Meaningful 15

Posted on April 28, 2020 by rpflee

無聊

~ no talk

~ nothing to talk

~ 無前途

~ 不能不斷地有下一步

~ no future

— Me@2011.07.14

反貼士搵笨大行動 1.4

Posted on April 26, 2020 by rpflee

…

這五篇文章的主旨是，

「無知」即是「缺乏足夠資料」；

「無知」不是「愚蠢」。

需不需要補習的一個指標是，你在日校專心聽課後，懂不懂做以往的公開試試題？

如果你大部分試題也不懂做，那就代表了，你的日校導師，沒有提供足夠的資料給你，簡稱「無料到」。那樣，解決辦法是，找過另一位，可以提供足夠物理資料的導師。

記住，如果需要「補習」的話，重點不在於「補習」（額外上課），重點在於，你可以選擇導師。

而「選擇導師」的重點則在於「選擇」，而不在於「導師」。

有補習導師並不代表，你就會懂得做試題。

補習導師和日校導師一樣，可能提供不到足夠資料，即是「無料到」。補習導師和日校導師一樣，質素都是沒有保證的。「沒有保證」的意思是，如果補習無用，導師並不會賠償，你所損失的，大量金錢和時閶。

所以，「選擇導師」的重點在「選擇」，不在「導師」。

選擇對導師，才會有成果。

而「有料到」的導師極少，不易找到。以下是選擇導師的方法：

請到本站底部，點擊到達本人的補習網站。

該站有三篇文章：頭兩篇有關「選擇導師」的方法，尾一篇是廣告。

廣告那篇可以忽略。頭兩篇的內容，則適用於大部分人。

— Me@2020-04-25 08:08:39 AM

1990s

Posted on April 23, 2020 by rpflee

— Me@2020-04-22 10:07:48 PM

Problem 2.2c

Posted on April 21, 2020 by rpflee

A First Course in String Theory

2.2 Lorentz transformations for light-cone coordinates.

Consider coordinates $\displaystyle{x^\mu = ( x^0, x^1, x^2, x^3 )}$ and the associated light-cone coordinates $\displaystyle{x^\mu = ( x^+, x^-, x^2, x^3 )}$ . Write the following Lorentz transformations in terms of the light-cone coordinates.

