做个小结

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口耐滴右手(48级)楼主2015-10-03 19:59:59发布于维多利亚
做个小结口耐滴右手 发表在步行街主干道 https://bbs.hupu.com/topic-daily

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啊啊啊啊啊,今天赶due比预期耗时更长啊。没来得及看正态分布的推导,明天一定不犯浑。哦不,今天。

不过经济学的due有一道题很有意思,忍不住做了一下research。

飞机上的座位调整往往是很蛋疼的事情。前面的人向后躺,后面的人立刻发毛。引起很多不必要的争执。所以题中问的是科斯定理怎么解决这个问题。

科斯定理是说在满足两个条件下,经济活动的外部性问题可以通过私下调解来解决掉。这两个条件是外部性的权力归属能够明确定义,以及交易成本可以忽略不计。

虽然昧着良心按照老师的意愿回答了这个问题。但还是要忍不住吐个槽

科斯定理完全无法用来解决飞机靠背问题,(其实科斯定理完全解决不了任何问题hhhhh)

按照科斯定理的解释,前后的乘客可以互相协商,比如后面的乘客可以支付给前面的乘客一笔钱,买走前面乘客向后放倒座椅的权力。但这想得太美了

首先是权利归属问题,坐在前面的乘客认为自己有权力向后放倒座椅。而坐在后面的乘客认为自己有权力获得更多的空间。所以座椅放倒所占用的这部分空间到底是归谁所有,前后两位乘客都各执一词。如果两方无法明确权力归属,那么就无法决定谁该向对方支付赔偿。No deal

其次是成本问题。和一个陌生人讨价还价是非常困难的。乘客需要在公开场合,众目睽睽之下做这种让人笑掉大牙的交易。没有乘客愿意做这么尴尬的事情吧哈哈。

最有有一点很有趣,除了第一排的乘客和最后一排的。其他所有人都同时是“坐在前面的”和“坐在后面的”。也就是说如果一个乘客A和前面的乘客达成协议,比如A支付前面的乘客10元来买下自己放腿的空间。那么乘客A需要确保自己和坐在后面的人达成的协议能和之前的协议互补——后面的乘客也要同意支付给A 10元来买下自己面前的空间。如果做不到这一点,乘客A可能首先不会和前面的乘客达成协议。而这是一个连锁反应,整个一列50多位乘客都要同意某一协议——即同意权力的归属,以及权力的价格。这一列中任何一个乘客不同意协议就会导致所有协议失效。

压根不现实。

我又想起来这周在公司里跟上司聊天时学到的东西。

公司在Geelong买了一块地用来发展豪宅区。但是这块地旁边有个采石场,土地污染比较严重。按照法律,公司可以起诉采石场,让采石场承担所有的环境维护费用。但问题在于一走法律程序,就会把整个案子拖得很长很长。而同时这块地因为环保标准未达标无法取得发展执照,如果公司就地起诉采石场的话,势必三年之内没办法发展这块地,也没有任何的招资和回报。同时还要支付巨额的律师费用,而且卷入法律纠纷影响公司形象,投资者甚至是合伙人都会颇有微词。

所以最后的结果就是公司坐下来和采石场谈判,公司和采石场承担清理费用。这样公司能更快开发这片地,采石场也能少花些钱(尽管他们应该支付全额)。最后皆大欢喜。

这个例子对于解决飞机上的空间可以问题有些启发。
啊啊啊啊啊,今天赶due比预期耗时更长啊。没来得及看正态分布的推导,明天一定不犯浑。哦不,今天。

不过经济学的due有一道题很有意思,忍不住做了一下research。

飞机上的座位调整往往是很蛋疼的事情。前面的人向后躺,后面的人立刻发毛。引起很多不必要的争执。所以题中问的是科斯定理怎么解决这个问题。

科斯定理是说在满足两个条件下,经济活动的外部性问题可以通过私下调解来解决掉。这两个条件是外部性的权力归属能够明确定义,以及交易成本可以忽略不计。

虽然昧着良心按照老师的意愿回答了这个问题。但还是要忍不住吐个槽

科斯定理完全无法用来解决飞机靠背问题,(其实科斯定理完全解决不了任何问题hhhhh)

按照科斯定理的解释,前后的乘客可以互相协商,比如后面的乘客可以支付给前面的乘客一笔钱,买走前面乘客向后放倒座椅的权力。但这想得太美了

首先是权利归属问题,坐在前面的乘客认为自己有权力向后放倒座椅。而坐在后面的乘客认为自己有权力获得更多的空间。所以座椅放倒所占用的这部分空间到底是归谁所有,前后两位乘客都各执一词。如果两方无法明确权力归属,那么就无法决定谁该向对方支付赔偿。No deal

其次是成本问题。和一个陌生人讨价还价是非常困难的。乘客需要在公开场合,众目睽睽之下做这种让人笑掉大牙的交易。没有乘客愿意做这么尴尬的事情吧哈哈。

最有有一点很有趣,除了第一排的乘客和最后一排的。其他所有人都同时是“坐在前面的”和“坐在后面的”。也就是说如果一个乘客A和前面的乘客达成协议,比如A支付前面的乘客10元来买下自己放腿的空间。那么乘客A需要确保自己和坐在后面的人达成的协议能和之前的协议互补——后面的乘客也要同意支付给A 10元来买下自己面前的空间。如果做不到这一点,乘客A可能首先不会和前面的乘客达成协议。而这是一个连锁反应,整个一列50多位乘客都要同意某一协议——即同意权力的归属,以及权力的价格。这一列中任何一个乘客不同意协议就会导致所有协议失效。

