何处安魂:悬浮着的学术精英

何处安魂:悬浮着的学术精英

作者: 李博文

前一阵子一个来自芝加哥的教会阿姨跟我说几年前有一个中国留学生在西北大学读博士,毕业后回国由于没有受到预想的待遇而抑郁自杀。教会阿姨说芝加哥的教会都为这个有才华的中国年青人逝世而惋惜,后悔没有早日领他见到主,若是他早日见到主了这个悲剧就能避免。

我当时不记得有看过相关的新闻,回来搜索了一下:涂序新,浙江金华人,清华大学水利工程学士、法学学士,美国西北大学岩土工程硕士、博士,发表SCI核心期刊3篇,2009年回到浙江大学工作,2009年9月11日向浙江大学填报申报副教授的信息,六天以后自杀于浙江大学玉泉校区,死前留下遗书:

“在此时刻,我认为当初的决定下得是草率的,事后的发展完全没有预计,感谢一些朋友事前的忠告。国内学术圈的现实:残酷、无信、无情。虽然因我的自以为是而忽视。”

很多人猜测,涂序新自杀之前,有人向他暗示了副教授的申请结果,虽然之后没有人站出来承认。和几个同学聊起这个事情,有人说国内学术界黑暗,有人怪这个人心态不好,大家看法上莫衷一是,感情上都很惋惜。

和很多其他美国商学院一样,UTD的商学院也在扩张,今年一年就招了20个faculty,昨天去学院拿了宣传手册,浏览了一下这些未来有可能成为自己老师的人,发现三个亚裔面孔,看罢简历,三人本科都毕业于清华北大两所学校之一,然后在美国常春藤或常春藤级的名校拿下了博士学位,年龄在三十上下,我真的由衷佩服这三位前辈,美国学界教职十分紧张,好多一流名校博士只能到次一级的学校教书,但是终身教授制度规定除非学者违反了法律,美国学术机构不能解聘获得终身教授身份的学者,这样优厚的待遇、自由而独立的工作、以及社会赋予学者的尊重,使得美国的professorship严重供不应求,这三人在中国成长、接受教育,用第二语言研究学问、表达学术观点,不但能受到美国学界的认可,还能在美国拿到教职,这意味着美国人愿意花自己的钱供养他们的智力创造,也意味着美国人放心把他们的next generation交给三人来塑造。

手册里,三人西装革履,自信满满,神采奕奕,眼神中仿佛世界朝他们打开了。百度百科上搜出涂序新生前的照片,也和他们一样,清秀俊朗,帅气阳光,只是现在,鲜活的生命已经变成了一个词条,被压在人们记忆的杂货柜底。我眼前浮现出教会阿姨想我讲述这个悲剧时的样子,我不禁想问她:若真有主,若主泛爱众生,为何他待人差别如此之大?

在UTD有幸结识Dr.Scotch,一个有俄罗斯血统的典型的西式老学者,三十多年前,他在芝加哥大学获得社会学学士学位,而后在哈佛大学获得了社会学博士,之后教书并从事关于disabled people的研究。来到他办公室,墙上挂着一幅马克斯·韦伯的画像,韦伯双眉微皱、目光如炬、炯炯有神,好像向前能刻穿任何和他对接的目光,背后又有不可测的渊深。Dr.Scotch看到我对韦伯的画像很感兴趣,从书架上拿出了一本皱巴巴的旧书,对我说This is the first sociology book that I read. At that time, I wasn’t in Harvard. I was in University of Chicago。我双手接过书,生怕不小心把老教授少年的记忆珍藏弄破了,定睛看看书名:The Protestant Ethic and Spirit of Capitalism,哎呀,这不是久违的《新教伦理与资本主义精神》吗?我尽量保持对仗的跟他说This is also the first the sociology book that I read. When I was reading its Chinese version, I wasn’t in America. I was in Xiamen University.

 

一学期下来旁听了Dr. Sctoch的课程,顺便观察了这个学者的生活,大致是看journal里的paper, 去conference和其他教授讨论paper,写自己的paper,改自己的paper,给学生布置paper,看学生的paper,改学生的paper。他那两大常春藤名校的光环随着接触变多而渐渐褪去,有时我会好奇,这个老爷爷研究了三十多年的disabled people,他到底研究出了什么?发的paper的名字都能写一页又一页了,这些paper有多少人看过?disabled people的生活又改变了多少?世界对disabled people的理解和认识又如何不一样了?

