The Local Inertial Reference Frame

[Project] Logarithmic correction to BH entropy (1)

2011-10-05T13:49:00.000-07:00

Review of basic thermodynamics and statistical mechanics
________________________________________________________

Thermodynamics

Zeroth Law
Equilibrium: _____________________
Time: ____________________________
Transitivity of the equilibrium: A~B && B~C --> A~C

First Law
Adiabatic process:
Quasi-stationary:

Second Law
Irreversible process:
Time axis direction:

Third Law

________________________________________________________

Ensemble theories
Ergodicity

[Project] Supersymmetric nonlinear sigma models (1)

2011-10-04T11:44:00.001-07:00

[nytimes] When Knowledge Isn’t Written, Does It Still Count?

2011-08-14T23:50:00.000-07:00

http://www.nytimes.com/2011/08/08/business/media/a-push-to-redefine-knowledge-at-wikipedia.html

By NOAM COHEN

Published: August 7, 2011

HAIFA, Israel

“MAKING fun of Wikipedia is so 2007,” a French journalist said recently to Sue Gardner, the executive director of the foundation that runs the Wikipedia project.

And so Ms. Gardner, in turn, told an auditorium full of Wikipedia contributors and supporters on Thursday in Haifa, Israel, the host city for the seventh annual Wikimania conference, where meetings and presentations focus on the world’s most used, and perhaps least understood, online reference work.

Once routinely questioned about its reliability — what do you mean, anyone can edit it? — the site is now used every month by upwards of 400 million people worldwide. But with influence and respect come responsibility, and lately Wikipedia has been criticized from without and within for reflecting a Western, male-dominated mindset similar to the perspective behind the encyclopedias it has replaced.

Seeing Wikipedia as The Man, in so many words, is so 2011.

And that’s a problem for an encyclopedia that wants to grow. Some critics of Wikipedia believe that the whole Western tradition of footnotes and sourced articles needs to be rethought if Wikipedia is going to continue to gather converts beyond its current borders. And that, in turn, invites an entirely new debate about what constitutes knowledge in different parts of the world and how a Western institution like Wikipedia can capitalize on it.

Achal Prabhala, an adviser to Ms. Gardner’s Wikimedia Foundation who lives and writes in Bangalore, India, has made perhaps the most trenchant criticism in a video project, “People are Knowledge,” that he presented in Haifa (along with its clunky subtitle, “Exploring alternative methods of citation for Wikipedia”).

The film, which was made largely with a $20,000 grant from the Wikimedia Foundation, spends time showing what has been lost to Wikipedia because of stickling rules of citation and verification. If Wikipedia purports to collect the “sum of all human knowledge,” in the words of one of its founders, Jimmy Wales, that, by definition, means more than printed knowledge, Mr. Prabhala said.

In the case of dabba kali, a children’s game played in the Kerala state of India, there was a Wikipedia article in the local language, Malayalam, that included photos, a drawing and a detailed description of the rules, but no sources to back up what was written. Other than, of course, the 40 million people who played it as children.

There is no doubt, he said, that the article would have been deleted from English Wikipedia if it didn’t have any sources to cite. Those are the rules of the game, and those are the rules he would like to change, or at least bend, or, if all else fails, work around.

“There is this desire to grow Wikipedia in parts of the world,” he said, adding that “if we don’t have a more generous and expansive citation policy, the current one will prove to be a massive roadblock that you literally can’t get past. There is a very finite amount of citable material, which means a very finite number of articles, and there will be no more.”

Mr. Prabhala, 38, who grew up in India and then attended American universities, has been an activist on issues of intellectual property, starting with the efforts in South Africa to free up drugs that treat H.I.V. In the film, he gives other examples of subjects — an alcohol produced in a village, Ga-Sabotlane, in Limpopo, South Africa, and a popular hopscotch-type children’s game, tshere-tshere — beyond print documentation and therefore beyond Wikipedia’s true-and-tried method.

There are whole cultures, he said, that have little to no printed material to cite as proof about the way life is lived.

