反貼士搵笨大行動 1.1

在中四升中五的那個暑假,有一位楊姓同學送了,當時某補習社一個講座的入場劵給同學們,包括我。(該補習社,現已不存在。)物理科的部分,由 Ken Chan 主講。

他的第一句是:「我正職唔係日校物理老師,我係做研究o既。」

然後,他自問:「嘩,阿 sir 好犀利呀!」

自答:「唔一定o既,可能係我俾人研究呢。」

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另一句金句是:「後生又唔代表無經驗o既。」

他宣稱他在當屆的會考物理中,選擇題中,貼中了多少題,而長題目中,又貼中了多少題。選擇題的命中數目,我不太記得;大概是 45 題中的 39 題。而長題目的貼中率,則是 5 題中有 4 題。

聽過了他的講座後,我感到他與別不同,有如半人半神。之後的那個星期,我立刻去補習社報讀他的課程。每星期上他的課,大概是該星期最快樂的時光,雖然他的課堂時間,定在星期六的早上八時半。那個年代,仍是一個真人授課的時代。

他在授課中,亦間中,但不常,提及他的試題預測命中率。

我是在中五初之前的那個月(八月),開始上 Ken Chan 的課。我不記得是當時還是後來,他在星期六的下午 5 時半,有開另一班;課程和進度,和上午 8 時半那班,大致相同。

幾個月(可能少於三個月)後,我有一次改了上,下午的那一課,遇到暑期介紹我去聽講座的那位楊姓同學。我發覺他在那時才開始補,所以他要借我九月以來的講義。他以外,他還介紹了我日校的另一位同學,去上那個補習班。那另一位同學姓馬。

幾個月後,考了物理科後的一晚,我和馬同學於電話傾談。他說他在見到試題時,十分生氣,因為不如傳說中的所謂「5 題貼中 4 題」。(根本就一題也沒有貼中,除非「貼中」的定義,就只是「同一課題」而已;例如,貼「力學」題目,又真是出了「力學」題目。)

我則不會有那樣的期望。我回答他說:「如果他真的可以貼中題目,他在平時又何須那麼用心去授課?他又何須在聖誕假和農曆年假中,再要不斷的補課呢?」

— Me@2020-02-19 05:33:09 PM

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2020.02.19 Wednesday (c) All rights reserved by ACHK

Problem 2.1b

A First Course in String Theory

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2.1 Exercises with units

(b) Explain the meaning of the unit K (degree kelvin) used for measuring temperatures, and explain its relation to the basic length, mass, and time units.

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{\displaystyle {\frac {1}{T}}=\left({\frac {\partial S}{\partial U}}\right)_{V,N}},

where \displaystyle{U} is the internal energy.
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The units of \displaystyle{k_B T} and \displaystyle{E} are the same.

\displaystyle{[k_B T] = [E]}

In other words, the Boltzmann constant \displaystyle{k_B} translates the temperature unit \displaystyle{K} to the language of energy unit \displaystyle{J}.

However, although the temperature unit \displaystyle{K} and the energy unit \displaystyle{J} have the relation

\displaystyle{k_B K = J},

just \displaystyle{k_B T} would not give the correct value of energy \displaystyle{E}, not to mention that we have not yet specified of which the energy \displaystyle{E} is.

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For an ideal gas,

\displaystyle{pV=Nk_B T}

and the average translational kinetic energy is

{\displaystyle {\frac {1}{2}}m{\overline {v^{2}}}={\frac {3}{2}}k_BT}

for 3 degrees of freedom. In 3D space, if there are only translational motions, there are only 3 degrees of freedom.

In other words, just the value of {k_B T} itself gives no physical meaning. Instead, {\tfrac{1}{2}k_B T} can be interpreted as the average translational kinetic energy of the particles in an one dimensional space. Equivalently, \displaystyle{\tfrac{3}{2}k_BT} gives that in our three dimensional space.

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Another main difference is that although energy is an extensive property, temperature is an intensive property.

