The universe in the handcuffs - The the universes in a handkerchief: Lewis Carroll
Seraph chutium - http://com.6to23.com/
Welcome to my message discussion: http://two.guestbook.de/gb.cgi?gid=584097&prot=uhsaif&
The book here is:
Martin Gardner,
The Universes IN A Handkerchief: Lewis Carroll ''s Mathematical Recreations, Games, Puzzles and Word Playscopernicus Springer-Verlag, 1996.
I sent this book in the mail on October 20, 1996. But I have been putting it in early 1999 to start reading. After reading, it happened to the day of Carroll one hundred and sixty-seven years old. It is also very close to the one hundred and anniversary of his death. It is a coincidence.
Gardner is not a mathematician, but in the mathematics circle, the name is not in the Won of Faulz. There is a column writer of Siam News (he is a mathematician, who is appointed in Brown University Applied Mathematics), appeals to mathematics agencies should consider a doctoral degree to Gardner. To thank his life for the contribution to mathematics. The introduction of Gardner is not that I have to record in this reading report. But I will not want to come with a few words.
After Gardner retired, Gardner has traveled over a causing day. About the 1950s, he was recommended to write a few articles on mathematics games for Scientific American. It may be that the reader has a good reaction, or it may be the editorial committee. His article developed into a column of mathematics entertainment, and he became a column writer and wrote a special article for every month. I wrote this for more than 30 years. After he retired, the past column articles will be added to the past, and they have been successfully published again, until 1998. Even serious mathematicians, mostly agreed, his mathematics entertainment article is not full of skin. In fact, he is known as the first good hand of rigorous and abstract mathematics by entertainment and game. Sometimes, even if the professional mathematicians of the inner line are also easily described by his easy, home, interesting and absolutely correct narrative. His article is no longer just entertainment. He can actually introduce very abstract and advanced mathematics, introduce the social love from ordinary education. In other words, his column articles can be seriously entered into the mathematics class. But Gardner did not have any mathematical degree.
I am most curious, not how Gardner understands those mathematics? How to write those articles? What I want most is that who introduces him to Scienific American? Who recommended him to serve as this job? Who will support him in his back? It was still so young, there was no correct degree, and there was no obvious experience. Who is it, I found him and dared to deliver this responsibility to him? My most feeling, not Gardner's genius and luck, but his society. Compare our own society, we must imagine, fifty years ago, it is already how open, fair and sound. I used to think that the United States is strong because of his liberal democracy. Later I think these are just the system. A deeper point is that this system makes a society more likely to become a healthy society. I am so called, simply, "I have a most appropriate person on every seat." Therefore, a benign cycle can begin. That proper person will work in his part. Because there is a proper person to do something that is not your own, everyone can work with their appropriate work wholeheartedly. Because some people who have appropriate talents are sitting in the appropriate seat, they will be appropriate when he wants to make judgments. Because of his proper talent, and the clear understanding of him, when he chooses a successor, it is certainly appropriate. This is what I called. I always imagine that when Gardner is young, there must be an appropriate vision with appropriate position, recognize his talent, so give him an appropriate seat. Maybe as sang in the American national anthem, God bless the United States. At the beginning of her, there was Washington and there were Jefferson, Franklin and Adams. Suppose her benign circular pipeline began to establish it, then her society has been strong for three hundred years, can it be strong? For our society, I believe it must be more than one hundred years ago, even more than 20 years ago. However, its sound pipeline is obviously not smooth enough, especially in bureaucratic systems. Perhaps, the Chinese youths that will be able to gradually change the old blood in the 21st century, which makes our society and sound. Go back to the original theme. Lewis Carroll is the pen name of Charles Lutwidge Dodgson. He was born on January 27, 1832, died on January 14, 1898. In 1865, Alice ''s Adventures In Wonderland was published. Seven years later (1872) published a similar sequel in the THROUGH THE LOOKING GLASS. He has a mathematical degree, graduated from Oxford at the age of 22, and stayed in that college as a mathematics teacher and lifelong. Although his life did not make a significant contribution in mathematics, he did not publish how many passions were published. But through other works, it also makes superior contributions to the overall mathematics, and the attitude of the public to mathematics. Therefore, it is necessary to have a person who is in place at the time, giving the appropriate seat of Carroll. This proper person is likely to be Henry Liddell. Two Alice in Alice in the love of Alice, all of Alice Liddell. Carroll likes children, and has made many children and leave hundreds of letters written to many different children. Alice three sisters are his good friend, and they are Henry Liddell daughters, and Mr. Liddell is the seniors of Christ Church College.