一天下课他跟我说,学院要选一个新的院长,但是他不想去选,他觉得当个学者就很好,每天他都可以慢慢的吃一顿午餐,如果他做了financial analyst,他恐怕就没有这个特权了。我恍然一小悟,什么contribute to the advancement of knowledge through cutting-edge research,什么facing the greatest intellectual challenge of our times,孩子,你不是想多了,你是想太多了!你以为每个学者都是马克思·韦伯啊?若是每个学者都像韦伯老爷子那么猛,《社会学入门》早就写爆了!你想累死社会学系大一新生啊?

大部分的学者一生只能重复咀嚼韦伯老爷子的观点,然后把咀嚼出来的成果吐给next generation,在读完同行几百篇paper之后,从一大堆重复的观点里挖掘出一点点新意,浩浩荡荡几千字,其实只在一个大话题的小问题里做出一点点进步。而若不是有其他学者也面临着相同的写作压力,很少有人再会从这佶屈聱牙的文字梳理出他的思路,他的“智力贡献”就此被封存到了书柜的角落里。与韦伯不同的是,没有一老一少会将它从书柜里重新拾起,然后重复Dr.Scotch和我的对话。

这个世界上大部分人都是普通人,学者也一样,也许,学者这份工作的特殊之处就是能慢慢的吃一顿午餐吧。但是学者在学生面前还要重复着勇于创造、大胆创新学术精神,尽管有时他要拉直嗓子说这些话才有底气,尽管他知道也许他本人也无法留下什么创造被人铭记,因为台下坐着的保不齐就有人有韦伯的笔力,潇潇洒洒便揭示人类发展的奥秘,而对于其余的人,还有他自己,也许在一开始就注定被遗忘,但是有过认真努力便是意义。

 

小时候常觉得读博士作学者是一件崇高伟大的事情,长大了发现周围很多好友都读了博士,其中去国外读博士的人也大有人在。Personal Statement里面为学为师的誓言写的令读者临表涕零、不知所言,然而私下里聊来大家的动机都莫衷一是:有人确实爱学术;有人觉得博士的光环很诱人;有人喜欢大学的环境、教授的待遇;有人想出国,硕士太贵了,博士倒贴奖学金,算一算比国内工作的同学挣得还多,这何乐不为;有的人压根没想好干什么,先读着,反正多读点书没有错。

在这一群人中,有极小一部分人有幸去到世界名校,有幸享受到世界上最精致的教育资源,翻开北美各名校网站,看一看博士生的简历,每个名校的项目一两年间都会招一个中国学生,涂序新的教育背景是这一群人的一个标准模版,本科清华或北大,博士常春藤或常春藤级名校。

犹记当年我在辽宁参加高考,三十多万人同进考场,清华北大也只要几百人而已,能考入这两所高等学府之一已经是几千人中的一个了。进入北大清华,他们要与这个国家最优秀的头脑竞争,GPA、语言考试、学生活动、学术论文,一切的一切都冲在前面,才有一定的几率进入梦寐以求的西方学府开始自己的PhD生活,走到这一步的人称得上是精英中的精英。若是来北美,PhD的学术训练要求又是惊人的严格,稍不留神又有奖学金停掉、资格考试不过、毕业论文写不出的障碍,于此同时还要在一流刊物上发尽可能多的文章以提高将来找到教职的概率。困难虽多,总有人能够克服万难,最终拿到博士学位,同时在世界级的top journal上发表了文章。我由衷的羡慕和钦佩这些人,因为超常的智力水平和坚韧意志,只要少了一样,他们都走不到这一步。

 

只要想想从应试教育的苦读到博士帽流苏的援正之间所有的希望、努力、坚持、辛苦和拼搏,我们便可以稍微理解涂序新的心情。他的成就是一步一个脚印踩出来的,是用paper的冷寂和实验室里的汗水交换来的,是他用最真实最纯粹的努力创造出来的。现在,他要社会给他应得的尊重和奖励,就像他做对了题就该得到相应的分数,他付出过了努力,也该有百分之百的正当性得到与之对应的评价和报酬。可惜生活不像是一场考试,更像是一次实验,结果有时和努力并不相关,因为大自然有自己的轨迹。

