Build cross-compiled ECL for Android, 3

Posted on December 30, 2018 by rpflee

EQL5-Android | Common Lisp for Android App Development 2018

d_2018_12_19__22_56_00_PM_

After successfully running the command ./1-make-ecl-host.sh, when I tried to run the command ./2-make-ecl-android.sh, I got the following errors:

d_2018_12_29__23_30_22_PM_

— Me@2018-12-29 11:21:46 PM

Problem 14.5c8

Posted on December 29, 2018 by rpflee

Counting states in heterotic SO(32) string theory | A First Course in String Theory

At any mass level $\displaystyle{\alpha' M^2 = 4k}$ of the heterotic string, the spacetime bosons are obtained by “tensoring” all the left states (NS’+ and R’+) with $\displaystyle{\alpha' M_L^2 = k}$ with the right-moving NS+ states with $\displaystyle{\alpha' M_R^2 = k}$ .

Similarly, the spacetime fermions are obtained by tensoring all the left states (NS’+ and R’+) with $\displaystyle{\alpha' M_L^2 = 4k}$ with the right-moving R- states with $\displaystyle{\alpha' M_R^2 = k}$ .

c) Calculate the total number of states in heterotic string theory (bosons plus fermions) at $\displaystyle{\alpha' M^2 =4}$ .

~~~

— This answer is my guess. —

When $\displaystyle{\alpha' M^2 =4}$ ,

$\displaystyle{\begin{aligned} \alpha' M_L^2 &= 1 \\ \alpha' M_R^2 &= 1 \end{aligned}}$

~~~

The left NS’+ sector:

$\displaystyle{\begin{aligned} \alpha'M^2=1,~~~&N^\perp = 2:~~~~~&\{ \bar \alpha_{-1}^I \bar \alpha_{-1}^J, \bar \alpha_{-1}^I \lambda_{\frac{-1}{2}}^A \lambda_{\frac{-1}{2}}^B, \lambda_{\frac{-3}{2}}^A \lambda_{\frac{-1}{2}}^B, \lambda_{\frac{-1}{2}}^A \lambda_{\frac{-1}{2}}^B \lambda_{\frac{-1}{2}}^C \lambda_{\frac{-1}{2}}^D \} |NS' \rangle_L \\ \end{aligned}}$

The left R’+ sector:

$\displaystyle{\begin{aligned} (-1)^{F_L} |R_\alpha \rangle_L &= + |R_\alpha \rangle_L \\ (-1)^{F_L} |R_\alpha \rangle_R &= - |R_\alpha \rangle_L \\ \end{aligned}}$

$\displaystyle{\begin{aligned} \alpha'M^2=1,~~~&N^\perp = 0:~~~~~&|R_\alpha \rangle_L \\ \end{aligned}}$

The right-moving NS+ states:

$\displaystyle{\begin{aligned} \alpha'M^2=1, ~~~&N^\perp = \frac{3}{2}: &\{ \alpha_{-1}^I b_{\frac{-1}{2}}^J, b_{\frac{-3}{2}}^I, b_{\frac{-1}{2}}^I b_{\frac{-1}{2}}^J b_{\frac{-1}{2}}^K \}~&|NS \rangle \otimes |p^+, \vec p_T \rangle, \\ \end{aligned}}$

The R- states (that used as right-moving states):