压根不现实。

我又想起来这周在公司里跟上司聊天时学到的东西。

公司在Geelong买了一块地用来发展豪宅区。但是这块地旁边有个采石场,土地污染比较严重。按照法律,公司可以起诉采石场,让采石场承担所有的环境维护费用。但问题在于一走法律程序,就会把整个案子拖得很长很长。而同时这块地因为环保标准未达标无法取得发展执照,如果公司就地起诉采石场的话,势必三年之内没办法发展这块地,也没有任何的招资和回报。同时还要支付巨额的律师费用,而且卷入法律纠纷影响公司形象,投资者甚至是合伙人都会颇有微词。

所以最后的结果就是公司坐下来和采石场谈判,公司和采石场承担清理费用。这样公司能更快开发这片地,采石场也能少花些钱(尽管他们应该支付全额)。最后皆大欢喜。

这个例子对于解决飞机上的空间可以问题有些启发。
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啊啊啊啊啊今天好多任务都没完成。碎片时间利用的太糟糕了QVQ。



看了半天notes其实还是自己已经会的,也没看出什么新东西。做题也没啥心得。



教量化分析的那个基佬终于换裤子了。



另外今天QM的课上想到了一个很有意思的问题:hypothesis test中有一个概念是type 1 2error。notes上给的type 1 error和2 error的critical value是相同的。 但是这个图只画出了one tail test,如果要做two tail test,这个极限值会有一边是重合的,另一边怎么算?

要搞清楚这个问题。还是问问我的美女tutor吧,无法直视那个基佬。



微积分学到了三维图形,还好还好。



LRC电路的微分方程精髓在于所有部分的电压加起来等于0。



i=dq/dt; 电源电压是q/c,电阻电压iR; Inductor电压应该是L*(di/dt) L是个系数



加起来就是q/c+L*(di/dt)+iR1+iR2+........iRn=0



di/st=d^2q/dt^2; 用e^x代入来解决掉。马克一下,以后留着复习用



数据的due满分!!!!bonus也拿到手了!!!!期末这一个H1有戏啊哈哈哈哈。然而基础金融还有due没写完,还有好多概念没有背。这周三的微经讲博弈论,明天抽个时间把reading看了。



虽然很不现实,但是从未有过如此强烈的愿望想考到年级第一。




啊啊啊啊啊今天好多任务都没完成。碎片时间利用的太糟糕了QVQ。



看了半天notes其实还是自己已经会的,也没看出什么新东西。做题也没啥心得。



教量化分析的那个基佬终于换裤子了。



另外今天QM的课上想到了一个很有意思的问题:hypothesis test中有一个概念是type 1 2error。notes上给的type 1 error和2 error的critical value是相同的。 但是这个图只画出了one tail test,如果要做two tail test,这个极限值会有一边是重合的,另一边怎么算?

要搞清楚这个问题。还是问问我的美女tutor吧,无法直视那个基佬。



微积分学到了三维图形,还好还好。



LRC电路的微分方程精髓在于所有部分的电压加起来等于0。



i=dq/dt; 电源电压是q/c,电阻电压iR; Inductor电压应该是L*(di/dt) L是个系数



加起来就是q/c+L*(di/dt)+iR1+iR2+........iRn=0



di/st=d^2q/dt^2; 用e^x代入来解决掉。马克一下,以后留着复习用



数据的due满分!!!!bonus也拿到手了!!!!期末这一个H1有戏啊哈哈哈哈。然而基础金融还有due没写完,还有好多概念没有背。这周三的微经讲博弈论,明天抽个时间把reading看了。



虽然很不现实,但是从未有过如此强烈的愿望想考到年级第一。




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hey...................
hey...................
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[quote][b]引用4楼 @梦凌枫潇 发表的[/b]:
hey...................[/quote]
你居然摸过来了QVQ

好吧,这里就是记录下我的邪思杂念。每天想太多,时间一长就忘了,然而又懒得写日记。就这样咯~

free to think, free to talk !

(其实这里还有好多好多黑历史,被我机智的删掉了XD)
[quote][b]引用4楼 @梦凌枫潇 发表的[/b]:
hey...................[/quote]
你居然摸过来了QVQ

好吧,这里就是记录下我的邪思杂念。每天想太多,时间一长就忘了,然而又懒得写日记。就这样咯~

free to think, free to talk !

(其实这里还有好多好多黑历史,被我机智的删掉了XD)
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https://www.youtube.com/watch?v=HON-9Z1Greo

肖斯塔柯维奇,列宁格勒交响曲

reading的时候千万不要听这么猎奇的交响曲,码一记。回来写些啥感受
https://www.youtube.com/watch?v=HON-9Z1Greo

肖斯塔柯维奇,列宁格勒交响曲

reading的时候千万不要听这么猎奇的交响曲,码一记。回来写些啥感受
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吐个槽,微积分练习册上有一道丧心病狂的求257阶导数的题...............

好吧,做法是很简单啦,把复数表达成三角函数形式,然后分割复数的实际域和虚拟域,再回归到极坐标形式,利用e^kx的导数是ke^kx的特点。再整理复数的式子。最后单独提取实际域或者虚拟域。

但是这些乱七八糟的式子,又是三角函数又是复数化简的,稍稍不慎就全错了...............口亨!!!!

啊,突然发现春天是色彩最丰富的季节。夏季满满都是刺眼的阳光,冬天则到处张扬着灰色与空白。秋天其实也很美,金黄的颜色铺满了视野,但是太单一,没有想象的空间。

只有缤纷斑斓的颜色交织着的春天,才能让人唤起心底那份对生活最真挚的热爱。

享受这可能非常短暂的美吧。
吐个槽,微积分练习册上有一道丧心病狂的求257阶导数的题...............

