逃避問題

這段改編自 2010 年 7 月 27 日的對話。

一般人云亦云的所謂「做人道理」,很多也是錯的。其中一個是:「千萬不要逃避問題。」

這句說話未必正確,因為,我可以追問,為什麼不可以逃避問題?

正確的講法應該是,問題有兩種。一種是不可以逃避的,一種是可以逃避的。不可以逃避的問題,你就不要逃避。可以逃避的,為什麼不逃避?

例如,有一隻獅子,正在追殺你。你總不能說:「千萬不要逃避問題。我一定面對問題,和獅子搏鬥一番。」

如果有獅子正在追殺你,最恰當的「面對」方法應該是,立刻逃走。

— Me@2013.11.30

2013.11.30 Saturday (c) All rights reserved by ACHK

Perl

心懷混亂 4

As we all know, reality is a mess.

This is a picture of many things. It’s a picture of air molecules bouncing around. It’s a picture of the economy. It’s a picture of all the relationships of the people in this room. It’s a picture of what the typical human language looks like. It’s a picture of your company’s information systems. It’s a picture of the World Wide Web. It’s a picture of chaos, and of complexity.

It’s certainly a picture of how Perl is organized, since Perl is modeled on human languages. And the reason human languages are complex is because they have to deal with reality.

Now, you may be wondering what all this has to do with Perl. The fact is, your brain is built to do Perl programming. You have a deep desire to turn the complex into the simple, and Perl is just another tool to help you do that–just as I am using English right now to try to simplify reality. I can use English for that because English is a mess.

This is important, and a little hard to understand. English is useful because it’s a mess. Since English is a mess, it maps well onto the problem space, which is also a mess, which we call reality. Similarly, Perl was designed to be a mess (though in the nicest of possible ways).

This is counterintuitive, so let me explain. If you’ve been educated as any kind of an engineer, it has been pounded into your skull that great engineering is simple engineering. We are taught to admire suspension bridges more than railroad trestles. We are taught to value simplicity and beauty. That’s nice. I like circles too.

However, complexity is not always the enemy. What’s important is not simplicity or complexity, but how you bridge the two.

— Open Sources: Voices from the Open Source Revolution

2013.11.30 Saturday ACHK

化到最簡 1.2

人格考試 2.2 | 速度準確表達 2.2 | Impossible to misunderstand, 2.2

這段改編自 2010 年 7 月 27 日的對話。

另外,每題的最終答案,你一定要化到最簡。即使你的答案正確,如果你的寫法奇怪,評卷員都不會給予分數。

(CYW:不是運算到正確答案就可以嗎?)

要明顯正確才可以。

(CYW:怎樣才為之「明顯正確」?)

換句話說,一定要最精簡。

一來,評卷員不會知道,亦不會有閒暇去檢驗,你那「不是最簡」的答案,是否真的「正確」。二來,如果最終答案沒有規定,一定要最簡,那又真的會造成世界大亂。例如,某一題的最終最簡答案是「x」,

有人卻答「x – x + x」;

有人則答「2x/2」;

有人更答「x^2/x + sin x – sin x」。

它們全部「正確」,但是評卷員絕對有權,不予評分。

— Me@2013.11.29

2013.11.29 Friday (c) All rights reserved by ACHK

師奶是怎樣煉成的

I think the important thing about the real world is not that it’s populated by adults, but that it’s very large, and the things you do have real effects. That’s what school, prison, and ladies-who-lunch all lack. The inhabitants of all those worlds are trapped in little bubbles where nothing they do can have more than a local effect. Naturally these societies degenerate into savagery. They have no function for their form to follow.

— Why Nerds are Unpopular

— Paul Graham

2013.11.19 Tuesday ACHK

人格考試 2.1

化到最簡 1.1 | 速度準確表達 2.1 | Impossible to misunderstand, 2.1

這段改編自 2010 年 7 月 27 日的對話。

留意,考試作答時,你的思路表達,一定要清晰。

如果你的答案陳述,艱深難明,就會導致一題本來,只需要用 30 秒批改的題目,評卷員要花上兩分鐘,才有機會看得明白。那樣,不論你混亂表達的背後,數學內容正不正確,評卷員也絕對有權,一開始就不花那兩分鐘去研究,而直接把你該題的答案,視作錯誤,不予分數。

評卷員有權那樣做的原因是,作為考生,你有絕對的責任,去清晰表達你的作答。如果你的作答,不能令評卷員一目瞭然,失職的人是你,而不是評卷員。

記住,考試是兩成考知識,八成考人格。換而言之,數學考試中,只有兩成是考「數學知識」,另外的八成,是考「數學人格」。人格方面主要考你的,是「速度」、「準確度」和「語文」。「速度」即是時間管理;「語文」即是清晰表達,自己思想的能力。

所以,「清晰表達」本身,正正是數學考試中,主要想考核你的環節。「我其實數學高超,只是表達欠佳」只要廢話,不能作為辯解理由。

— Me@2013.11.19

We should not write so that it is possible to understand, but so that it is impossible to misunderstand.