“Publishing is a system of power and I mean that in a completely pleasant, accepting sense,” he said mischievously. “But it leaves out people.”

But Mr. Prabhala offers a solution: he and the video’s directors, Priya Sen and Zen Marie, spoke with people in African and Indian villages either in person or over the phone and had them describe basic activities. These recordings were then uploaded and linked to the article as sources, and suddenly an article that seems like it could be a personal riff looks a bit more academic.

For example, in his interview with a South African villager who explained how to make the alcoholic drink, morula, she repeatedly says that it is best if she demonstrates the process. When the fruit is ready, said the villager, Philipine Moremi, according to the project’s transcript of her phone conversation, “we pry them open. We are going to show you how it is done. Once they are peeled, we seal them to ferment and then we drink.” The idea of treating personal testimony as a source for Wikipedia is still controversial, and reflects the concerns that dominated the encyclopedia project six years ago, when arguably its very existence was threatened.

After a series of hoaxes, culminating in a Wikipedia article in 2005 that maligned the newspaper editor John Seigenthaler for no discernible reason other than because a Wikipedia contributor could, the site tried to ensure that every statement could be traced to a source.

Then there is the rule “no original research,” which was meant to say that Wikipedia doesn’t care if you are writing about the subway station you visit every day, find someone who has written reliably on the color of the walls there.

“The natural thing is getting more and more accurate, locking down articles, raising the bar on sources,” said Andrew Lih, an associate professor of journalism at the University of Southern California, who was an early contributor to Wikipedia and has written a history of its rise. “Isn’t it great we have so many texts online?”

But what works for the most developed societies, he said, won’t necessarily work for others. “Lots of knowledge is not Googleable,” he said, “and is not in a digital form.”

Mr. Lih said that he could see the Wikipedia project suddenly becoming energized by the process of documenting cultural practices around the world, or down the street.

Perhaps Mr. Prabhala’s most challenging argument is that by being text-focused, and being locked into the Encyclopedia Britannica model, Wikipedia risks being behind the times.

An 18-year-old is comfortable using “objects of trust that have been created on the Internet,” he said, and “Wikipedia isn’t taking advantage of that.” And, he added, “it is quite possible that for the 18-year-old of today that Wikipedia looks like his father’s project. Or the kind of thing his father might be interested in.”

Ouch
.

A version of this article appeared in print on August 8, 2011, on page B4 of the New York edition with the headline: When Knowledge Isn’t Written, Does It Still Count?.

The Reference Frame: Rationalism vs empiricism

2011-08-13T20:09:00.000-07:00

The Reference Frame: Rationalism vs empiricism: "Sean Carroll reasonably discusses the tension between 'rationalism' and 'empiricism'. These are two competing philosophical paradigms whe..."

3.1415926535897....

2009-03-14T08:23:00.000-07:00

It can be of no practical use to know that Pi is irrational, but if we can know, it surely would be intolerable not to know.
-- Edward C. Titchmarsh

I am ashamed to tell you to how many figures I carried these calculations, having no other business at that time.
-- Isaac Newton

一个有趣的网站请见
http://3.141592653589793238462643383279502884197169399375105820974944592.com/

关于Pi的公式:
http://mathworld.wolfram.com/PiFormulas.html

关于Bailey-Borwein-Plouffe Pi Algorithm的介绍:
这个算法及其简单, BBP用它算了第10000000000位的Pi的数值.
不过, 这个数值是用16进制写的, 也就是说, 3.243f6a8885a308d...^#$%@^@%&*~
更令人吐血的是, 计算第10000000000位的数字, 竟然不需要计算第9999999999位...
计算公式:
http://www.andrews.edu/~calkins/physics/Miracle.pdf

中国古代数学家刘徽的割圆术

(不断更新中...)

关于科大的学习生活

2009-02-14T20:40:00.000-08:00

关于科大的学习生活
(转载自
http://zsb.ustc.edu.cn/bbs/viewthread.php?tid=7765&extra=page%3D1
我写给新生看的,也是给自己.)