好吧,做法是很简单啦,把复数表达成三角函数形式,然后分割复数的实际域和虚拟域,再回归到极坐标形式,利用e^kx的导数是ke^kx的特点。再整理复数的式子。最后单独提取实际域或者虚拟域。

但是这些乱七八糟的式子,又是三角函数又是复数化简的,稍稍不慎就全错了...............口亨!!!!

啊,突然发现春天是色彩最丰富的季节。夏季满满都是刺眼的阳光,冬天则到处张扬着灰色与空白。秋天其实也很美,金黄的颜色铺满了视野,但是太单一,没有想象的空间。

只有缤纷斑斓的颜色交织着的春天,才能让人唤起心底那份对生活最真挚的热爱。

享受这可能非常短暂的美吧。
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远期汇率好绕啊,看学校的notes根本不知所云,上网搜了一下居然搜到了普林斯顿的notes,好吧,依然很绕。不过好歹算是理清了丝路。


1 假设A用澳元兑换M美元,市场即期汇率AUD/USD:S(注意这里AUD是commodity currency,USD是term currency,单位一是AUD,意味着1AUD等价S USD,而不是说AUD除以USD=S),A要支付M/S澳元


2 B提供给A,N天远期汇率合同。现在假设澳币国债利率Ra,美元国债利率Ru。如果B要确保九十天后能给A支付M美元,B需要先买成熟期位N天,面值为M的美元债券。则B需要在现在支付 M / (1+Ru·N/365),即面值为M的美债的即期价格。


3 如果要得到 M / (1+Ru·N/365)的美元, B需要用澳币以即期汇率兑换,则B需要澳币M / S·(1+Ru·N/365)。


4 为了支付澳币M / (1+Ru·N/365), B需要发行年化利率Ra,即期价格M / (1+Ru·N/365)的N天澳币债券。


5 N天过后,B购买的美债成熟期到期,拿回面值M美元。同时B要兑现澳币债券,此时澳币债券面值为[M / (1+Ru·N/365)]·(1+Ra·N/365)=[M·(1+Ra·N/365)]/[ (1+Ru·N/365)] 


6 B支付给A M美元,同时作为价格,A应支付[M·(1+Ra·N/365)]/[ (1+Ru·N/365)] 澳币,那么对于A来说,90天后实际支付的利率F=M/{[M·(1+Ra·N/365)]/[ (1+Ru·N/365)]}= (1+Ru·N/365)/(1+Ra·N/365)


7 然后真正的公式中把Ru表示成Rterms,即term currency的债券利率,Ra变成Rcom


F=S·(1+Rterms·N/365)/(1+Rcom·N/365)


其实从公式里面就能看出来远期汇率和即期汇率的关系,和即期汇率,两种货币债券的利率以及期限的时间相挂钩的。最重要的还是两种货币债券利率的比较,对于B来说,有利的情况是Rterm>Rcom,对于A来说就恰恰相反了。






远期汇率好绕啊,看学校的notes根本不知所云,上网搜了一下居然搜到了普林斯顿的notes,好吧,依然很绕。不过好歹算是理清了丝路。


1 假设A用澳元兑换M美元,市场即期汇率AUD/USD:S(注意这里AUD是commodity currency,USD是term currency,单位一是AUD,意味着1AUD等价S USD,而不是说AUD除以USD=S),A要支付M/S澳元


2 B提供给A,N天远期汇率合同。现在假设澳币国债利率Ra,美元国债利率Ru。如果B要确保九十天后能给A支付M美元,B需要先买成熟期位N天,面值为M的美元债券。则B需要在现在支付 M / (1+Ru·N/365),即面值为M的美债的即期价格。


3 如果要得到 M / (1+Ru·N/365)的美元, B需要用澳币以即期汇率兑换,则B需要澳币M / S·(1+Ru·N/365)。


4 为了支付澳币M / (1+Ru·N/365), B需要发行年化利率Ra,即期价格M / (1+Ru·N/365)的N天澳币债券。


5 N天过后,B购买的美债成熟期到期,拿回面值M美元。同时B要兑现澳币债券,此时澳币债券面值为[M / (1+Ru·N/365)]·(1+Ra·N/365)=[M·(1+Ra·N/365)]/[ (1+Ru·N/365)] 


6 B支付给A M美元,同时作为价格,A应支付[M·(1+Ra·N/365)]/[ (1+Ru·N/365)] 澳币,那么对于A来说,90天后实际支付的利率F=M/{[M·(1+Ra·N/365)]/[ (1+Ru·N/365)]}= (1+Ru·N/365)/(1+Ra·N/365)


7 然后真正的公式中把Ru表示成Rterms,即term currency的债券利率,Ra变成Rcom


F=S·(1+Rterms·N/365)/(1+Rcom·N/365)


其实从公式里面就能看出来远期汇率和即期汇率的关系,和即期汇率,两种货币债券的利率以及期限的时间相挂钩的。最重要的还是两种货币债券利率的比较,对于B来说,有利的情况是Rterm>Rcom,对于A来说就恰恰相反了。






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提到reading,由于这学期四门课两门是数学相关,基础金融半文半理,只有微经还是纯粹的文科。所以reading从来不是很繁琐的项目。

博弈论的reading只有72页,而且还是影音的旧版书。排版间的空隙估计能写下一本脂砚斋平红楼梦。文字阅读量压根不多。两个晚上随随便便就完事了。

不过我很惊讶的是学校文学院的学生上课reading也不多。相反很多该有的reading都是老师在课上按照学生在这一阶段应当掌握的水平而给出digest。这倒是很省事,毕竟学术书中大部分都是论证的过程,而作者的主要观点总结起来不到三分之一。

听过很多其他学校reading如何变态,学文科之类的课程reading很多我觉不是怪事。

但是为什么其他学校学数学或者计算机会有很多的reading?? 我的学校数学系中reading最多也最重要的是大二的实分析这门课,而且reading多也是因为课程设置中有很多关于数学的哲学理论。

按理说大一数学是基础的不能在基础的课程了。而且不做好数学基础的教育,压根没有办法进行实分析这种哲学境界的数学课程。所以可以排除大一数学的reading和实分析的reading是一个境界的可能性。

那么这些数学的reading到底是在看什么?

