Small and large categories

A category C is called small if both ob(C) and hom(C) are actually sets and not proper classes, and large otherwise. A locally small category is a category such that for all objects a and b, the hom-class hom(a, b) is a set, called a homset. Many important categories in mathematics (such as the category of sets), although not small, are at least locally small.

— Wikipedia on Category (mathematics)

2010.03.31 Wednesday ACHK


Past papers 14

“Past papers” means “past HKCEE/HKAL examination papers”. The topic is for Hong Kong students who are facing HKCEE or HKAL. But the general principles can also be used for tackling other public examinations.

這段改篇自2010年 1 月 3 日的對話。


那就應該算是「情緒病」,因為你這個問題十分浪費你的考試作答時間。如果那導致你整份試卷損失幾分的話,你該科隨時會低一個 grade(成績等級)。那就是我所講的「實質影響」。









— Me@2010.03.30

2010.03.30 Tuesday (c) All rights reserved by ACHK

Lisp macros

Lisp’s uniform, parenthesized syntax works especially well with macros. Languages of the Lisp family, such as Common Lisp and Scheme, have powerful macro systems because the syntax is simple enough to be parsed easily. Lisp macros transform the program structure itself, with the full language available to express such transformations. Common Lisp and Scheme differ in their macro systems: Scheme’s is based on pattern matching, while Common Lisp macros are functions that explicitly construct sections of the program.

Being able to choose the order of evaluation (see lazy evaluation and non-strict functions) enables the creation of new syntactic constructs (e.g. control structures) indistinguishable from those built into the language. For instance, in a Lisp dialect that has cond but lacks if, it is possible to define the latter in terms of the former using macros.

Macros also make it possible to define data languages that are immediately compiled into code, which means that constructs such as state machines can be implemented in a way that is both natural and efficient.

— Wikipedia on Macro (computer science)

2010.03.30 Tuesday ACHK

多次元宇宙 7


















— Me@2010.03.29

2010.03.29 Monday (c) All rights reserved by ACHK


Mainland China and Taiwan

The People’s Republic of China (PRC) and the Republic of China (ROC) do not recognise each other as sovereign states. They both claim themselves as the only legal government representing the whole China.

Consistent with the 1992 Consensus, the PRC and ROC legally consider both citizens in mainland China and Taiwan as their own citizens, but residing in different areas of the same nation. Neither the PRC nor the ROC accepts passports issued by the other as entry documents.

Citizens in Taiwan use identity documents issued by PRC public-security authorities to enter mainland China. Citizens in mainland China entering Taiwan must also use identity documents issued by the ROC authority, and have their mainland documents surrendered. The identity documents cannot be used for international travel, and an endorsement must be obtained separately to enable travel.

The ROC used to require its citizens who intended travel to mainland China to obtain official approval for the travel, and prescribed an administrative fine of NT$20,000 to NT$100,000 for those who did not. However, the fine was often unenforceable because such travel was untraceable by examination of travel documents, except if an ROC citizen lost his ROC passport while on the mainland, and, so, had to report the loss. The official-approval requirement was abolished, except in relation to ROC officials, of whom applications are required.

— Wikipedia on Passport

2010.03.29 Monday ACHK

Clebsch-Gordan coefficients software

This program is written by me to calculate the Clebsch-Gordan coefficients.

To use it, copy-and-paste the text of this file onto DrScheme and run it.

Within DrScheme, you have to select the Language “Pretty Big”.

You can contact me if you find any bugs in this program.

2010.03.28 Sunday (c) All rights reserved by ACHK

Batman Begins


Blogger Mark Fisher states that Bruce’s search for justice requires him to learn from a proper father figure, with Thomas Wayne and Ra’s al Ghul being the two counterpoints. Alfred provides a maternal figure of unconditional love, despite the overall lack of focus on a mother figure in Bruce’s life.


