# The Hong Kong Way

The Hong Kong Way (Chinese: 香港之路) was a peaceful political campaign held in Hong Kong on the 30th anniversary of the Baltic Way. Organisers estimated that 210,000 people participated, to draw attention to the 2019 anti-extradition bill movement and the five demands for government accountability and expanded democratic freedoms. In the early night time hours on 23 August 2019, Hongkongers joined hands to create a human chain 50 kilometres long, stretching across both sides of Hong Kong harbour and over the top of Lion Rock.

The action was inspired by the Baltic Way demonstration of 1989, which involved 2 million people, and contributed to the collapse of Soviet Russian control of the region. The Hong Kong Way event assembled participants along routes that corresponded to the three main MTR lines, forming a chain of people that stretched nearly 50 kilometres through Hong Kong Island, Kowloon and the New Territories, and without any disruptions to traffic.

— Wikipedia on Hong Kong Way

.

.

2019.08.28 Wednesday ACHK

# Problem 13.6

A First Course in String Theory

.

13.6 Orientifold Op-planes

(a) For an O23-plane the two normal directions $\displaystyle{x^{24}, x^{25}}$ can be represented by a plane. A closed string at a fixed $\tau$ appears as a parameterized closed curve $\displaystyle{X^a(\tau, \sigma)}$ in this plane. Draw such an oriented closed string that lies fully in the first quadrant of the $\displaystyle{(x^{24}, x^{25})}$ plane. Draw also the string $\displaystyle{\tilde{X}^a(\tau, \sigma) = -X^a(\tau, 2\pi - \sigma)}$.

~~~

This one is wrong.

.

.

— Me@2019-08-26 10:31:07 PM

.

.

# Quantum Computing, 3

Instead of requiring deterministic calculation, you allow (quantum) probabilistic calculation. What you gain is the extra speed.

— Me@2018-02-08 01:50:06 PM

.

.

# 年年齡 10.2

We don’t stop playing because we grow old; we grow old because we stop playing.

.

— Me@2011.10.11

— Me@2019.08.24

.

.

# 財政自由 1.1

（問：根據你的講法，好像大部分情況下，都不應該讀研究院似的。）

.

（問：那樣，你心目中的理想情況是什麼？）

.

（問：那就即是話，要在還年青時，就賺到一生夠用的金錢？

.

（問：但是，財政自由，又可以如何實現呢？）

「售賣時間」的致命傷是，收入不可倍增放大。那就是所謂的「一分耕耘，一分收穫」。

（問：「一分耕耘，一分收穫」有什麼問題？）

— Me@2019-08-21 07:40:35 PM

.

.

# Physical laws are low-energy approximations to reality, 1.6

QM GR

too many particles

when you cool down the system, you see something that your equations cannot predict

only by experiment, you discover that you can go to there

the system state goes from one local minimum to another

.

Since each theory is valid only when near a particular energy local minimum, we cannot use it to predict other local minima (other physical realities). That’s why we need to keep doing experiments that are designed for stress-testing existing theories. For example, one experiment can put a system in extreme high pressure. Another experiment can put a system in extreme high temperature.

Once a theory breaks down in one of those experiments, we see phenomena that we have never seen before. From there, we construct new theories to explain those phenomena.

Once a theory breaks down in one of those experiments, we see phenomena that we have never seen before. In this sense, experimental physics is much richer.

Computational physics goes further in only one direction. Only experiments let you try randomly.

— Me@2019-08-18 07:51:05 PM

.

.

# Literal numbers

All primitive mathematical procedures are extended to be generic over
symbolic arguments. When given symbolic arguments, these procedures
construct a symbolic representation of the required answer. There are
primitive literal numbers. We can make a literal number that is
represented as an expression by the symbol “a” as follows:

(literal-number 'a)        ==>  (*number* (expression a))


The literal number is an object that has the type of a number, but its
representation as an expression is the symbol “a”.

(type (literal-number 'a))          ==>  *number*

(expression (literal-number 'a))    ==>  a


— SCMUTILS Reference Manual

.

.

2019.08.17 Saturday ACHK

# Multiple dimensions of time

What would be the implications of multiple dimensions of time?

That means the (past) history itself can change, as commonly seen in time travel stories.

But wouldn’t that be the case with one dimension also?

In reality, there is only one dimension of time, meaning that the state of a system keeps changing, forming the timeline. But the timeline itself cannot be changed once formed. In other words, (past) history cannot be changed.

— Me@2019-08-11 04:07:48 PM

.

.

# （反對）開夜車 4.2

.

— Me@2019-07-30 11:11:42 PM

.

.

# Hong Kong

.

.

.

2019.07.29 Monday ACHK

# Quick Calculation 15.1.2

A First Course in String Theory

.

Recall that a group is a set which is closed under an associative multiplication; it contains an identity element, and each element has a multiplicative inverse. Verify that $\displaystyle{U(1)}$ and $\displaystyle{U(N)}$, as described above, are groups.

