# 凌晨舊戲 2.2

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（問：但是，道理又怎樣為之「境界極高」呢？）

（以下的「瀕死經驗者」，是「自稱經歷瀕死經驗人仕」的簡稱。同理，「瀕死經驗後」，是「所宣稱的瀕死經驗後」的縮寫。）

（問：那樣，你又如何呢？

（問：那樣，你又可否舉例，哪些是帶來「好果」的真道理，而哪些卻是帶在「壞果」的假道理？）

（問：即是話，要足夠老？）

— Me@2018-11-08 11:24:23 AM

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# A pretty girl, 2

Women are directly fitted for acting as the nurses and teachers of our early childhood by the fact that they are themselves childish, frivolous and short-sighted; in a word, they are big children all their life long–a kind of intermediate stage between the child and the full-grown man, who is man in the strict sense of the word. See how a girl will fondle a child for days together, dance with it and sing to it; and then think what a man, with the best will in the world, could do if he were put in her place.

— Of Women

— Arthur Schopenhauer

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When the elderly Schopenhauer sat for a sculpture portrait by the Prussian sculptor Elisabet Ney in 1859, he was much impressed by the young woman’s wit and independence, as well as by her skill as a visual artist. After his time with Ney, he told Richard Wagner’s friend Malwida von Meysenbug, “I have not yet spoken my last word about women. I believe that if a woman succeeds in withdrawing from the mass, or rather raising herself above the mass, she grows ceaselessly and more than a man.

— Wikipedia on Arthur Schopenhauer

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Anybody can look at a pretty girl and see a pretty girl. An artist can look at a pretty girl and see the old woman she will become. A better artist can look at an old woman and see the pretty girl that she used to be. But a great artist — a master — and that is what Auguste Rodin was — can look at an old woman, portray her exactly as she is… and force the viewer to see the pretty girl she used to be…. and more than that, he can make anyone with the sensitivity of an armadillo, or even you, see that this lovely young girl is still alive, not old and ugly at all, but simply prisoned inside her ruined body. He can make you feel the quiet, endless tragedy that there was never a girl born who ever grew older than eighteen in her heart…. no matter what the merciless hours have done to her. Look at her, Ben. Growing old doesn’t matter to you and me; we were never meant to be admired — but it does to them. Look at her! (UC)

— Robert A. Heinlein

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2018.10.27 Saturday ACHK

# Existence and Description

Bertrand Russell, “Existence and Description”

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§1 General Propositions and Existence

“Now when you come to ask what really is asserted in a general proposition, such as ‘All Greeks are men’ for instance, you find that what is asserted is the truth of all values of what I call a propositional function. A propositional function is simply any expression containing an undetermined constituent, or several undetermined constituents, and becoming a proposition as soon as the undetermined constituents are determined.” (24a)

“Much false philosophy has arisen out of confusing propositional functions and propositions.” (24b)

A propositional function can be necessary (when it is always true), possible (when it is sometimes true), and impossible (when it is never true).

“Propositions can only be true or false, but propositional functions have these three possibilities.” (24b)

“When you take any propositional function and assert of it that it is possible, that it is sometimes true, that gives you the fundamental meaning ‘existence’…. Existence is essentially a property of a propositional function. It means that the propositional function is true in at least one instance.” (25a)

— Brandon C. Look

— University Research Professor and Chair

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2018.10.07 Sunday ACHK

# Problem 14.5a1

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

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(a) Consider the left NS’ sector. Write the precise mass-squared formula with normal-ordered oscillators and the appropriate normal-ordering constant.

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$\displaystyle{\alpha' M_L^2 = \frac{1}{2} \sum_{n \ne 0} \bar \alpha_{-n}^I \bar \alpha_n^I + \frac{1}{2} \sum_{r \in \mathbf{Z} + \frac{1}{2}}r \lambda_{-r}^A \lambda_r^A}$

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What is normal-ordering?

Put all the creation operators on the left.

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What for?

p.251 “It is useful to work with normal-ordered operators since they act in a simple manner on the vacuum state. We cannot use operators that do not have a well defined action on the vacuum state.”

