驗算校對 2.3

活在當下 6.3 | 唔識就飛 10.2

這段改編自 2010 年 7 月 27 日的對話。

留意,驗算校對有兩個大方向。其一是做了所有題目後,才開始作驗算。其二是完成了一題的一個部分後,就立刻作校對。有時候,第一個進路會好一點;有時候,第二個進路會較合適。

大部分情況下,我會建議使用第二個進路 —— 每題每部後,就即時驗算,因為這方法特別適合用於,時間緊迫的公開試。

例如,我當年高考 Pure Maths(純數學)試卷的結構,會令人在考試時,繁忙到不會有時間「返轉頭」 —— 完成了的題目,不可能第二次閱讀修正的機會;除非,中途我有很多題目,也因為不懂做而留空跳過,導致「節省」了大量時間。那絕對是一件,非常不幸事件。

所以,如果你打算,做完所有題目後,才開始作驗算,那就相當於打算了,從來不作驗算。

— Me@2013.10.31

2013.10.31 Thursday (c) All rights reserved by ACHK

ER-EPR

物理定律團 2 | 語意互相推卸責任論 3

Allowed topology changes (e.g. conifold transitions) may always be described as a condensation of objects on the original background; allowed (non-traversable) wormholes may be described as entangled states of objects (on a wormhole-free background) whose details reflect the properties of the wormhole.

So what is doomed isn’t a spacetime in the sense of our right of using the concept; what is doomed is the idea that a classical spacetime is unambiguously associated with states or processes. The association is not only refusing to be unique but to a large extent, the spacetime may be chosen arbitrarily (even its topology may be chosen differently, even if the topology change involves time in a nontrivial way). An inconvenient choice of the spacetime background for a given physical situation will be manifested in the complexity of the collections of particles and objects that live on top of the chosen spacetime but the theory will never say that the choice is “fundamentally wrong”.

So the advances in string/M-theory and quantum gravity have eliminated the idea that the reality canonically carries a “particular spacetime background”. At the fundamental level, the separation of the reality to the “spacetime” and “the objects that live on the spacetime” is highly redundant if not arbitrary. This fact may be viewed as a manifestation of the inevitable unification of gravity with other forces or matter. You just can’t objectively or canonically determine which part of the state or process or reality is gravity (space and time); and which part is the information about the objects or phenomena taking place on that background! Only some combination of theirs retains its unambiguous meaning.

— Is space and time emergent? ER-EPR correspondence adds a voice

— Lubos Motl

2013.10.31 Thursday ACHK

Amazing Gags 6

對牛彈琴 3

留意,通常自以為高智力的人,都是傻瓜人士。

如果你真才實學,客觀地智力高過一般人,大部人就不能感受到你的高智力,因為,別人感受到你高智力的先決條件是,他的智力相若。但是,你的智力與眾不同地高的話,大眾的智力就自然與你不同。

如果你要一個智力平庸的人,都能感受到你的高智力,「搞 gag」(弄笑話)是一個有效捷徑。你的說話散發幽默感的話,別人就自然不知不覺地感受到,你的智力高過一般人。

但是,如果對方的智力真的太低,可能會連最簡單的笑話,也不明白。

— Me@2013.10.30

2013.10.30 Wednesday (c) All rights reserved by ACHK

知己知彼

「知己知彼,百戰不殆」的原因是:

如果你「知己知彼」,

你就可以在事前知道,你會哪些戰爭中贏、哪些戰爭中輸,

從而選擇不參加,那些你會輸的戰爭。

— Me@2010.08.05

— Me@2013.10.30

2013.10.30 Wednesday (c) All rights reserved by ACHK

活在當下 6.2

驗算校對 2.2 | 唔識就飛 10

這段改編自 2010 年 7 月 27 日的對話。

而我慣常使用的,是這方法一個絕一點的版本。即使是對於同一題而言,如果它分了例如 a,b,c,d 四部分,做 a 部分時,我不會容許自己看到 b 部分;做 b 部分時,我亦不會容許自己看到 c 部分;如此類推。因為在每一步,我也只專心閱讀那一個部分、那一句句子,錯誤理解題目的機會,就會大大減少。

完成了 a 部分後,我會立刻驗算該部分。驗算完畢,我就會在 a 部分旁邊剔一剔(✓)。那樣,即使在運算 b 部分時,我仍然和必須看到 a 部分,我也不會覺得煩擾,反而,我會覺得愉快滿足。

留意,驗算校對有兩個大方向。其一是做了所有題目後,才開始作驗算。其二是完成了一題的一個部分後,就立刻作校對。有時候,第一個進路會好一點;有時候,第二個進路會較合適。

大部分情況下,我會建議使用第二個進路 —— 每題每部後,就即時驗算。

— Me@2013.10.29

2013.10.29 Tuesday (c) All rights reserved by ACHK

Logical arrow of time, 6

The source of the macroscopic time asymmetry, aka the second law of thermodynamics, is the difference of prediction and retrodiction.