— De Institutione Oratoria, Book VIII, 2, 24 (ca. 95AD)

— Me@2013.11.19

2013.11.19 Tuesday (c) All rights reserved by ACHK

Pain 2

In general usage, “sense” and “feel” have the same meaning. However, in special usage, they do not. For example, “I sense pain” is a little bit different from “I feel pain“.

I feel pain

~ I sense that my body is hurt

~ My mind has got the data “my body is hurt”

I sense pain

~ I sense that I feel pain

~ I sense that I sense that my body is hurt

~ My mind has got the data “I feel pain”

sensing ~ getting data of the outside world

feeling ~ a state of the mind

— Me@2013-11-16 3:43 PM

2013.11.18 Monday (c) All rights reserved by ACHK

權力來源 1.3

這段改編自 2010 年 4 月 24 日的對話。

「權力」是一個「自我實現預言」(self-fulfilling prophecy)。

「權力」結構的其中一個性質是:

我猜想你在想什麼;你猜想我以為你在想什麼;然後,我又猜想你以為我以為你在想什麼;如此類推。

所以,「權力」在大家一同覺得「有」時,就立刻「有」;在大家一同覺得「無」時,就立刻「無」。

— Me@2013.11.17

2013.11.17 Sunday (c) All rights reserved by ACHK

Infinite loop 2

Recursion 12.3 | Paradox 6 | Life as a recursion, 3

Paradox is due to the mixing of para-level (meta-level) and original level.

— Me@2012-09-29 02:22:14 PM

The mixing of levels creates a causal/reasoning loop, resulting an infinite long chain.

In short, infinite loop is due to mixing levels.

— Me@2012.10.15

If there is no progress or no terminating condition, a loop cannot stop.

With progress (change of some values of some variables), each iteration is different. In this sense, each iteration is at a different level.

Without progress, all iterations are at the same level, creating a mixing-level problem, aka “a paradox”.

— Me@2013-11-16 5:55 AM

Level 1: Life is a repetition.  /* an infinite loop */

Level 2: Life is an iteration.

Level 3: Life is a recursion.

— Me@2011.12.24

— Me@2013.11.16

2013.11.16 Saturday (c) All rights reserved by ACHK

Discovery

厭倦 5 | 心懷混亂 3

being tired of something

~ no difference

~ nothing new

No distraction, no discovery.

— Me@2011.05.28

Sometimes, a little bit of distraction is a good thing, because it prevents your daily life from being 100 percent repetitions.

— Me@2013.11.15

2013.11.15 Friday (c) All rights reserved by ACHK

驗算校對 2.7

這段改編自 2010 年 7 月 27 日的對話。

近乎每種題目,都有對應的高速驗算方法。而那些驗算方法背後的精神,或者大方向,就是做完每一小題後,立刻用另一個完全不同的方法,去做多一次。記住,驗算時千萬不要,用原本的思路重做一次,因為如果原本有錯,你驗算時很可能會錯在同一個步驟。

如果不幸遇上了一題,當時沒有「另一個方法」的題目,你就唯有在運算時格外小心 —— 寫完每一行的運算時,就立刻望一望、瞥一瞥,看看有沒有寫錯東西。而這個「望一望」,如果要做到快而準,是一種「超能力」。換而言之,沒有平日的反覆訓練的話,你考試時不會做得到。

留意,這個「每步也驗」的方法比較費時,應該在逼不得已時,才拿出來使用。

— Me@2013.11.15

2013.11.15 Friday (c) All rights reserved by ACHK

Godel 17

The truth of the Godel sentence

The proof of Godel’s incompleteness theorem just sketched is proof-theoretic (also called syntactic) in that it shows that if certain proofs exist (a proof of P(G(P)) or its negation) then they can be manipulated to produce a proof of a contradiction. This makes no appeal to whether P(G(P)) is “true”, only to whether it is provable. Truth is a model-theoretic, or semantic, concept, and is not equivalent to provability except in special cases.

By analyzing the situation of the above proof in more detail, it is possible to obtain a conclusion about the truth of P(G(P)) in the standard model (\mathbb{N}) of natural numbers. As just seen, q(n,G(P)) is provable for each natural number n, and is thus true in the model (\mathbb{N}). Therefore, within this model,

P(G(P)) = \forall y\, q(y,G(P))

holds. This is what the statement “P(G(P)) is true” usually refers to — the sentence is true in the intended model. It is not true in every model, however: If it were, then by Godel’s completeness theorem it would be provable, which we have just seen is not the case.