$\displaystyle{\begin{aligned} \alpha'M^2=1,~~~&N^\perp = 1:~~~~&\alpha_{-1}^I |R_{a} \rangle,~d_{-1}^I |R_{\bar a} \rangle ~~&||~~ ... \\ \end{aligned}}$

~~~

spacetime bosons:

$\displaystyle{NS'+ \otimes NS+}$

$\displaystyle{\begin{aligned} \left( \{ \bar \alpha_{-1}^I \bar \alpha_{-1}^J, \bar \alpha_{-1}^I \lambda_{\frac{-1}{2}}^A \lambda_{\frac{-1}{2}}^B, \lambda_{\frac{-3}{2}}^A \lambda_{\frac{-1}{2}}^B, \lambda_{\frac{-1}{2}}^A \lambda_{\frac{-1}{2}}^B \lambda_{\frac{-1}{2}}^C \lambda_{\frac{-1}{2}}^D \} |NS' \rangle_L \right) \otimes \left( \{ \alpha_{-1}^{I'} b_{\frac{-1}{2}}^J, b_{\frac{-3}{2}}^{I'}, b_{\frac{-1}{2}}^{I'} b_{\frac{-1}{2}}^J b_{\frac{-1}{2}}^K \}~|NS \rangle \otimes |p^+, \vec p_T \rangle \right) \end{aligned}}$

$\displaystyle{R'+ \otimes NS+}$

$\displaystyle{\begin{aligned} \left( |R_\alpha \rangle_L \right) \otimes \left( \{ \alpha_{-1}^I b_{\frac{-1}{2}}^J, b_{\frac{-3}{2}}^I, b_{\frac{-1}{2}}^I b_{\frac{-1}{2}}^J b_{\frac{-1}{2}}^K \}~|NS \rangle \otimes |p^+, \vec p_T \rangle \right) \end{aligned}}$

spacetime fermions:

$\displaystyle{NS'+ \otimes R-}$

$\displaystyle{\begin{aligned} \left( \{ \bar \alpha_{-1}^I \bar \alpha_{-1}^J, \bar \alpha_{-1}^I \lambda_{\frac{-1}{2}}^A \lambda_{\frac{-1}{2}}^B, \lambda_{\frac{-3}{2}}^A \lambda_{\frac{-1}{2}}^B, \lambda_{\frac{-1}{2}}^A \lambda_{\frac{-1}{2}}^B \lambda_{\frac{-1}{2}}^C \lambda_{\frac{-1}{2}}^D \} |NS' \rangle_L \right) \otimes \left( \alpha_{-1}^{I'} |R_{a} \rangle,~d_{-1}^{I'} |R_{\bar a} \rangle \right) \\ \end{aligned}}$

$\displaystyle{R'+ \otimes R-}$

$\displaystyle{\begin{aligned} \left( |R_\alpha \rangle_L \right) \otimes \left( \alpha_{-1}^{I} |R_{a} \rangle,~d_{-1}^{I} |R_{\bar a} \rangle \right) \\ \end{aligned}}$

— This answer is my guess. —

— Me@2018-12-28 11:12:59 PM

The problem of induction 3.3

Posted on December 28, 2018 by rpflee

“Everything has no patterns” (or “there are no laws”) creates a paradox.

If “there are 100% no first order laws”, then it is itself a second order law (the law of no first-order laws), allowing you to use probability theory.

In this sense, probability theory is a second order law: the law of “there are 100% no first order laws”.

In this sense, probability theory is not for a single event, but statistical, for a meta-event: a collection of events.

Using meta-event patterns to predict the next single event, that is induction.

Induction is a kind of risk minimization.

— Me@2012-11-05 12:23:24 PM

understand \neq agree

Posted on December 28, 2018 by rpflee

$\displaystyle{\text{understand} \neq \text{agree}}$

Seek first to understand, then to be understood

— The Habit 5

— The 7 Habits of Highly Effective People

— Stephen Covey

To understand does not mean to agree.

— Stephen Covey

2018.12.28 Friday by ACHK

Ken Chan 時光機 2.1

Posted on December 27, 2018 by rpflee

當年是 1996 年，我 9 月開始上他的課程。每星期上 1.5 小時，由星期六早上 8 時半，上到 10 時正。所以，每個星期六，我也要在還未睡夠時，就很早起床。去補習社的路程中，往往是一邊行，一邊流鼻水；唯有勉勵自己：「即使再辛苦，只要捱過『會考』（公開試），就可以有好日子過。」

記憶所及，大概在聖誕前，剛好完成了力學分部。

然後，他於聖誕假期中，有額外補課—歷時三天的全日課程，不再是每天 1.5 小時。就在那三天，他要完成波動分部。

他在公佈有這個聖誕波動補課時，我有兩點不開心。

第一點是，我要交額外的學費。不過，相對於第二點而言，那也只是小問題。

第二點是，那補課的學額有限，只有常規課程的兩成。我現在的記憶可能有誤，未必真的是兩成，但也必定是，遠少於他常規課程的學生數目。換句話說，如果供不應求，我就可能報讀不到。幸好，正正是因為這個擔憂，我及早報名，爭取到一個補課學位。

— Me@2018-12-27 03:50:13 PM

Build cross-compiled ECL for Android, 2

Posted on December 25, 2018 by rpflee

EQL5-Android | Common Lisp for Android App Development 2018

The step 2 is to “build cross-compiled ECL for Android”. It should have been straightforward to follow the instructions in the README page of the EQL5-Android project.

d_2018_12_19__22_56_00_PM_

However, when trying to run the command ./1-make-ecl-host.sh, I got the following error messages:

d_2018_12_19__23_11_14_PM_

The error was caused by the fact that my Ubuntu 18.04’s 64-bit gcc toolchain could not compile any source code to create 32-bit executables.

The solution is to run the following command to install the 32-bit gcc toolchain first:

sudo apt-get install g++-multilib libc6-dev-i386

— Me@2018-12-25 09:51:02 PM

Problem 14.5c7

Posted on December 25, 2018 by rpflee

Counting states in heterotic SO(32) string theory | A First Course in String Theory

c) … Write out the massless states of the theory (bosons and fermions) and describe the fields associated with the bosons.

