前两天，甜甜盯着墙上挂钟看了很久，很兴奋地跟我说她有一个重要发现：”Dad, I have a discovery: if you multiple the minute hand number by 4, and then add it to the minute hand number, we get the reading! This is a rule with no exception, and I have tried every minute hand in whole numbers. This rule works!”。大体是说，要想知道分针所在读数，可以拿4乘以分钟所指整数，再加上分钟所指整数。比如，５分钟等于１乘４加１；１０分钟等于２乘４加２；１５分钟等于３乘４加３，以此类推。这是甜甜独立思考，用归纳法总结出来的规律，说明这个九岁的小家伙是个爱琢磨的孩子。我随她一起逐一验证，果然正确，心里有些诧异，她怎么绕过这个弯的呢，因为美国小学数学教育远比国内落后，四年级才刚开始介绍代数的概念，还没有用到代数。我问她，你是不是从书上或者老师那里看到的，她摇头，说这完全是她自己的发现。 为了表明是她自己的得意发现，她又注视挂钟良久，继而大叫：“Dad, come here, I have another theory: if you multiple the minute hand number by 3, and then add it to the even number in sequence, we also get the reading! Isn’t this also a discovery？”甜甜的第二个理论是，分针所在读数等于３乘以分钟所指整数，再加上分钟顺序向下的偶数，比如，５分钟等于１乘３加偶数２，１０分钟等于２乘３加偶数４，以此类推。甜甜问我这算不算一大发现。我说，如果理论经实践验证无误，就可以算是发现。”So let’s verify it”，甜甜说，”1 times 3 plus 2 equals 5 minutes; 2 times 3 plus 4 equals 10 minutes; 3 times 3 plus 6 equals 15 minutes, ……. They are all verified: I got another discovery!” 我跟甜甜说，我也有一个发现：分针所在读数等于５乘以分钟所指整数。甜甜不屑一顾地说，这算什么发现呀，这是 common sense（常识），人人都知道呀。这时候，我觉得有必要因势利导，上升到代数的高度了。我说，“Let’s represent your discoveries in algebra, ok？”甜甜一直想超前学代数，好在同学面前炫耀，很高兴。我说，其实，你的两个理论和我的”发现”在代数上是等价的，正因为我的发现是常识，不证自明的，所以，如果你的理论跟我的发现等价，我们甚至不必一一验证，也可以证明你的理论是正确的。“Dad, you are confusing me!（你把我搞糊涂了）”我本来想教育孩子，世界上除了归纳法以外，还有演绎法，可惜操之过急，有点揠苗助长了。我说，好，我们先写代数表达式吧，假设X是分针所指的整数（X=1,2,…,12），Y是分钟读数： 爸爸的 “发现”（常识）：Y = 5*X 甜甜的第一个发现：Y = 4*X+X 甜甜的第二个发现：Y = 3*X+2*X 我接着试图讲解代数运算的方法：4X+X=4X+1X=(4+1)X=5X; 3X+2X=(3+2)X=5X，可是甜甜的兴趣到此为止，已经不耐烦了，要求玩游戏去：”Ok, ok, Dad, it’s too complicated. Let’s do it another time. Can I play gameboy now?”。大概超出了这个岁数的专心时间限度了，我虽然意犹未尽，也只好作罢了。看样子，我家这个小鬼头，天才有余，耐性不足，要想成才，也不容易。不过，还是顺其自然吧。 2005年11月9日记于水牛城 ［补记：甜甜舅舅看了这篇花絮，给了以下评论，夸赞甜甜有天才：“我觉得，数学就是透过世间万物中简单的数字组合，从中发现奥妙，好学生和天才的区别在于发现和创造，在简单的表针上发现奥秘，甜甜比舅舅聪明。继续努力！”。甜甜很依恋舅舅，经常念叨舅舅舅妈和大宝弟弟。我跟甜甜说舅舅夸她比舅舅聪明，甜甜很开心。］ 另外， 甜甜本学期的 Science project，取材甜甜的上述数学发现：Clock Reading Experiment。为了把幻灯制作得丰富多彩，甜甜上网用Google寻找图片 icons （clock.gif,thinker.gif,happyperson.gif之类）。 ２００５年六月十一日 于美国水牛城 见： 孩子的思维实验 06.01.23, 甜甜本学期的 Science project，取材甜甜的数学发现： Clock Reading Experiment: myscienceproject.pdf 甜甜本来想做一个物理或者化学实验，可是想到的实验要不太简单，要不太难施行，所以我提议用她在时钟上的实验验证她早先发现的数学假设。甜甜总觉得这不象所要求的实验，我说，数学实验是“思维实验”，同样遵循科学的一般方法：（一）提出问题；（二）研究探索；（三）形成假设；（四）实验验证；（五）观察和结论。甜甜勉强同意了。为了把幻灯制作得丰富多彩，甜甜上网用Google寻找图片 icons （clock.gif,thinker.gif,happyperson.gif之类）。 《朝华午拾》总目录（置顶）