V0.8
再一次走进科大招生论坛的时候,我已经是大三的学生了.突然就想写点什么.于是我试着回忆...
先是在电脑中找出了大一时候经常听的几首歌,放到播放列表里.其中有一首<<光辉岁月>>.播这个倒不是因为我大一的日子有多'光辉',而是我的第一次在舞台上正式的表演.开学时有个迎新晚会,我和刚认识的也会弹琴的同学就上去演了.那次表演很成功,据说晚会之后的一段时间,周围琴行的吉他销量猛增^_^.

那时我以为我的大学生活会是这样那样的有趣.

但接下来我能想到的事,就是线性代数.教课的老师讲的东西很不和我口味,几节课后我索性就延续高中的'传统'--自学--经常游荡在教师最后一排.我看的书也不是老师用的课本,而是科学出版社的樊恽/郑延履编的<<线性代数与几何引论>>.当然这样的结果是有得有失:我把自己的书完整的看过,却发现它和老师的要求相去甚远.很多内容老师没讲,而很多老师提到的计算技巧我都落下了.这些是我后来与同学交流时才意识到的.

讲微积分课的老师是一名很有经验的老教授.可惜那时自以为是的我竟然也选择了自学:找来了数学系的<<数学分析教程>>(常庚哲/史济怀)开始啃.甚至有时候不去上课,自己在自习室闷着头琢磨.高中时做惯了竞赛题的我在那套书的'问题'(练习题后的附加题目)上消耗了很多精力.

现在回想起来,不听课是我入大学后做得最糟糕的事情.虽然自学收获也很多,但这远不及老师上课不时的经验之谈.没有人带路,弯子自然绕了不少.

英语的快班也给我带来不少郁闷.开学的教学分级考试题基本是四级的难度,但我'竟然'做得一塌糊涂,当然没有被分到所谓高级班.那时心里是很不好受的,因为高中的英语考试我很少在90%之下.再加上不适应科大的英语教学方式,最终我没有选择'努力超过'高级版的同学,而是选择放弃--我的英语课也被自己安排去读英文的数学教材了.偶尔会下载一些VOA听听,去英语角练练口语.

有些事情我是不太喜欢讨论'是对还是错'的.就在这些英语课上,我读完了第一本英文教材(很菜的一本Linear Algebra,选这个内容来读的原因是我对它比较了解).之后的几个学期,基本上我感兴趣的课都读了一些网上推荐的教材,西图12楼也成了我常去的地方.较早接触英文教材我在之后的学习中受益很多.

那时我是班上的C语言的课代表.高中时候的编程经历使我能为大多数人解决上机时的困难.当然我并没有止步.侯捷翻译的基本C++的书我也是花大力气读的(不过都没看完),甚至还做了笔记.高中时没来得及学的STL模板库这时也有机会看了.不过很可惜的是之后的几个学期中,作为物理系的学生,这些对我没什么用处,学过的很多细节都忘记了,只是在和人闲聊的时候可以说几个名词吓唬人^_^.

编程方面的学习并不是没有用处,相反,在大三我们开设了<<计算物理>>这门课,作业大部分是需要编程求解的.谭浩强老师的那本绿色的书在这时又被大家翻了出来.我的个人意见是,学C的时候一定要借一本美国人写的C语言的书,并且多上机实践;谭的书学完可以直接赠给师弟师妹,原因如果你读了老美书自然就会知道. 但是总之认真学C语言是有很多好处的.我们不妨在此扯远一点,当时在Unix终端上机调试的时候,有个问题是整型变量可以有32bit的long int,也可以有64bit的long long int.我就突发奇想试了一下long long long int,结果编译器报错说" 'long long long' is too long for gcc."当时笑的肚子都疼了^_^.

好笑的事有很多,不过全部属于书呆子之间的冷笑话.为了不让大家受冻,我就不讲了.

考试并不好笑.由于忽视计算能力的训练,我成了眼高手低型,成绩自然不太理想.

