Ken Chan 時光機 3.3

他答了我很久,阻礙了他的工作,十分抱歉,萬分感激。

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他當時和我對話的最大作用是,在我在最無助時,舒緩了我的情緒。

至於在長遠上、實際上,讀書時所需的策略設計、時間編排 和 心態管理,則未有提供。

.

當然,要他在百忙之中抽出時間,答了我物理問題後,再要完整設計一個,適合我溫習時間表,是沒有可能的。

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那些所謂的「策略設計、時間編排 和 心態管理」,雖然當年不知道,但在之後讀預科、大學本科、研究院時,經過無數的撞板碰壁後,二十九歲時有所領悟。

(問:你研究院碩士畢業時,才二十四歲。為什麼要在二十九歲時,才有所領悟?)

當然,經驗是一年比一年多。

「二十九歲時才有所領悟」的意思是,我在那時才有一個,(我覺得)完整的讀書策略體系,適合大部分人使用。

如果有一個特級極超聰明的人,當然就毋須所謂「策略」。但是,不幸地,我並不是那類人。我相信,我提議的方法,適合那些像我一樣,不太聰明,智力正常的人。

(問:你又怎樣知道,你的讀書策略體系完整,適合大部分人使用?)

當然不會百分百肯定,亦不會有方法,可以去百分百的證實。但是,有一定證據,因為碩士後,我到過高中教書三年;發現了原來我當年,有關讀書的心理或情緒問題,竟然大部人也有。

What is most personal is most general.

— Carl Rogers

另外,之後我重回大學,讀第二個碩士。再做學生後,令我深層領會我那時(28歲)和當年(17歲)的讀書問題。

(問:那些是什麼問題?)

問題太多,不能盡錄。但願有一天,我有時間,把那些問題,一一詳述,令到其他人,毋須再犯。

而這正正是這個網站的作用。

.

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。

— Me@2020-01-20 10:26:20 PM

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2020.01.20 Monday (c) All rights reserved by ACHK

Quick Calculation 13.2

A First Course in String Theory

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Verify that

\displaystyle{\left[ \bar L_0^\perp, X^I (\tau, \sigma) \right] = - \frac{i}{2} \left( {\dot{X}}^I + {X^I}' \right)},