http://news.nationalgeographic.com/news/2009/12/091202-top-ten-discoveries-2009-year-science-news.html Top Ten Discoveries of 2009: Nat Geo News's Most Viewed 美国《国家地理》新闻频道评选出2009年度最受欢迎的十大自然发现： 1. 艾达化石或可弥补人类进化中缺失的一环；2. 发现头部透明海鱼的活体标本；3. 发现新云型；4. 灭绝鸟类重现；5. 最古老人类祖先骨骼化石；6. 找到淘金热时期的幽灵船残骸；7. 发现最长蛇化石；8. 美国三分之一地区面临外来巨蟒威胁；9. 古代镶宝石牙齿；10. 超罕见巨口鲨。 December 02, 2009 National Geographic News's most popular coverage of 2009 scientific finds is swarming with megamouth sharks, giant snakes, a transparent-headed fish, and rare species rescued from obscuritythen eaten. 10. Ultra-Rare Megamouth Shark Found, Eaten In March, the 41st megamouth shark ever found went from swimming in Philippine waters to simmering in coconut milk. 9. Ancient Gem-Studded Teeth Show Skill of Early Dentists The glittering grills of some hip-hop stars aren't exactly unprecedented. Sophisticated dentistry allowed Native Americans to add bling to their teeth as far back as 2,500 years ago, a May study said. 8. Alien Giant Snakes Threaten to Invade Up to 1/3 of U.S. Nine giant snakes could be on the verge of causing ecological catastrophe if they establish themselves in the U.S. wildat least two have already set up shop in Floridaaccording to an October report. See pictures 7. Biggest Snake Discovered; Was Longer Than a Bus The 60-million-year-old reptile was also heavier than a car, scientists said in February, adding that the fossil could shed light on climate change. See pictures 6. Gold Rush-Era Ghost Ship Wreck Found With boots thrown hastily on deck and cooking utensils scattered, the last moments of the crew aboard the gold rush-era paddleboat A.J. Goddard are preserved in the ship's recently found wreck, archaeologists announced in November. 5. Oldest Skeleton of Human Ancestor Found There was never a chimp-like missing link between humans and today's apes, according to an October fossil-skeleton study that could rewrite human evolutionary history. Said one scientist, It changes everything. See pictures 4. Extinct Bird Seen, Eaten Long believed to be extinct, a rare quail from the Philippines was photographed for the first time everthen sold at a poultry market, experts said in February. 3. New Cloud Type Discovered? Nicknamed Jacques Cousteau clouds, these turbulent seas in the sky could be examples of the first official new cloud type since 1951, experts said in June. 2. Fish With Transparent Head Seen Alive for First Time Perhaps the most bizarre nature discovery of the yearthough Stephen Colbert put it a bit less delicately a Pacific barreleye fish shows off its transparent head and barrel-like eyes in pictures released on February of the first specimen ever found alive. Watch video 1. Missing Link Found: Fossil Connects Humans, Lemurs? The publicity frenzy made National Geographic News's brief coverage our most viewed page of the yearand inspired a backlash as some experts, including one here at Nat Geo HQ , suggested Ida was more media event than milestone. The 47-million-year-old, exceptionally preserved primate fossil Ida, unveiled on May 20, was hailed by some as a major discovery in human evolution.
标签: 发现