我认为reading的存在是因为教科书中没有涵盖某些重要的知识理论。大一的数学居然难道这种境界了么.............要真是这样也挺恐怖的QvQ.....

我现在学的微积分所涵盖的topic只是正本教科书的四分之三而已。难怪没有什么reading╮(╯▽╰)╭
提到reading,由于这学期四门课两门是数学相关,基础金融半文半理,只有微经还是纯粹的文科。所以reading从来不是很繁琐的项目。

博弈论的reading只有72页,而且还是影音的旧版书。排版间的空隙估计能写下一本脂砚斋平红楼梦。文字阅读量压根不多。两个晚上随随便便就完事了。

不过我很惊讶的是学校文学院的学生上课reading也不多。相反很多该有的reading都是老师在课上按照学生在这一阶段应当掌握的水平而给出digest。这倒是很省事,毕竟学术书中大部分都是论证的过程,而作者的主要观点总结起来不到三分之一。

听过很多其他学校reading如何变态,学文科之类的课程reading很多我觉不是怪事。

但是为什么其他学校学数学或者计算机会有很多的reading?? 我的学校数学系中reading最多也最重要的是大二的实分析这门课,而且reading多也是因为课程设置中有很多关于数学的哲学理论。

按理说大一数学是基础的不能在基础的课程了。而且不做好数学基础的教育,压根没有办法进行实分析这种哲学境界的数学课程。所以可以排除大一数学的reading和实分析的reading是一个境界的可能性。

那么这些数学的reading到底是在看什么?

我认为reading的存在是因为教科书中没有涵盖某些重要的知识理论。大一的数学居然难道这种境界了么.............要真是这样也挺恐怖的QvQ.....

我现在学的微积分所涵盖的topic只是正本教科书的四分之三而已。难怪没有什么reading╮(╯▽╰)╭
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原来泰勒极限的到处是根据极限式的导数是其本身的特点,进而用e的幂数形式可以进行估算。

我还以为是什么高深的定义呢口亨。
原来泰勒极限的到处是根据极限式的导数是其本身的特点,进而用e的幂数形式可以进行估算。

我还以为是什么高深的定义呢口亨。
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1 固定成本是沉没成本,短期内不能够影响企业的产出与定价决定



2 离岸资本市场存在的好处有三,一为企业提供了多元化的资金来源,二降低企业购置外汇的成本,三为企业提供潜能更大的资本市场。

3 切记弹簧在负重平衡的时候已经有一部分延展长度,而当重量块开始做周期运动的时候,他的均衡位置其实是带着原始的延展长度,因此弹簧拉力是K(T+S) 
1 固定成本是沉没成本,短期内不能够影响企业的产出与定价决定



2 离岸资本市场存在的好处有三,一为企业提供了多元化的资金来源,二降低企业购置外汇的成本,三为企业提供潜能更大的资本市场。

3 切记弹簧在负重平衡的时候已经有一部分延展长度,而当重量块开始做周期运动的时候,他的均衡位置其实是带着原始的延展长度,因此弹簧拉力是K(T+S) 
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I as a bank manager can manipulate the reference rate (eg, Libor) and get profit from financial products or derivatives whose prices are derived from the reference rate.
For example, I can purchase a 90-day security today with face value of 1milllion. The interest rate which is derived from the Libor is assumed to be 5%. The price of the security will be
P=1000000/(1+(o.o5*90/365)) =$987821.3802.
On the next business day, assume I will sell this security.If the interest rate remains at 5%, price will be
P=1000000/(1+(o.o5*89/365))=$987955.0683
I make a profit of $133.6881.
However, if I can manipulate the Libor, I can potentially make more profit by purposely keeping it low. I can approach my colleagues in charge of submitting the preferred Libor rate to BBA and Thomas Reuters, let them to lower their reported rates. I can also collude with the rest of the 16 banks who are also in the panel to lower the Libor.
Assume on the next day the Libor drops 10 basis points, the interest rate will adjust itself accordingly to 5%-0.1%=4.9%. So this time if I were to sell that 90-day security. I will receive P=1000000/(1+(o.o49*89/365))=$988193.1227
I make a profit of $371.7425174. This is almost 3 folds more than the profit I can get if Libor doesn’t change or even goes higher.
I as a bank manager can manipulate the reference rate (eg, Libor) and get profit from financial products or derivatives whose prices are derived from the reference rate.
For example, I can purchase a 90-day security today with face value of 1milllion. The interest rate which is derived from the Libor is assumed to be 5%. The price of the security will be
P=1000000/(1+(o.o5*90/365)) =$987821.3802.
On the next business day, assume I will sell this security.If the interest rate remains at 5%, price will be
P=1000000/(1+(o.o5*89/365))=$987955.0683
I make a profit of $133.6881.
However, if I can manipulate the Libor, I can potentially make more profit by purposely keeping it low. I can approach my colleagues in charge of submitting the preferred Libor rate to BBA and Thomas Reuters, let them to lower their reported rates. I can also collude with the rest of the 16 banks who are also in the panel to lower the Libor.
Assume on the next day the Libor drops 10 basis points, the interest rate will adjust itself accordingly to 5%-0.1%=4.9%. So this time if I were to sell that 90-day security. I will receive P=1000000/(1+(o.o49*89/365))=$988193.1227
I make a profit of $371.7425174. This is almost 3 folds more than the profit I can get if Libor doesn’t change or even goes higher.
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突然想起来一个思维的盲点。