“The vacuum expectation value of a normal ordered product of creation and annihilation operators is zero. This is because, denoting the vacuum state by $|0\rangle$, the creation and annihilation operators satisfy”

$\displaystyle{\langle 0 | \hat{a}^\dagger = 0 \qquad \textrm{and} \qquad \hat{a} |0\rangle = 0}$

— Wikipedia on Normal order

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— This answer is my guess. —

$\displaystyle{\sum_{n \ne 0} \bar \alpha_{-n}^I \bar \alpha_n^I}$

$\displaystyle{= \sum_{n \in \mathbf{Z}^-} \bar \alpha_{-n}^I \bar \alpha_n^I + \sum_{n \in \mathbf{Z}^+} \bar \alpha_{-n}^I \bar \alpha_n^I}$

$\displaystyle{= \sum_{n \in \mathbf{Z}^+} \bar \alpha_{n}^I \bar \alpha_{-n}^I + \sum_{n \in \mathbf{Z}^+} \bar \alpha_{-n}^I \bar \alpha_n^I}$

$\displaystyle{= \sum_{n \in \mathbf{Z}^+} \left[ \bar \alpha_{n}^I \bar \alpha_{-n}^I - \bar \alpha_{-n}^I \bar \alpha_{n}^I + \bar \alpha_{-n}^I \bar \alpha_{n}^I \right] + \sum_{n \in \mathbf{Z}^+} \bar \alpha_{-n}^I \bar \alpha_n^I}$

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$\displaystyle{= \sum_{n \in \mathbf{Z}^+} \left[ \bar \alpha_{n}^I, \bar \alpha_{-n}^I \right] + \sum_{n \in \mathbf{Z}^+} \bar \alpha_{-n}^I \bar \alpha_{n}^I + \sum_{n \in \mathbf{Z}^+} \bar \alpha_{-n}^I \bar \alpha_n^I}$

$= \displaystyle{\sum_{n \in \mathbf{Z}^+} n \eta^{II} + 2 \sum_{n \in \mathbf{Z}^+} \bar \alpha_{-n}^I \bar \alpha_{n}^I}$

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c.f. p.251:

$\displaystyle{\sum_{n \ne 0} \bar \alpha_{-n}^I \bar \alpha_n^I}$

$\displaystyle{= \sum_{n \in \mathbf{Z}^+} n \eta^{II} + 2 \sum_{n \in \mathbf{Z}^+} \bar \alpha_{-n}^I \bar \alpha_{n}^I}$

$\displaystyle{= \frac{-1}{12} (D - 2) + 2 \sum_{n \in \mathbf{Z}^+} \bar \alpha_{-n}^I \bar \alpha_{n}^I}$

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Equation at Problem 14.5:

$\displaystyle{\alpha' M_L^2}$

$\displaystyle{= \frac{1}{2} \sum_{n \ne 0} \bar \alpha_{-n}^I \bar \alpha_n^I + \frac{1}{2} \sum_{r \in \mathbf{Z} + \frac{1}{2}}r \lambda_{-r}^A \lambda_r^A}$

$\displaystyle{= \frac{1}{2} \left[ \frac{-1}{12} (D - 2) + 2 \sum_{n \in \mathbf{Z}^+} \bar \alpha_{-n}^I \bar \alpha_{n}^I \right] + \frac{1}{2} \sum_{r \in \mathbf{Z} + \frac{1}{2}}r \lambda_{-r}^A \lambda_r^A}$

$\displaystyle{= \frac{-1}{24} (D - 2) + \sum_{n \in \mathbf{Z}^+} \bar \alpha_{-n}^I \bar \alpha_{n}^I + \frac{1}{2} \sum_{r \in \mathbf{Z} + \frac{1}{2}}r \lambda_{-r}^A \lambda_r^A}$

$\displaystyle{= \frac{-1}{8} + \sum_{n \in \mathbf{Z}^+} \bar \alpha_{-n}^I \bar \alpha_{n}^I + \frac{1}{2} \sum_{r \in \mathbf{Z} + \frac{1}{2}}r \lambda_{-r}^A \lambda_r^A}$

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$D = 10$

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$\displaystyle{\sum_{r \in \mathbf{Z} + \frac{1}{2}}r \lambda_{-r}^A \lambda_r^A}$

$\displaystyle{= \sum_{r = - \frac{1}{2}, - \frac{3}{2}, ...} r \lambda_{-r}^A \lambda_r^A + \sum_{r = \frac{1}{2}, \frac{3}{2}, ...} r \lambda_{-r}^A \lambda_r^A}$

$\displaystyle{= \sum_{r = \frac{1}{2}, \frac{3}{2}, ...} (-r) \lambda_{r}^A \lambda_{-r}^A + \sum_{r = \frac{1}{2}, \frac{3}{2}, ...} r \lambda_{-r}^A \lambda_r^A}$

$\displaystyle{= \sum_{r = \frac{1}{2}, \frac{3}{2}, ...} r \left[ (-1) \lambda_{r}^A \lambda_{-r}^A + \lambda_{-r}^A \lambda_r^A \right]}$

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$\displaystyle{= \sum_{r = \frac{1}{2}, \frac{3}{2}, ...} r \left[ (-1) \lambda_{r}^A \lambda_{-r}^A + \lambda_{-r}^A \lambda_r^A \right]}$

$\displaystyle{= \sum_{r = \frac{1}{2}, \frac{3}{2}, ...} r \left[ \lambda_{-r}^A, \lambda_r^A \right]}$

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Equation (14.29):

