阿达·洛夫莱斯Ada Lovelace

奥古斯塔阿达·洛夫莱斯的父亲是著名诗人乔治Gordon Byron勋爵，母亲是安妮·伊莎贝尔·米尔班克。阿达·洛夫莱斯的父母于1815年1月2日结婚，但在1816年1月16日分居，那时她出生才一个月。1816年4月25日，Lord Byron出国，阿达·洛夫莱斯此后再也没有见过父亲。Lord Byron再也没有回到英格兰，在阿达·洛夫莱斯八岁时死于希腊。阿达·洛夫莱斯夫人获得了女儿阿达·洛夫莱斯的单独监护权，后者于1817年4月被宣布为衡平法院受监护的未成年人，她竭尽所能抚养孩子，以确保她不会像父亲那样成为诗人。

阿达·洛夫莱斯夫人本人曾对数学研究感兴趣。Lord Byron在结婚前曾称他未来的妻子为“平行四边形公主”，并于1812年10月18日写信给她（例如参见[3]，其中引用了这封信）：-

我在数学方面也完全同意你的看法——并且只能满足于在不可理解的距离之外钦佩它们——总是把它们加入我遗憾的清单——我知道二加二等于四——如果我能证明这一点我也会很高兴——尽管我必须说，如果通过某种过程我能把二加二变成五，那会给我大得多的乐趣。我记得唯一给我很大乐趣的部分是那些定理（是这个词吗？），在其中在对A、B和C、D等等进行变换之后，我最后来到“这是荒谬的——这是不可能的”，而这一点我总是达到，并且我担心一生中总会达到……

鉴于这种数学心态，Lord Byron显然并不具有，阿达·洛夫莱斯夫人自然应该试图在那个方向上鼓励阿达·洛夫莱斯。此外，她认为数学是训练心智的好科目，可以确保她的女儿采取有纪律的方法。阿达·洛夫莱斯夫人认为，音乐是为女孩提供正确社交技能的主题，因此这在阿达·洛夫莱斯的教育中也受到强调。然而，尽管阿达·洛夫莱斯夫人投入了大量精力来组织阿达·洛夫莱斯的教养，她本人似乎很少与她相处。Lord Byron一定听说过这些问题，因为他于1816年3月1日写信给阿达·洛夫莱斯夫人（例如参见[3]，其中引用了这封信）：-

他们告诉我，年幼的阿达·洛夫莱斯身体很好，并且显示出对保姆和祖母的熟悉程度令人惊叹——也许她该开始认识另一位亲戚了。

Lord Byron在这段引文中提到的祖母是诺埃尔夫人，即阿达·洛夫莱斯夫人的母亲，她与阿达·洛夫莱斯的日常接触确实比阿达·洛夫莱斯的母亲多得多。然而，诺埃尔夫人于1822年去世。

为了指导阿达·洛夫莱斯的教育，家里聘请了多位家庭教师，往往只聘用很短一段时间。大约六岁时，她有一位拉蒙特小姐做家庭教师，尽管母亲强调数学，阿达·洛夫莱斯最喜欢的科目却是地理，而算术她只是为了取悦母亲才勉强学习。在发现阿达·洛夫莱斯更喜欢地理而非算术后，阿达·洛夫莱斯夫人坚持要把阿达·洛夫莱斯的一节地理课换成一节算术课，此后不久，拉蒙特小姐就被替换掉了，不再担任阿达·洛夫莱斯的家庭教师。家里有些人担心阿达·洛夫莱斯夫人坚持对女儿逼得太紧。

阿达·洛夫莱斯夫人不顾家中的事务，不断向女儿施压，要她长时间刻苦学习功课。虽然有时给予一些奖励，但通常施加压力的方式是给阿达·洛夫莱斯惩罚，如单独禁闭、让她一动不动地躺着，并要求她写道歉信，例如（参见[3]）：-