\displaystyle{\left[ L_0^\perp, X^I (\tau, \sigma) \right] = - \frac{i}{2} \left( {\dot{X}}^I - {X^I}' \right)},

~~~

Equation (13.24):

\displaystyle{X^{\mu} (\tau, \sigma) = x_0^\mu + \sqrt{2 \alpha'} \alpha_0^\mu \tau + i \sqrt{\frac{\alpha'}{2}} \sum_{n \ne 0} \frac{e^{-in\tau}}{n} (\alpha_n^\mu e^{i n \sigma} + \bar \alpha_n^\mu e^{-in \sigma})}

Equation (13.39):

\displaystyle{{\dot{X}}^- + {X^-}' = \sqrt{2 \alpha'} \sum_{n \in \mathbb{Z}} \bar \alpha_n^- e^{-in (\tau + \sigma)}}

\displaystyle{{\dot{X}}^- - {X^-}' = \sqrt{2 \alpha'} \sum_{n \in \mathbb{Z}}  \alpha_n^- e^{-in (\tau - \sigma)}}

Equation (13.51):

\displaystyle{\left[\bar L_m^\perp, \bar \alpha_n^J \right]  = - n \bar{\alpha}_{m+n}^J}

\displaystyle{\left[L_m^\perp, \alpha_n^J \right] = - n \alpha_{m+n}^J}

Equation (13.52):

\displaystyle{\left[L_m^\perp, \bar \alpha_n^J \right] = 0}

\displaystyle{\left[\bar L_m^\perp, \alpha_n^J \right] = 0}

Equation (13.53):

\displaystyle{\left[ \bar L_m^\perp, x_0^I \right] = - i \sqrt{\frac{\alpha'}{2}} \bar \alpha^I_m}

\displaystyle{\left[ L_m^\perp, x_0^I \right] = - i \sqrt{\frac{\alpha'}{2}} \alpha^I_m}

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\displaystyle{\left[ \bar L_0^\perp, X^I (\tau, \sigma) \right]},

\displaystyle{= \left[ \bar L_0^\perp, x_0^I + \sqrt{2 \alpha'} \alpha_0^I \tau + i \sqrt{\frac{\alpha'}{2}} \sum_{n \ne 0} \frac{e^{-in\tau}}{n} (\alpha_n^I e^{i n \sigma} + \bar \alpha_n^I e^{-in \sigma}) \right]}

\displaystyle{= - i \sqrt{\frac{\alpha'}{2}} \bar \alpha^I_0 + i \sqrt{\frac{\alpha'}{2}} \sum_{n \ne 0} \frac{e^{-in\tau}}{n} e^{-in \sigma} (-n \bar \alpha_n^I)}

\displaystyle{= - i \sqrt{\frac{\alpha'}{2}} \bar \alpha^I_0 - i \sqrt{\frac{\alpha'}{2}} \sum_{n \ne 0} e^{-in(\tau + \sigma)} ( \bar \alpha_n^I)}

\displaystyle{= - \frac{i}{2} \sqrt{2\alpha'} \sum_{n \in \mathbb Z} \bar \alpha_n^I e^{-in(\tau + \sigma)}}

— Me@2020-01-06 11:30:38 PM

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2020.01.06 Monday (c) All rights reserved by ACHK

Compare results

Within a universe, any two observers can, at least in principle, compare results.

When they compare, they will have consistent results for any observables/measurables.

— Me@2018-02-06 08:48:24 PM

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being entangled ~ being consistent, with respect to any two observers, when they compare the results

— Me@2018-02-05 10:11:45 PM

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2020.01.04 Saturday (c) All rights reserved by ACHK

時間止血 1.6.2

止蝕 3.6.2 | 活在當下 4.6.2

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又例如,我年青時往往會因為.浪費了時間而內疚。後來我發現,人其實有「浪費時間」的心理需要。

我不容許自己浪費時間,往往導致我浪費過多的時間。當我的思考顯意識,企圖毫無保留地,迫自己百分百「善用時間」時,我的身體潛意識,就會不留餘地地,浪費人類所能達到,最多的時間。

如果你在編時間表時,預早安排了一些,用來「浪費時間」的空格,那樣,「浪費時間」這活動,就自然受到控制。

— Me@2013.06.25
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有如睡覺一樣,如果不安排時間睡覺,你身體就會反抗,在不應該睡覺的時候,例如駕車時,睡覺,十分危險。

— Me@2019-12-24 11:15:13 AM

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2020.01.02 Thursday (c) All rights reserved by ACHK

財政自由 1.3.3

PhD, 3.8.3

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(問:你即是話,財政充裕前,讀研究院時,即使智力再高,往往沒有自由去,研究自己喜歡的課題。但是,要等到財政自由時,才研究學術的話,又未必仍然有足夠的智力。)

無錯。那是兩難。

有如人生目標一樣,不會只有一個。當兩個目標有衝突時,要麼取一捨一、要麼雙方妥協。有時靈機一觸的話,則可以協同互生,合而為一。

(問:協同互生?如何執行?可否舉一個例?)