经济学中最基本的概念就是机会成本,而和机会成本遥相呼应的就是沉没成本。这是整个经济学研究的最基本框架。



所有的教科书上都告诉我们沉没成本不应参与决策。我们日常做决定的时候需要参考的只是预期收益和机会成本,沉没成本不应参与考量。但是教科书却没有告诉我们为什么现实中我们会对沉没成本念念不忘。 


沉没成本在成为沉没成本之前也会被当做机会成本参与决策,现在先想到这些。留着接着码字
突然想起来一个思维的盲点。



经济学中最基本的概念就是机会成本,而和机会成本遥相呼应的就是沉没成本。这是整个经济学研究的最基本框架。



所有的教科书上都告诉我们沉没成本不应参与决策。我们日常做决定的时候需要参考的只是预期收益和机会成本,沉没成本不应参与考量。但是教科书却没有告诉我们为什么现实中我们会对沉没成本念念不忘。 


沉没成本在成为沉没成本之前也会被当做机会成本参与决策,现在先想到这些。留着接着码字
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今天回家下车的时候手机正好放到了拉二的第一乐章。突然抬头看见满天的星星,再配着背景音乐,感觉好梦幻!~
今天回家下车的时候手机正好放到了拉二的第一乐章。突然抬头看见满天的星星,再配着背景音乐,感觉好梦幻!~
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hmmmm 今天是公司的family day & pets day..............举目四望,并没有什么family QAQ
hmmmm 今天是公司的family day & pets day..............举目四望,并没有什么family QAQ
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如何欣赏老柴

On Tchaikovsky



How is one to put into words those indeterminate feelings that engulf one during the composition of an instrumental work? It is a purely lyrical process, the outpourings of a soul marked by the vicissitudes of life but destined by its very nature to express itself in music.” Tchaikovsky wrote that in 1878, after the completion of his fourth symphony, in a letter to his benefactress, Nadezhda Von Meck, the widow of an industrialist. Her generosity enabled him to devote himself entirely to composition. In the letter, Tchaikovsky has more to say about the vicissitudes of life, “This is fate, that inexorable force; it is inescapable and invincible. There is no other course but to submit and to lament in vain.”



He was convinced that this idea of fate or providence was crucial and that it was beyond the powers of mere mortals to do anything about it. This conviction is reflected in his music, notably in his symphonic works. For Tchaikovsky, music was not just the arrangement of notes on the page; it was the language of emotion, the mirror of his own feelings. Eleven years later Tchaikovsky composed his fifth symphony. By then he was Russia’s most prominent composer at home and abroad. Again, the idea of fate ran through the whole work. He noted, “Introduction: complete surrender to fate or—and this is the same thing—to the inscrutable decrees of providence.” 

Tchaikovsky was highly sensitive. Outwardly, the impression he made was balanced and self-controlled, but in reality he was very insecure; an unstable, tormented personality. He was prey to dire visions and nightmares and his diary is full of astonishing and distressing disclosures about the psychological agonies he went through. He wrote to Nadezhda Von Meck expressing his fear that he was “written out”, but he completed the fifth symphony within the space of three months. Tchaikovsky conducted the first performance himself on the fifth of November, 1888, in St. Petersburg. His brother, Modeste, was present. After the symphony Pyotr Ilyich received a rapturous applause. The orchestra played three flourishes for him and he was presented with flowers. But despite its great success with the audience, many critics found fault with the new symphony. 

But by no means all of them. After the first German performance five months later, the Hamburg reviewer Josef Zitaud, wrote, “The E-minor symphony can rightly be hailed as one of the most significant symphonic works of the age.” Today, Tchaikovsky’s “Fifth” is among the most famous symphonies ever written.

 Pyotr Ilyich Tchaikovsky was born on the 7th of May, 1840, in a small mining town west of the Urals called Votkinsk. His mother, Alexandra Andreyevna, played the piano and introduced her son to the world of music. The highly sensitive boy responded with passionate interest. Though his musical gifts were encouraged by his parents, the lowly social standing of professional musicians meant they never seriously contemplated a musical career for him. At the age of ten he was sent to the School of Jurisprudence in St. Petersburg, which he left nine years later to take up a junior post in the Ministry of Justice. He described himself as “a poor civil servant”. 

Finally, in 1862, he enrolled at the new St. Petersburg Conservatory of Music established by Anton Rubenstein. Rubenstein persuaded him to devote himself entirely to music. In a letter to his sister, Tchaikovsky says, “This is my vocation and I must follow it. Whether I become a great composer or a poor music teacher is immaterial. At all events my conscience will be clear and I shall no longer have any cause to complain about my lot.” After successfully completing his studies in St. Petersburg, Tchaikovsky spent twelve years teaching music theory at the new conservatory in Moscow. His first four symphonies and many other works date from this period, so it was productive for him as a composer, but it was also a time of distress and unrest. 

Tchaikovsky was homosexual and that was a social stigma. To avoid the inevitable ostracism associated with it, he resolved to marry Antonina Miliukova, a woman he hardly knew. The marriage was a disaster. Tchaikovsky suffered a complete nervous breakdown and tried to kill himself. After separating from his wife in 1878, Tchaikovsky continued as an extremely successful freelance composer. The vicissitudes he had been through strengthened his firm belief in the force of destiny. The mysterious circumstances surrounding his early death at the age of 53 have given rise to a great deal of speculation. We know that he drank a glass of unboiled water in a restaurant in St. Petersburg when cholera was raging in the city. Some believe that he did this intentionally.