我，阿达·洛夫莱斯，没有把笔记做得很好，但我会努力明天做得更好。

阿达·洛夫莱斯的数学教育由多位私人教师承担。威廉·弗伦德曾教过阿达·洛夫莱斯夫人数学，也参与了阿达·洛夫莱斯的数学教育，但此时他已年迈，未能跟上数学的发展。威廉·金博士也在1829年被聘为阿达·洛夫莱斯的教师，但他对数学的兴趣并不很深，他承认自己学习数学是靠阅读而非实践。他继续提供建议数年，并在1834年与阿达·洛夫莱斯的通信中写道：-

……你很快会在学习中难住我。

很明显，作为家庭教师的King有些力不从心。我们称King为“家庭教师”，因为到1834年，阿达·洛夫莱斯的生活中出现了第二位William King，也就是她次年将要嫁的人。

回到阿达·洛夫莱斯夫人为教十三岁的阿达·洛夫莱斯而聘请的教师，我们还可以提到Arabella Lawrence小姐，阿达·洛夫莱斯夫人指示她改变阿达·洛夫莱斯的“好争论的性情”。很少有人能像阿达·洛夫莱斯夫人那样为塑造孩子的性格付出更多！然而，年轻的阿达·洛夫莱斯长期遭受一些健康问题，并在1829年染上麻疹，花了很长时间才康复。

1833年，阿达·洛夫莱斯被引见入宫，同年6月5日，她在一次聚会上遇到了查尔斯·巴贝奇。两周后，阿达·洛夫莱斯和她的母亲参观了查尔斯·巴贝奇的伦敦工作室，那里展示着差分机。阿达·洛夫莱斯为之着迷，据Sophia Frend——William Frend的女儿、后来成为奥古斯塔斯·德摩根的妻子——记载，她写道：阿达·洛夫莱斯：-

……尽管她年纪尚小，却理解其工作原理，并看到了这项发明的非凡之美。

1834年，当阿达·洛夫莱斯十八岁时，她遇到了玛丽·费尔法克斯·萨默维尔 [3]：-

玛丽·费尔法克斯·萨默维尔夫人给阿达·洛夫莱斯寄数学书，指导她学习，为她出题，最重要的是，与她这位年轻的门生谈论数学。谈话的部分内容涉及查尔斯·巴贝奇和他的机器。查尔斯·巴贝奇和玛丽·费尔法克斯·萨默维尔夫人已是多年好友，并定期通信。

阿达·洛夫莱斯喜欢与玛丽·费尔法克斯·萨默维尔一起参加数学和科学演示，但她也喜欢在其他场合有她作伴。1835年6月，她写信给William King，她未来的丈夫（例如参见[3]，信中引用了这封信）：-

今晚我要去我的朋友玛丽·费尔法克斯·萨默维尔夫人家过夜。她好意提出带我去听音乐会，我对音乐的热爱使我无法拒绝。

阿达·洛夫莱斯金在1838年她的丈夫威廉·金被授予伯爵爵位后成为阿达·洛夫莱斯伯爵夫人，她于1835年7月8日与威廉·金结婚。他们有三个孩子；阿达·洛夫莱斯生于1836年5月12日，安娜贝拉生于1837年9月22日，拉尔夫·戈登生于1839年7月2日。此后，在1841年，阿达·洛夫莱斯开始由奥古斯塔斯·德摩根提供的高等数学学习。

正如我们上面提到的，1833年阿达·洛夫莱斯（当时她仍是这个名字）对查尔斯·巴贝奇的分析机产生了兴趣，十年后，她完成了一篇带注释的费德里科·路易吉的Notions sur la machine analytique de Charles Babbage（1842年）译本。查尔斯·巴贝奇[2]描述了这是如何发生的：-