$\displaystyle{ \begin{aligned} \begin{bmatrix} c t' \\ z' \\ x' \\ y' \end{bmatrix} &= \begin{bmatrix} \gamma & -\beta \gamma & 0 & 0 \\ -\beta \gamma & \gamma & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 1 \\ \end{bmatrix} \begin{bmatrix} c\,t \\ z \\ x \\ y \end{bmatrix} \\ \end{aligned} }$

~~~

$\displaystyle{ \begin{aligned} \begin{bmatrix} c t' \\ x' \\ y' \\ z' \end{bmatrix} &= \begin{bmatrix} \gamma & 0 & 0 & -\beta \gamma \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ -\beta \gamma & 0 & 0 & \gamma \\ \end{bmatrix} \begin{bmatrix} c\,t \\ x \\ y \\ z \end{bmatrix} \\ \end{aligned} }$

$\displaystyle{ \begin{aligned} \begin{bmatrix} 1 & 1 & 0 & 0 \\ 1 & -1 & 0 & 0 \\ 0 & 0 & \sqrt{2} & 0 \\ 0 & 0 & 0 & \sqrt{2} \\ \end{bmatrix} \begin{bmatrix} (x^+)' \\ (x^-)' \\ y' \\ z' \end{bmatrix} &= \begin{bmatrix} \gamma & 0 & 0 & -\beta \gamma \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ -\beta \gamma & 0 & 0 & \gamma \\ \end{bmatrix} \begin{bmatrix} 1 & 1 & 0 & 0 \\ 1 & -1 & 0 & 0 \\ 0 & 0 & \sqrt{2} & 0 \\ 0 & 0 & 0 & \sqrt{2} \\ \end{bmatrix} \begin{bmatrix} x^+ \\ x^- \\ y \\ z \end{bmatrix} \\ \end{aligned} }$

$\displaystyle{ \begin{aligned} \begin{bmatrix} (x^+)' \\ (x^-)' \\ y' \\ z' \end{bmatrix} &= \frac{1}{2} \begin{bmatrix} \gamma + 1 & \gamma - 1 & 0 & -\sqrt{2}\,\beta\,\gamma \\ \gamma - 1 & \gamma + 1 & 0 & -\sqrt{2}\,\beta\,\gamma \\ 0 & 0 & 2 & 0 \\ - \sqrt{2}\,\beta\,\gamma & - \sqrt{2}\,\beta\,\gamma & 0 & 2 \gamma \end{bmatrix} \begin{bmatrix} x^+ \\ x^- \\ y \\ z \end{bmatrix} \\ \end{aligned} }$

— Me@2020-04-19 11:52:09 PM

Omnipotence 4.2

Posted on April 19, 2020 by rpflee

When responding to the question “can X create a stone that it cannot lift”, another flawed argument is

X can create the stone that it cannot lift but it chooses not to create it. So there is no stone it cannot lift yet. So X has not failed the omnipotence test.

This argument is wrong.

When we ask “can X choose to create a stone that it cannot lift”, we are discussing whether X has an ability. When we discuss ability, it is always about a potential, a possibility.

Y is able to do action B

always means that

“Y does B” is possible,

which is equivalent to

“Y does B” is not contradictory to any logical laws nor physical laws.

“Whether Y has already done B or will do B” is not the point.

If we allow such “Y can do B but it chooses not to” argument, then anyone is omnipotent. For example,

Can you fly?

I can fly but I choose not to. So even though you have never seen me flying and will never see me flying, it is not because I cannot fly; it is just because I choose not to.

Can you choose to fly?

I can choose to fly but I choose not to choose to fly.

This type of arguments make the word “can“ meaningless.

— Me@2020-03-30 06:52:58 AM

Superpower

Posted on April 19, 2020 by rpflee

Impossible self, 2 | 電腦輪迴觀 4.2

ability 能力

~ you can access your own time to do things

power 權力

~ weighted ability

~ amplified ability

~ super ability

~ 超過一人之力

~ you can access also our people’s time to do things

— Me@2020-04-17 09:00:44 PM

Freedom is being able to make decisions that affect mainly you; power is being able to make decisions that affect others more than you. If we confuse power with freedom, we will fail to uphold real freedom.

