他能够完全投身于研究。到1566年,为了降低生活费用,他与母亲住在伦敦的莫特莱克。在那里,他在自己的图书馆中积累了一批非凡的学术著作,还收集了一批天文仪器、地球仪(包括墨卡托送给他的一个)和精确的时钟。
1568年,他出版了Propaedeumata Aphoristica,并将这部作品呈献给伊丽莎白女王。伊丽莎白印象深刻,迪伊给她上数学课,使她能够理解它。这本书混合了优秀的物理学和数学,也有大量占星术和魔法。让我们强调,我们不应因为迪伊对魔法感兴趣而轻视他;他那个时代以及更晚得多的大多数伟大科学家和数学家都有这样的兴趣。例如,第谷·布拉赫坚定地相信炼金术和占星术,博纳文图拉·卡瓦列里和约翰内斯·开普勒也是如此,而艾萨克·牛顿和迪伊一样,痴迷于研究炼金术。在Propaedeumata Aphoristica中,我们可以描述为“优秀科学”的内容包括一个陈述:不等质量以相同速度下落。迪伊提到了早先也声称这一事实的科学家。他还指出,宇宙中的每个物体都对所有其他物体施加力。
1570年,迪伊编辑了一版由Billingsley翻译的欧几里得的Elements。迪伊为这一版写了一篇著名的序言,为研究数学辩护:——
啊,令人慰藉的诱惑,啊,令人陶醉的说服,去研究一门其主题如此古老、如此纯粹、如此卓越、如此环绕一切受造之物的科学,它被造物主全能与不可理解的智慧所使用,在一切受造之物的独特创造中:在它们所有独特的各部分、属性、本性和德能中,藉着秩序和最为绝对的数,从无中被带出,进入其存在与状态的形式。
迪伊观测了那颗常被称为“第谷·布拉赫1572年超新星”的“新星”,并在次年撰写了Parallacticae commentationis praxosque,其中给出了用于测定到这颗新星距离的三角学方法。他曾与助手Thomas 托马斯·迪格斯一起进行精确观测,二人很可能就这颗星与第谷·布拉赫有通信往来。当然,第谷·布拉赫极为钦佩迪伊的贡献。
迪伊在1551年返回时从欧洲大陆带回了航海仪器。从1555年起,他担任莫斯科公司的顾问。莫斯科公司由航海家兼探险家Sebastian Cabot与一些伦敦商人于1555年成立。它获得了英俄贸易的垄断权,其目标之一是寻找东北航道。在接下来的32年里,迪伊为公司准备了航海信息,包括极地航行用的海图。1576年,在船员们出发前往北美航行之前,他向他们教授几何学和宇宙志。
1579年,迪伊的母亲将她在莫特莱克的房子(他至少已在此居住13年)给了他;次年她去世。迪伊于1578年2月与Jane Fromands结婚,他们共育有八个孩子。她是他的第三任妻子——他的第二任妻子在婚后次年,即1576年3月去世。他与前两任妻子没有孩子(至少没有存活下来的)。
Edward Kelley于1582年3月进入了迪伊的生活。他是一位灵媒,声称能够与天使和灵魂沟通,他通过凝视水晶球来做到这一点。尽管这不是迪伊第一次参与此类实践,但起初他仍然高度怀疑约翰·L·凯利的幻象是否真实。然而,有两件事说服了他:凯利在他的技艺上非常娴熟,其次迪伊如此渴望理解宇宙的终极真理,而他通过其他方式未能找到。其他人对他的科学工作缺乏反应也是一个因素,还有他一生中经常被指控使用魔法的事实。迪伊通过凯利越来越深入地参与与天使和灵魂的对话,可悲的是,这主导了他生命的后期。这发生在大约五年的时间里。一些参考文献详细描述了这些对话,迪伊将其记录在日记中;例如参见[6]、[9]和[10]。我们注意到,在他的日记中,迪伊称自己为Δ,这是一个巧妙的双关语,因为Δ是字母“dee”的希腊字符,也是一个魔法符号。
迪伊于1583年2月向伊丽莎白女王提出了历法改革建议。他提议删除十一天,使历法与天文年一致。当然,这恰恰是正确的做法,迪伊的提议得到了伊丽莎白几位顾问的支持。然而,坎特伯雷大主教反对该方案,部分原因是他与伊丽莎白长期争执,部分原因是他认为该方案与天主教会在前一年所采纳的历法相近。不过,迪伊的方案比教皇格里高利十三世颁布后欧洲所采纳的方案更好。格里高利历以325年尼西亚会议日期为基础,而迪伊提议的历法以天文为基础,而非政治基础,他明确指出了这一点。迪伊历法改革提案的失败意味着英格兰保留的历法直到1752年都与欧洲其他地区不一致。
迪伊和凯利访问了波兰和波希米亚(1583-89),在诸侯宫廷表演魔法。凯利获得了名声和财富,并被封为骑士。另一方面,迪伊仍然面临严重的经济问题,于1589年12月回到莫特莱克,发现他的大部分藏书被盗,科学仪器也被盗。大约在这个时候,迪伊一定与托马斯·哈里奥特成为了朋友。两人讨论了针对罗利学派的无神论指控,并讨论了其中哪一位被称为“其主人的魔术师”。他们在1590年代还讨论了科学和数学问题。1590年,托马斯·哈里奥特寄给迪伊一本他的书,他在书中写下了“致我亲爱的朋友”。
多年来,迪伊一直试图为他多年来的收入损失争取补偿,但未能成功。他试图获得圣约翰十字架堂主教的任命,该任命经伊丽莎白女王批准,但须经坎特伯雷大主教批准——然而这一批准从未实现。1596年,他被任命为曼彻斯特学院教堂的监管人,几乎可以肯定这是为了让他离开伦敦。1605年,曼彻斯特遭受瘟疫,迪伊的妻子和几个孩子去世。他回到伦敦,几年后在那里去世。
John Dee's father was Roland Dee who was of Welsh descent. Roland Dee dealt in textiles and, in addition, was a gentleman sewer at the court of Henry VIII. In this latter capacity he would have made clothing for the royal household as well as buying and supplying fabrics for the King. John Dee's mother was Jane Wild. Jane married Roland when she was fifteen years of age and, three years later, John (who was their first and only child) was born.