在[费德里科·路易吉的]关于该主题的论文在《日内瓦万有文库》上发表后一段时间，已故的阿达·洛夫莱斯伯爵夫人告诉我她翻译了费德里科·路易吉的论文。我问她为什么不自己就这个她如此熟悉的主题写一篇原创论文？对此，阿达·洛夫莱斯夫人回答说她没有想到这一点。然后我建议她在费德里科·路易吉的论文中加一些注释；这个想法立即被采纳了。

我们一起讨论了可以加入的各种说明：我提出了几个建议，但选择完全由她自己决定。各个问题的代数推导也是如此，只有与numbers of Bernoulli有关的那个例外，那是我主动提出替阿达·洛夫莱斯夫人做的，以免她费事。这个她寄回给我要求修改，因为她发现我在推导过程中犯了一个严重错误。

阿达·洛夫莱斯伯爵夫人的注释长度约为原论文的三倍。其作者几乎完全进入了与该主题相关的所有极为困难和抽象的问题。

这两篇论文合在一起，为那些能够理解推理的人提供了一个完整的证明——分析的所有展开和运算现在都能够由机器执行。

在被称为“注释”的注解中，阿达·洛夫莱斯描述了分析机如何编程，并给出了许多人认为是第一个计算机程序的东西。她这样描述分析机[6]：-

分析机的独特之处，以及使它能够被赋予如此广泛的功能、有望成为抽象代数得力助手的原因，在于它引入了雅卡尔所设计的原理，即通过穿孔卡片来调控锦缎织物制造中最复杂的花样。两种机器的区别正在于此。差分机中不存在任何类似的东西。我们可以最恰当地说，分析机编织代数图案，正如雅卡尔织机编织花朵和叶子。

她还在注释[6]中写道：-

再者，[分析机]除了数之外，还可以作用于其他事物，只要找到这样的对象，其相互之间的基本关系能够用抽象运算科学的关系来表达，并且这些对象也能够适应发动机的运算记号与机构的作用……例如，假设和声学与音乐作曲科学中音高的基本关系能够进行这样的表达和适应，那么发动机就可以创作出任何复杂程度或篇幅的精巧而科学的音乐作品。

阿达·洛夫莱斯的注释于1843年发表在理查德.泰勒的《科学回忆录》第3卷中，作者署名AAL。这是她成就的巅峰，有一段时间她沉浸在知道AAL是谁的朋友们的钦佩之中，但这些朋友已经对她的健康表示担忧。到那年年底，她因困扰她的各种健康问题而服用多种药物。

注释出版后，她的生活每况愈下，几乎可以肯定缺乏科学项目，尤其是她缺少可以讨论数学和科学问题的朋友，是她衰落的主要原因。当然，她将注释视为自己的第一部数学出版物，并在许多信件中写到她预期将随之而来的许多数学著作。她考虑写一篇长评，也许以她注释的风格，评论格奥尔格·欧姆的著作On galvanic series, mathematically determined，但她寻求鼓励的查尔斯·巴贝奇，因自己为计算机开发筹资缺乏成功而变得沮丧，未能给她必要的支持。1844年，阿达·洛夫莱斯写信给奥古斯塔斯·德摩根的妻子说，由于最近的一场病：-

……我完全无法思考，甚至连我的研究都无法想。我昨天重新开始了；但有一段时间我每天只能给它们半小时到一小时。请告诉奥古斯塔斯·德摩根先生这一切；他一定奇怪为什么没有收到我的信。

阿达·洛夫莱斯曾与几位男性熟人调情，并因此闹出过几桩丑闻。她的丈夫确保销毁了她写给这类朋友的100多封信。此外还有过度饮酒的问题，当饮酒佐餐变成以酒代餐后，情况变得更糟。有一度她考虑根据自身经历写一篇关于鸦片和葡萄酒影响的科学研究。赛马赌博是这些年的另一大嗜好，她典当了一些珠宝来筹措赌资。去世时，她欠下了2000英镑的赌债。