— Freedom or Power?

— Bradley M. Kuhn and Richard M. Stallman

So the term “superpower” is actually redundant, because “power” already means “super-ability”, the ability to access more than one person’s time.

— Me@2020-04-18 07:41:36 PM

In daily life, “power” is often used as a synonym of “ability”. In this sense, “superpower” is the ability to access more than one person’s time.

In this context, with our people’s agreement, other people are your superpower. Also, you are our people’s superpower.

— Me@2020-04-18 03:58:32 PM

太極滅世戰

Posted on April 18, 2020 by rpflee

機遇創生論 1.5

這段改編自 2010 年 4 月 18 日的對話。

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
間書原理
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。

下一個定律，就是「間書原理」。

「間書原理」的意思，其實是「陽之極為陰；陰之極為陽」。但那不易理解，所以，我在十多年前，舉了「間書」的例子：

我們平日看書時會間書：用紅筆間低重要的句子。

間書的一個極端是一句也不間。那我們就不知哪些是重要句子。

間書的另一個極端是句句間。那我們也不知哪些是重要句子。

— Me@2003-2004

其他例子有：

順其自然：在生活中百分百地「順其自然」，是一件十分不自然的事。

不要執著：要求自己在任何情況下也「不要執著」，本身是一個執著。

— 改編自李天命先生

知道這個原理後，你在生活處世，凡事就自然不會走得太盡，因為你知道，企圖走得太盡的後果是，輕則過猶不及，重則物極必反。

間書原理水清則無魚

另外，運氣太好時，你會格外小心，因為，好事可以引發壞事，而大好事可以引發大壞事。運氣太差時，你亦不要過份擔心，因為，只要保命，運氣比「太差」更差的話，隨事引發大好事。

我一直以為，尋尋覓覓，兩把年紀，仍然未找到另一半，不幸也。但是，在 2019 滅世戰開始後，我發覺仍然單身，是極大的福份。

或許，到 2021 時，地球和我都仍然存在的話，宇宙會把我一切的夢想，化身成人，和我一同去創造，無限個嶄新的世界。

好事可以變好事

壞事可以變壞事

好事可以變壞事

壞事可以變好事

不要奢望，你可以控制到事情，向這四個方向中的哪一個去發展。你只可以引導，你只可以鼓勵，你不可以控制。

這正正呼應我剛剛講的「種子論」。你可以控制起點，卻不可以控制結果。

當你對「間中原理」深刻心領神會後，你不會輕易羨慕別人的「運氣」或者「天份」，因為通常，凡事有代價。看到別人好時，你反而會問：「他付出了什麼代價，作出了什麼犧牲？」

當你對「間中原理」深刻心領神會後，有時，你更可以主動使用。

例如，以前的眾多考試中，有時，有溫習的那一次，成績反而比沒有溫習的那一次低。

其實，原因並不是「有沒有溫習」本身，而是你「是不是太過刻意」，去奪取成績。

不如，你試試積極溫習，然後，不理成績地，盡情發揮。或許，你有意想不到的收穫。

（問：「不理成績」而又要「盡情發揮」？自相矛盾也？）

你只能提升獲得佳績的機會率，所以，要試前積極溫習，試試盡情發揮；但是，你卻不能直接控制，將要奪得什麼成績，所以，要「不理成績」。

又例如，你下次失眠時，你試試躺下，然後張開雙眼，嘗試迫自己清醒。或者，不知不覺間，你會睡著了。

再例如，如果你由於怕做得不好，而遲遲拖延著一些必須事務的話，你不妨反轉心態，試試在你的能力範圍內，把該事做到最差。或許那樣，你不會再拖延，反而會極早基本完成了該事，剩下了時間，給你改善那「草稿」。

間書原理置之於死地而後生

主動版的「間中原理」，其實就是「種子論」。

把手緊握什麼都沒有
把手放開你得到一切

主動版的「間中原理」，可以戲稱為「耍太極」。

Wikipedia
public domain image
陽之極為陰陰之極為陽

— Me@2020-04-13 06:58:18 PM

CSS, 3

Posted on April 12, 2020 by rpflee


blockquote {
	font-family: Helvetica;
	font-style: normal;
	color: #4f7499;
	background: #EAEFF3;
	border-left: solid 2px #9ab3cb;
	padding-left: 10px;
	margin-left: 20px;
}

#infinite-handle {
	display: none;
}

.infinite-scroll #nav-below {
	display: block;
}

.infinite-scroll #content {
	margin-bottom: 0;
}

.wp-caption .wp-caption-text:before {
    display:none;
}
 
.wp-caption .wp-caption-text {
    text-align:center;
    padding:5px 7px 0;
}

— Me@2020-03-14 04:30:08 PM

2020.03.14 Saturday ACHK

Ex 1.8.2.1 Implementation of $\delta$

Posted on April 11, 2020 by rpflee

Structure and Interpretation of Classical Mechanics

b. Use your delta procedure to verify the properties of $\displaystyle{\delta}$ listed in exercise 1.7 for simple functions such as implemented by the procedure f:

(define (f q)
  (compose
    (literal-function ’F
          (-> (UP Real (UP* Real) (UP* Real)) Real))
    (Gamma q)))

This implements an n-degree-of-freedom path-dependent function that depends on the local tuple of the path at each moment. You can define a literal two-dimensional path by

(define q (literal-function ’q (-> Real (UP Real Real))))

You should compute both sides of the equalities and subtract the results. The answer should be zero.

