It's Layla's labyrinth

Tag: 数学 (page 1 of 1)

The power of simple

When step back to the entire student life over the 20 years, I can say that the most magic course I’ve taken is no doubt to be mathematics.Everybody learns mathematics for at least 12years, from primary to senior high, the only difference is someone enjoys, someone suffers.


I’ve been the latter for sure. No mathematics intelligence is inherited from my parents though they are both talented in dealing with mathematics. Father studies physics, which is based on mathematics training. Mother studies engineering, fundamental mathematics is in great need of which.

However, after graduation from primary school, I fell in a strange math-phobia. Troubles kept showing up to ridicule my clumsiness and brainless effort. I tried so many ways to get it better but failed thereafter.

Mathematic is COMPLEX. I said to myself during every-night-fight with maths.


I can’t remember how I survived before I finally met physics. Physics is  the last straw. I was totally defeated by this charming sister of mathematics. I envy my peers who can easily deal with these twin sisters, after all, I can’t.


So I can’t understand why I’ve choose finance and finance engineering as major of college. My mathematics teacher in high school told me economics is mathematics. How could I just forget that….


Regret? No, absolutely not. Actually I felt so fortunate to have made this decision. Otherwise, I might have missed a lot of great experiences now.

Change happened in my college year..

To tell the significance of changes, let’s extract a piece of my memory: On Tuesday I attended my class of derivatives,  professor tried to tell us a phenomenon that the distances in premium of call option with different strike price is shorter than the distance  in the strike prices. He tried to tell us verbally in the first 15 minutes, but failed. Verbally is institutionally indeed, but not convincing.

He would have no alternative to turn to mathematics, I guessed. Why not use function convexity to illustrate that? Quite simple, right? You might say the function is not continuous, but so what? Try convex set, you’ll get the conclusion.

Just as expected, he went the the whiteboard and drew  a plot, and started to explain in Mathematics way. Only 5 minutes, things got clear.

See? Mathematics is SIMPLE.

The existent of mathematics is aimed at making the world more simple and clarified, especially applied mathematics. Statistics, algorithm, operational research….everything is meant to MAKE IT SIMPLER.

Take operational research and linear programming as another example. Everybody who ever enrolled in this course learnt about queue theory and simplex method. Simplify the business decision: manufacturer management, price setting,selling plans…and other complex real business problems into relatively simple mathematics model, and solve them using random variables or basic constraints, and then find possible optimal solution.

Got it? Mathematic is used to deduct the complexity of real world problems.

We have to admit that mathematics itself may be hard to learn. Many many art students are going crazy with calculus or probabilities. Many many engineering students are busy with graph theory and combination. Many many science students are fighting against analysis, differential equations, number theory….

But the NATURE of mathematics is simple. Complexity inside mathematics is served to accompany the simpleness with convince.Look at Taylor expansion, many of us feel uncomfortable to memorize the equation, but when applied into practice, and by ignoring high order terms, Taylor expansion does contribute to dealing with high order polynomial.Another example is algorithm. Applying algorithm into programming will help decrease meaningless duplication. However, it might be time-costing or space costing quite often. To find or develope a clear and good algorithm can be quite hard. But we have to experience and shoulder the hardship and complexity to be simple.

In some field, simple is not enough. For example, literature. When studying comparative literature, people have to master two or more languages to do the research.Art will get dull without complexity. But not mathematics. We are not meant to make these look complex and “zhuangbility”, all we need is to make things simple but also convincing.


Try to think in this way: Can I abstract the nature of problem? Can I express them in a more clear way? Can I recount this problem to another person in an most efficient way?


If you do think like this, I believe finally the method is to use mathematics, for most of the case.

Look, this is the power of simple.



今天在上数学选修课,Alex突然从天而降(其实我一直觉得你还在南通做项目……),又很惊喜的发现金丹姐姐也选了这门数学课,所以三个人决定下了 课去喝奶茶。在奶茶店聊到Alex工作的事情,然后就聊到英语能力,接着聊到最近大热的瑞银女PK渣打小三的英文邮件,然后就聊到爱情的问题了。

金 丹姐说,认识1-2年结婚是很好的选择,因为如果周期太长,爱情就会消失,就像是七年之痒。而Alex反对,他抛出周董的爱情经济学理论:即两人认识的时 间越长,信息不对称的差异就越小,这样两人的生活中信息成本就会降低很多,可以避免很多矛盾。如果相识的时间太少,这些矛盾就会在婚姻生活中放大,最终带 来可能很坏的后果。

就他们俩的讨论,我个人认为,周董的爱情经济学的理论所认为的“相处时间”和“问题发现&解决”构建成了一个线 性相关的联系,就像是一个回归函数一样~但是现实中往往并不是如此。爱情的效用和时间的关系就像是一个库兹涅兹倒U型曲线,在到达顶点之前,一对 couple享受着爱情的甜蜜满足感,并在不断地发现问题解决问题中推动着爱情的成长,但过了顶点之后,当双方的了解过了维持婚姻必要的临界点的时候,无 婚姻的爱情所带来的效用指数就开始跌跌跌……也许这就是所谓七年之痒吧。




2、 在定量研究的过程中需要很多假设前提。比如最重要的理性人假设。也就是说爱情中的每一个参与方(GG/MM/甚至是小三)都能够根据所掌握的已有信息理性 的做出最有利于自己的判断。事实上这基本上是不切实际的,因为在爱情中能保持理智的人太少了(……或许引入神经生物学可以解决这个变量的偏差纠正问题,呼 唤neuro大神!)

但是,爱情还是可以用一些基本的经济学思想来看待的。比如如何定义最好的爱情。个人认为,最好的爱情或者婚姻就是相爱 成本最低的爱情。我们现在所谓的“相处的很舒服”、“不用努力维系关系就很开心”说的就是爱情成本的minimum~不过爱情成本也的确是一个很难量化的 东西,因为每个人对于爱情成本的理解,和他们的边际成本负荷率(也就是他们对于承担成本的意愿的指标)也是不同的,这种独立但不同分布的大量样本的分 析……还是交给张涤新老师去研究吧……调皮

那 如果这样说的话,爱情和友情的区别在哪儿?我也可以拽出一个友情成本来描述友情啊。实际上这两者最大的不同就是变量是完全不一样的。影响友情和影响爱情的 因素有很大不同,所以两者的分析方法可以一样,但分析结果和所建模型应该是不同的。比如友情一般就很少有七年之痒之说对吧~

OK,其实网上还是有很多的关于爱情定量分析的好案例,作者强大的数学功底让定量分析成为了可能,最著名的应该是那篇IT男写的《why I don’t have a girlfriend》吧……



最 后补一句牢骚,实际上经济学的视角总是很有意思的,最近google撤出的消息中,大多数更关注信息自由化和个人权利的诉求,但是从经济的角度来看。自从 google放出要撤出的消息之后,google的股价持续下点的将近10个百分点(当然这也跟google在德国、中东等国家遭遇“数字图书馆门”和 “gmail门”事件有关),于此相对的,百度在大力发展贴吧业务( i 贴吧)和强化服务功能(中老年人群基本不会去维基百科的,他们只要百度百科就够了)的背景下,股价上升了30%+~