John was educated at a school in Chelmsford in Essex from 1535, then entered St. John's College, Cambridge in November of 1542. There he studied Greek, Latin, philosophy, geometry, arithmetic and astronomy. Woolley writes [10]:-
He was so eager to learn, he later recalled, so "vehemently bent to study", that he worked eighteen hours a day, allowing just four hours for sleep and two for meals. Mathematics was his passion ...
During 1546, his final year as an undergraduate, he began to make astronomical observations. Using a quadrant and a cross-staff he made (as he later wrote in Compendious Rehearsal):-
... observations (very many to the hour and minute) of the heavenly influences and operations actual in this elemental portion of the world. Of which sort I made some thousands in the years then following.
Perhaps we should say a few words at this stage to explain this quotation. One would not expect a modern astronomer to say "observations of the heavenly influences" but Dee, in common with the general practice in his time, believed in astrology. However, Dee sought a scientific explanation for the reasons that the positions of the planets at the moment of a person's birth would affect their future. He would argue that each body emitted rays of force which acted on all other bodies. One could view this as an early form of the law of universal gravitation, but this might be somewhat overstating Dee's idea. However, Newton's concept of force certainly derived from concepts of magic powers such as those of Dee. We should stress, however, that Dee's approach was always through mathematics and he sought a scientific explanation.
Dee graduated with a B.A. in 1546 and became a Fellow of St John's College. In December 1546 he became a Fellow of Trinity College, Cambridge. Henry VIII founded Trinity College, the largest of the Cambridge colleges, in 1546 and Dee became one of its founding Fellows.
Being unhappy with the scientific attitude in England, Dee travelled on the Continent between 1548 to 1551. He first made a visit to Louvain near Brussels, arriving on 24 June 1548, where he studied with Gemma Frisius and Gerardus Mercator. Soon Mercator became a particularly close friend of Dee's and together they discussed new models for the universe. Dee later wrote:-
It was the custom of our mutual friendship and intimacy that, during three whole years, neither of us lacked the other's presence for as much as three whole days.