大一下学期过的很平淡,现在我已经想不起什么来了.因为性格原因,我没有参加任何社团,所以没有'活动',每日专心看书练琴.本来还受好友鼓舞去追一个女生,结果因为每次约她打羽毛球都被她菜而打消了高攀此女杰的念头.

给我印象最深的还是有关学习的事情.那时我逃课去数学系旁听史济怀老师讲数学分析II中的R_n点集拓扑的内容.这段旁听对我影响很大.史老师的讲课把我完全吸引.若不是顾及到点名,我就一直听下去了.R_n中的点集拓扑是很有用的,在后面学到复变函数的时候我意识到了这一点.而再往后,我在书店偶遇一本<>,之后就成了它的忠实读者.这本书是给我数学上帮助最大的一本书.它使我具备了和数学系同学争辩问题的能力.

突然觉得有些'吹牛'了.我就说上一段真正大牛的故事,让自己清醒一下^_^.他叫-***-.就在我刚接触拓扑的时候,他还没转到数学系.他(大一)选了胡森老师的大三年级数学系课程<<拓扑学>>.他期末考试得了全班最高分.他使胡森老师惊讶了,并因此开始传奇.现在他已经不和我们是同一级别的人了,并且马上要到国外去访问学习.

好了我清醒了.继续写.

在学过隐函数及反函数定理之后我听说了Manifold(流形)这个东西,也听说了Arnold的<<经典力学中的数学方法>>这本书.随后的一段时间我就陷入了对微分流形的定义的苦苦研读之中.那时候我的思考能力以及数学准备还不太充分,所以学得一异常艰难.不过通过大量翻阅各种相同话题的书,我总算从泥潭里淌了出来.绕了好多弯后,我认识到关于流形的讲解最好的是S.S.Chern, Arnold以及Frankel的书.其它的初学时就没必要看了.

大一的下学期有一门对物理系学生至关重要的课--<<普物.力学>>.我们的课是向守平老师(<<时间之箭>><<引力与时空>>等书的译者,科大威望很高的老师)带的.我很庆幸能有这样的老师给我上物理的启蒙课.除了讲课,他被同学们谈论最多的是半开卷的考试方法--考生允许将一张写满公式的A4纸带入考场做参考.现在想,来唯一对不起他老人家的是我没有写期末的课程小论文.

说起物理(总算到了本行),不得不提张量分析(又是数学-_-).科大有一门著名的选修课叫'张量分析'.之所以著名,是它本身入门比较难,尤其是在学习微积分和线性代数时没有对相关部分给予从充分重视的情况;还有就是吕老师比较'狠'--给分(科大学生普遍关注)很出奇.我倒是不关心他给分多少.他编的讲义在众多教材中算得上是优秀,引入的方法很独特,书自成体系.但是他讲课的方式多少令人畏惧:来得总比大部分学生早,上课之前先把一堆公式抄在黑板左边,上课就推导一个擦掉一个;课间休息时再抄.那时听课我总是被噎的直冒汗,不停的喝水.

其实张量分析需要的就是一点线性代数(Multilinear)和多元微积分中的Jacobi矩阵的知识.学的时候可以先从n维欧空间开始,到正交曲线坐标,最后到一般流形上的张量分析.学习时最好配合广义相对论一起.书可以选S.Weinberg的(只看公式推导即可,不过Weinberg的书写的很通俗易懂);也可以选郭硕鸿的<<电动力学>>的附录.张量分析是学习理论物理必备的知识.

我们那时候军训是安排在大一的暑假的.虽然大学的军训相对轻松(科大如此),但仍然有人在军训开始的十五分钟内就晕倒了.他站在我后面,我们当时在练站姿.因为没有防备,所以我没有接住他.由此看来,身体还是很重要的,不能只顾学习,不顾后半生的幸福.呵呵.