六年的苦读后从西北大学拿到博士学位,也许是因为照顾家人的考虑,他没有留在美国而是选择了到浙江大学教书,也许在他心中,自己去浙大是overqualified,也许评上副教授是他给自己不能再退的底线。当他带着北美名校的荣耀重踏故土,被浙大安排在57平方米的教师公寓里,现实的感官刺激太强烈了,即使你是那么优秀、那么上进、那么努力,即使你有那么多成绩,生活依然不容易,作为一个新人,这里有副教授们、教授们、院长们,你名校的荣耀不能免除你和他们经营关系的负担,你要考虑岩土的构造,也要以相同的审慎去考虑见到什么样的人该怎样说话;你可能看惯了美国人的大house,但是以杭州高企的房价57平米的房子已经是浙大腾出的一笔价值不小的资产,想要大一点的房子,靠工资收入也只能一平米一平米的挣,一间厕所一个厨房的积攒。

很容易知道,现实的这一切和涂序新想象的太不一样了,他开始怀疑自己曾经的努力,一切是否值得,若是不值,青春也覆水难收。也许副教授的职称是他最后的慰藉,但是生活严酷的说:这,我也不能给你。遗言中,他斥责中国学术界的“残酷、无情、无信”,他的评价或有几分偏激或有几分真,实际上不仅是中国学界,整个生活似乎都在骗他。

 

假如生活欺骗了你,不要悲伤,不要心急。

忧郁的日子里需要镇静,相信吧,快乐的日子终将会来临。

一切都是瞬息,一切都将会过去。

 

夜半观影,随便一选竟是一部德州的电影,No Country for Old Man,中译《老无所依》。结尾处,牛仔的妻子对杀手说:你没有必要杀我,你已经拿到了钱,也杀了我丈夫。

杀手拿出一枚钱币,抛过后掷出生死一问:告诉我,是正面还是反面?

牛仔的妻子说:钱币不能决定什么,决定权在你。

杀手不高兴的回复道:我来到这里的原因,和这枚钱币来到这里的原因,没有什么不同。

这个世界任何一件事的发生都是有逻辑的,一件事情确有另一件事情的引导,又确凿的引导另一件事情的发生。然而这个逻辑并不掌握在人手上,有时生活总向希望的反向行走,而且走的理直气壮,有时你用你的逻辑去框定它,它便告诉你它的那些必然而不期然的偶然。

The finity can’t comprehend the infinity.

影片里的老警察无法继承父辈们惩凶除恶的荣耀,无论多么努力,杀手的狡猾精明面前,他总是幼稚无力。最后,他决定退出这场不是为他的智商设定的游戏: I always figured when I got older, God would sort of come into my life somehow. But he didn’t。

 

体制之过?人心之恶?涂序新之错?神之责?

我想到了教会的阿姨跟我讲述这个悲剧时的样子,我想问问她:如果真的有主,如果主全知全能全善,那么他能不能告诉我,悲剧为何?

 

xmmxmu最近有一条微博:“我渐渐开始意识到,我这辈子极有可能成不了富二代他爹官二代他爹,只能当一个平凡的我娃他爹了。。。每每想到这里,我就觉得眼前的生活开阔亮丽了不少。”

David呆回复他说:“有时候觉得接受自己终将平庸的事实也算是成熟的表现啊。”

 

不知怎的,毕业三个月后,这些当年被我视作不上进的语言,现在听起来都有道理了。拿出毕业前为班级毕业大戏写的朗诵词,勤勉与善良,智识与理想,悲悯与传奇,凌云寺里写下的文字,我还信着。只是,我也许一生最传奇的事情就是在毕业季给已经毕业、正在毕业、将要毕业的同学讲文庆校长的传奇;只是,我也许一生也没有能力在宏大的背景里演绎悲悯,但是我还是有可能完成小学生守则里的要求,做几件助人为乐的好人好事。总是梦想改变世界,慢慢发现世界早有自己的安排,不需要我去改变,我需要改变自己,那样也是在改变世界,因为我也是世界的一部分。

慢慢感知到自己的普通、平常,只是属于正态分布一个标准差里的一份子,没有什么“异禀”,不见什么“大用”,只是一个比较努力的平常人吧,而这个世界努力的平常人很多,况且不平常的人也在努力。我知道自己还会努力,但是我也承认一生极有可能只能做些平常事,父母都是平常的人啊,有我平常的乖儿子不是也挺幸福的。我骨子里留着百姓的血,百姓的血带着百姓的命,也带着百姓的福。

承认自己平常,没有那么难。卸下荣耀,也是卸下重量。还原自己,也是上进。

 