Igor Stravinsky, a great admirer of Tchaikovsky, said this about his countryman, “Tchaikovsky had a powerful sense of melody. It is the centre of gravity in all his symphonies, operas and ballets. There is no doubt that he was an inspired creator of melody and that is a rare and precious gift.” The beginning of the second movement takes us into an entirely different world. With quiet piano-pianissimo chords in the lower strings, it’s a very gentle introduction. Then comes a cantilena on the horn; this is the main theme. The movement is marked “Andante Cantabile con alcuna licenza”, a songful andante with a degree of license. This is an allusion to the licenza of operatic arias, allowing the singer to modify the tempo at his or her discretion.



The horn cantilena is followed by an oboe theme that Tchaikovsky refers to in his sketches as “a ray of light”. Both these themes culminate in passionate climaxes, which, however, subside again almost as soon as they appear. If you think of the symphony in terms of a novel, I would say that this is an idyllic episode. In fact, I think you could even call it a love scene. It opens as a dialogue between the horn melody and the oboe theme. In the central section you have constant give and take between different instruments or groups of instruments. Then there’s the indication “Con desiderio e passione”, which is very unusual. 

The central section introduces a new theme that builds to a forte-fortissimo climax. At this point the full orchestra hammers out the “fate” theme. After a general pause, the recapitulation sets in. Again, the two main themes are developed into a passionate climax. The “fate” theme intrudes once more before the coda brings the movement to a melancholy close built around the second theme.
如何欣赏老柴

On Tchaikovsky



How is one to put into words those indeterminate feelings that engulf one during the composition of an instrumental work? It is a purely lyrical process, the outpourings of a soul marked by the vicissitudes of life but destined by its very nature to express itself in music.” Tchaikovsky wrote that in 1878, after the completion of his fourth symphony, in a letter to his benefactress, Nadezhda Von Meck, the widow of an industrialist. Her generosity enabled him to devote himself entirely to composition. In the letter, Tchaikovsky has more to say about the vicissitudes of life, “This is fate, that inexorable force; it is inescapable and invincible. There is no other course but to submit and to lament in vain.”



He was convinced that this idea of fate or providence was crucial and that it was beyond the powers of mere mortals to do anything about it. This conviction is reflected in his music, notably in his symphonic works. For Tchaikovsky, music was not just the arrangement of notes on the page; it was the language of emotion, the mirror of his own feelings. Eleven years later Tchaikovsky composed his fifth symphony. By then he was Russia’s most prominent composer at home and abroad. Again, the idea of fate ran through the whole work. He noted, “Introduction: complete surrender to fate or—and this is the same thing—to the inscrutable decrees of providence.” 

Tchaikovsky was highly sensitive. Outwardly, the impression he made was balanced and self-controlled, but in reality he was very insecure; an unstable, tormented personality. He was prey to dire visions and nightmares and his diary is full of astonishing and distressing disclosures about the psychological agonies he went through. He wrote to Nadezhda Von Meck expressing his fear that he was “written out”, but he completed the fifth symphony within the space of three months. Tchaikovsky conducted the first performance himself on the fifth of November, 1888, in St. Petersburg. His brother, Modeste, was present. After the symphony Pyotr Ilyich received a rapturous applause. The orchestra played three flourishes for him and he was presented with flowers. But despite its great success with the audience, many critics found fault with the new symphony. 

But by no means all of them. After the first German performance five months later, the Hamburg reviewer Josef Zitaud, wrote, “The E-minor symphony can rightly be hailed as one of the most significant symphonic works of the age.” Today, Tchaikovsky’s “Fifth” is among the most famous symphonies ever written.

 Pyotr Ilyich Tchaikovsky was born on the 7th of May, 1840, in a small mining town west of the Urals called Votkinsk. His mother, Alexandra Andreyevna, played the piano and introduced her son to the world of music. The highly sensitive boy responded with passionate interest. Though his musical gifts were encouraged by his parents, the lowly social standing of professional musicians meant they never seriously contemplated a musical career for him. At the age of ten he was sent to the School of Jurisprudence in St. Petersburg, which he left nine years later to take up a junior post in the Ministry of Justice. He described himself as “a poor civil servant”. 

Finally, in 1862, he enrolled at the new St. Petersburg Conservatory of Music established by Anton Rubenstein. Rubenstein persuaded him to devote himself entirely to music. In a letter to his sister, Tchaikovsky says, “This is my vocation and I must follow it. Whether I become a great composer or a poor music teacher is immaterial. At all events my conscience will be clear and I shall no longer have any cause to complain about my lot.” After successfully completing his studies in St. Petersburg, Tchaikovsky spent twelve years teaching music theory at the new conservatory in Moscow. His first four symphonies and many other works date from this period, so it was productive for him as a composer, but it was also a time of distress and unrest. 

Tchaikovsky was homosexual and that was a social stigma. To avoid the inevitable ostracism associated with it, he resolved to marry Antonina Miliukova, a woman he hardly knew. The marriage was a disaster. Tchaikovsky suffered a complete nervous breakdown and tried to kill himself. After separating from his wife in 1878, Tchaikovsky continued as an extremely successful freelance composer. The vicissitudes he had been through strengthened his firm belief in the force of destiny. The mysterious circumstances surrounding his early death at the age of 53 have given rise to a great deal of speculation. We know that he drank a glass of unboiled water in a restaurant in St. Petersburg when cholera was raging in the city. Some believe that he did this intentionally.