大二开学不久,我又开始逃课了:那次是逃<<概率与数理统计>>,原因是感觉那科实在简单.当我从宿舍出来,准备到楼层内的自习室看书时,惊奇地发现那个教室人都溢出到了楼道里.挤进去一看,一位老者在讲台上大讲"MM从合肥坐飞机到北京去开会,我们可以说MM从合肥湮灭了,然后又在北京产生了?" 他的讲课立即吸引了我.四处打问才知道他是张永德老师(黑色物理题典全套的总编,科大重量级人物).讲到电子的单缝衍射,我才知道这课是量子力学."(量子态)她就是个小女孩,你用good news 逗她,她就表现出笑面孔;你用bad news 逗她,她就表现出哭面孔." "量子力学是十分重要的课啊,它'一美遮百丑',你们不要觉得自己以前的课没学好就学不好量子力学..." 那堂课后我坚定了'将逃课进行到底'的决心.后来教室移到了新盖起的五教去了,那里屋子大了许多,但是通风很糟糕(那时五教还没正式运行).古稀之年的老人在汗流浃背地写板书,那个场面很是令人感动.

虽然我这个量子力学课听得很不是时候(太早),虽然我经常是云山雾罩云雾缭绕盘龙云海腾云驾雾云里雾里,但听他的课我还是有非常多的收获.老人家毫无保留地将自己学术上的经验传授给学生,从"大道"到"小道",无微不至.不仅如此,他对消失的'科大五年制',CUSPEA班,Min.of Edu.与清北之间的关系,朱校长,以及上完课不擦黑板的老师等的尖刻评论,也启发我们对社会,及为人处世方面进行一些思考.

不过最终我没能进行到底,原因是我被概率老师连续三次点名,马上就要移交教务处审理.无论我和她怎样解释她就是无法理解她和张老师之间的差距.(我没有讽刺的意思,概率那课比较难讲.在我听她最后的几节课时能体会出来她是很认真备过课的.)

电磁学也碰到了很好的老师.他的讲课是学校公认的出色.他也是我见到的将多媒体教学设备利用的最充分的老师.虽然使用备受争议的ppt讲课,但从我个人感觉来讲他的教学效果是极好的.那时候我在读Landau&Lifshitz的Vol.8,他对我的'傻'问题总是很耐心的解答,并时常鼓励我.这门课的小论文我认真做了,写的是有关经典电动力学拉氏量推导的一些细节.虽然有班门弄斧之感,但那篇小文仍然得到了他的赞许.我很少得到那样多的真心的鼓励的,所以对他印象很深.

数学当然是放不下的东西.我有空闲的时间,就跑去数学系听<<常微分方程>>.那时是沈维孝老师在带这门课.其实叫沈哥都行--他和我们同辈,三十出头,有人开玩笑说"(若未婚)本班女生都可以去追他了."他讲课完全脱稿,定理证明虽不能说行云流水,但也像极了技艺高超的F1车手:偶尔有出入弯的小失误,他会对大家说"这个定理先欠大家的,下节课补上."他的思路很敏捷,各个定理证明都很利索;在讲解的存在唯一性时,他向我们就提前灌输泛函分析中'压缩映射'的概念,而且叙述清晰明了,听来毫无困难.在讲课时若不书写板书则必在讲台上穿梭云行:一节课下来他的总里程可以从科大开到大蜀山.他的研究做得也及出色.可惜的是他怀才不'遇'(传统地理解,实际他本人可能未必要求'遇'),在我们眼中总有些低调暗淡,甚至可能消失.

还有不能不说的就是胡森老师.我倾向于叫做'先生',因为他做的高深的弦问是我一直以来追求和仰慕的.那时我跑去18楼旁听了他的<<物理学中的几何>>,知道了陈省身在Riemann流形上证明GB定理的大略,知道了直觉和整体把握在数学中的重要性,还知道了一本Frankel的书,'捞'到了一本他的课的讲义.我没有把讲义还他,是因为今后我还会去找他的.他的课听过前半程,由于实在准备不足消化不良,就放弃了.

关于讲课还要说说潘海俊老师讲的<<经典力学>>.这也是一位年轻的老师,但讲课内容却非常精彩.他在清楚叙述基本概念的同时,还力求多样,比如在讲变分与最短路径的Hamilton原理时就花了不短的时间介绍Feynman路径积分.听他的家乡口英也是倍感轻切.接下来一个学期的<<近代数学物理方法>>,他讲得同样精彩.