也许如果她的丈夫个性更强，特别是如果他能够与她的智力相匹配，一些问题本可以避免，因为整个家庭是由阿达·洛夫莱斯夫人主导的。然而在1850年前后，阿达·洛夫莱斯与她的母亲闹翻了，几乎可以肯定是在她发现多年来母亲一直就她的父亲Lord Byron对她撒谎时。阿达·洛夫莱斯夫人一生都试图确保她的女儿尽可能与Lord Byron不同，最终阿达·洛夫莱斯发现了母亲操纵的程度。

到1852年1月，阿达·洛夫莱斯饱受疼痛折磨，因为那很可能早已是她一段时间以来健康问题主因的癌症，变得更加严重。然而她的头脑依然像以往一样敏锐。她的丈夫写道（例如见[5]）：-

她的心智因她所款待的知识分子宾客的交往而焕发活力。……她能极其细致地掌握问题的数学方面……她的概括能力确实最为出众，而这又与细致而复杂的分析能力结合在一起。查尔斯·巴贝奇是她恒久的智识伴侣，她总能在他身上找到与自己强大理解力相匹配的人，他们不断的哲学讨论只会带来更多的敬重和相互喜爱。

1852年，年仅37岁的阿达·洛夫莱斯死于癌症。

Augusta Ada Byron's father was the famous poet Lord George Gordon Byron and her mother was Anne Isabelle Milbanke. Ada's parents married on 2 January 1815 but separated on 16 January 1816, a month after she was born. On 25 April 1816 Lord Byron went abroad and Ada never saw her father again. Lord Byron never returned to England and died in Greece when Ada was eight years old. Lady Byron was given sole custody of her daughter Ada, who was declared a Ward in Chancery in April 1817, and she tried to do everything possible in bring up her child to ensure that she would not become a poet like her father.

Lady Byron had been interested in the study of mathematics herself. Lord Byron, before his marriage, had called his future wife "the Princess of Parallelograms" and had written to her on 18 October 1812 (see for example [3] where the letter is quoted):-

I agree with you quite upon Mathematics too - and must be content to admire them at an incomprehensible distance - always adding them to the catalogue of my regrets - I know that two and two make four - and should be glad to prove it too if I could - though I must say if by any sort of process I could convert two and two into five it would give me much greater pleasure. The only part I remember which gave me much delight were those theorems (is that the word?) in which after ringing the changes upon A, B and C, D etc I at last came to "which is absurd - which is impossible" and at this point I have always arrived and I fear always shall through life ...

Given this mathematical frame of mind, which Lord Byron clearly did not share, it was natural that Lady Byron should try to encourage Ada in that direction. Also she considered mathematics a good subject for training the mind to ensure that her daughter took a disciplined approach. Music, Lady Byron believed, was a topic that provided a girl with the right social skills so this was also emphasised in Ada's education. However although Lady Byron devoted much energy to organise Ada's upbringing she herself seems to have spent very little time with her. Lord Byron must have heard about the problems for he wrote to Lady Byron on 1 March 1816 (see for example [3] where the letter is quoted):-

They tell me young [Ada] is well and shows marvellous indications of acquaintance with her nurse and her grandmother - it is perhaps time she should begin to recognise another of her relations.

The grandmother that Lord Byron refers to in this quote was Lady Noel, Lady Byron's mother, who was indeed much more in daily contact with Ada than was her mother. Lady Noel, however, died in 1822.

A number of tutors were employed, often for only a short period, to direct Ada's education. At age about six she had a Miss Lamont as a tutor and, despite her mother's emphasis on mathematics, Ada's favourite subject was geography while arithmetic she only studied reluctantly in order to please her mother. On discovering that Ada preferred geography to arithmetic, Lady Byron insisted that one of Ada's geography lessons be replaced by an arithmetic lesson and shortly after this Miss Lamont was replaced as Ada's tutor. Some members of the family feared that Lady Byron was insisting that her daughter be driven too hard.