~~~

— This answer is my guess. —

spacetime bosons:

$NS'+ \otimes NS+$

$\displaystyle{\begin{aligned} \left( \{ \bar \alpha_{-1}^I , \lambda_{\frac{-1}{2}}^A \lambda_{\frac{-1}{2}}^B \} |NS' \rangle_L \right) \otimes \left( b_{-1/2}^J~|NS \rangle \otimes |p^+, \vec p_T \rangle \right) \end{aligned}}$

$\displaystyle{\begin{aligned} = \{ \bar \alpha_{-1}^I , \lambda_{\frac{-1}{2}}^A \lambda_{\frac{-1}{2}}^B \} b_{-1/2}^J |NS' \rangle_L \otimes \left( |NS \rangle \otimes |p^+, \vec p_T \rangle \right) \end{aligned}}$

What is the nature of each of the indices $I, J, A, B$ ?

The vector index $J$ runs over eight values.

— c.f. p.323 A First Course in String Theory (Second Edition)

$\displaystyle{I = 2,3,...,9}$

$\displaystyle{A, B = 1, 2, ..., 32}$

— c.f. the blog post Problem 14.5a3

— Me@2018-12-24 10:04:52 PM

For the states in the form

$\displaystyle{ \bar \alpha_{-1}^I b_{-1/2}^J |NS' \rangle_L \otimes \left( |NS \rangle \otimes |p^+, \vec p_T \rangle \right)}$ ,

they

carry two independent vector indices $I$ , $J$ that run over eight values. There are therefore 64 bosonic states. Just like the massless states in bosonic closed string theory[,] they carry two vector indices. We therefore get a graviton, a Kalb-Ramond field, and a dilation:

(NS+, NS+) massless fields: $g_{\mu \nu}, B_{\mu \nu}, \phi$ .

— p.323 A First Course in String Theory (Second Edition)

Then how about the states in the form

$\displaystyle{\begin{aligned} \lambda_{\frac{-1}{2}}^A \lambda_{\frac{-1}{2}}^B b_{-1/2}^J |NS' \rangle_L \otimes \left( |NS \rangle \otimes |p^+, \vec p_T \rangle \right) \end{aligned}}$ ?

What kinds of fields do they represent?

— Me@2018-12-24 10:42:03 PM

— This answer is my guess. —

— Me@2018-12-23 11:16:56 PM

Afshar experiment, 2

Posted on December 23, 2018 by rpflee

Double slit experiment, 8.2

In the double slit experiment, the screen is used to detect interference pattern itself, causing the photon wavefunctions to “collapse”.

In the Afshar experiment, there is no classically definite position for a photon when the photon passes “through” the vertically wire slits. So there is no interference patterns “formed”, unless you put some kind of screen afterwards. [Me@2015-07-21 10:59 PM: i.e. making the observation, c.f. delayed choice experiment]

— Me@2012-04-09 12:19:52 AM

Being massless, they cannot be localized without being destroyed…

— Photon dynamics in the double-slit experiment

— Wikipedia on Photon

Universe City

Posted on December 22, 2018 by rpflee

A university is a city.

