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

OCD 4

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。

(KYH:我考試有時明明某一題做完做對了,但是覺得寫得很混亂,所以會擦掉,重新寫一次。)

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」。

你的問題算是「情緒病」,因為你的問題對你有「實質影響」。

我說我在二十八歲時,可以排除了九成的情緒病。我有很多方法,其中一個方法可能對你有用,可以用來解決你這個問題。

那個方法是:「不要百份百跟足你的感覺行事。」

例如,你的感覺是,你的字體不美,想擦掉,重新寫一次。哪應不應該聽從這個感覺,真的把那些字重新寫一次呢?

完全不聽從的話,心裡會極不舒服。完全聽從的話,又會浪費大量的時間。哪怎麼辦呢?

你可以只聽從一部分,但不聽從全部。例如,感覺是要你擦掉一整頁,重新寫一次。但你堅持只擦掉半頁。一方面,你不是完全聽從感覺,所以你不會浪費太多的時間。另一方面,你不是完全不聽從感覺,你心裡即使有不舒服的感覺,也不會大至不能接受的程度。

還有,你長期這樣做的話,慢慢就會習慣了「只擦掉半頁」。當你「只擦掉半頁」也不會有不舒服的感覺時,你就可以試試「只擦掉四分之一頁」,如此類推。

你會這樣(擦掉,重新寫一次),是因為你不容許自己有不舒服的感覺(覺得寫得很混亂)。我這個方法的原理是,要你容許自己有不舒服的感覺。有時,容許自己有不舒服的感覺,不舒服的感覺反而傷害不到你。

— 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

為什麼《心經》說「色『即是』空」?「即是」在這裡是什麼意思?

(安:暫時也不是很明白。除了說「即是」之外,《心經》還說「不異」:「色不異空,空不異色」。

首先要問,「色」和「空」是不是同一個意思?

如果不是同一個意思,它們有什麼分別?(「色即是空」這句話是錯誤的。)

如果是同一個意思,《心經》為什麼要講多一次?(「色即是空」這句話是多餘的。))

《心經》說「色『即是』空」,意思是:

我們如何可以觀察到「本體」呢?

唯有透過「現象」。

「本體」是不能直接被觀察到的,因為我們不能『直接看到』「本體」。我們只能透過「現象」去觀察「本體」。「透過『現象』去觀察『本體』」是「觀察『本體』」的唯一方法。

正如,一隻杯的「本身」是不能直接被觀察到的,因為我並不能一次過觀察到那隻杯的「整體」。我每次所看到的,只是那隻杯的某個角度,投射在我視網膜上的平面影像。在任何一個角度觀察到的「影像」,都只是其中一個「投影」。任何一個「投影」,都不是那隻杯「本身」。但是,我們除了靠那隻杯的「影像」外,並沒有任何方法可以觀察到杯的「本身」。所以,「透過『投影』去觀察『杯本身』」是「觀察『杯本身』」的唯一方法。

「色即是空,空即是色」的意思是,雖然「現象」和「本體」是不同的東西,但是,要觀察「本體」,我們只能透過「現象」去觀察「本體」。正如,雖然「杯的影像」和「杯本身」是不同的東西,但是,要觀察「杯本身」,我們只能透過「杯的影像」去觀察「杯本身」。

「色即是空,空即是色」中的「即是」,是指當我們說

「我的眼睛接收到一隻『杯』的『影像』。」時,意思即是

「我看到一隻『杯』。」;

而當我們說

「我看到一隻『杯』。」時,意思又即是

「我的眼睛接收到一隻『杯』的『影像』。」

— Me@2010.03.29

2010.03.29 Monday (c) All rights reserved by ACHK

Passport

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

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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.

Impact

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

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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

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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

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2010.03.27 Saturday copyright ACHK

OCD 3

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。

我當年(十九歲,高考時期)另外一個大問題是,我有情緒病。我當時沒有「情緒病」這個概念。到大約在二十三歲時,看紀錄片才知道我的所謂「弱點」原來不是我個人的性格問題,而是一種很普遍的情緒病。到了二十八歲時,我發明了一些方法,導致我可以排除了九成的情緒病。

我所講的「情緒病」大概是這個意思:例如,考試時計了一題數後,我怕自己計錯數,所以計完以後,會檢查一次。那是正常。但是,我檢查了一次後,仍然不安心,所以會再檢查。明明只需要檢查一次,我卻檢查超過一次,自然會浪費很多時間,導致拿不到最好的成績。

(KYH:我的是另外一個類似的問題。我有時寫了一東西,例如計完一題數,我覺得字體不夠好,會擦掉,重新寫一次。那算不算是情緒病?)

輕微的不算。比喻說,間中一次打噴嚏,不算是病。但是,如果一天之中多次打噴嚏的話,那就是患了傷風感冒。

你的問題算不算「情緒病」,要視乎嚴不嚴重。你的問題嚴不嚴重?

(KYH:OK 啦 …)

「OK」即是「頗為嚴重」?

(KYH:我也不知道算不算嚴重。)

「嚴重」的意思是,你的問題,除了令你心裡不舒服外,對你還有「實質影響」。你的問題對你有沒有「實質影響」?

(KYH:我考試有時明明某一題做完做對了,但是覺得寫得很混亂,所以會擦掉,重新寫一次。)

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」。

你的心理問題算是「情緒病」,因為你的心理問題對你有心理以外的「實質影響」。

我說我在二十八歲時,可以排除了九成的情緒病。我有很多方法,其中一個方法可能對你有用,可以用來解決你這個問題。

— 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

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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

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2010.03.26 Friday ACHK

50 50

無關重要的選擇,應該擲毫決定。

那可以節省很多時間。

— Me@around 2000

如果有兩個抉擇:甲或乙,你只能選一個。

如果你花了三日三夜也不能決定選哪一個比較好,即是甲和乙的好處多少,其實十分相近。所以你選哪一個,對你的影響也分別不大。

既然分別不大,何不擲毫決定?

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

如果擲毫所做的決定,令你心裡有少許不舒服的話,那就選相反的一個。

— an updated version by Me@around 2007-2008

— Me@2010.03.25

2010.03.25 Thursday (c) All rights reserved by ACHK

University-academic

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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

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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

天才省略

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

「天才」,就是知道什麼可以省略的人。但是要「知道什麼可以省略」,本身就要有強大的背景知識,一般人也沒有。所以如果你是「一般人」,又要「知道什麼可以省略」的話,你可以用以下兩個捷徑:

一、 靠做 pastpapers(歷來試題),歸納出重點;

二、 靠高人老師的提點。

老師的主要責任是告訴學生,什麼可以省略,什麼不可以。

— Me@2010.03.24

2010.03.24 Wednesday (c) All rights reserved by ACHK