在写作此文想法出现的第二天,网上便传出MIT投行女郭衡自杀的消息。郭衡在华尔街投行、私募对冲基金都做过,就读蜚声世界的MIT斯隆管理学院MBA,还自己开办过公司。从博客里看,她不是一个书呆子,而是有很多独立的想法的人。透过MIT,她仔细的观察着世界上流社会的精英们,发现自己无法与他们竞争。她还忧心中国传统文化的陨落,渴望振兴传统文化,这里摘录她博客里的一段文字:

“今年是龙年,我依然用着这传了五千年的宝贵文字纪录我的人生。在我生日之际,我真心希望所有龙的传人能够睁开双眼,看看我们所面对的真实世界,客观地分析一下我们民族的未来在哪里。”

想想民族的未来,也想想自己的现在:自己开心吗?自己喜欢什么?自己在做自己喜欢的事吗?如果没有,为什么?有时候我们觉得自己是强者,其实我们同情弱者的同时,自己也许就是弱者,是需要帮助的人。我们要尽一切可能帮助人,但是自己病的咬牙坚持的时候,治愈自己便是对世界很大的帮助,因为自己轰塌的时候,这个世界中与自己有联系的部分也会颤抖。

任何人都需要一个宏愿。任何一种伟大都是自然发生的。

谈及涂序新的悲剧,教会的阿姨说其实侍奉神不需要什么地位,哪怕是一个普通老师,在讲台之上,如果能充分演绎神性的伟大,也能为神创造不少荣耀。

作为非基督徒,我尊重她对世界的理解,就像她尊重我对世界的理解一样。

涂序新临死时还有一个女儿在由她姥姥姥爷抚养,我想,如果真的有所说的神性的伟大荣耀,那必然在他女儿嫩嫩的掌心。

The exam feedback conundrum

The exam feedback conundrum

By this point in the semester, I have given two exams in my Calculus class and one in my Real Analysis class. Grading is always a pain, but I have struggled much more recently with what to say as I hand out the exams. Giving statistics on the exam might be helpful for students so they can see how they stand with respect to the rest of the class. But is that really important? Isn’t it more important that the student only know how they did, and perhaps how they can improve? I really don’t know the answer to this question. I used to never give statistics on the exam. If my students asked, I would say that averages and medians were not a great way to summarize their performance, and that they should really only worry about their own performance. But I have recently caved, mostly because I realized I was one of the few people who did not give any stats on the overall class performance, and the students were sort of expecting it. After a couple of awkward incidents this semester, I’m considering going back to my “no stats” policy.

 

The first thing to think about is why would you want to know how everyone else did? Especially if the professor doesn’t curve, and so the performance of others will not affect your own individual performance. So what does it matter if you were the only A, or one of the many A’s? But of course, it matters.  Everyone wants to feel like they’re doing better than average, so they want to know the average. The paradox here is that there have to be people below the average! I remember telling my Calculus students, on their first exam, that the median was an 89. I was congratulating them, because as a class they performed well. But as soon as I explained (to the few who didn’t know) that the median was the cut-off between the top 50% and the bottom 50%, a lot of them looked very concerned. They realized that 50% of them had gotten an 89 or less. So somehow, this makes the people who didn’t get an A feel worse, and at the same time it makes the people who did feel less special. So my attempt to congratulate and praise kind of backfired.

And then we have the problem of what that praise does to the students’ performance later. For example, the average and median on the second exam were a lot worse. And I know in part it was because the material got harder (the material always gets harder), but I wonder if maybe they got a bit complacent and overconfident, and decided to blow off this exam. Of course, I have no way to prove this, and because I had done it for the first exam, I gave them the stats for the second. One student asked for more information, like what was the spread of the grades. This is a good statistical question, but I don’t like to give the highest and lowest scores, since then I make the student with the lowest score feel really bad. I gave the highest score, because I decided no one would mind, and then the student with the highest score came up to me and said that that made them a little uncomfortable. I didn’t say any names or indicate that they had been the student with the highest score, but then I realized that their friends could probably figure it out, and I guess that’s something that people are not always comfortable with sharing.

This reminds me a bit of my Real Analysis exam, where the median was an A-. I wanted to share that with the class because the exam wasn’t easy, Real Analysis is not easy, and I wanted to congratulate them on their accomplishment. But again, my mistake was in forgetting that there were still people who had not done very well, and thus I was essentially making them feel very bad about themselves. I am also not sure if this improved morale in the class, since an A in Analysis, which would normally be exciting, now didn’t seem like such a hard thing to attain and thus was made less special.