— Me@2011.08.23

University ~ Universe City

— Me@2011.09.02

宇宙大戰 1.1

Posted on December 21, 2018 by rpflee

PhD, 2.3 | 故事連線 1.1.5 | 碩士 3.3

…

（問：你好似講到，人類那麼危險？）

因為事實上，人類的確是，那麼危險。

剛才所講，有關選擇碩士或博士論文導師，所需的技巧，背後的精神，其實是通用的—同時適用於你將來選擇公司、上司、生意合作伙伴、配偶，等等。

選擇錯誤，同樣是有改變一生的後果。

（問：人類真的那麼危險嗎？）

你一日未試過，同一個人有工作關係，或者錢銀來往，你也不會知道，他的真面目。

時常會聽到一類故事：

「

甲和乙是幾十年的要好朋友。他們決定合作創業。不料，一同工作不出幾個月，就反目收場。

」

（問：我也遇過類似的情境。

我和一位好朋友合作做小組習作時，雖然未至於反目，但總會有很多爭拗。和他合作前，明明和他感情要好。各自有什麼困難時，對方總會杖義相助。

為什麼人類會，那麼奇怪呢？）

簡單地說，即使是同一個人，其實也有不同方面，各樣性格。

做朋友時，你只需要接受小部分—你可以選擇，只接受他，最好的優點。但是，做工作伙伴時，你卻要接收大部分—你未必可以選擇，不接受他，最壞的缺點。

（問：那樣，如果要「複雜地說」呢？）

— Me@2018-12-20 11:06:49 PM

Build cross-compiled ECL for Android

Posted on December 19, 2018 by rpflee

EQL5-Android | Common Lisp for Android App Development 2018

The step 2 is to “build cross-compiled ECL for Android”. It should have been straightforward to follow the instructions in the README page of the EQL5-Android project.

d_2018_12_19__22_56_00_PM_

However, when trying to run the command ./1-make-ecl-host.sh, I got the following error messages:

d_2018_12_19__23_11_14_PM_

A more serious problem was that I could not even locate the error log file config.log.

Another abnormality was that while the process claimed that it was

Creating directory 'build',

the directory build was actually not created at all.

So I manually created that directory before running the command ./1-make-ecl-host.sh again. Only then, I could find the error log file config.log in the build directory, after the failure of the compilation.

— Me@2018-12-19 10:50:31 PM

Problem 14.5c6

Posted on December 18, 2018 by rpflee

Counting states in heterotic SO(32) string theory | A First Course in String Theory

At any mass level $\displaystyle{\alpha' M^2 = 4k}$ of the heterotic string, the spacetime bosons are obtained by “tensoring” all the left states (NS’+ and R’+) with $\displaystyle{\alpha' M_L^2 = k}$ with the right-moving NS+ states with $\displaystyle{\alpha' M_R^2 = k}$ .

c) Are there tachyonic states in heterotic string theory?

Write out the massless states of the theory (bosons and fermions) …

~~~

— This answer is my guess. —

The left NS’+ sector:

$\displaystyle{\begin{aligned} \alpha'M^2=0,~~~&N^\perp = 1:~~~~~&\{ \bar \alpha_{-1}^I , \lambda_{\frac{-1}{2}}^A \lambda_{\frac{-1}{2}}^B \}|NS' \rangle_L \end{aligned}}$

The left R’+ sector has no massless states.

The right-moving NS+ states:

$\displaystyle{\begin{aligned} \alpha'M^2=0, ~~~&N^\perp = \frac{1}{2}: &b_{-1/2}^I~&|NS \rangle \otimes |p^+, \vec p_T \rangle, \\ \end{aligned}}$

The R- states (that used as right-moving states):

$\displaystyle{\begin{aligned} \alpha'M^2=0,~~~&N^\perp = 0:~~~~&|R_a \rangle \\ \end{aligned}}$

~~~

Since R’+ has no massless states:

spacetime bosons:

$NS'+ \otimes NS+$

$\displaystyle{\begin{aligned} \left( \{ \bar \alpha_{-1}^I , \lambda_{\frac{-1}{2}}^A \lambda_{\frac{-1}{2}}^B \} |NS' \rangle_L \right) \otimes \left( b_{-1/2}^I~|NS \rangle \otimes |p^+, \vec p_T \rangle \right) \end{aligned}}$

$\displaystyle{\begin{aligned} = \{ \bar \alpha_{-1}^I , \lambda_{\frac{-1}{2}}^A \lambda_{\frac{-1}{2}}^B \} b_{-1/2}^I |NS' \rangle_L \otimes \left( |NS \rangle \otimes |p^+, \vec p_T \rangle \right) \end{aligned}}$

spacetime fermions:

$NS'+ \otimes R-$

$\displaystyle{\begin{aligned} \{ \bar \alpha_{-1}^I , \lambda_{\frac{-1}{2}}^A \lambda_{\frac{-1}{2}}^B \} |NS' \rangle_L \otimes |R_a \rangle \\ \end{aligned}}$

— This answer is my guess. —

— Me@2018-12-18 07:46:15 PM

The problem of induction 3.1.2

Posted on December 18, 2018 by rpflee

Square of opposition

“everything has a pattern”?