The best translation of Alice roaming, of course, is the version of Mr. Zhao Yuan. At the end of 2000, the translation of Mr. Zhao used Mr. Zhao, with a new illustration of the Award in Europe in 1999, re-moved the book on Taiwan's children's book market, and the reaction was warm. Mr. Zhao also continued to translate the mirror after returning to the country, but unfortunately the original is ruined. He may have rewritten in his later years, but there is no formal publication, but it is published in the 2nd book of the three books in his compiled, I have never seen this book. In mathematics, Carroll has some original contribution to logic and chance, but it is insignificant than his literary work. His handed down is the aforementioned two Alice. In addition, he also wrote several books like Alice travel: The hunting of the snark (1876), two series Sylvie and Bruno (1889, 1893); they all contain many mathematics, logic, benefit Wisdom games and a variety of strange English poems. In addition, he left a thousand sings and notes, many of the small manuals describing the playing card or English writing gameplay. He is still a famous and creative amateur photographer. In short, he has circulated the name of the later generation, not mathematician, but a writer and "player". (In Taiwan, there is also a gentleman who claims to be writer and players, but I don't intend to compare the talents and ability of these two people. This is not very fair.)
Also until today, many Carroll fans have been retained. Discussing him with a special book of this person. In the United States, there is a Carroll Association, which is probably more mature than the songs participating in the teenagers. When Gardner read Alice tour after Middle age, Gardner began to interested in Carroll's character, and later, it was more in-depth, the more found it, the two were in essence. Therefore, gradually Gardner became one of the authoritative characters of Carroll. This book, in addition to collecting the mathematical game creation of the story book, letters, diary, and small manual, and collects some other creations, including the strange poems, English writing games, and cards. . Three small manuals in the unnamed printing were also typed in the first rules, describing several kinds of CARROLLs invented the rules of the game. So this book has functions that collect, organize and archae.
Just start from the title of this book. What is "the universe in the handcuffs"? That is in the second volume of sylvie and bruno, Mein Herr performs how to use two stand-in-one pockets with two stand-up signs to the Lady Muriel. This is the promotion of Mobius, which is the famous Klein bottle. Because it is, it is inside, so it contains all the outside. Therefore, it is exaggerated that this pocket contains the full universe. There is a print illustration in the book. But there is no career from the original content. Interested parties can go to check the original text, there is currently a revision version of Dover (1988). In fact, as long as the reader knows how to make Mobius belts, it is not difficult to imagine how to make this pocket.
Carroll has many special functional poems. Some correspondence to our "崁 崁", some are not easy to find corresponding in Chinese literature (probably because I am ignorant). For example, the following famous 崁崁 poems, writing in the mirror, hiding the real name of the heroism of Alice dreaming of the fairyland. Just read each of the first letters of each line, you will find the answer. "Forest is translated", including the translation of Mr. Zhao Yuan, the translation of the translation of the translation of the translation of the translation of the translation.
A Boat, Beneath a sunny skyling, beneath a sunny skylining of july --- 阳 照 小 天 天 天 天 天 天 天 天 天 天 , PLLASED A SIMPLE TO HEAR --- Toddler Three Three Leaning on the Pillow The Ears Wish I want to listen to the story. I want to have a story. LONG HAS PALED THAT SKY; Echoes Fade and Memories Die; Autumn Frosts Have Slain July. That year Scholars blocked ,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,, Tale to Hear, Eager Eye and Willing Ear, Lovingly Shall Nestle Near. There is also a child. I will want my eyes. I'm squeezing. I should squeeze people Telling in a Wonderland, Dreaming as the day, dreaming as the summers Die: It is the dream of dreams, dreams, dreams, dream, dream, dream, DRIFTING, DOWN, THEAM --- LINGERING in the golden gleam --- life, what is it but a dream? Follow the water Following the sun and looked at the life. If you are a dream, you are not bad to recite Zhao Yuan's translation, there is a very moving taste. But Mr. Zhao's translation poem did not take the name of Alice into it. Her full name is Alice Pleasance Liddell, if the voice is translated into Chinese, may be the word "Alice · Puertois Lidel" or other homophonic. Chinese people are not difficult to use this ten words and do a word poem. In the poem, three children should refer to Alice Liddell and other three sisters. There is another poem that darkly refers to the three sisters. The three Liddell hide in poetry for a long time before they discovered:
All in The GoldenAfternoon
Full Leisurely We glide;
For Both Our Oars, with
LittleSkill,
BY
Littlearms Are Plied,
While
Littlehands make Vain Pretence
Our Wanderings to Guide.