Lady Byron ignored the family concerns and kept a constant pressure on her daughter to work hard and long at her lessons. Some rewards were offered but pressure was usually applied by giving Ada punishments like solitary confinement, making her lie motionless, and demanding that she write apologies such as (see for example [3]):-

I, Ada, have not done the Notes very well, but I'll try to do it better tomorrow.

Ada's mathematical education was undertaken by a number of private tutors. William Frend, who had tutored Lady Byron in mathematics, was involved in Ada's mathematical education but by this time he was an old man who had not kept pace with mathematical developments. Dr William King was also engaged as a tutor to Ada in 1829 but his interest in mathematics was not very deep and he confessed that he had studied mathematics by reading it rather than by doing it. He continued to give advice for some years and in correspondence with Ada Byron in 1834 he wrote:-

... you will soon puzzle me in your studies.

It is evident that King, the tutor, was rather out of his depth. We say King "the tutor" since by 1834 there was a second William King in Ada Byron's life, namely the man she would marry in the following year.

Returning to the tutors Lady Byron employed to teach the thirteen year old Ada we might also mention Miss Arabella Lawrence who Lady Byron instructed to change Ada's "argumentative disposition". Few can have done more to mould the character of their child than Lady Byron did! The young Ada, however, had long suffered some health problems and in 1829 contracted measles from which she took a long while to recover.

In 1833 Ada Byron was presented at court and, on the 5 June that year, she met Charles Babbage at a party. Two weeks later Ada and her mother visited Babbage's London studio where the Difference Engine was on display. Ada was fascinated and, according to Sophia Frend, William Frend's daughter and later De Morgan's wife, wrote that Ada:-

... young as she was, understood its working, and saw the great beauty of the invention.

In 1834, when Ada was eighteen years old, she met Mary Somerville [3]:-

Mrs Somerville sent Ada mathematics books, advised her on study, set problems for her, and above all, talked to her young protégée about mathematics. Some of the conversation was about Babbage and his engines. Babbage and Mrs Somerville had been friends for years and corresponded regularly.

Ada Byron enjoyed attending mathematics and scientific demonstrations with Mary Somerville, but she also enjoyed her company on other occasions. In June 1835 she wrote to William King, her future husband (see for example [3] where the letter is quoted):-

I am going this evening to my friend Mrs Somerville's to stay the night. She has kindly offered to take me to a concert, which my love of music could not resist.

Ada King became Countess of Lovelace when her husband William King, whom she married on 8 July 1835, was created an Earl in 1838. They had three children; Byron born 12 May 1836, Annabella born 22 September 1837 and Ralph Gordon born 2 July 1839. It was after this, in 1841, that Lovelace began advanced study in mathematics which was provided by De Morgan.

As we mentioned above, in 1833 Ada Byron (as she still was at that time) had become interested in Babbage's analytic engine and, ten years later, she produced an annotated translation of Menabrea's Notions sur la machine analytique de Charles Babbage (1842). Babbage [2] describes how this came about:-

Some time after the appearance of [Menabrea's] memoir on the subject in the "Bibliothèque Universelle de Genève," the late Countess of Lovelace informed me that she had translated the memoir of Menabrea. I asked why she had not herself written an original paper on a subject with which she was so intimately acquainted? To this Lady Lovelace replied that the thought had not occurred to her. I then suggested that she should add some notes to Menabrea's memoir; an idea which was immediately adopted.

We discussed together the various illustrations that might be introduced: I suggested several, but the selection was entirely her own. So also was the algebraic working out of the different problems, except, indeed, that relating to the numbers of Bernoulli, which I had offered to do to save Lady Lovelace the trouble. This she sent back to me for an amendment, having detected a grave mistake which I had made in the process.

The notes of the Countess of Lovelace extend to about three times the length of the original memoir. Their author has entered fully into almost all the very difficult and abstract questions connected with the subject.

These two memoirs taken together furnish, to those who are capable of understanding the reasoning, a complete demonstration - That the whole of the developments and operations of analysis are now capable of being executed by machinery.