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We define the temperature unit Kelvin \displaystyle{K} by requiring the water triple point temperature,

\displaystyle{T_{tp} \equiv 273.16K}

Once this value is fixed, the Boltzmann constant \displaystyle{k_B} value can be estimated by using, for example, the ideal gas law

\displaystyle{pV = N k_B T},

because \displaystyle{k_B} always comes with \displaystyle{T}.

— Me@2020-02-16 11:14:24 AM

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2020.02.16 Sunday (c) All rights reserved by ACHK

Unix

Linux is headache. It gives you too many choices.

— Me@2011.07.14

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But Linux is necessary.

— Me@2020-01-23 08:53:29 PM

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Applicants must also have extensive knowledge of Unix, although they should have sufficiently good programming taste to not consider this an achievement.

— MIT job advertisement

— Hal Abelson

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2020.02.15 Saturday (c) All rights reserved by ACHK

大腦物理性損毀不是比喻

99.85%的人不會,終身被匪欺騙教育,大腦已經物理性損毀了,假如說匪的謊言灌輸有20層,那麼絕大多數人遭鐵拳之後的反思,最多只能突破一兩層,達到“我愛國所以要說話”的程度,離理解台人港人藏人維人還非常遠,至少還需要十幾個層次的突破。所以覺醒者極少極少,而且沒有力量。很悲哀,但事實如此。

所以匪的滅亡,恐怕不會是由於覺醒後的民眾起來反抗,而是傳統的王朝滅亡現象,天災加人禍造成經濟崩潰,引發統治崩潰,帶來的不是社會進步,而是社會危機。

大腦物理性損毀不是比喻,而是 literally 如此,人腦的神經細胞本身不構成思想,神經細胞之間的連接方式才是,從嬰兒出生到不斷學習成長,就是逐步構建神經細胞連接到過程,連接完成之後,是不可逆的,所以經匪教育的人,99.85%都是終身殘疾,剩下那點點漏網之魚,只是教育失敗而已。

肉體也是一樣,從受精卵、胚胎開始,細胞都是幹細胞,然後分化成各種完全不同的組織細胞,成長為肉體,這個分化、成長、發育的過程是非常可塑的,外界條件可以對肉體發育造成很大影響,但是一旦發育完成,還有可能退回去變成幹細胞,再重新發育一次,變成一個不一樣的肉體嗎?沒有可能的。

所以您國成年人99.85%都是無救的,不要對他們抱任何希望,期待發生什麼什麼事件能夠改變他們的思維,從這個意義上看,他們都是已經死亡的人。唯一的希望恐怕在還沒有受匪教育或受教育不多的小孩子,以及還沒有出生的下一代,只有趕緊跑路,把他們帶離地獄,才有一點點挽救的希望。

所以逃離匪區最大的收穫是什麼,不是自己能賺錢,能自由,而是孩子可以不用再經歷我們曾經經歷的那些毫無意義的痛苦、摧殘、扭曲,孩子可以有機會做個正常人。我們自己每個人都已經多多少少被毀滅了一部分,但是能救孩子,下一代還有新的希望,還有什麼比這更重要的呢。

— 李穎

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People do not change. They die, replaced by other people.

Most people do not change. They die, replaced by a new generation of people.

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You cannot change the people around you, but you can change the people you choose to be around.

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2020.02.15 Saturday ACHK

機遇創生論 1.2

這段改編自 2010 年 4 月 18 日的對話。

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還有,「人生攻略理論」令人聯想到很多東西,而大部分也不是,我們那個合體大理論的內容。

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「緣份攻略」都不行,因為感覺有點怪。

(安:那就不如叫做「緣份理論」。)

「理論」很空泛。不應把「理論」,視為名字的一部分。

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不如就直接收做「機械人生論」啦,因為那個大統一理論,其實就即是「人生攻略」。

這個大統一理論的成員,包括(但不止於):

精簡圖:

種子論
反白論
完備知識論

自由決定論

它們可以大統一的成因,在於它們除了各個自成一國外,還可以合體理解和應用。

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詳細圖:

種子論 可遇不可求

你只能控制因,不能控制果。事情結果,除了受你的因以外,還受千百萬樣其他因素影響。所以,人生的大目標之中,很多也只有極細的成功機會率。

第一方面,如果你很努力做事,事情仍不能如你所願的話,不要覺得很奇怪。

第二方面,做事時,不要過份用力之外,亦不要在不適當的地方用力。

比喻說,你向心儀示愛後,就只能等待她的答覆,讓她決定,接不接受你的愛意。

示愛以後,並沒有任何東西你可以做,從而控制到她去喜歡你,因為,那是她的自由。

你唯一可以做的是,遠在示愛之前,就積極提升自己的外貌和人格等,從而提高,她喜歡你的機會率。

在適當的地方用力以後,要懂得「放手」,讓事情自己發展。

把手緊握 什麼都沒有
把手放開 你得到一切

萬事俱備,只欠東風時,就應該立刻離開,讓東風做事,不要阻礙東風。

亦即是話,一件事情的發展結果,受眾多因素影響。有些你控制得到,有些你控制不到。你既要盡力處理,你控制得到的部分,亦同時要盡力去忽略,你控制不到的部分。

千萬不要干涉,大自然的內政,因為,那只會弄巧反拙。

— Me@2020-02-15 07:17:00 AM

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2020.02.15 Saturday (c) All rights reserved by ACHK

scmutils, 2.3

Within the MIT Scheme environment, it is not the original command line (bash) anymore. I can neither repeat the last command by just pressing the up key once, nor select the last command by mouse in order to copy it.

So I think I have to use an older version of scmutils.

However, this method is not easy to implement, because the author’s website does not provide an older version. Luckily, I have found an old version in my computer. You can download it here:

scmutils-20160827-x86-64-gnu-linux

Note: Since the installation of the library scmutils requires the root access of your Linux system, please do NOT use it on your working computer. Instead, create an isolated virtual machine to use it.

— Me@2020-02-09 10:27:32 PM

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2020.02.09 Sunday (c) All rights reserved by ACHK

Black hole information paradox, 4

So we seem to have a direct contradiction between [QM and unitarity] and [GR and causality]. Both of these principles, unitarity and causality, cannot be exactly correct because a contradiction arises from their explosive mixture.

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As most quantum mechanicians have known from the very beginning, it is the unitarity, a principle of quantum mechanics, that wins in the battle and remains universally valid.

On the other hand, causality becomes an approximate principle that is only valid in the limit of infinitely large causal diamonds. In the presence of black holes, the internal causal structure is modified by quantum phenomena and the information can “tunnel” out of the black hole.

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It shouldn’t be so surprising that unitarity survives completely while causality doesn’t. After all, the basic postulates of quantum mechanics, including unitarity, the probabilistic interpretation of the amplitudes, and the linearity of the operators representing observables, seem to be universally necessary to describe physics of any system that agrees with the basic insights of the quantum revolution.

On the other hand, geometry has been downgraded into an effective, approximate, emergent aspect of reality. The metric tensor is just one among many fields in our effective field theories including gravity. In string theory, there are, in some sense, infinitely many such fields besides the metric tensor – the whole “stringy tower”. The metric tensor doesn’t have to exist as a good degree of freedom at the Planck scale or in other extreme conditions. We know many other fields that are only good enough at low energies – e.g. the pion field.

— Black hole information puzzle

— Lubos Motl

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2020.02.09 Sunday ACHK

Ken Chan 時光機 3.4

如果可以用時光機,把那些讀書策略傳送到 16 歲時的自己,而又只能夠長話短說的話,我會提醒自己,

不要企圖去,違反「自然定律」。 

比喻說,如果你企圖把二公升的水,倒進只有一公升的杯中,悲劇注定會發生。

同理,如果有一件工作,正常人要花十小時,才能圓滿完成,而我企圖去,僅僅用五小時的話,質素必然會奇差。

一切要符合邏輯和自然定律。

第一定律是:

相對於當年香港中學會考(中五公開試)的課程時間長度和深淺程度而言,一個平均智力的人,只要運用一些簡單的時間管理系統,都可以在各科之中,獲得上佳成績。

會考課程由中四開始,至中五開考,大約有一年零七個月的時間。

但是,當時我詢問 Ken Chan 讀書方法,或者時間管理技巧時,情境並不是那樣的。

(問:何出此言呢?)