Igor Stravinsky, a great admirer of Tchaikovsky, said this about his countryman, “Tchaikovsky had a powerful sense of melody. It is the centre of gravity in all his symphonies, operas and ballets. There is no doubt that he was an inspired creator of melody and that is a rare and precious gift.” The beginning of the second movement takes us into an entirely different world. With quiet piano-pianissimo chords in the lower strings, it’s a very gentle introduction. Then comes a cantilena on the horn; this is the main theme. The movement is marked “Andante Cantabile con alcuna licenza”, a songful andante with a degree of license. This is an allusion to the licenza of operatic arias, allowing the singer to modify the tempo at his or her discretion.



The horn cantilena is followed by an oboe theme that Tchaikovsky refers to in his sketches as “a ray of light”. Both these themes culminate in passionate climaxes, which, however, subside again almost as soon as they appear. If you think of the symphony in terms of a novel, I would say that this is an idyllic episode. In fact, I think you could even call it a love scene. It opens as a dialogue between the horn melody and the oboe theme. In the central section you have constant give and take between different instruments or groups of instruments. Then there’s the indication “Con desiderio e passione”, which is very unusual. 

The central section introduces a new theme that builds to a forte-fortissimo climax. At this point the full orchestra hammers out the “fate” theme. After a general pause, the recapitulation sets in. Again, the two main themes are developed into a passionate climax. The “fate” theme intrudes once more before the coda brings the movement to a melancholy close built around the second theme.
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不仅仅在于无理数的存在,有理数为正整数比值的这个定义也在另一个方面限制了古希腊数学的发展,那就是单位的问题。

古希腊人一直认为能够用来做比值的物体必须是相同单位的,比如五个点比三个点。五个苹果比三个苹果。但假如五个点除以三条线,这个比值就显得毫无意义。古希腊人的定义中,比值的意义在于同类事务的数量之间的关系。而不同类的事务之间的数量关系并没有太多的意义。

另一个原因还有一条线段有无数个点,一个面包含无数条线,一个立方体包含无数个横切面。因此用不同的事务去比较还会出现如何除以“无限”这个很纠结的概念。比如一条线段有无数个点,而五个点比上一条线段,显然就不可能进行比较。

但是今天的数学,任何数字都可以用来比较。比如速度,加速度,加速度的加速度。这些都是用毫不相干的单位的数量关系来表示的。在古希腊人看来,用距离除以时间并没有任何的意义。可这和根号二的纠结是一个意思,古希腊人没有意识到,再原有定义框架下毫无意义的东西,在新的定义体系下会有意义。如果两个不同单位量的比值看起来是没有意义的,那我们完全可以把这两个不同单位量的比值当做新的单位。速度就是这一例子。

同样五个点和一条线的比例我们也可以理解成一个单位线段上,我划定五个点,然后这就是我的新的单位,新的单位可以用来去比较其他的单位然后寻求数量之间的关系。

其实古希腊人还是有速度的概念的,但是他们对于速度的概念比较奇特。古希腊人把速度当做恒定的值,然后这种情况下两端不同的旅途中,路程的比例等于所用时间的比例。而古希腊人因为不能接受不同单位之间的比值,因此就无法理解速度的改变。

亚里士多德就曾经写道,motion of motion is beyond our ability to measure.

当然今天物理学中加速度的定义必须用微积分的关系来导出才显得有意义。因为只有微积分中的极限理论才能解释瞬间速度这个定义。

根据亚里士多德,也给根据我们的常识,无论什么物体,他在一瞬间的速度都是0,因为一瞬间没有任何时间区间,因此就没有任何移动距离可言。也就没有任何的速度可以求得。但相反如果我把每一个点状的时间叠加起来,我就有了时间区间,我就能有移动距离,可没一个点状时间的速度都是零,加起来为什却不是零呢?这是亚里士多德无法解释的。

但是微积分给这看似没有意义的概念,赋予了意义。

这就是极限,以后再展开。
不仅仅在于无理数的存在,有理数为正整数比值的这个定义也在另一个方面限制了古希腊数学的发展,那就是单位的问题。

古希腊人一直认为能够用来做比值的物体必须是相同单位的,比如五个点比三个点。五个苹果比三个苹果。但假如五个点除以三条线,这个比值就显得毫无意义。古希腊人的定义中,比值的意义在于同类事务的数量之间的关系。而不同类的事务之间的数量关系并没有太多的意义。

另一个原因还有一条线段有无数个点,一个面包含无数条线,一个立方体包含无数个横切面。因此用不同的事务去比较还会出现如何除以“无限”这个很纠结的概念。比如一条线段有无数个点,而五个点比上一条线段,显然就不可能进行比较。

但是今天的数学,任何数字都可以用来比较。比如速度,加速度,加速度的加速度。这些都是用毫不相干的单位的数量关系来表示的。在古希腊人看来,用距离除以时间并没有任何的意义。可这和根号二的纠结是一个意思,古希腊人没有意识到,再原有定义框架下毫无意义的东西,在新的定义体系下会有意义。如果两个不同单位量的比值看起来是没有意义的,那我们完全可以把这两个不同单位量的比值当做新的单位。速度就是这一例子。

同样五个点和一条线的比例我们也可以理解成一个单位线段上,我划定五个点,然后这就是我的新的单位,新的单位可以用来去比较其他的单位然后寻求数量之间的关系。

其实古希腊人还是有速度的概念的,但是他们对于速度的概念比较奇特。古希腊人把速度当做恒定的值,然后这种情况下两端不同的旅途中,路程的比例等于所用时间的比例。而古希腊人因为不能接受不同单位之间的比值,因此就无法理解速度的改变。

亚里士多德就曾经写道,motion of motion is beyond our ability to measure.

