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[英漢文摘] 幾十年來,他讓人們迷醉于數學之中

幾十年來,他讓人們

迷醉于數學之中

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.

說到今天的數學趣題,會想到1956年時紐約有一本兒童雜志,名字取自一個大蛋形人,日日漢普蒂·鄧普蒂,他足這本雜志的名義主編。

    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.

鄧普蒂先生有個真人編輯做幫手,名叫馬丁·加德納他負責編寫“兒童活動特寫”欄目的內容,并目_每個月寫篇小故事,講述蛋形人的孩子小漢普蒂·鄧普蒂的歷險記。加德納每個月的另一個任務足寫一首詩,模仿老漢普蒂·鄧普蒂的日吻給小漢普蒂·鄧普蒂講述做人的道理。

    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.

    那時,加德納37歲,自高中以后再也沒有上過一節數學課微積分足令他頭疼的東西,他自認為不擅解決基本的數學趣題,更不要說出題了。但是當《科學美國人》雜志的出版人問他能否湊夠材料來出一個“趣味數學”(1956年,“趣味數學”這個詞聽上去要比今天顯得史自相矛后)每月專欄時,加德納決定貼一把。

 

    He quit his job with Humpty Dumpty.

于是,他辭去了《漢普蒂·鄧普蒂》雜志的工作。

    On Wednesday, Mr. Gardner will celebrate his 95th 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),加德納將慶祝他的95歲壽辰,同時另一本書也要出版,這是他今年將要出版的第一本收錄隨筆和數學趣題的書。一生出書70多本的他,是世界上最著名的趣味數學家,他啟發人們去享受數學的樂趣,其感召力或許無人能及。

 

    How is this possible?

這是怎么實現的呢?

   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?

    實際上,這里有兩個小同的問題一是每天仍然還在老式打字機上工作的加德納是靠什么挑戰讀者的腦筋并愉悅讀者的,而且還堅持了這么長的時間。另外就是為什么我們中有這么多人總是無法抗拒這種謎題的誘惑。當我們聽到有個人想把一只狼、一只羊和一顆圓白菜用一條小船運到河對岸去,為什么我們會按捺小住地要去解決這個擺渡難題呢?

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.

我從來沒有想到數學能這么有意思,直到上小學的某一天父親送給我一本書,上而是加德納收錄的19世紀數學趣題—碰巧那也是加德納的父親在他上學的時候曾拿來吸引他興趣的難題。代數學和幾何學被包裹上精巧的故事和美妙的插圖,如長頸鹿賽跑、臺球房里的日角、夜盜行為以及詭計多端的游藝場拉客者。

    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.

    那些趣題雖沒有讓加德納成為職業數學家—他在芝加哥大學主修哲學—但他在公關和新聞行業從事最初幾份工作時,一直都是個熱情的數學愛好者。當他得知數學家們對把一定量的紙折成小同形狀產生興趣之后,便把一篇有關“折紙”的文章賣給了《科學美國人》,于是就有了后來每個月的“數學游戲”專欄,這一寫就是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.

為了撰寫這個新開的每月專欄,他遍覽曼哈頓的二手書店,尋找數學趣題和游戲。如果小是在這一行,這種做法恐有抄襲之嫌,但是對于智力題編撰者來說,這卻是他們長久以來的慣例:好的智力題跨越時空。

    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,那個關于把狼、山羊和圓白菜擺渡過河的趣題就曾訪日分靈存一術1200年前的智力題集中,它是專門為查理曼大帝所編的—有人推測它也是查理曼手下出題人借用來的劃船問題在世界各地的文化中流傳,衍生出各種版本,有衛兵與罪犯、醋壇子夫妻、傳教士、食人族與各種食肉動物等等。

    "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.

加德納說:“我自己編寫的智力題屈指可數”在他的數百篇專欄和數學一本書中,他總是感謝別人提供了索材,并堅持說自己連一個好的數學家都算不上。

    "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.

他說:“我想我寫的專欄里沒有哪一篇用得上微積分的我的專欄之所以成功,最大的秘訣在于我對數學知之甚少。”

    "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."

“在寫專欄前我一定會竭力搞懂所有的東西,這就意味著我能把它寫得通俗易懂。”

    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年停比專欄寫作之后,加德納仍然筆耕小輟,撰文、出書,而他在數學家、智力題出題人和魔術師中的聲譽也繼續與日俱增從1994年開始,這些人每兩年要在亞特蘭大聚會一次,交換智力題和觀點創意這個活動被稱為G4G,即“加德納聚會。”

 "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."

加州大學圣迭戈分校的數學家羅納德·格雷厄姆說:“許多人試圖模仿他,但沒有人成功。馬丁讓成千上萬的孩子變成了數學家,也把成千上萬的數學家變成了孩子。”

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.

加德納說,他很欣慰地看到越來越多的老師把智力題融入數學課教學中如他所見,解智力題的快感是進化的一個副產品。

 "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.

他說:“比如說一頭牛,它就小具備黑猩猩的解決問題能力,后者知道如何把棍子伸進自蟻洞里掏出自蟻來”

"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."

“進化使大腦發展出解決謎題的能力,同時也讓我們的大腦中產生出解決問題的快感。”

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.

加德納最喜歡的一類智力題是那些需要靈機一動的智力題在他看來,手毛何一類智力題都可能出現這種“哎呀,原來如此”的時刻,但足數學上的這種頓悟是一種很特別的愉悅,所以也是永恒的在他的新書《你是州州,我是角》中,他解釋了為什么在數學方而他是個“毫小諱言的柏拉圖主義者”。

  "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."

他寫道:“假女日宇宙間有感知力的生命全部消失,仍會留有-種感覺,即數學對象和數學定理將永存,縱使沒有人寫卜來或者談論它。即使無人加以證明,但那些大質數仍然是質數。”

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.

 我對他在數學上的柏拉圖主義抱有同感,我認為這最終解釋了智力題的魅力所在。表而上看,它們說的是劃船、臺球房或長頸鹿等等,但實際上講的卻是超驗的數字和定理。

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.

當你找到答案,你就會知道你發現了放之四海而皆準的東西。在這一剎那,宇宙變得完全合情合理。

    (涂頒譯自The New York Times Oct. 20, 2009)

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幸运28是国家开奖的吗