Of course, it could be much worse. When I was in college, my Linear Algebra prof liked to hand out exams in descending order. So if your name was called first, you knew you had the best grade in the class. As names were called, you got increasingly worried. Whoever was called last had to do the long walk of shame to the front of the class to pick up their exam, which we all knew was the worst. I was called first only once, and I was very pleased with myself, so I guess the method did improve my self-esteem. I’m not sure this method helped anyone in the bottom half, though. In any case, I believe that this would be illegal due to FERPA rules, so it’s not even something to consider.

All of this is a long way to say that I’m considering not giving any statistical feedback on the exam. Maybe just focus on common mistakes and things to work on for the final exam, and perhaps I could take a bit more time on each exam and write personalized feedback on the exam instead. I do tell everyone who got less than a 70 to come talk to me during office hours, so that’s another place to give feedback and comments or suggestions on a student’s individual performance. It is tempting to praise a class that did well, but it’s possible that I’m doing that more to stroke my own ego (look how great a teacher I am!) than to improve their morale. Each one of them knows how they’re doing, and I think now that that should be enough.

How about you, dear readers? How much feedback do you give to the class as a whole on their performance in an exam? Have you had uncomfortable situations stemming from this? Do you have suggestions for how to praise the students without making others feel bad? Please share your thoughts in the comments section below.

– See more at: http://blogs.ams.org/phdplus/2013/11/17/the-exam-feedback-conundrum/#sthash.mQsafZxP.dpuf

Five (math) things to do before you die

Five (math) things to do before you die

An interesting question was posed to me recently. If you were told you were going to die tomorrow, which 5 math topics/questions would you be most sad you never got to learn about/have answered? First of all, I must admit I freeze any time people ask me to rank my top five anything. It feels so final, and I really want to think about it carefully before I answer. Also, honestly, if I were told I had 24 hours to live I would be sad and upset but probably not about the math I was going to miss. But that is not the point of the question, I guess. In this post I will attempt to answer this question, with full awareness that I may change my mind in a few days. But I will also pose a few other questions and then leave it to you, my readers, to ponder them.

1. My immediate response to the question was the Riemann hypothesis. Not that given 100 more years to live I would have any hope of solving this problem, but I would like to see it proved in my lifetime. Especially because we are all pretty certain that it’s true.

Of course, then one can go through the list of Millenium Problems and I would add two more things:

2. the Birch and Swinnerton-Dyer Conjecture, and

3. the P vs NP problem.

Again, I am not saying I have any chance of solving them, just that I would like to see the solutions to these problems. But this is where it gets tricky. I basically have a list of three things that probably anyone could have made (these are some of the most famous problems in math!). So how do I add two more things to it? Nothing will seem as important (nothing else I can think of would make you a millionaire!). OK, there are three other millenium problems, but I’m just not as interested in them. So then I started thinking about the math topics I would be sad not to have learned if I were to die tomorrow.

4. I have gotten interested in mirror symmetry and its relation to physics and number theory, so I guess I would be sad if I died tomorrow without learning more about it.

5. Arithmetic dynamics, since I am very interested but kind of new to it.

But doesn’t the list become weak after I add these two things? Anyway, please share your Top 5 in the comments below.

The original question got me thinking about other fun questions on might ask:

– Which 5 math books would you take to a desert island? The funny thing is that I can’t think of a top 5 but I can always think of at least one or two things. For example, I would bring Serre’s A Course in Arithmetic. But of course, if you asked me to bring just one I would be stuck.

– Who are your Top 5 mathematicians of all time? Gauss? Ramanujan?

-Slight variation: which 5 mathematicians would you take to a desert island? See, here I would probably pick some fun/handy mathematicians. I don’t know if Gauss would be very good at building a hut.

– What are the best 5 math formulas? Euler’s formula is widely regarded as one of the most beautiful formulas in mathematics. Do you agree? Can you think of others?

– What are your 5 favorite functions? I know one: hypergeometric functions!

As a final comment, I wanted to say the first question was suggested by my friend Casey Douglas, who is an Assistant Professor at St. Mary’s College of Maryland. He thought of this question as he was preparing a talk for the SMCM math department’s annual “MATH WEEK OF AWESOME”, which sounds, indeed, awesome.