“everything follows some pattern” –> no paradox

“everything follows no pattern” –> paradox

— Me@2012.11.05

My above statements are meaningless, because they lack a precise meaning of the word “pattern”. In other words, whether each statement is correct or not, depends on the meaning of “pattern”.

In common usage, “pattern” has two possible meanings:

1. “X has a pattern” can mean that “X has repeated data“.

Since the data set X has repeated data, we can simplify X’s description.

For example, there is a die. You throw it a thousand times. The result is always 2. Then you do not have to record a thousand 2’s. Instead, you can just record “the result is always 2”.

2. “X has a pattern” can mean that “X’s are totally random, in the sense that individual result cannot be precisely predicted“.

Since the data set X is totally random, we can simplify the description using probabilistic terms.

For example, there is a die. You throw it a thousand times. The die lands on any of the 6 faces 1/6 of the times. Then you do not have to record those thousand results. Instead, you can just record “the result is random” or “the die is fair”.

— Me@2018-12-18 12:34:58 PM

Best 1.2

Posted on December 17, 2018 by rpflee

The point is not to eliminate a risk, which is always impossible, but to minimize it, which is always possible.

— Me@2018-12-10 02:41:14 PM

迷宮直升機 5.3

Posted on December 17, 2018 by rpflee

Ken Chan 時光機 1.4.3

…

其實，那種情形，對現為中四的你而言，並不只是一個「假設」，因為，你現正修讀， G.Maths（核心數學）和 A.Maths（附加數學）。

「附加數」比「基礎數」而言，艱深非常，大部分人也覺得，十分辛苦。但是，亦正正是因為「附加數艱深非常」，你才會覺得「核心數容易萬分」。

那又為什麼，會有這個現象呢？

（問：程度高了？）

無錯。水平高了。

試想想，你參加了一個走迷宮比賽—與另外幾位參賽者，鬥快逃出同一個迷宮。

在那個情況下，「勤力」一點，跑快一些，是沒有什麼大作用的；因為，你只要在其中一個分岔路口，做錯決定，你就已經可以，前功盡廢。

走迷宮的致勝之道—在現埸極速逃出的方法是，在事前用大量時間準備，一架直升機，在比賽期間，把你釣出迷宮。

即使沒有那麼多資源，至起碼，在比賽開始前，你就要準備好，該迷宮的平面圖。

（問：無論是直升機，或者是鳥瞰圖，好像都是犯規？）

那要視乎，具體是哪一個遊戲。

試想想，中學生自修大學程度的課程，有沒有犯規？

（問：似乎沒有。但是，那又好像十分辛苦。）

一般而言，世間少有不勞而獲的東西。鉅大的好處，很多時也需要付出，鉅大的代價。

還有，如果策略妥當，閱讀大學程度書籍，所需的額外時間，未必如想像中的那麼多。

比喻說，假設你修讀 A.Maths（附加數學）的唯一目的是，提升 G.Maths（核心數學）。那樣，你的「附加數」成績，並不需要保證，名列前茅。

反而，即使在最壞情況，你的「附加數」成績不合格，只要你曾經用心研習過，「附加數」也會令你覺得，「核心數」容易了很多。

同理，如果你閱讀大學物理書籍的主要目的是，提升中學物理的話，你並不需要完成，整本「大學物理」的課文和習題。

反而，最重要的是，你嘗試過「大學物理」中，部分題目的難度；那就足以令你感到，中學的版本，顯淺非常。

— Me@2018-12-17 07:05:34 PM

The Android NDK Tools

Posted on December 16, 2018 by rpflee

EQL5-Android | Common Lisp for Android App Development 2018

After installing the Android SDK Tools by installing Android Studio, originally, you would be able to install the Android NDK through Android Studio’s SDK Manager.

d_2018_12_16__17_27_49_PM_

However, since EQL5-Android requires an old version of the NDK (version 10e), you have to download the NDK from the Android’s official NDK webpage.

d_2018_12_16__16_22_31_PM_

In Ubuntu, move the file android-ndk-r10e-linux-x86_64.zip to the same location as the Android SDK and then unzip it.