Shawn Adler of MTV stated after Batman Begins, a trend of darker genre films, that either retold back-stories or rebooted them altogether, began.
Examples he cited were Casino Royale, as well as the in-development RoboCop, Red Sonja, and He-Man. Filmmakers, screenwriters and producers who have mentioned the film to describe their projects include: Jon Favreau and Iron Man, Edward Norton and The Incredible Hulk, McG and Terminator Salvation (which also stars Bale), Damon Lindelof and Star Trek, Robert Downey, Jr. and Sherlock Holmes, Lorenzo di Bonaventura and G.I. Joe: The Rise of Cobra, and even Hugh Jackman and X-Men Origins: Wolverine.

— Wikipedia on Batman Begins




2010.03.28 Sunday ACHK

Copyleft 4

The Open Invention Network (OIN) is a company that acquires patents and licenses them royalty free to entities which, in turn, agree not to assert their own patents against Linux or Linux-related applications.

— Wikipedia on Open Invention Network

2010.03.27 Saturday ACHK

浮水 2


真姐也講過,當你遇到一個難講的題目時,唯有對考官承認:「我個人的經歷尚淺,所以不能完全掌握此題目。若果真的要我講的話,我會 … 」有如遇溺時,越爭扎  只會浸得越快。唯有放鬆,等水浮起你。

– Diary, Me@2000.04.28




2010.03.27 Saturday copyright ACHK


Past papers 13

“Past papers” means “past HKCEE/HKAL examination papers”. The topic is for Hong Kong students who are facing HKCEE or HKAL. But the general principles can also be used for tackling other public examinations.

這段改篇自2010年 1 月 3 日的對話。






(KYH:OK 啦 …)





那就應該算是「情緒病」,因為你這個問題十分浪費你的考試作答時間。如果那導致你整份試卷損失幾分的話,你該科隨時會低一個 grade(成績等級)。那就是我所講的「實質影響」。



— Me@2010.03.26

2010.03.26 Friday (c) All rights reserved by ACHK

The Maxwell’s equations of programming

Interactive means that programming is a dialog with Lisp. You enter an expression and Lisp computes the side effects (for example output) and the value.

So your programming session is like ‘talking’ with the Lisp system. You work with it until you get the right answers.

Alan Kay (of Smalltalk fame) calls the original definition of Lisp evaluation in Lisp the Maxwell’s equations of programming.

— Rainer Joswig

2010.03.26 Friday ACHK

Be rewritten


Another group was worried when they realized they had to rewrite their software from scratch. I told them it would be a bad sign if they didn’t. The main function of your initial version is to be rewritten.

— Paul Graham




2010.03.26 Friday ACHK

50 50



— Me@around 2000




— Me, based on Mr Lee@around 2007-2008


— an updated version by Me@around 2007-2008

— Me@2010.03.25

2010.03.25 Thursday (c) All rights reserved by ACHK



The way to get an academic position is to write great books, proving your academic competence. But you may not want an university-academic life.

— Me@around 2007



















The way to get an academic position is not to get a PhD first, but to write great books, proving your academic competence. But you may not want an university-academic life.

2010.03.25 Thursday copyright ACHK


Past papers 12

“Past papers” means “past HKCEE/HKAL examination papers”. The topic is for Hong Kong students who are facing HKCEE or HKAL. But the general principles can also be used for tackling other public examinations.

這段改篇自2010年 1 月 3 日的對話。

我當年的主要問題是,我打算「讀完所有東西」。那不是正確的讀書心態,因為書是沒有所謂讀得「完」的。任何一個 topic(課題)都可以無限深入研究。正確的心態是,即使你打算於某一科拿到 A 級的成績,無論是各個課題之間,還是同一個課題的不同部分之間,都應該要權衡取捨。如果花太多時間於不太重要的部分,你將會不夠時間溫習重要的部分。

我當年溫習時不懂得「取捨」,任何課題、任何部分也企圖「徹底完成」,導致沒有足夠的時間集中火力進攻真正的重點,結果拿不到 A 級的成績。所以你要拿好成績的話,就要學懂「權衡取捨」。

The art of being wise is the art of knowing what to overlook. –- William James


一、 靠做 pastpapers(歷來試題),歸納出重點;

二、 靠高人老師的提點。


— Me@2010.03.24

2010.03.24 Wednesday (c) All rights reserved by ACHK