我也不知道呀。如果我知道詳細的解答,我的生活就不會那麼悲慘。

(問:你的生活悲慘?)

大部分人也是那麼吧。每天上班下班,直到退休。最終也做不到,自己最終想做的東西。簡稱「遺撼」也。

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(問:你真的完全不知道嗎?)

又不是完全不知道。只是嘗試當中,尚未成功。所以我不好意思講出來。

(問:只作參考,無傷大雅吧?)

短期而言,先找一份全職,而不全天候的工作,以作維生之用。

並非所有全職工作,都是全天候的。有不少工作職位,有真正下班時間。亦即是話,下班後到下一天上班前,都暫時毋須操心,那份正職的份內事務。

(問:即是有工餘時間。)

無錯。當然,要找到這種工作,並非毫無難度。

例如,你每天下班後,至睡覺前,有三個小時的集中精神時間。你就用那三小時,從事你真正嚮往的事業。

(問:用空閒時間,做自己喜歡的事情?

那太明顯吧?)

未講完。

重點是,要極度認真。那並不是純粹是「做自己喜歡的事情」,而更是「從事自己想發展的事業」。換句話說,那並不只是「每天的娛樂」,而亦是「人生的目標」。

而要做到「極度認真」,就必須無止境地創作和無間斷地發表。

(當然,你亦同時要,做好版權的保護,避免別人盜取你的作品後,反過來指控你抄襲了他。)

— Me@2019-12-30 09:56:25 PM

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2019.12.31 Tuesday (c) All rights reserved by ACHK

Simcity, 2

d_2019_12_29__15_35_29_PM_

I bought this SimCity 2000 box in 1995. It was the first time I went to a big computer centre (mall).

At the first glance, I thought that it was sold at the price 800 HKD, which I could not afford. Luckily, the price label was actually NT800, which meant 800 New Taiwan Dollars.

So I could buy it at 200 Hong Kong Dollars.

— Me@2019-12-29 03:42:26 PM

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2019.12.29 Sunday (c) All rights reserved by ACHK

scmutils, 2

The original method of setting up Emacs for scmutils does not work anymore if you uses the newest (August 2019) version of scmutils, because its installation directories are not the same as those in the previous version.

Either use an older version of scmutils in order to follow the previous instructions for setting up Emacs for scmutils, or give up using Emacs for scmutils for the time being.

Using command line is the best way to go, so far.

Do not use the Edwin editor, since you cannot easily run, edit, or copy existing lines of code, unless you are familiar with it. I do not like it anyway, because after all, it does not provide syntax highlighting.

— Me@2019-12-28 07:50:32 PM

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2019.12.28 Saturday (c) All rights reserved by ACHK

Ken Chan 時光機 3.2

有一次,他在晚上十一時多,回覆我的致電。他說先要關掉實驗機器。他回答了我的物理題目後,我順道問他讀書方法,訴苦說,來不及溫習應試。

你識得咁樣問,幾好喎。(你懂得那樣問,相當好。)

他的意思是,欣賞我有上進心。

.

他答了我很久,花了他大概一個小時多,非常抱歉。

他講了一些東西。以下不依次序。

中五(會考年)每天溫習五、六小時,很正常的事。

你化學不好,為什麼不補化學?

我答:補得太多的話,我沒有足夠溫習。

他說:咁又係。(那又是。)

他問我附加數學有哪些課題。

如果讀了那幾個課題就不會有大問題。

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他暫時不表達立場地,問我喜不喜歡生物科。我答不太喜歡後,他才和應。

係囉,成日有好多嘢背。都唔知背嚟做乜。(是的,時常有很多東西要背。都不知背來為了什麼。)

.

我又問中六時,應該選化學還是應用數學。(其實我一早就想選,應用數學。)我問他當年是讀什麼科。他說他預科時毋須二選一。

我兩科也有讀。

他中六預科時修讀的科目是,英文、純數學、應用數學、物理 和 化學,共五科。

我那時沒有中文必修科。[所以毋須犧牲,化學或應用數學。]

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我又講到另外一些東西。我現在不記得是什麼。他答我:

你完成了力學的 MC(多項選擇題)沒有?

我大概回答,雖然完成了,但仍然沒有把握。(那些 MC,總共花了我三個月,沒有可能重新做一次。)

你試試逐題看一看,不需做多一次,只需嘗試對自己,講一講該題的做法。如果講得出,就為之學懂了該題。如果講不出,才詳細研究該題。

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他答了我很久,阻礙了他的工作,十分抱歉,萬分感激。

— Me@2019-12-26 06:59:01 PM

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2019.12.27 Friday (c) All rights reserved by ACHK

Quick Calculation 13.1

A First Course in String Theory

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Verify that

\displaystyle{\left[ \bar L_m^\perp, x_0^I \right] = - i \sqrt{\frac{\alpha'}{2}} \bar \alpha^I_m},

\displaystyle{\left[ L_m^\perp, x_0^I \right] = - i \sqrt{\frac{\alpha'}{2}} \alpha^I_m}.