当然今天物理学中加速度的定义必须用微积分的关系来导出才显得有意义。因为只有微积分中的极限理论才能解释瞬间速度这个定义。

根据亚里士多德,也给根据我们的常识,无论什么物体,他在一瞬间的速度都是0,因为一瞬间没有任何时间区间,因此就没有任何移动距离可言。也就没有任何的速度可以求得。但相反如果我把每一个点状的时间叠加起来,我就有了时间区间,我就能有移动距离,可没一个点状时间的速度都是零,加起来为什却不是零呢?这是亚里士多德无法解释的。

但是微积分给这看似没有意义的概念,赋予了意义。

这就是极限,以后再展开。
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法拉利上市的新闻,里面提到了承销商的一串名单。

其中很多非常容易辨认的老牌子,摩根大通,桑坦德,瑞银等等等等。不过Allen&co是一个很熟悉但却完全想不起来搞什么的名字。

今天一翻旧新闻,啊,这不正是可口可乐,华纳,FB,谷歌以及京东等等一系列大公司上市的幕后推手么。。。。。。。。。

小巧精致的规模,刻意避免媒体曝光的公关策略,但却在资本市场的每一次大动作背后留下自己的痕迹。

资本主义大法好。
法拉利上市的新闻,里面提到了承销商的一串名单。

其中很多非常容易辨认的老牌子,摩根大通,桑坦德,瑞银等等等等。不过Allen&co是一个很熟悉但却完全想不起来搞什么的名字。

今天一翻旧新闻,啊,这不正是可口可乐,华纳,FB,谷歌以及京东等等一系列大公司上市的幕后推手么。。。。。。。。。

小巧精致的规模,刻意避免媒体曝光的公关策略,但却在资本市场的每一次大动作背后留下自己的痕迹。

资本主义大法好。
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天鹅湖最吸引人的艺术高光点就是白天鹅和黑天鹅的设定。

白天鹅象征纯洁,高雅,善良,一切你能想象的美好品格。

黑天鹅象征妖艳,黑暗,精明。一切你能想象的邪恶本质。

白天鹅和黑天鹅在和王子对戏的时候,都同样有一段和王子若即若离的片段。

第二幕中小天鹅的群舞片段结束后,白天鹅会和王子有一段双人独舞。他们亲密相拥,但随后又立刻转身远离王子;王子再一次靠近白天鹅,白天鹅依旧回到王子怀中,而后又转身远离王子,但这一次白天鹅转身的动作就没有上一次那么急促和慌张;这一套动作大概重复四次,每一次天鹅转身远离王子的动作幅度都会有所减小。这个细节是为了体现白天鹅内心的矛盾。看到了心爱的王子,但又想到自己受到的诅咒,便要决心离开王子,犹豫再三又回到王子的怀中,反反复复之后,这种犹豫和矛盾再三减弱。最终白天鹅像王子透露出了自己所受的诅咒。

黑天鹅与王子的双人舞中也有一套类似的动作,但是演员在此时要展现出的精神面貌就完全不同了。黑天鹅每一次从王子的怀中挣脱时,都要做出一种玩弄王子的感觉。因为黑天鹅的目的是为了吸引王子的注意力,吸引王子上钩,用一种顾此言他的遮遮掩掩来“勾引”王子。这时的黑天鹅内心充满了邪恶的算计和策划。要表现出邪恶妩媚,同时还要给人一种勾引的感觉,这对于上一幕刚刚演完纯洁善良的白天鹅的演员来说是巨大的挑战,在短时间内完全要切换整套精神面貌和相应的技术动作,这是非常困难的。

不过很有意思的一点是,黑天鹅和白天饿这两种人格设定其实都是寄托在一个人——公主奥杰塔的形象之内。

也许这就是在暗示,我们每个人心中都有一只白天鹅,还有一只黑天鹅。
天鹅湖最吸引人的艺术高光点就是白天鹅和黑天鹅的设定。

白天鹅象征纯洁,高雅,善良,一切你能想象的美好品格。

黑天鹅象征妖艳,黑暗,精明。一切你能想象的邪恶本质。

白天鹅和黑天鹅在和王子对戏的时候,都同样有一段和王子若即若离的片段。

第二幕中小天鹅的群舞片段结束后,白天鹅会和王子有一段双人独舞。他们亲密相拥,但随后又立刻转身远离王子;王子再一次靠近白天鹅,白天鹅依旧回到王子怀中,而后又转身远离王子,但这一次白天鹅转身的动作就没有上一次那么急促和慌张;这一套动作大概重复四次,每一次天鹅转身远离王子的动作幅度都会有所减小。这个细节是为了体现白天鹅内心的矛盾。看到了心爱的王子,但又想到自己受到的诅咒,便要决心离开王子,犹豫再三又回到王子的怀中,反反复复之后,这种犹豫和矛盾再三减弱。最终白天鹅像王子透露出了自己所受的诅咒。

黑天鹅与王子的双人舞中也有一套类似的动作,但是演员在此时要展现出的精神面貌就完全不同了。黑天鹅每一次从王子的怀中挣脱时,都要做出一种玩弄王子的感觉。因为黑天鹅的目的是为了吸引王子的注意力,吸引王子上钩,用一种顾此言他的遮遮掩掩来“勾引”王子。这时的黑天鹅内心充满了邪恶的算计和策划。要表现出邪恶妩媚,同时还要给人一种勾引的感觉,这对于上一幕刚刚演完纯洁善良的白天鹅的演员来说是巨大的挑战,在短时间内完全要切换整套精神面貌和相应的技术动作,这是非常困难的。

不过很有意思的一点是,黑天鹅和白天饿这两种人格设定其实都是寄托在一个人——公主奥杰塔的形象之内。

也许这就是在暗示,我们每个人心中都有一只白天鹅,还有一只黑天鹅。
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