In a prediction, the deduction direction is the same as the physical/observer time direction.

In a retrodiction, the deduction direction is opposite to the physical/observer time direction.

.

— guess —

If a retrodiction is done by a time-opposite observer, he will see the entropy increasing. For him, he is really doing a prediction.

However, it may not be possible for such an observer to exist. Me@2018-02-02 09:37:48 PM

— guess —

.

— Me@2013-10-25 3:33 AM

.

.

.

2013.10.29 Tuesday (c) All rights reserved by ACHK

Tactics and Strategy

What’s the difference between the adjectives “strategic” and “tactical”?

Tactics is knowing what to do when there is something to do. Strategy is knowing what to do when there is nothing to do.

— Savielly Tartakower

2013.10.28 Monday ACHK

物理定律團 1.4

這段改編自 2010 年 4 月 3 日的對話。

什麼東西是「軟件」,什麼東西是「硬件」,雖然非常客觀,但不是絕對客觀。有時會出現一些模稜兩可的情況。

從這個角度看,一樣東西究竟應該叫做「硬件」還是「軟件」,其實是一種 convention(習俗慣例)。

convention ~ the most convenient labeling system

所謂的「習俗慣例」,「最方便的標籤系統」也。至於那個標籤方法最方便,則需要視乎上文下理而定。例如,對於「硬碟」而言,在一般情況下,我們會標籤為「硬件」,因為「硬碟」是「物件」,你可以用手拿著它;拿著它時,你又可能會擔心稍一不慎,會把它掉在地下弄壞。

但是,如果你是硬碟工程師,你拿著一個硬碟設計圖和同事討論時,那個「硬碟」,就仍然只是一個「設計」,暫時未有實物。那時,你標籤它為「軟件」比較恰當。

同理,什麼東西是「物理定律」,什麼東西是「物理系統」,雖然非常客觀,但不是絕對客觀。有時會出現一些模稜兩可的情況。

— Me@2013.10.28

2013.10.28 Monday (c) All rights reserved by ACHK

Recursion 12.2

Recursion in programming is not paradoxical, because a recursive function is not really calling itself. In a correct recursive function,

1. at least one variable has different values in each iteration, and

2. there is a terminating condition.

That’s why a valid recursion creates no mixing-level problems.

— Me@2012.10.01

— Me@2013.10.28

2013.10.28 Monday (c) All rights reserved by ACHK

Citizen of the universe

[The happy] man feels himself a citizen of the universe, enjoying freely the spectacle that it offers and the joys that it affords, untroubled by the thought of death because he feels himself not really separate from those who will come after him. It is in such profound instinctive union with the stream of life that the greatest joy is to be found.

— Ch. 17: The happy man

— The Conquest of Happiness

— Bertrand Russell

2013.10.27 Sunday ACHK

活在當下 6

驗算校對 2.1

這段改編自 2010 年 7 月 27 日的對話。

還有另一個方法,可以令你在閱讀長題目時,快一點和準一點,你可以同時使用。

對我來說,考試是一個十分厭惡的過程,尤其是數學科。在數學科的考試中,每每有十幾題有很多文字的長短題目,而即使精確地明白了那堆文字,亦不代表你知道,如何運算作答;即使知道如何作答,你又不知道,中途有沒有運算錯誤。所以,為了減低厭惡程度,我習慣在做第一題時,用答案紙順勢遮蓋住,第二題和其他題目。那會令我舒服一點。

到要做第二題時,我才會讓自己看到第二題。在我的視線範圍內,就只有第一和第二題,而第三題或以後的,就會仍然遮蓋著。雖然,在運算第二題時,我會看到第一題,但是,因為那時的第一題是「已答之題」,所以並不會構成,我額外的心理壓力。

而我慣常使用的,是這方法一個絕一點的版本。即使是對於同一題而言,如果它分了例如 a,b,c,d 四部分,做 a 部分時,我不會容許自己看到 b 部分;做 b 部分時,我亦不會容許自己看到 c 部分;如此類推。

— Me@2013.10.27

2013.10.27 Sunday (c) All rights reserved by ACHK

Confirmation

Ideal clock 4 | 物理定律團 1.1.2 | Verification principle, 6

confirm = is compatible with

A confirms B

= A is compatible with B

The assumptions that are compatible with most other physical laws and events are called physical laws. In this sense, physical laws are conventions.

conventions ~ convenience

The physical laws are the most convenient assumptions to describe the physical world.

most convenient ~ most cost-effective

— Me@2013.10.25 19.32.56

2013.10.26 Saturday (c) All rights reserved by ACHK

Transparency and Privacy

Ygg2 4 days ago

Power demands transparency. Lack of power should give you some privacy.