So now I open it to you. Do you have answers to these questions? Do you also find it slightly frustrating when these questions are posed (if so, I apologize)? Can you think of other questions like this?

– See more at: http://blogs.ams.org/phdplus/2012/03/23/five-math-things-to-do-before-you-die/#sthash.y1aLpLP5.dpuf

http://blogs.ams.org/phdplus/2012/03/23/five-math-things-to-do-before-you-die/

44个精彩的物理趣题 (转自MATRIX67)

Shirley was saying...

44个精彩的物理趣题 (转自MATRIX67)

 

 这个 Blog 几乎一直在讲数学趣题,却很少提到物理趣题。其实,我个人觉得,物理也是相当好玩的(我是化学不好才选的文科)。隐约记得初中搞物理竞赛时,曾见过大量让人大呼过瘾的好题。前几天看到了一个绝好的网站,里面有相当多的物理题目,让我激动了好一阵子。我搜集整理了里面的一些好题,加上了我自己的一些补充,在这里和大家分享。不过,由于我的物理实在不怎么样,如果出现什么错误,请大家及时纠正。

    那个网站上的“官方解答”并不见得靠谱,也不知是因为我没有悟到,还是因为它真的不靠谱。不管怎样,我给出的基本上还是它的官方答案。其实,阅读过程中你会发现,答案是次要的,真正有趣的其实是问题本身。

    几乎从没写过物理题目的 Blog ,想要用一篇文章总结物理趣题,因此毫无疑问——这是一篇非常,非常,非常长的文章。建议大家用自己喜欢的方式做个书签,一天看一点。如果觉得还不过瘾,推荐订阅物理大牛 EagleFantasy 的 Blog

    另外,此日志一出,想必又会收到无数邮件,询问我作图用的什么工具的。在此就先回答了——请见 FAQ 。

    开始吧。

 

 
    有一块 V 字形木板,两侧与地面的夹角都是 θ 。一根密度均匀的绳子放在木板上,绳子与木板之间的摩擦系数为 1 。整个系统左右对称。没挨着木板的那段绳子所占的比例最大是多少?此时 θ 是多少度?

    

    用一些非常初等的方法可以得到,答案是 (√2 – 1)2 ≈ 0.172 ,此时 θ = 22.5° 。具体解答可以见 http://star.tau.ac.il/QUIZ/05/sol_rope.pdf 。

 
 
    一个长、宽、高分别为 a 、 b 、 c 的长方体物块,斜靠在一个墙角。由于墙壁和地面都是完全光滑的,因此物块将会开始下滑。什么时候,物块会脱离墙壁?

    

    为了解决这个问题,首先需要把物块和地面的夹角记作 θ ,物块下滑过程中的各种物理量都可以用 θ 来表示。然后,解决这个问题的关键就在于,当物块脱离墙壁时,物块向右的加速度就消失了,这个临界点就由等量关系 dvx / dθ = 0 给出。不过,由此产生的方程非常复杂,我们只能用数值的方式去解它。

 
 
    有一个半圆柱体横放在水平桌面上,截面的半径为 R 。我们在半圆柱体上放一块木板,试图让它在半圆上保持平衡。假如这块木板非常薄,那么这块木板很容易放稳,即使有些小动静,木板也会自动恢复平衡。但考虑 另外一个极端,假如这是一块非常厚非常厚的木板(甚至是大楼一般的形状),它显然不能稳放在这个半圆上。那么,这中间一定会有一个临界点。这个临界点在哪 里?换句话说,这个半圆上最多能放稳一块多厚的木板?

    

    把半圆的半径记作 R ,把木板的厚度记作 t 。如果把木板平放在半圆上,其重心的高度就是 R + t/2 。假如这块木板倾斜了一个微小的角度 θ ,那么图中 M’T 的长度等于弧 MT 的长度,即 2πR·(θ/2π) = R·θ 。此时,木板的重心 G’ 的高度变为了 (t/2)cosθ + (R·θ)sinθ + R·cosθ。为了让木板保持平衡,不会自动往下滑,我们需要让新的重心高度大于原来的重心高度,即 (t/2)cosθ + (R·θ)sinθ + R·cosθ > R + t/2。解出不等式,再令 θ→0 ,即可得到 t < 2R。也就是说,一旦木板的厚度超过半圆的直径,木板就无法放稳了。

 
 
    假如你面向东边,站在冰面上,鞋底与冰面完全没有摩擦。你能否做出一系列动作,使得自己最后能面向西边站立?

