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**几十年来，他让人们**

**迷醉于数学之中**

F or D ecades，

Puzzling People with Mathematics

For today's mathematical puzzle, assume that in the year 1956 there was a children's magazine in New York named after a giant egg, *Humpty Dumpty, who purportedlyz served as its chief editor.

说到今天的数学趣题，会想到1956年时纽约有一本儿童杂志，名字取自一个大蛋形人，日日汉普蒂·邓普蒂，他足这本杂志的名义主编。

Mr. Dumpty was assisted by a human editor named Martin Gardner, who prepared "activity features" and wrote a monthly short story about the adventures of the child egg, Humpty Dumpty Jr. Another duty of Mr. Gardner's was to write a monthly poem of moral advice from Humpty Sr. to Humpty Jr.

邓普蒂先生有个真人编辑做帮手，名叫马丁·加德纳他负责编写“儿童活动特写”栏目的内容，并目_每个月写篇小故事，讲述蛋形人的孩子小汉普蒂·邓普蒂的历险记。加德纳每个月的另一个任务足写一首诗，模仿老汉普蒂·邓普蒂的日吻给小汉普蒂·邓普蒂讲述做人的道理。

At that point, Mr. Gardner was 37 and had never taken a math course beyond high school. He had struggled with calculus and considered himself poor at solving basic mathematical puzzles, let alone creating them. But when the publisher of Scientific American asked him if there might be enough material for a monthly column on "recreational mathematics," a term that sounded even more oxymoronic in 1956 than it does today, Mr. Gardner took a gamble.

那时，加德纳37岁，自高中以后再也没有上过一节数学课微积分足令他头疼的东西，他自认为不擅解决基本的数学趣题，更不要说出题了。但是当《科学美国人》杂志的出版人问他能否凑够材料来出一个“趣味数学”(1956年，“趣味数学”这个词听上去要比今天显得史自相矛后)每月专栏时，加德纳决定贴一把。

He quit his job with Humpty Dumpty.

于是，他辞去了《汉普蒂·邓普蒂》杂志的工作。

On Wednesday, Mr. Gardner will celebrate his 95^{th} birthday with the publication of another book-his second book of essays and mathematical puzzles to be published just this year. With more than 70 books to his name，he is the world’s best-known recreational mathematician, and has probably introduced more people to the joys of math than anyone in history.

本周三(10月21日)，加德纳将庆祝他的95岁寿辰，同时另一本书也要出版，这是他今年将要出版的第一本收录随笔和数学趣题的书。一生出书70多本的他，是世界上最著名的趣味数学家，他启发人们去享受数学的乐趣，其感召力或许无人能及。

How is this possible?

这是怎么实现的呢?

Actually, there are two separate puzzles here. One is how Mr. Gardner, who still works every day at his old typewriter, hasvmanaged for so long to confound and entertain his readers. The other is why so many of us have never been able to resist this kind of puzzle. Why, when we hear about the guy trying to ferry a wolf and a goat and a head of cabbage across the river in a small boat, do we feel compelled to solve his transportation problem?

实际上，这里有两个小同的问题一是每天仍然还在老式打字机上工作的加德纳是靠什么挑战读者的脑筋并愉悦读者的，而且还坚持了这么长的时间。另外就是为什么我们中有这么多人总是无法抗拒这种谜题的诱惑。当我们听到有个人想把一只狼、一只羊和一颗圆白菜用一条小船运到河对岸去，为什么我们会按捺小住地要去解决这个摆渡难题呢?

It never occurred to me that math could be fun until the day in grade school that my father gave me a book of 19th-century puzzles assembled by Mr. Gardner-the same puzzles, as it happened, that Mr. Gardner's father had used to hook him during his school days. The algebra and geometry were sugar-coated'' with elaborate stories and wonderful illustrations of giraffe races, pool-hall' squabbles, burglaries and scheming carnival" barkers.

我从来没有想到数学能这么有意思，直到上小学的某一天父亲送给我一本书，上而是加德纳收录的19世纪数学趣题—碰巧那也是加德纳的父亲在他上学的时候曾拿来吸引他兴趣的难题。代数学和几何学被包裹上精巧的故事和美妙的插图，如长颈鹿赛跑、台球房里的日角、夜盗行为以及诡计多端的游艺场拉客者。

The puzzles didn't turn Mr. Gardner into a professional mathematician-he majored in philosophy at the University of Chicago-but he remained a passionate amateur through his first jobs in public relations and journalism. After learning of mathematicians' new fascination with folding certain pieces of paper into different shapes, he sold an article about these "Hexagons';" to Scientific American, and that led to his monthly "Mathematical Games" column, which he wrote for the next quarter-century.

那些趣题虽没有让加德纳成为职业数学家—他在芝加哥大学主修哲学—但他在公关和新闻行业从事最初几份工作时，一直都是个热情的数学爱好者。当他得知数学家们对把一定量的纸折成小同形状产生兴趣之后，便把一篇有关“折纸”的文章卖给了《科学美国人》，于是就有了后来每个月的“数学游戏”专栏，这一写就是25年.

Mr. Gardner prepared for the new monthly column by scouring Manhattan's second-hand bookstores for math puzzles and games. In another line of work, that would constitute plagiarism, but among puzzle makers it has long been the norm a good puzzle is forever.