In the annotations, which were called "Notes", Ada Lovelace described how the Analytical Engine could be programmed and gave what many consider to be the first ever computer program. She described the Analytical Engine in the following way [6]:-

The distinctive characteristic of the Analytical Engine, and that which has rendered it possible to endow mechanism with such extensive faculties as bid fair to make this engine the executive right-hand of abstract algebra, is the introduction into it of the principle which Jacquard devised for regulating, by means of punched cards, the most complicated patterns in the fabrication of brocaded stuffs. It is in this that the distinction between the two engines lies. Nothing of the sort exists in the Difference Engine. We may say most aptly that the Analytical Engine weaves algebraical patterns just as the Jacquard loom weaves flowers and leaves.

She also wrote in the Notes [6]:-

Again, [the Analytical Engine] might act upon other things besides number, were objects found whose mutual fundamental relations could be expressed by those of the abstract science of operations, and which should be also susceptible of adaptations to the action of the operating notation and mechanism of the engine . . . Supposing, for instance, that the fundamental relations of pitched sounds in the science of harmony and of musical composition were susceptible of such expression and adaptations, the engine might compose elaborate and scientific pieces of music of any degree of complexity or extent.

Lovelace's Notes were published in Richard Taylor's Scientific Memoirs Volume 3 in 1843 with the author's name given as AAL. This was the high point of her achievements and for a while she basked in the admiration that she received from her friends who knew who AAL was, but already these friends were showing concern about her health. By the end of the year she was taking several medicines for different health problems which troubled her.

Following the publication of the Notes her life deteriorated, almost certainly the lack of a scientific project, and particularly the fact that she lacked friends with whom she could discuss mathematical and scientific problems, being a major reason for her decline. Certainly she regarded the Notes as her first mathematical publication and wrote in many letters about the many mathematical works that she anticipated would follow. She considered writing a long review, perhaps in the style of her Notes, of Ohm's work On galvanic series, mathematically determined but Babbage, whom she looked to for encouragement, was becoming depressed at his own lack of success with financing the development of his computers and failed to give her the necessary support. In 1844 Lovelace wrote to De Morgan's wife saying that because of a recent illness:-

... I have been utterly unable to think even of my studies. I yesterday resumed them; but for some time I must only give them half an hour to an hour a day. Pray tell Mr De Morgan all this; he must wonder at not having heard from me.

Lovelace flirted with several of her male acquaintances and there were several scandals. Her husband made sure that over 100 of her letters to such friends were destroyed. There was also a problem with over indulgence in wine which became worse when drinking with her meals changed to drinking instead of meals. At one point she considered writing a scientific study of the effects of opium and wine gained from her own experiences. Gambling on horses was another passion in these years and she pawned some of her jewels to finance it. She owed £2000 in gambling debts when she died.

Perhaps had her husband been a stronger personality, particularly had he been able to match her intellectual abilities, some of the problems might have been avoided, for it was Lady Byron who dominated the whole family. However around 1850 Lovelace fell out with her mother, almost certainly when she discovered that for years her mother had lied to her about her father Lord Byron. Lady Byron had tried all her life to make sure her daughter was as different from Lord Byron as possible and eventually Lovelace discovered the extent of her mother's manipulation.

By January 1852 Lovelace was wracked with pain, as the cancer which presumably had been a major cause of her health problems for some time, became more acute. Her mind however remained as sharp as ever. Her husband wrote (see for example [5]):-

Her mind was invigorated by the society of the intellectual men whom she entertained as guests. ... She mastered the mathematical side of a question in all its minuteness ... her power of generalisation was indeed most remarkable, coupled as it was with that of minute and intricate analysis. Babbage was a constant intellectual companion and she ever found in him a match for her powerful understanding, their constant philosophical discussions begetting only an increased esteem and mutual liking.

In 1852, when only 37 years of age, Ada died of cancer.