    

    可以。只需要重复“伸臂-挥臂-屈臂”的动作,你的身体便会向反方向转动一点。期待实验党。

 
 
    用过多年的插座(尤其是插过大功率电器的插座),右边的孔(火线)往往会有过热的迹象。如果是劣质插座,加上经常插拔插头的话,右边的孔甚至会有烧黑了的痕迹。明明是通过相同大小的电流,为什么右边的孔会被烧得更厉害呢?

    目前,这个问题没有一个所谓的标准答案。当然,这个现象本身是否存在也是存疑的。大家不妨来说说自己家里插座的情况。

 
 
    呼拉圈是怎么转起来的?人应该做一个什么样的运动?呼拉圈的转动频率是由什么决定的?和人的体形、运动速度、运动方式有关系吗?是否存在一个最优的频率?⋯⋯

    我有几件事情死活搞不明白,吹泡泡是怎么吹出来的,小舌颤音是怎么发出来的,骑车不动把手是怎么实现拐弯的⋯⋯当然,还有呼拉圈是怎么转起来的。和呼拉圈有关的问题似乎永远也列举不完。如果你真的把它当成一回事仔细分析,你会发现这不是一般的困难。
    2004 年, Biological Cybernetics 上发表了一篇长达 15 页的论文,论文题目是 Coordination Modes in the Multi-Segmental Dynamics of Hula-Hooping 。这篇论文终于不负众望,成功地摘得了诺贝尔奖——当然,是搞笑版的。

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What the world would look like if all the ice melts

http://www.smh.com.au/environment/climate-change/what-the-world-would-look-like-if-all-the-ice-melts-20131107-2x2p9.html

It seems Charles Sturt, Thomas Mitchell and other early European explorers tramping the scorching deserts of Australia in search of an inland sea were a few thousand years too early.

According to maps published by National Geographic, Australia will one day get an inland sea if global warming continues and melts the world’s ice caps and glaciers, lifting sea levels by about 70 metres.

The US-based organisation said it would take about 5000 years for all the ice to melt, although impacts will hit coastal communities much sooner – and having an inland sea won’t be much consolation to Australians.

What if all the ice melted? National Geographic's map of a shrinking Australia.What if all the ice melted? National Geographic’s map of a shrinking Australia.

Neville Nicholls, a climate expert at Monash University whose work has included research on Australia’s shrinking snow season, said scientists have known for decades the upper end of sea-level rises from melting the cryosphere would be about 70 metres.

While the complete melting of the world’s ice would potentially take thousands of years, the pace of global warming caused by human activities is putting us on such a course, Professor Nicholls said.

“The amount of warming you need isn’t out of the realms of what we’d expect from business-as-usual emissions scenarios,” Professor Nicholls said.

Europe in an ice-free world.Europe in an ice-free world. Photo: National Geographic

Once you get to warming of about 5 degrees, it would be hard to see how the melting would stop, given the long-lived consequences of a build-up of greenhouse gases, he said.

“You don’t need to wait for 70 metres to really disrupt Melbourne, Sydney, New York and many more low-lying coastal cities around the world,” Professor Nicholls said. “It’s the first metre or two that you have to worry about.”

The sea level has been rising at the rate of about 3 millimetres a year globally, and “there are worries that it will accelerate as warming increases”, Professor Nicholls said.

North America in an ice-free world.North America in an ice-free world. Photo: National Geographic

The World Meteorological Organisation overnight released its latest annual report, showing that the concentration of greenhouse gases that trap more of the sun’s heat in the earth’s biosphere are at record levels, with the increase accelerating.

National Geographic noted that the last time the earth was ice-free was 34 million years ago during the Eocene period, when alligators swam in Arctic swamps.

An ice-free world would see present-day London underwater, the Netherlands and Denmark lost. Bangladesh, home to 160 million people,would no longer exist and land now home to 600 million Chinese would be submerged. The US would have a lot fewer states, with the east coast including Florida lost to the sea, the National Geographic maps show.

Asia in an ice-free world.Asia in an ice-free world. Photo: National Geographic

The world’s ice caps, glaciers and permanent snow contain about 24 million cubic kilometres of water, according to the US Geological Survey. Antarctica and Greenland make up about 90 per cent of the total ice.

Read more: http://www.smh.com.au/environment/climate-change/what-the-world-would-look-like-if-all-the-ice-melts-20131107-2x2p9.html#ixzz2jxKQ4a1H