为了撰写这个新开的每月专栏，他遍览曼哈顿的二手书店，寻找数学趣题和游戏。如果小是在这一行，这种做法恐有抄袭之嫌，但是对于智力题编撰者来说，这却是他们长久以来的惯例:好的智力题跨越时空。

For instance, that puzzle about ferrying the wolf, the goat and the cabbage was included in a puzzle collection prepared for the emperor Charlemagne 12 centuries ago-and it was presumably borrowed by Charlemagne's puzzlist. The row-boat problem has been passed down in cultures around the world in versions featuring guardsvand prisoners, jealous spouses, missionaries, cannibals'' and assorted carnivores".

例如，那个关于把狼、山羊和圆白菜摆渡过河的趣题就曾访日分灵存一术1200年前的智力题集中，它是专门为查理曼大帝所编的—有人推测它也是查理曼手下出题人借用来的划船问题在世界各地的文化中流传，衍生出各种版本，有卫兵与罪犯、醋坛子夫妻、传教士、食人族与各种食肉动物等等。

"The number of puzzles I've invented you can count on your fingers," Mr. Gardner says. Through his hundreds of columns and dozens of books, he always credited others for the material and insisted that he wasn't even a good mathematician.

加德纳说:“我自己编写的智力题屈指可数”在他的数百篇专栏和数学一本书中，他总是感谢别人提供了索材，并坚持说自己连一个好的数学家都算不上。

"I don't think I ever wrote a column that required calculus," he says. "The big secret of my success as a columnist was that I didn't know much about math.

他说:“我想我写的专栏里没有哪一篇用得上微积分的我的专栏之所以成功，最大的秘诀在于我对数学知之甚少。”

"I had to struggle to get everything clear before I wrote a column, so that meant I could write it in a way that people could understand."

“在写专栏前我一定会竭力搞懂所有的东西，这就意味着我能把它写得通俗易懂。”

After he gave up the column in 1981, Mr. Gardner kept turning out essays and books, and his reputation among mathematicians, puzzlists and magicians just kept growing. Since 1994, they have been convening in Atlanta every two years to swap puzzles and ideas at an event called the G4G: the Gathering for Gardner.

1991年停比专栏写作之后，加德纳仍然笔耕小辍，撰文、出书，而他在数学家、智力题出题人和魔术师中的声誉也继续与日俱增从1994年开始，这些人每两年要在亚特兰大聚会一次，交换智力题和观点创意这个活动被称为G4G，即“加德纳聚会。”

"Many have tried to emulate" him; no one has succeeded," says Ronald Graham, a mathematician at the University of California, San Diego. "Martin has turned thousands of children into mathematicians, and thousands of mathematicians into children."

加州大学圣迭戈分校的数学家罗纳德·格雷厄姆说:“许多人试图模仿他，但没有人成功。马丁让成千上万的孩子变成了数学家，也把成千上万的数学家变成了孩子。”

Mr. Gardner says he has been gratified to see more and more teachers incorporating puzzles into the math curriculum. The pleasure of puzzle-solving, as he sees it, is a happy byproduct of evolution.

加德纳说，他很欣慰地看到越来越多的老师把智力题融入数学课教学中如他所见，解智力题的快感是进化的一个副产品。

"Consider a cow," he says. "A cow doesn't have the problem-solving skill of a chimpanzee, which has discovered how to get termites out of the ground by putting a stick into a hole.

他说:“比如说一头牛，它就小具备黑猩猩的解决问题能力，后者知道如何把棍子伸进自蚁洞里掏出自蚁来”

"Evolution has developed the brain's ability to solve puzzles, and at the same time has produced in our brain a pleasure of solving problems."

“进化使大脑发展出解决谜题的能力，同时也让我们的大脑中产生出解决问题的快感。”

Mr. Gardner's favorite puzzles are the ones that require a sudden insight. That aha! moment can come in any kind of puzzle, but there's a special pleasure when the insight is mathematical- and therefore eternal, as Mr. Gardner sees it. In his new book, "When You Were a Tadpole'"and I Was a Fish," he explains why he is an "unashamed" Platonist" when it comes to mathematics.

加德纳最喜欢的一类智力题是那些需要灵机一动的智力题在他看来，手毛何一类智力题都可能出现这种“哎呀，原来如此”的时刻，但足数学上的这种顿悟是一种很特别的愉悦，所以也是永恒的在他的新书《你是州州，我是角》中，他解释了为什么在数学方而他是个“毫小讳言的柏拉图主义者”。

"If all sentient beings in the universe disappeared," he writes, "there would remain a sense in which mathematical objects and theorems would continue to exist even though there would be no one around to write or talk about them. Huge prime numbers would continue to be prime even if no one had proved them prime."

他写道:“假女日宇宙间有感知力的生命全部消失，仍会留有-种感觉，即数学对象和数学定理将永存，纵使没有人写卜来或者谈论它。即使无人加以证明，但那些大质数仍然是质数。”

I share his mathematical Platonism, and I think that is ultimately the explanation for the appeal of the puzzles. They may superficially involve row boats or pool halls or giraffes, but they're really about transcendent numbers and theorems.

我对他在数学上的柏拉图主义抱有同感，我认为这最终解释了智力题的魅力所在。表而上看，它们说的是划船、台球房或长颈鹿等等，但实际上讲的却是超验的数字和定理。

When you figure out the answer, you know you've found something that is indisputably true anywhere, anytime. For a brief moment, the universe makes perfect sense.

当你找到答案，你就会知道你发现了放之四海而皆准的东西。在这一刹那，宇宙变得完全合情合理。

(涂颁译自The New York Times Oct. 20, 2009)