至于课余生活,那学期也是很不错的,主要是我有了电吉他,有了自己的乐队,认识了大孟,剑宇,李矜.我们玩原创Punk,玩Nirvana,谢天笑.当我站在酒吧舞台上,那个Marshall音箱前面的时候,我感受到吉他就是AK47,手中的Pick是扳机,身上的热情是子弹.主唱大孟是少有的'黑嗓',和轰鸣的金属失真音色有绝佳的搭配;鼓手剑宇时常会有令人惊讶的即兴发挥.那段日子我特别留恋.怀念我们提着冲锋枪(吉他,别误会)和人抢出租车的场景,怀念那个已经被烟味熏得发甜的酒吧,怀念那振聋发聩的轰鸣.虽然我那时拮据到不得不一周带两次家教,但仍然觉得心甘情愿.但那样的日子怕是再也不会有了......

转眼到了该考虑GRE的时候.07年底,我试着开始准备作文,但由于没考虑清楚到底要不要选择毕业后出国深造,没多久就打了退堂鼓.这也是我比较后悔的一件事.那时的时间多充裕,都被我轰轰烈烈了.关于英语我没有提四六级的事,因为这被我们大多数同学'秒杀'.

大二下学期是在断断续续的背GRE单词和东奔西跑的旁听中度过的.我认识了我们寝室现在的导师.(注:物理系实行寝室导师制,即每个寝室可以分配一名科研一线的教授作为学习生活的导师)他待人很平和,很耐心,很愿意与我们交流.在他的鼓励下,我去旁听了那时他正在带的一门<<量子信息导论>>课.这门课上下来,在他带领下我是真正到科研的靠前部分去溜了溜.他的课很多人都觉得难,但我听过后,尤其是在接下来的一学期继续选<<量子计算>>选修时,深切体会到,若以后要投身与有关研究,这个课的所有内容都是及其基本且实用的.

可能是已经有些习以为常,或许是我写累了,大二下的生活就没想起多少.扭头看看书架,只记得读过一些书.在这也推荐给大家.Frankel, "Geometry in Physics",有很多图;尤承业,<<基础拓扑学讲义>>,精彩简练而内容却不平凡;J.D.Jackson,"Classical Electrodynamics",兵家必读; Landau &Lifshitz 的Vol.2(前6章),非常个性地讲解电动力学;其他记不清了.

大三的这个学期比较挑战.虽然有了几何学上的准备,但我没有接触广义相对论.也就是说我是'从头学'.幸好又碰上了好老师----年轻的杨老师,以及一本非常出色的入门书----Hartle写的教材.加上断断续续地啃Hawking的那本硬骨头,这门外系看来很难很枯燥的课也变得充实和有趣起来.在杨老师的课上我总能听到很有启发性的讲解,而这样渐渐地我对广义相对论的畏惧也转变成了兴趣.

其实我的每一门课,每一个老师都值得仔细讲.比如量子力学的石老师,对于这门课中思辨性的内容讲得很到位.这基于他本人对量子力学基本问题的相当数量的研究和思考.还有量子计算的杜老师,他本人在科研一线是非常活跃的,我们参加他的 Seminar,就相当于参加了他的科研组,充分接触到了这个领域的一些前沿问题.再说天体物理概论的袁老师,他对物理图像的充分阐释使我对一些物理过程印象深刻;群论的朱老师,一份出色的讲义使我们省掉许多自己的摸索.

经过慎重考虑,我决定'冒险'去听量子场论.说冒险,是因为当时只听说它很难,又听说它是必须,而从前又没有看过.不过几节课后井老师非常细致的课堂讲解便消除了我的顾虑."老师的作用就是给大家带带路",这是他老人家轻描淡写却又意味深长的话.

现如今又一个学期来到了,我的课表依然被排得满满的.我喜欢这种充实的感觉.充实,就是科大的感觉.

(Version 0.8)