$\displaystyle{\left\{ b_r^I, b_s^J \right\} = \delta_{r+s, 0} \delta^{IJ}}$

$\displaystyle{b_r^I b_s^J = - b_s^I b_r^J + \delta_{r+s, 0} \delta^{IJ}}$

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$\displaystyle{\sum_{r \in \mathbf{Z} + \frac{1}{2}}r \lambda_{-r}^A \lambda_r^A}$

$\displaystyle{= \sum_{r = \frac{1}{2}, \frac{3}{2}, ...} r \left[ (-1) \lambda_{r}^A \lambda_{-r}^A + \lambda_{-r}^A \lambda_r^A \right]}$

$\displaystyle{= \sum_{r = \frac{1}{2}, \frac{3}{2}, ...} r \left[ (-1) \left( - \lambda_{-r}^A \lambda_r^A + \delta_{r-r, 0} \delta^{AA} \right) + \lambda_{-r}^A \lambda_r^A \right]}$

$\displaystyle{= \sum_{r = \frac{1}{2}, \frac{3}{2}, ...} r \left[ \lambda_{-r}^A \lambda_r^A + \lambda_{-r}^A \lambda_r^A - 1 \right]}$

$\displaystyle{= \sum_{r = \frac{1}{2}, \frac{3}{2}, ...} r \left[ 2 \lambda_{-r}^A \lambda_r^A - 1 \right]}$

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$\displaystyle{\sum_{r \in \mathbf{Z} + \frac{1}{2}}r \lambda_{-r}^A \lambda_r^A}$

$\displaystyle{= - \sum_{r = \frac{1}{2}, \frac{3}{2}, ...} r + \sum_{r = \frac{1}{2}, \frac{3}{2}, ...} r \left[ b_{-r}^A b_r^A + \lambda_{-r}^A \lambda_r^A \right]}$

$\displaystyle{= - \frac{1}{2} \sum_{r = 1, 3, ...} r + \sum_{r = \frac{1}{2}, \frac{3}{2}, ...} r \left[ b_{-r}^A b_r^A + \lambda_{-r}^A \lambda_r^A \right]}$

$\displaystyle{= \left[ - \frac{1}{24} + \sum_{r = \frac{1}{2}, \frac{3}{2}, ...} r \left( b_{-r}^A b_r^A + \lambda_{-r}^A \lambda_r^A \right) \right]}$

— This answer is my guess. —

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— Me@2018-08-06 10:23:48 PM

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# CSS

— Me@2018-04-05 06:09:36 PM

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# Cat

— Me@2018-02-19 02:33:42 PM

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# The Sixth Sense, 2

It is difficult only for the others.

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It is also true when you are stupid.

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2018.01.26 Friday ACHK

# Teachers, 2

The most important teachers in my life, 2

6. 程兆海 (pure maths)

7. Christopher Nolan (film director)

8. Lubos Motl (physicist)

# 如何拯救眾生 2

How to improve the world indefinitely?

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There is law of conservation of energy.
There is law of conservation of mass.
But, there is no law of conservation of ideas.

— Me

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If you have an apple and I have an apple, and we exchange apples, we both still only have one apple. But if you have an idea and I have an idea, and we exchange ideas, we each now have two ideas.

— George Bernard Shaw

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. . . it is the action of the thinking power called an idea, which an individual may exclusively possess as long as he keeps it to himself; but the moment it is divulged, it forces itself into the possession of every one, and the receiver cannot dispossess himself of it. Its peculiar character, too, is that no one possesses the less, because every other possesses the whole of it. He who receives an idea from me, receives instruction himself without lessening mine; as he who lights his taper at mine, receives light without darkening me.

That ideas should freely spread from one to another over the globe, for the moral and mutual instruction of man, and improvement of his condition, seems to have been peculiarly and benevolently designed by nature, …

— Thomas Jefferson

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# 如何拯救眾生 1

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The meeting of two personalities is like the contact of two chemical substances: if there is any reaction, both are transformed. — Carl Jung

Generalized Newton’s Third Law: You cannot change others without being changed. — John Wheeler

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You are an A person. You befriend with an F person. The result is that your friend becomes a better person, you become a worse person. In theory, you become a C person. Your friend becomes a C person. In practice, since being a bad person is much easier than being a good person, you two will become both F people. — Me

Be slow in making friends, slower in changing. — Benjamin Franklin

You have to know how to accept rejection and reject acceptance. — Ray Bradbury

If you hire all A people, he said, they’ll also hire A people. But if you hire B people, they’ll hire the C people and then it’s all over. — Joel Spolsky

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So that means you cannot help anyone weaker than you?

NO.

Instead, you should help others. But you have to help others in a smart way. — Me

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How?