我在中四時,大部分時間,都用來擔憂和內疚,真正用來讀書時間奇少。所以,我是在中五開始時,才真正(企圖)開始準備會考的。而最慘的是,那時,我仍然花了不少的時間,去擔憂和內疚。

當時我詢問 Ken Chan 讀書方法,或者時間管理技巧時,已經是中五的中段時期;距離應考,只剩幾個月的時間,並沒有一年零七個月的時間。所以,心態上,我不應想像,仍然有什麼方法,可以令我可以在所有科目,都奪取 A 級成績。合理的問題應該是:

如何善用那剩下的幾個月,把它發揮最大的功效?

有多少科目,仍然有機會奪 A?

有哪些科目,只能退而求其次,奪 B 了事?

又有哪些科目,其次也不行,只能期望守住 C?

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第二定律是:

假設某一科奪 A 需要的分數是 100 分,而對應需要研習時間 1000 小時。

如果奪 B 需要的分數是 80 分的話,對應需要研習時間,必定遠低於 800 小時;因為凡事該科課程中,最艱深和最費時的題目,你都可以選擇放棄。

— Me@2020-02-08 11:36:41 AM

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2020.02.08 Saturday (c) All rights reserved by ACHK

Problem 2.1

A First Course in String Theory

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2.1 Exercises with units

Construct and evaluate a dimensionless number using the charge \displaystyle{e} of the electron (as defined in Gaussian system of units), \displaystyle{\hbar}, and \displaystyle{c}. (In Heaviside-Lorentz units, the Gaussian \displaystyle{e^2} is replaced by \displaystyle{\frac{e^2}{4 \pi}}.)

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\displaystyle{ \begin{aligned} \alpha &= \frac{e^2}{(4 \pi \varepsilon_0)\hbar c} \\ \alpha &= \frac{1}{137.035\,999\,679(94)} \\ \end{aligned} }

— Me@2010

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2020.02.04 Tuesday (c) All rights reserved by ACHK

Spacetime interval

Two contrasting viewpoints on time divide prominent philosophers.

One view is that time is part of the fundamental structure of the universe – a dimension independent of events, in which events occur in sequence. Isaac Newton subscribed to this realist view, and hence it is sometimes referred to as Newtonian time.

The opposing view is that time does not refer to any kind of “container” that events and objects “move through”, nor to any entity that “flows”, but that it is instead part of a fundamental intellectual structure (together with space and number) within which humans sequence and compare events.

This second view, in the tradition of Gottfried Leibniz and Immanuel Kant, holds that time is neither an event nor a thing, and thus is not itself measurable nor can it be travelled.

— Wikipedia on Time

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Special relativity declares a similar law for all motion: the combined speed of any object’s motion through space and its motion through time is always precisely equal to the speed of light.

— The Fabric of the Cosmos: Space, Time, and the Texture of Reality

— Brian Greene

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Space is relative, in the sense that the space interval, \Delta d, (aka distance) between two events can have different values for different observers.

\displaystyle{ \begin{aligned}   \Delta {d} &= \sqrt{{\left(\Delta {x}\right)}^{2}+{\left(\Delta {y}\right)}^{2}+{\left(\Delta {z}\right)}^{2}} \\    \end{aligned} }

Time is relative, in the sense that the time interval, \Delta t, (aka duration) between two events can have different values for different observers.

Spacetime is absolute, in the sense that the spacetime interval, (\Delta s)^2, between two events cannot have different values for different observers.

\displaystyle{  \begin{aligned}  (\Delta s)^{2}  &= (\Delta ct)^{2}-(\Delta x)^{2}-(\Delta y)^{2}-(\Delta z)^{2} \\  &= (\Delta ct)^{2}-(\Delta d)^{2} \\  \end{aligned} }

— paraphrasing The Fabric of the Cosmos

— Me@2020-01-26 12:46:41 AM

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2020.02.03 Monday (c) All rights reserved by ACHK