The first poem appeared three little Little, just right and Liddell rhyme. This is a gift from Carroll to the Liddell three sisters. Talking about Carroll's special poems, most interesting is a "symmetric poem":
I offen wondered gen i CURSED, I OFTEN WONDERED WHEN I. CURSED OFTEN FEARED WHERE I Would Be --- Offen Fere I Would Be Wondred Where She ''d Yield Her Love, Wondred Where She''d Yield Her Love When i Yield , So Will She Pitied! I Would Her Will Be Pitied! I Would Her Will Be Pitied CURSED BE Love! She Pitied Me ... CURSED BE LOVE SHE PITIED ME This poem is six columns, each column 6 A word. If you ignore the punctuation, the thirty-six words in the poem are neatly arranged, see it? This is a symmetric matrix of sixteen six. That poem, no matter how it is reading or reading, it is the same! Chen Sili, the Eighth Central University of the Chinese University, made a symmetrical campmine poem, she put the "Alice Dream of Xiu Xianjing" on the diagonal of the poem. Liu Dexin, a mathematics, eight eight, has also created a symmetrical poem, and her work seems to be an ornament with a commercial value. Because both works are very wonderful, it is included in this.
Eshan Le Shui Yi leisurely mountain Lichuan show refreshing heart Hui Chuanz distorted East to the water show sentiment dreams to the worsi, the ultimate, the singer, the singer, the singer, the singer, the singer, the singer, the singer, the singer, the singer, the singer, the singer, the singer, the singer, the singer, the singer, the singer, the singer] Tolerance is non-vestigial people who are not afraid of laid
In both mathematics games, Carroll has some puzzle issues suitable for beginners. For example, he asked, in the middle of the following formula, any X, how does the answer is always X?
(x 7 10) * (1000-8) ------------------------ - 17992
He asked a question in a letter to a little boy. Let X = 1 and y = 1, then 2 * (x2-y2) = 0 and 5 * (x-y) = 0. Therefore, 2 * (x2-y2) = 5 * (x-y) is now removed from the (x-Y) of the equation to obtain 2 * (x y) = 5. But X Y = 2, so 2 * 2 = 5. what happened?
In addition to algebra games, he has more logic and opportunities. The logic is interlaced, and it often appears in his book and is fascinating. The Carroll is one of the people who will co-invented and promoted symbolic logic. Many of his logic can make it clear after using symbolic operations. Sometimes it is a Boolean operation, sometimes it is a collection picture. For example, McCarthy, which creating artificial intelligence, has borrowed Carroll's logical puzzle, as an application example of LISP program language (this is McCarthy creation, not Carroll). Suppose Cheshire Cat said to Alice
Either I am Mad or the Hatter is Mad
Repeatedly
Either you or the harder is MAD
Then
Only One of the Three of US IS MAD
If CHSHIRE CAT is true, and we use A represents Alice is Mad, with C represents CAT is mad, and C represents Hatter is mad. Then the first two sentences are logical symbols.
(("
C OR
H) and
A OR
H))
This narrative is true, must
(
C OR
H) True and
A OR
H) true
These two are true, and there is only one true in A, C, and, obviously visible to H true. In other words, only Hatter has been crazy. Often, Carroll logic games may not appear in the form of complex relationships, but only extremely violated the normal and creative, making readers mistaken. For example, in the mirror, there is a similar design of a butterfly dream with Zhuangzi. When the Red King dreams to Alice, she just asleep dreams of the king. Alice in the Dream of the Red King also dreams this red king. This is such an unlimited backup relationship. In the end, Alice didn't dare to be sure. Who is real, who is dreaming? Another example is, if you are often quoted when discussing modern information society: "You must run more quickly, you can stay in the same place." This situation is not very appropriate to reach a modern rapid change in modern times?
Carroll is also some original discovery in terms of chance. We will give two examples. These two issues appear inside the "Pillow Problems" published in 1893. At first he used a subtitle Thought Out During Sleepless Nights. At the time of retest, Carroll used a relatively positive statement; he changed the "Sleepless Nights" to "Wakeful Hours". It seems to have changed from the "repeated war and repeated defeat" to "repeated defeat".