During his time in Louvain Dee wrote two texts on astronomy. In 1550 he went to Brussels to meet the mathematicians working there. It seems that around this time he met Nunes and they became close friends. In the same year Dee went to Paris where he lectured on Euclid's Elements. He must have been an impressive lecturer for it was reported that people flocked to hear his lectures which filled the lecture rooms to overflowing. In 1551 Dee was offered an appointment as professor of mathematics in Paris but declined. He also declined a lectureship in mathematics at Oxford three years later.
Back in England Dee entered the service of the Earl of Pembroke in February 1552, then he entered the service of the Duke of Northumberland near the end of the same year. While holding this latter post he wrote a work on tides.
After the death of King Edward VI, there were great problems between Catholics and Protestants as to the succession. The Catholic Queen Mary came to the throne very much against the wishes of many Protestants who feared for their safety. Indeed they were right to have such fears as Mary instigated a campaign against eminent Protestants and one person to be arrested was Roland Dee, John Dee's father, who was taken prisoner in August 1553. He was released, but only after he had been deprived of all his financial assets. John, who had expected to inherit considerable wealth from his father and be in a position to carry out scientific studies free from worries about earning an income, was put in a difficult position. He might have solved his financial problems by accepting a mathematics post at the University of Oxford which he was offered in 1554, but his views on the lack of scholarship in the English universities led him to turn the offer down.
On 28 May 1555 Dee was arrested and charged with "calculating". At this time mathematics in England was considered to be equivalent to the possession of magical powers and Aubrey writes (see [22]) that the authorities had:-
... burned mathematical books for conjuring books.
Although he was guilty of the charges brought against him, Dee was released in August after being held for three months. Although he was released as a free man his sources of income were removed putting him in severe financial problems. Dee's father died in 1555 without being able to recover his wealth. As to Dee's religious position this seems a little harder to ascertain. He seems, with good reason, to have tried to avoid taking sides in the Catholic-Protestant argument, but after his release from prison he seemed completely at home in the Catholic regime which had imprisoned him. He may have changed sides for political convenience, but we shall see in a moment that there is a theory that he was acting as a spy.
Dee presented plans for a national library to Queen Mary on 15 January 1556. It was a superb scheme to preserve learning by finding copies of all important books and keeping them in a Royal Library which men could consult to settle:-
... such doubts and points of learning, as might cumber and vex their heads [and] learning [would] wonderfully be advanced.
The scheme did not receive official backing, but nevertheless Dee, despite his financial difficulties, set out to create his own library. See [7] for the library catalogue from the library that he built up.
Queen Mary died in 1558 and the Protestant Elizabeth became Queen. Dee quickly found favour with Elizabeth and was even asked to use his astrological skills to select the most appropriate day for her coronation. This he did but one is left wondering how someone so closely associated with the previous Catholic administration might have found favour so soon. Woolley [10] suggests that Dee may have acted as a spy for Elizabeth in Mary's administration and this would certainly be consistent with events and explain some otherwise puzzling ones.
During the next five years Dee spent time abroad collecting books for his library, and studying astronomy, astrology, mathematics, coding, and magic - all topics which were linked in his mind as he struggled to understand the ultimate truths about the universe. Despite being close to Queen Elizabeth, and advising her frequently, he never achieved from her the financial security that he longed for to enable him to devote himself completely to his studies. By 1566 he was living with his mother at Mortlake, in London, to reduce his living costs. There he built up a remarkable collection of scholarly works in his library as well as a collection of astronomical instruments, globes (including one given to him by Mercator) and accurate clocks.
In 1568 he published Propaedeumata Aphoristica and presented the work to Queen Elizabeth. Elizabeth was impressed and Dee gave her mathematics lessons to enable her to understand it. The book contains a mixture of good physics and mathematics, and also a lot of astrology and magic. Let us emphasise that we should not think any the less of Dee because of his interests in magic; most of the great scientists and mathematicians of his time, and much later, had such interests. For example Brahe firmly believed in alchemy and astrology as did Cavalieri and Kepler while Newton, like Dee, was obsessed with studying alchemy. Among what we would describe as "good science" in Propaedeumata Aphoristica is a statement that unequal masses fall at the same speed. Dee refers to earlier scientists who also claimed this fact. He also states that every object in the universe exerted a force on all others.