— Wikipedia on Proof sketch for Godel’s first incompleteness theorem

2013.11.14 Thursday ACHK

原始時代 4

每個時代的人,都覺得自己的時代是「現代」。

每個時代的人,都不覺得自己的時代是「古代」。

— Me@2010.03.29

任何時代的人,都是當時有史以來,最先進的人類。

— Me@2013.10.11 02.27.10

2013.11.14 Thursday (c) All rights reserved by ACHK

權力來源 1.2

這段改編自 2010 年 4 月 24 日的對話。

那十個士兵中的任何一個,都以為另外的九位同事,會聽命於那位將軍。「如果我不服從將軍,他會命令另外九人拘捕我。任我的武功再好,也敵不過九個人。」而另外的九位同事,亦都會聽命於那位將軍的原因,正正是因為有同樣的想法。

這個人性社會結構,學名為「勢」,是「權力」的來源,可以十分堅固,因為人數越多,要摧毀這個「勢」就越困難,除非發生了一些特殊的情況。

那樣,怎樣才可以令那個「勢」消失呢?

就是要那十個士兵中的全部,或者大部分人,同時不服從那個將軍。但是,這個目標很難化成,實際的執行步驟,因為,「十人同時不服從將軍」有兩個先決條件:

第一,十人都不想服從;

第二,十人中的每一個,都知道其餘九人,都不想服從。

試想想,如果你是其中一位士兵,你可以怎樣做,去確定其餘九人,是否都是不想服從將軍呢?

唯一的方法,就是逐一問他們。但是,你要冒很大風險,因為,只要有其中一人仍然忠於將軍,他就會告發你,導致你被將軍下令拘捕。即使餘下的八人,心裡其實都是不想忠於將軍,也不會幫到你,因為,他們中的每一個,也尚未知道,原來十人之中,已經有九人想造反。

除非,發生了一些特殊的情況,導致那十位士兵的每一個,也立刻知道,原來大部分人也不想服從將軍。例如,將軍突然宣佈:「你們這一年的薪金,全歸我所有。」那樣,即使沒有任何形式的溝通,每一個士兵也會立刻知道,其餘九人中的每一個,都不可能想服從將軍。那樣,那將軍即時由「強勢」變成「弱勢」。

在那個極端不穩定的權力結構下,只差一聲號令,「弱勢」就會變成「無勢」,甚至是「負勢」。只要有其中一位士兵,有少許的膽量,大叫:「拘捕他!」將軍就立刻被那十人制伏。

那就是「兵變」,又名「革命」。

— Me@2013.11.13

2013.11.13 Wednesday (c) All rights reserved by ACHK

驗算校對 2.6

活在當下 6.6 | 唔識就飛 10.5

這段改編自 2010 年 7 月 27 日的對話。

所以,有很大的機會,「完成了一題的一個部分後,就立刻作校對」這個策略,會令你的考試成績好一點。

那様,你怎樣可以肯定,對你來說,「每題即驗」是否真的好過「做完卷才驗」呢?

你一定要在平時先行測試。你在「按年份、計時間、計分數」做 past paper(歷屆試題)時,就應留意一下,兩個驗算策略之中,哪個對你最有利。

即使假設你選定了「每題即驗」,你還要研究,面對各種情境時,應該如何自處。例如,每種題目有何高速驗算方法?甚至,有哪些題目,你根本不應該驗算?

近乎每種題目,都有對應的高速驗算方法。例如,一題如果需要三分鐘運算,通常 15 秒內就可以完成驗算。那些高速驗算方法,你一定要在平時先行收集,因為,你不可能在考試的緊迫時間之中,即製即用。

但是,有時候,你會遇到一些新奇一點的題目,沒有你已知的高速驗算技巧,只能靠低速。例如,那一題運算需要五分鐘,而驗算亦需要五分鐘。那樣,你就要立刻取捨,決定值不值得花那額外的五分鐘,去驗算校對。

如果那一題是某長題目的第一部分,你就應該花,因為,那長題目之後幾部分的對錯,會建基於第一部分答案的正確與否。相反,如果那一題是某長題目的最後一部分,你就可以考慮,在題號上寫一個「C」字,代表暫時擱置驗算。

要掌握這些隨機應變的能力,就要靠試前日積月累的修行。考試時的清晰頭腦,來自平日的混亂心靈。

— Me@2013.11.12

2013.11.12 Tuesday (c) All rights reserved by ACHK