~~~

# Definition

A group is a set, G, together with an operation $\displaystyle{\bullet}$ (called the group law of G) that combines any two elements a and b to form another element, denoted $\displaystyle{a \bullet b}$ or $\displaystyle{ab}$. To qualify as a group, the set and operation, $\displaystyle{(G, \bullet)}$, must satisfy four requirements known as the group axioms:

Closure

For all a, b in G, the result of the operation, $\displaystyle{a \bullet b}$, is also in G.

Associativity

For all a, b and c in G, $\displaystyle{(a \bullet b) \bullet c = a \bullet (b \bullet c)}$.

Identity element

There exists an element e in G such that, for every element a in G, the equation $\displaystyle{e \bullet a = a \bullet e = a}$ holds. Such an element is unique, and thus one speaks of the identity element.

Inverse element

For each a in G, there exists an element b in G, commonly denoted $\displaystyle{a^{-1}}$ (or $\displaystyle{-a}$, if the operation is denoted “+”), such that $\displaystyle{a \bullet b = b \bullet a = e}$, where e is the identity element.

— Wikipedia on Group (mathematics)

.

The axioms for a group are short and natural… Yet somehow hidden behind these axioms is the monster simple group, a huge and extraordinary mathematical object, which appears to rely on numerous bizarre coincidences to exist. The axioms for groups give no obvious hint that anything like this exists.

— Richard Borcherds in Mathematicians: An Outer View of the Inner World

.

.

2019.07.28 Sunday ACHK

# Alfred Tarski, 3

The undefinability theorem shows that this encoding cannot be done for semantic concepts such as truth. It shows that no sufficiently rich interpreted language can represent its own semantics. A corollary is that any metalanguage capable of expressing the semantics of some object language must have expressive power exceeding that of the object language. The metalanguage includes primitive notions, axioms, and rules absent from the object language, so that there are theorems provable in the metalanguage not provable in the object language.

— Wikipedia on Tarski’s undefinability theorem

.

Tarski’s 1969 “Truth and proof” considered both Gödel’s incompleteness theorems and Tarski’s undefinability theorem, and mulled over their consequences for the axiomatic method in mathematics.

— Wikipedia on Alfred Tarski

.

.

2019.07.20 Saturday ACHK

# Constructive competition

Habit 4: Think Win-Win or No-Deal

.

Constructive competition means that, whoever wins, the whole society wins.

— Me@2011.10.11

.

.

# PhD, 3.7.2

.

（問：根據你的講法，好像大部分情況下，都不應該讀研究院似的。）

（問：那樣，你心目中的理想情況是什麼？）

1. 如果你是自資，就即是不拿學校的資助。那樣，你就不是僱員。研究以外的工作，例如做助教等，可以一概不理。

2. 同理，你的博士導師再不會是，你工作上的上司。反而，你是消費者，他是你的僱員。

（問：怎樣為之「有財政自由」呢？）

（問：那就是即是「退了休」？）

（問：那就即是話，要在還年青時，就賺到一生夠用的金錢？

（問：那麼玄？什麼意思？）

— Me@2019-07-06 10:57:22 PM

.

.

# Physical laws are low-energy approximations to reality, 1.5

… difficult, as you have to heat up [the system] …

… messenger …

… collider particle …

… cool it down to discover new physics …

— Me@2019-06-27 11:23:18 PM

.

.

# Ex 1.7 Properties of $\delta$

Let $\displaystyle{F}$ be a path-independent function and $\displaystyle{g}$ be a path-dependent function; then

$\displaystyle{\delta_\eta h[q] = \left( DF \circ g[q] \right) \delta_\eta g[q]~~~~~\text{with}~~~~~h[q] = F \circ g[q].~~~~~(1.26)}$

— 1.5.1 Varying a path

— Structure and Interpretation of Classical Mechanics

.