In 1570 Dee edited an edition of Euclid's Elements translated by Billingsley. Dee wrote a famous preface to this edition justifying the study of mathematics:-
O comfortable allurement, O ravishing persuasion to deal with a science whose subject is so ancient, so pure, so excellent, so surrounding all creatures, so used of the almighty and incomprehensible wisdom of the Creator, in distinct creation of all creatures: in all their distinct parts, properties, natures, and virtues, by order, and most absolute number, brought from nothing to the formality of their being and state.
Dee observed the "new star" which is often called "Tycho Brahe's supernova of 1572" and in the following year he wrote Parallacticae commentationis praxosque which gives trigonometric methods which were applied to find the distance to the new star. He had made accurate observations with his assistant Thomas Digges and the two probably corresponded with Brahe about the star. Certainly Brahe greatly admired Dee's contributions.
Dee brought instruments of navigation back from the Continent when he returned in 1551. From 1555 he was a consultant to the Muscovy Company. The Muscovy Company was formed in 1555 by the navigator and explorer Sebastian Cabot together with a number of London merchants. It was granted a monopoly of Anglo-Russian trade and had as one of its aims the search for the Northeast Passage. Dee prepared nautical information, including charts for navigation in the polar regions, for the company during the next 32 years. He instructed the crews on geometry and cosmography before they left for voyages to North America in 1576.
In 1579 Dee's mother gave her house at Mortlake (which he had lived in for at least 13 years) to him; she died the following year. Dee had married Jane Fromands in February 1578 and together they had eight children. She was his third wife - his second wife had died in March 1576 in the year following their marriage. He had no children (at least none that survived) from his first two marriages.
Edward Kelley entered Dee's life in March of 1582. He was a medium who claimed to be able to contact angels and spirits and he did so by gazing into a crystal ball. Although this was not the first time Dee had been involved in such practices, at first he was still highly suspicious that Kelley's visions were real. Two things convinced him, however: Kelley was highly skilled in his art, and secondly Dee so longed to understand the ultimate truth about the universe which he had failed to find by other means. The lack of reaction of others to his scientific work was also a factor, as was the fact that he had been accused of magic so often in his life. Dee became more and more deeply involved in conversing with angels and spirits through Kelley and, sadly, it dominated the latter part of his life. This took place over a period of about five years. Several of the references give details of these conversations which Dee recorded in a diary; see for example [6], [9], and [10]. We note that in his diaries Dee refers to himself as Δ, a clever pun on the fact that Δ is the Greek character for the letter "dee" and also a magical symbol.
Dee made a proposal to Queen Elizabeth for calendar reform in February 1583. He proposed the removal of eleven days to bring the calendar into line with the astronomical year. It was, of course, exactly the right course of action and Dee's proposal gained support from several of Elizabeth's advisors. However, the Archbishop of Canterbury opposed the scheme, partly because he was engaged in a longstanding argument with Elizabeth, partly because he considered such a scheme to be close to what the Catholic Church had adopted in the previous year. Dee's scheme was, however, a better one than that adopted across Europe after the proclamation by Pope Gregory XIII. The Gregorian calendar was based on the date of the Council of Nicaea in 325, while Dee proposed a calendar with an astronomical base rather than a political one as he clearly pointed out. The failure of Dee's calendar reform proposal would mean that England retained a calendar at odds with that in the rest of Europe until 1752.
Dee and Kelley visited Poland and Bohemia (1583-89), giving displays of magic at the courts of princes. Kelley achieved fame and wealth and was knighted. On the other hand Dee, still in severe financial problems, returned to Mortlake in December 1589 to discover that much of his library had been stolen, as were his scientific instruments. Around this time Dee must have become friendly with Thomas Harriot. The two discussed the allegations of atheism made against Raleigh's school and discussed which of them was being referred to as "the conjurer that is master thereof". They also discussed scientific and mathematical matters in the 1590s. In 1590 Harriot sent Dee a copy of one of his books in which he had written "To my dear friend".
For a number of years Dee tried unsuccessfully to gain compensation for the income he had lost over the years. He tried to gain an appointment as Master of St John's Cross which was approved by Queen Elizabeth subject to approval by the Archbishop of Canterbury - but this approval never materialised. In 1596 he was appointed warden of the Collegiate Chapter in Manchester, almost certainly as a means of removing him from London. In 1605 Manchester was hit by the plague and Dee's wife and several of his children died. He returned to London where he died a few years later.
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