There are seventy-two problems in this booklet, many of the probability. For example, consider a bag, which can be used as a black or white ball. If you put a white ball, then take a ball at random, and that is a ball is white. What is the chance of the ball in the bag in the bag? Of course, the answer is no longer 1/2. Imagine another situation, if you take a black ball after being put into the white ball, then the bag is a white ball, it will be 1. That is, when we have made some experiments on an unknown collection, we have obtained some information, so it can do more accurate judgment.
The second example is actually a joke. But Carroll is written in the book through eight hundred fields. This is the last question of his seventy-two questions! Perhaps his joke is to tell us that it is too harmful to life, and even his head is confused. He said that if there are two balls in a bag, each is black or white, he can prove that the two balls must be a black white. The following is his "prove". Two balls in the bag, the chance of two blacks is 1/4, and the chance of the interior is 1/4. The chance of one black white is 1/2 (the same size is the same, no order difference). Suppose it is now put into a black ball, then the chance of three blacks is 1/4, and the chance of black two white is also 1/4, and the chance of two black is 1/2. Now, the chance of taking a black ball from this bag with three balls is
(1/4 * 1) (1/4 * 1/3) (1/2 * 2/3) = 1/4 1/12 1/3 = 8/12 = 2/3
Conversely, if a black ball is drawn from a bag with three black or white balls is 2/3, then there are two black balls and one white ball in the bag. We know that it is a black ball that just put it, so, there is no previous two balls, it must be a black white. "Say".
Carroll has a lot of invention, some of which are very popular today. For example, in the 1887 inventive algorithm, he can get any number of weeks of a DC date. This algorithm will also appear in many children's books or math entertainment books. Professor Princeton's Conway published a more simplified algorithm in 1973 at Eureka. Many people have heard a puzzle issue: someone carries a wolf, a sheep and a broth, he can only bring the same thing once, so when he is in the river, There are two things to stay on the shore. But you can't keep the wolf and your sheep, because the wolf will eat sheep; you can't leave the sheep and glasses, because the sheep will eat altitude. How do you cross the river? This is also the problem of the inventions of Carroll. In addition, such as using 1/7 of the circular festival number (142857) playing, and using 12345679 * 9 = 11111111, this fact is often played, and these are often in today's mathematical entertainment, which is also the invention of Carroll. There is also a problem, I think it has exceeded the range of "puzzle". It is a very serious problem. If a pulley is fixed on the roof, across a rope on the pulley so that it is naturally sagged. Now bring a monkey, and a lead block with monkeys. If the lead block is laid on the tail end of the rope on the side of the pulley, and pull it up in the air; then let the monkey catch on the other side of the rope, and the lead block is contrary. Excuse me, when the monkey climbs the rope and even temporarily loosen the hand, how will the other side change its height? Carroll presents this issue in 1893, which is discussed earnestly near the physics and mathematicians.
Carroll is obviously a person with strong "text". Among the many English writing games invented by his, I am the most fascination, or a word Links or a Word Ladder. He mentioned this game design in the diary in 1878. There are two kinds of gameplay. Perhaps you can have a question of one person, that is, an English word, other people think about a word, the letter length of each word needs to be with the previous word, and only one letter is different. A bit like I often play Chinese text interface games. But the usual rules of the interface game are connected to the heads of the two words. Another way of play is a question of someone, specifies the first and tail, and see who is the fastest way to find the shortest path. It should be noted that this topic may not be impossible. For example, from a set of pairs of cold (WARM), and one of the shortest paths evolved from the orangutan (APE) to the shortest path of human (Man),
ColdcordCardwardWARM ApeAptoptoatmatman
SwordsworesporesparespacespateskateslateplatePlacepece The University of Stanford is also a famous person with a famous person. He also wrote a computer program to help him play this game. He uses the model of graphh, which is identified as the length but only one letter is "adjacent". After the computer checked all English words, he found some words isolated, that is, there is no adjacent word. For example, Aloof (indifferent, alienation, not participating in something, such as He Stands Aloof from the crowd) is a isolated word. It's really a word like it. Therefore, the Knuth is double-clefly defines all the words in which no neighboring words are Aloof Words. If there is an appearance when playing this game, some people have the same topic happening happened to the waist, and they can't play. In the English word of five letters, there are 671 Aloof words. Earth, Ocean, Sugar, Laugh, First, Third, and NINTH, etc. Knuth showed the eleventh paradise of war (Sword) to peace (Peace) on the 1992 Christmas card. I don't know what the Knuth is solved, but the Chinese English Department of Eighth eight-eight-level Chen Xiaozhong found the formation of the right. In addition to text games, Carroll also invented a number of playing cards and origami games. But I personally is not interested. So, stop here.