Prove that

$\displaystyle{\delta_\eta F \circ g[q] = \left( DF \circ g[q] \right) \delta_\eta g[q]}$

~~~

$\displaystyle{RHS = \lim_{\Delta t \to 0} \left( \frac{F \circ g[q](t+\Delta t) - F \circ g[q](t)}{\Delta t} \right) \lim_{\epsilon \to 0} \left( \frac{g[q+\epsilon \eta]-g[q]}{\epsilon} \right)}$

\displaystyle{ \begin{aligned} LHS &= \delta_\eta F \circ g[q] \\ &= \lim_{\epsilon \to 0} \left( \frac{F \circ g[q+\epsilon \eta]-F \circ g[q]}{\epsilon} \right) \\ &= \lim_{\epsilon \to 0} \left( \frac{F \left[ g[q+\epsilon \eta] \right] - F \left[ g[q] \right]}{\epsilon} \right) \\ \end{aligned}}

Since $\displaystyle{F}$ is path-independent,

\displaystyle{ \begin{aligned} LHS &= \lim_{\epsilon \to 0} \left( \frac{F \left( g[q+\epsilon \eta ] \right) - F \left( g[q] \right)}{\epsilon} \right) \\ \end{aligned}}

Let $\displaystyle{ g[q+\epsilon \eta] = g + \Delta g}$.

\displaystyle{ \begin{aligned} LHS &= \lim_{\epsilon \to 0} \left( \frac{F \left( g[q] + \Delta g[q]] \right) - F \left( g[q] \right)}{\epsilon} \right) \\ &= \lim_{\epsilon \to 0} \left( \frac{F \left( g[q] + \Delta g[q]] \right) - F \left( g[q] \right)}{\Delta g[q]}\frac{\Delta g[q]}{\epsilon} \right) \\ \end{aligned}}

When $\displaystyle{ \epsilon \to 0}$, $\displaystyle{ \Delta g \to 0 }$.

\displaystyle{ \begin{aligned} LHS &= \lim_{\substack{\epsilon \to 0 \\ \Delta g \to 0}} \left( \frac{F \left( g[q] + \Delta g[q]] \right) - F \left( g[q] \right)}{\Delta g[q]}\frac{\Delta g[q]}{\epsilon} \right) \\ &= \lim_{\Delta g \to 0} \left( \frac{F \left( g[q] + \Delta g[q]] \right) - F \left( g[q] \right)}{\Delta g[q]} \lim_{\epsilon \to 0} \frac{g[q + \epsilon \eta] - g[q]}{\epsilon} \right) \\ &= DF \left( g[q] \right) \delta_\eta g[q] \\ &= RHS \\ \end{aligned}}

— Me@2019-06-24 10:55:28 PM

.

.

# From classical to quantum

From this viewpoint, the move from a classical to a quantum mechanical system is not a move from a comutative to a non-commutative algebra $\displaystyle{\mathcal{A}}$ of a real-valued observables, but, instead, a move from a commutative algebra to a partial commutative algebra of observables.

Of course, every non-commutative algebra determines an underlying partial commutative algebra and also its diagram of commutative subalgebras.

That fact that assuming the structure of a non-commutative algebra is the wrong assumption has already been observed in the literature (see, for example, [19]),

but it is often replaced by another wrong assumption, namely that of assuming the structure of a Jordan algebra.

These differing assumptions on the structure of $\displaystyle{\mathcal A}$ affect the size of its automorphisum group and, hence, of the allowable symmetries of the system (the weaker the assumed structure on $\displaystyle{\mathcal A}$, the larger is its automorphism group).

— The Mathematical Foundations of Quantum Mechanics

— David A. Edwards

.

.

2019.06.18 Tuesday ACHK

# Free will, 6

The factors are so many and so complex that no single observer can ever predict my actions with 100% accuracy, even in principle.

$\displaystyle{\equiv}$

I have free will.

— Me@2018-05-06 12:21:36 AM

.

.

# （反對）開夜車 4.1

（問：但是，在現今社會，無論是上班，或是讀書，完全不「開夜車」，又好像不切實際。）

.

（問：那樣說有意思嗎？我正正是問你，在時間管理失宜，需要「開夜車」時，該如何自處？）

• 只可以間中，不可以經常。

• 日間中途要有小睡。

• 平均而言，你仍必須要有，充足的睡眠。亦即是話，某一天睡少了，必須於在當個星期，還回「睡債」。

• 例如，如果你的充足睡眠是，每天七小時，而你在某一天只睡了六小時的話，你就有義務，在當個星期的另一天，睡多一小時。

.

— Me@2019-06-06 08:23:56 PM

.

.