— Me@2018-12-16 09:25:10 PM

Problem 14.5c5

Posted on December 15, 2018 by rpflee

Counting states in heterotic SO(32) string theory | A First Course in String Theory

c) Are there tachyonic states in heterotic string theory?

Write out the massless states of the theory (bosons and fermions) …

~~~

We have the following well-known bosonic string mass formulae:

open string:

$\displaystyle{\alpha' M^2 = N - a}$

closed string:

$\displaystyle{\frac{1}{4} \alpha' M^2 = N_L - a}$
$\displaystyle{\frac{1}{4} \alpha' M^2 = N_R - a}$

p.55

— Solutions to K. Becker, M. Becker, J. Schwarz String Theory And M-theory

— Mikhail Goykhman

How come there is an extra $\displaystyle{\frac{1}{4}}$ at the beginning of the closed string formula?

p.322

$\displaystyle{\frac{1}{2} \alpha' M^2 = \alpha' M_L^2 + \alpha' M_R^2}$

$\displaystyle{\begin{aligned} \alpha' M_L^2 &= \alpha' M_R^2 \\ \frac{1}{2} \alpha' M^2 &= \alpha' M_L^2 + \alpha' M_R^2 \\ \alpha' M^2 &= 2 \left( \alpha' M_L^2 + \alpha' M_R^2 \right) = 4 \alpha' M_L^2 \\ \end{aligned}}$

— Me@2018-12-15 08:59:18 PM

Wavefunction of a single photon

Posted on December 14, 2018 by rpflee

Photon dynamics in the double-slit experiment, 3

What equation describes the wavefunction of a single photon?

The Schrödinger equation describes the quantum mechanics of a single massive non-relativistic particle. The Dirac equation governs a single massive relativistic spin-½ particle. The photon is a massless, relativistic spin-1 particle.

What is the equivalent equation giving the quantum mechanics of a single photon?

— edited Jun 3 ’13 at 19:42

— Ben Crowell

— asked Nov 9 ’10 at 20:38

— nibot

There is no quantum mechanics of a photon, only a quantum field theory of electromagnetic radiation. The reason is that photons are never non-relativistic and they can be freely emitted and absorbed, hence no photon number conservation.

— answered Nov 10 ’10 at 20:00

— Igor Ivanov

You can also say that the wavefunction of a photon is defined as long as the photon is not emitted or absorbed. The wavefunction of a single photons is used in single-photon interferometry, for example. In a sense, it is not much different from the electron, where the wave-function start to be problematic when electrons start to be created or annihilated…

– Frédéric Grosshans Nov 17 ’10 at 10:19

— Physics StackExchange

2018.12.14 Friday ACHK

The fallacy of average

Posted on December 14, 2018 by rpflee

Those in the print media who dismiss the writing online because of its low average quality are missing an important point: no one reads the average blog. In the old world of channels, it meant something to talk about average quality, because that’s what you were getting whether you liked it or not. But now you can read any writer you want. So the average quality of writing online isn’t what the print media are competing against. They’re competing against the best writing online. And, like Microsoft, they’re losing.

— What Business Can Learn from Open Source

— Paul Graham

— Me@2011.08.23

2018.12.14 Friday ACHK

PhD, 2.2

Posted on December 14, 2018 by rpflee

故事連線 1.1.4 | 碩士 3.2

這段改編自 2010 年 4 月 18 日的對話。

…

有很多人的「個人形象」和「公眾形象」，都是差天共地的。

（問：即是表裡不一？）

有時，甚至是「表裡相反」。

（問：那應該怎麼辦？

除了在本科生年代，修讀心目中候選導師的課以外，還可以有什麼「測試」？）

可以試試找他，做你的本科畢業論文的導師。但是，這個風險仍然太大。我不太建議。

風險較小的方法有，詢問一下，他現時的研究生。他們最知道，該教授的真正面目，究竟是真材實學，還是欺世盜名。

還有，即使他真材實學，也不代表他肯花時間，用心教導研究生。他會不會那樣做，只有他以前或現時的研究生，才會知道。

（問：你好似講到，人類那麼危險？）

因為事實上，人類的確是，那麼危險。

選擇錯誤，同樣是有改變一生的後果。

— Me@2018-12-13 10:33:47 PM

Physics Town

continues

Monthly Archives: December 2018

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