~~~

Equation (13.37):

\displaystyle{\bar L_m^\perp = \frac{1}{2} \sum_{p \in \mathbf{Z}} \bar \alpha_p^J \bar \alpha_{n-p}^J},\displaystyle{~~~L_m^\perp = \frac{1}{2} \sum_{p \in \mathbf{Z}} \alpha_p^J \alpha_{n-p}^J}.

.

\displaystyle{ \begin{aligned} \left[ \bar L_m^\perp, x_0^I \right] &= \frac{1}{2} \sum_{p \in \mathbb{Z}} \left[ \bar \alpha^J_p \bar \alpha^J_{m-p}, x_0^I \right] \\  &= \frac{1}{2} \sum_{p \in \mathbb{Z}} \bar \alpha^I_p \left[ \bar \alpha^J_{m-p}, x_0^I \right] + \frac{1}{2} \sum_{p \in \mathbb{Z}} \left[ \bar \alpha^J_p, x_0^I \right] \bar \alpha^I_{m-p} \\  &= \frac{1}{2} \bar \alpha^J_m \left[ \bar \alpha^J_{0}, x_0^I \right] + \frac{1}{2} \left[ \bar \alpha^J_0, x_0^I \right] \bar \alpha^J_{m} \\  \end{aligned} }

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By Equation (13.33):

\displaystyle{ \begin{aligned}  \left[ \bar L_m^\perp, x_0^I \right]  &= - \frac{1}{2} \bar \alpha^J_m \left[ i \sqrt{\frac{\alpha'}{2}} \eta^{IJ} \right] - \frac{1}{2} \left[ i \sqrt{\frac{\alpha'}{2}} \eta^{IJ} \right] \bar \alpha^J_{m} \\  &= - i \sqrt{\frac{\alpha'}{2}} \eta^{IJ} \bar \alpha^I_m \\  \end{aligned} }

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Since I and J are transverse coordinate indices, neither of them can be zero.

\displaystyle{ \begin{aligned}  \left[ \bar L_m^\perp, x_0^I \right]  &=  - i \sqrt{\frac{\alpha'}{2}} \bar \alpha^I_m \\  \end{aligned} }

— Me@2019-12-25 10:56:15 AM

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2019.12.25 Wednesday (c) All rights reserved by ACHK

Two dimensional time 5.2.3

The first time direction is uncontrollable; the second is controlled by making choices, traveling through different realities. Future is a set of parallel universes.

— Me@2017-12-15 10:59:49 AM

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The first time direction, which is along the timeline, is uncontrollable, because one can only travel from the past to the future, not the opposite.

The second direction, which is across different timelines, is controlled by making choices, forming different realities.

— Me@2019-12-21 11:03:23 PM

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2019.12.22 Sunday (c) All rights reserved by ACHK

Two dimensional time 5.2.2

time direction ~ direction of change

multiple time directions ~ multiple directions of change

— Me@2019-12-22 04:38:47 PM

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the first dimension of time ~ direction of change

the second dimension of time ~ direction of change of changes

— Me@2019-12-22 04:46:47 PM

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2019.12.22 Sunday (c) All rights reserved by ACHK

Pandemonium, 2

Batman: You sold us out, Clark. You gave them the power that should have been ours. Just like your parents taught you. My parents taught me a different lesson… lying on this street… shaking in deep shock… dying for no reason at all. They showed me that the world only makes sense when you force it to.

— Batman

— The Dark Knight Returns

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2019.12.21 Saturday ACHK

PhD, 3.8.2

財政自由 1.3.2

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讀研究院的最大作用是,獲取獨家資料和人脈。

做到物理學家的其中一個,近乎先決條件是,認識一些一流的物理學家,從而可以跟他們對話。換句話說,讀研究院的主要目的是,爭取跟一些物理神人,對話的機會。
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(問:但是,你又提議最好在,已經有財政自由時,才讀研究院?那樣,豈不是起碼要三、四十歲時,才可以讀研究院?

那時,頭腦都已經,大大不如十多二十歲了。)

無錯。那是兩難。

有如人生目標一樣,不會只有一個。當兩個目標有衝突時,要麼取一捨一、要麼雙方妥協。有時靈機一觸的話,則可以協同互生,合而為一。

(問:那即是怎樣?)