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. . . it is the action of the thinking power called an idea, which an individual may exclusively possess as long as he keeps it to himself; but the moment it is divulged, it forces itself into the possession of every one, and the receiver cannot dispossess himself of it. Its peculiar character, too, is that no one possesses the less, because every other possesses the whole of it. He who receives an idea from me, receives instruction himself without lessening mine; as he who lights his taper at mine, receives light without darkening me.

— Thomas Jefferson

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# Amazing Gags 7

Chapter 7 Painting

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The secret source of Humor itself is not joy but sorrow.

– Mark Twain

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– Translation by Me

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2008.10.17 Friday (c) CHK2

# 3 Storyline

3 Storyline

3.1 In the beginning,
…3.1.1 in a sense, we are all time travellers

3.2 Now is the past of the future, the future of the past

3.3 You are nowhere but now-here

3.4 Living in now-here

3.5 Time messenger
…3.5.1 how to send messages to your past self
…………接收來自未來的訊息
…3.5.3 deja vu 似曾相識
…3.5.4 how to send messages to your future self
…3.5.5 regrets
…3.5.6 have no regrets
…3.5.7 palm
…3.5.8 preserve time

3.6 Now-here-I
…3.6.1 Foresight: prequel
…3.6.3 You are all of yourselves
…3.6.4 Now-here-I: the holographic universe
…3.6.6 Nothing less
…3.6.7 No persistence needed
…3.6.8 Eliminate the passage of time 與時並進
…3.6.9 Event realism 事件實在論
…3.6.10 Lost in time

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# Chrono Trigger 3

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Masato Kato confirmed that Cross featured a central theme of parallel worlds, as well as the fate of Schala, which he was previously unable to expound upon in Chrono Trigger. Concerning the ending sequences showing Kid searching for someone in a modern city, he hoped to make players realize that alternate futures and possibilities may exist in their own lives, and that this realization would “not … stop with the game”.

— Wikipedia on Chrono Cross

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2011.05.02 Monday ACHK

# Ra’s al Ghul

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Planned cast

Bale said he would return if Nolan did. Aaron Eckhart had expressed his enthusiasm to return for a sequel if asked, although he later stated Nolan verified that his character, Harvey Dent, is dead. Nolan confirmed that the ensemble cast from the first two films will be returning. Tom Hardy and Anne Hathaway have been cast as Bane and Selina Kyle. Juno Temple has been cast in a role described as a “street-smart Gotham girl”. Josh Pence was cast as a young Ra’s al Ghul, with his scenes to take place thirty years before the events of Batman Begins. Nestor Carbonell is in negotiations to reprise his role as Mayor Anthony Garcia. Joseph Gordon-Levitt has been cast as John Blake, “a Gotham City beat cop,” along with Marion Cotillard, who will be portraying Miranda Tate, “a Wayne Enterprises board member eager to help a still-grieving Bruce Wayne resume his father’s philanthropic endeavors for Gotham”.

— Wikipedia on The Dark Knight Rises

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2011.04.30 Saturday ACHK

# Teachers 4

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I’m about to become a teacher. How can I be a good one?

The best teachers I remember from school had three things in common:

(1) They had high standards. Like three year olds testing their parents, students will test teachers to see if they can get away with low-quality work or bad behavior. They won’t respect the teachers who don’t call them on it.

(2) They liked us. Like dogs, kids can tell very accurately whether or not someone wishes them well. I think a lot of our teachers either never liked kids much, or got burned out and started not to like them. It’s hard to be a good teacher once that happens. I can’t think of one teacher in all the schools I went to who managed to be good despite disliking students.

(3) They were interested in the subject. Most of the public school teachers I had weren’t really interested in what they taught. Enthusiasm is contagious, and so is boredom.

— Paul Graham

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2011.04.05 Tuesday ACHK

# Socialising

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Socialising on the internet is to socialising, what reality TV is to reality.

— Aaron Sorkin

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2011.04.04 Monday ACHK

# PayPal

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No, because I think we didn’t know what we were doing. I think the hallmark of a really good entrepreneur is that you’re not really going to build one specific company. The goal — at least the way I think about entrepreneurship — is you realize one day that you can’t really work for anyone else. You have to start your own thing.

— Max Levchin

— Founders at Work

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2011.03.31 Thursday ACHK

# Great Idea 4

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If so, this is good news indeed. Good ideas always tend to win eventually. The problem is, it can take a very long time. It took decades for relativity to be accepted, and the greater part of a century to establish that central planning didn’t work. So even a small increase in the rate at which good ideas win would be a momentous change — big enough, probably, to justify a name like the “new economy.”

— Paul Graham

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2011.03.29 Tuesday ACHK

# Blog 4

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In an attempt to avoid that trap, and to clarify my own thinking, I’ve decided to write for a very limited audience: me, and people who might be similar to me.

— Paul Buchheit

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2011.03.22 Tuesday ACHK