An individual has right to privacy and to waive said privacy when it considers appropriate. The case with Stallman you mention was waiving some of his rights to give his colleagues easier access.

Powerful organization should be forced to be transparent to maximum extent that is reasonable – you shouldn’t be forced to give out your trade/state secrets, but classifying everything as such and hiding is a worse transgression. They don’t have the right to waive their transparency when it suits them.

— Hacker News

2013.10.26 Saturday ACHK

物理定律團 1.3

這段改編自 2010 年 4 月 3 日的對話。

又例如,你電腦內的資料和程式是「軟件」,而裝載那些資料和程式的硬碟是「硬件」。但是,那個硬碟的設計 —— 外形、結構、運作模式 和 使用方法 等,可以視為一堆「軟件」。在這個角度下,你的電腦硬碟,亦可以視為一個「軟件團」。

而正正是因為硬碟是一個「軟件團」,同一型號的硬碟,才可以大量生產、無限複製。「硬件」和「軟件」的主要分別在於「可否複製」。我們把同一樣東西之中 ,可以複製的性質,歸納成「軟件」;不可以複製的性質,統稱為「硬件」。

「同一個」硬件,不可同時存在於兩個地方,所以「硬件」又名「物質」。「同一個」軟件,可以同時存在於兩處空間,因為「軟件」都是「模式」。

— Me@2013.10.25

2013.10.25 Friday (c) All rights reserved by ACHK

Principia Mathematica, 3.2

Why truth table is not used in logic?

In Principia, the authors wanted to produce an explicit list of purely logical ideas, including an explicit finite list of axioms and rules of inference, from which all of mathematics could be derived. The method of truth tables is not such a finite list, and in any case would only deal with propositional logic.

— This work is licensed under a Creative Commons Attribution-ShareAlike 3.0 Unported License.

— Mathematics – Stack Exchange

— Andre Nicolas

2013.10.25 Friday ACHK

物理語言 3

這段改編自 2010 年 7 月 27 日的對話。

(CYW:有沒有方法,可以解題解得快一點?)

什麼意思?

(CYW:我在閱讀長題目時,往往要用很長時間去理解。)

明白。

(CYW:還有,我要極度專心,才有機會理解得到。否則,我的腦袋就會去想其他東西,到頭來理解不到題目。)

這一科是 Mathematics and Statistics(數學與統計)。你要先行熟習,這一科試卷的語言,因為,試卷所用的語言雖然是英文,但其實那不是日常生活中的英文。所以,即使你平日的英文造詣深厚,也不代表你可以,立刻駕馭這科的長英文段落。

第二,即使只考慮數學科目,Pure Maths(純數學)、Applied Maths(應用數學)和 Maths and Stat(數學與統計)的語言風格和專門術語,都各有不同。

試想想,雖然我年青時有修讀 Pure Maths 和 Applied Maths,但是現在面對 Maths and Stat 的題目時,都未必一定可以,在第一次閱讀時,就百分之一百明白。所以,你現在的首先目標是,先行熟習 Maths and Stat 的語言。需要熟習到什麼程度呢?

你要熟習到一個地步,看長題目時,再不需要逐字閱讀,而是逐個 phrase(詞組)去閱讀。意思是,你能夠即時辨認到一些,在 Maths and Stat 這一科考試題目中,時常出現的專間術語和句子格式。

要達到這個目標,方法很簡單。你只要繼續使用,我教的「魔法筆記」技巧就可以。你在平日做改正時,每當發現自己對題目理解錯誤,或者捉錯用神時,就立刻檢討一下,你是因為不熟悉哪些詞彙、詞組 或者 句式,而引起那些誤會。

你就把那些生疏文字,記錄在你的「魔法筆記」,不容許自己,再犯同一個或同一堆錯誤。漸漸地,你 Maths and Stat 的「魔法筆記」,就會有一大部分,成了你的「 Maths and Stat 字詞句典」。

— Me@2013.10.22

2013.10.24 Thursday (c) All rights reserved by ACHK

Information 2

Event Realism 3 | 事件實在論 3 | Cumulative concept of time, 17 | Recursion 8.3 | I am a Strange Loop, 3.3

memory ~ information of the past

Part of the past still exists, in the sense that some states and events of the past are entangled with those of the present.

— Me@2013-10-09 6:50 PM

2013.10.23 Wednesday (c) All rights reserved by ACHK