每個人不同,沒有一定的答案。但是,你可以參考學術界中,成功或失敗人士的經驗,從而避開一些宏觀的錯誤。之於其他細節,只能隨機應變,見步行步,行步見步。

例如,有些人年輕時專心賺錢,暫時放棄讀書;打算老一點時,才重操學業。但是,老一點時,已經沒有心思了。

沒有「心」的原因是,年紀越大,機會成本越高。亦即是話,研究學術的時間,往往可以用於更偉大的地方。沒有「思」的原因是,年紀越大,一般而言,身體和智力也不如年輕時。

(問:你即是話,財政充裕前,讀研究院時,即使智力再高,往往沒有自由去,研究自己喜歡的課題。但是,要等到財政自由時,才研究學術的話,又未必仍然有足夠的智力。)

無錯。那是兩難。

有如人生目標一樣,不會只有一個。當兩個目標有衝突時,要麼取一捨一、要麼雙方妥協。有時靈機一觸的話,則可以協同互生,合而為一。

(問:協同互生?如何執行?可否舉一個例?)

— Me@2019-10-22 09:44:23 PM

— Me@2019-12-17 09:35:51 PM

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2019.12.18 Wednesday (c) All rights reserved by ACHK

University

d_2019_09_29__17_29_36_PM_

In this picture, he was at his 15.

Later on, he studied at another university.

— Me@2019-12-15 03:27:25 PM

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2019.12.15 Sunday (c) All rights reserved by ACHK

Varying the action, 2.2

\displaystyle{ \begin{aligned} &= \int_{t_1}^{t_2} (D L \circ \Gamma[q]) \delta_\eta \Gamma[q] \\ \end{aligned}}

\displaystyle{ \begin{aligned} &= \int_{t_1}^{t_2} [\partial_0 L (t, q, v), \partial_1 L (t, q, v), \partial_2 L (t, q, v)] (0, \eta(t), D\eta(t)) \\  \end{aligned}}

There are two kinds of tuples: up tuples and down tuples. We write tuples as ordered lists of their components; a tuple is delimited by parentheses if it is an up tuple and by square brackets if it is a down tuple.

— Structure and Interpretation of Classical Mechanics

So \displaystyle{\left[\partial_0 L (t, q, v), \partial_1 L (t, q, v), \partial_2 L (t, q, v)\right] (0, \eta(t), D\eta(t))} is really a dot product:

.

\displaystyle{ \begin{aligned} & \int_{t_1}^{t_2} (D L \circ \Gamma[q]) \delta_\eta \Gamma[q] \\ &= \int_{t_1}^{t_2} [\partial_0 L (t, q, v), \partial_1 L (t, q, v), \partial_2 L (t, q, v)] (0, \eta(t), D\eta(t)) \\ &= \int_{t_1}^{t_2} [\partial_1 L (t, q, v) \eta(t) + \partial_2 L (t, q, v) D\eta(t)] \\ \end{aligned}}

— Me@2019-12-14 06:11:22 PM

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2019.12.14 Saturday (c) All rights reserved by ACHK

Classical physics

Quantum Mechanics 6

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As Gene and Sidney Coleman have pointed out, the term “interpretation of quantum mechanics” is a misnomer encouraging its users to generate logical fallacies. Why? It’s because we should always use a theory, or a more accurate, complete, and universal theory, to interpret its special cases, to interpret its approximations, to interpret the limits, and to interpret the phenomena it explains.

However, there’s no language “deeper than quantum mechanics” that could be used to interpret quantum mechanics. Unfortunately, what the “interpretation of quantum mechanics” ends up with is an attempt to find a hypothetical “deeper classical description” underneath the basic wheels and gears of quantum mechanics. But there’s demonstrably none. Instead, what makes sense is an “interpretation of classical physics” in terms of quantum mechanics. And that’s exactly what I am going to focus in this text.

Plan of this blog entry

After a very short summary of the rules of quantum mechanics, I present the widely taught “mathematical limit” based on the smallness of Planck’s constant. However, that doesn’t really fully explain why the world seems classical to us. I will discuss two somewhat different situations which however cover almost every example of a classical logic emerging from the quantum starting point:

  1. Classical coherent fields (e.g. light waves) appearing as a state of many particles (photons)

  2. Decoherence which makes us interpret absorbed particles as point-like objects and which makes generic superpositions of macroscopic objects unfit for well-defined questions about classical facts

— How classical fields, particles emerge from quantum theory

— Lubos Motl

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There is no interpretation problem for quantum mechanics. Instead, if there is a problem, it should be the interpretation of classical mechanics problem.

— Lubos Motl

— paraphrased

— Me@2011.07.28

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2019.12.14 Saturday (c) All rights reserved by ACHK