## 2009年1月29日 星期四

### Finite simple group of order 2

I'm sure many of you have seen this before. This is a really mathematical song, by a group of students from Northwestern University who call themselves "The Klein Four Group". Pay attention to the lyrics; it's amazing how many mathematical terminologies they could fit in a simple song of finite length!

Finite Simple Group (of Order Two)
The Klein Four Group

The path of love is never smooth
But mine's continuous for you
You're the upper bound in the chains of my heart
You're my Axiom of Choice, you know it's true

But lately our relation's not so well-defined
And I just can't function without you
I'll prove my proposition and I'm sure you'll find
We're a finite simple group of order two

I'm losing my identity
I'm getting tensor every day
And without loss of generality
I will assume that you feel the same way

Since every time I see you, you just quotient out
The faithful image that I map into
But when we're one-to-one you'll see what I'm about
'Cause we're a finite simple group of order two

Our equivalence was stable,
A principal love bundle sitting deep inside
But then you drove a wedge between our two-forms
Now everything is so complexified

When we first met, we simply connected
My heart was open but too dense
To have a finite limit, in some sense

I'm living in the kernel of a rank-one map
From my domain, its image looks so blue,
'Cause all I see are zeroes, it's a cruel trap
But we're a finite simple group of order two

I'm not the smoothest operator in my class,
But we're a mirror pair, me and you,
So let's apply forgetful functors to the past
And be a finite simple group, a finite simple group,
Let's be a finite simple group of order two
(Oughter: "Why not three?")

I've proved my proposition now, as you can see,
So let's both be associative and free
And by corollary, this shows you and I to be
Purely inseparable. Q. E. D.

## 2009年1月22日 星期四

### 普選

「爭取普選」是本港近年一個熱門的政治話題，但究竟普選是甚麼？根據維基百科的定義，「普選權是選舉權的延伸，就是對一個成年人來說，無論他的性別、年齡、種族、信仰、社會狀況，都有在選舉參政及投票的權利」。這個定義非常廣泛，如果根據這個定義的話，現時香港立法會選舉也是一種普選。

「所有成年人都有均等的參政及投票的權利」，聽下去很合理，但如果以為這樣就算得上普選的話，那就大錯特錯了。大家看看以下故事吧。

## 2009年1月6日 星期二

### Attending Conference in New York City

This is long time from my last entry. Recently I am busy with my trip to USA, training MO in my mother school and preparing my presentation in the conference I am attending.

My first station is New York City. This is my second time to visit here. The conference I am attending is called Symposium on Discrete Algorithms. It is a Computer Science conference, but I would say many of the stuff are really Mathematics, and a few of them are related to Physics and Biology.

Okay, let me bring back to topic to Mathematics. In a talk, the speaker gave the following cute problem: In how many permutations of size n will two elements i and j in the same cycle? There is a one-line solution.

BTW, as some of you may know, I am the teaching assistant of the course Game Theory in HKUST in the recent two years. I have just found in the conference that a game "Atomic Game Flow" is an excellent example of applications of Game Theory to Computer Science. And its nature is so simple that undergraduate students should have no difficulty to understand it (certainly, as in most branches of Mathematics, if you go deeper, it can be very difficult :p).