~~~

(define (((delta eta) f) q)
  (define (g epsilon)
    (f (+ q (* epsilon eta))))
    ((D g) 0))

(define (f q)
  (compose (literal-function 'f (-> (UP Real Real Real) Real))
           (Gamma q)))

(define eta (literal-function 'eta))

(define q (literal-function 'q))

(print-expression ((((delta eta) f) q) 't))

— Patrick Eli Catach

(print-expression ((((delta eta) f) q) 't))

(+ (* ((D eta) t) (((partial 2) f) (up t (q t) ((D q) t)))) 
   (* (eta t) (((partial 1) f) (up t (q t) ((D q) t)))))

(show-expression ((((delta eta) f) q) 't))

d_2020_04_11__11_59_10_AM_

— Me@2020-04-11 12:01:04 PM

Omnipotence 4.1

Posted on April 10, 2020 by rpflee

Please read these 2 posts first:

For all, 3 | Omnipotence

For all, 3.2 | Omnipotence 2

You can find them by searching “omnipotence” using this blog’s search box.

— Me@2020-04-08 03:17:34 PM

If X is omnipotent, X can create a stone that it cannot lift. Then X is not omnipotent, because there is a stone it cannot lift. So omnipotence is a self-contradictory concept.

What if we define omnipotence not as “being able to do anything” but as “being able to do anything except logical self-contradictory ones“?

In order words, omnipotence means that being able to do anything logically possible. Omnipotence does not mean that being able to do also logically impossible things.

This re-definition is not useful, because the original meaning of “being omnipotent” already is “being able to do anything except logical self-contradictory ones“.

There is no re-definition needed. You can only say that the re-definition clarifies the original meaning of “being omnipotent”. However, this clarification cannot eliminate the self-contradictory nature of the meaning of “omnipotence” itself. For example, the following argument is wrong.

If X is omnipotent, “X can create a stone that it cannot lift” is self-contradictory because it is contradictory to “X is omnipotent”.

Since “X can create a stone that it cannot lift” is logically impossible, it should not be a requirement of being omnipotent.

This argument is wrong because:

1. “X can create a stone that it cannot lift” is not SELF-contradictory.

2. “X can create a stone that it cannot lift” is not logically impossible, because, for example, even a human being can create an object that he cannot lift. For example, human beings can create a car that no single person can lift.

Then someone might keep arguing that

But if X is omnipotent, “X can create a stone that it cannot lift” means that “X is omnipotent and X can create a stone it cannot lift”, which is logically impossible. So “X cannot create a stone that it cannot lift” does not make X non-omnipotent.

In other words, “whether X can create a stone that it cannot lift” should not be the requirement of the omnipotence test.

The argument is wrong, because what we are questioning is

Can someone X be omnipotent?

Is omnipotence logically possible?

Remember:

“Being logically possible” means “not self-contradictory”.

If “X is omnipotent” is true,

then “X can create a stone that it cannot lift” is true.

Then “there is a stone that X cannot lift” is true.

Then “X is not omnipotent” is true.

But “X is not omnipotent” is contradictory to the assumption “X is omnipotent“.

So “X is omnipotent” is self-contradictory.

So the question “whether an entity X can be omnipotent and create a stone that it cannot lift” is illegitimate because “an entity X is omnipotent” is logically impossible in the first place. It should not be placed within a question.

Note that our omnipotent test is

“whether an entity X can create a stone that it cannot lift”,

NOT “whether an entity X can be omnipotent and create a stone that it cannot lift”,

NOR “whether an omnipotent entity X can create a stone that it cannot lift”.

— Me@2020-03-30 06:52:58 AM

Time Travel OCD

Posted on April 6, 2020 by rpflee

Once you have DECIDED that you are not going to fear, you will not fear because you know that you are not going to fear.

— Me@2009.09.21

反貼士搵笨大行動 1.3

Posted on April 5, 2020 by rpflee

無足夠資料 12

中六時，我日校的同學中，有些在中五時和我一樣，都有補 Ken Chan 的物理班。升上中六後，他們大部分也補 MC Chan 的物理班。我在中六時則沒有補習。

哪我為什麼在中六時，不去補 MC Chan 的物理班呢？

一方面，那時我覺得，只要足夠勤力，不補也沒有大所謂。另外，補習本身，就要花很多，我原本可以用來，研習的時間。

會考的兩年課程中，因為不開心，荒廢了第一年。所以，中五時的補習，是必須的。但是，我在預科一開始的中六時，就立刻起步讀書，所以，我覺得我可能，毋須補習物理。

思前想後，結果，我在中六升中七的暑假，才去上 MC Chan 的物理班。那算是有點兒幸運，因為太多人報讀，不一定有學位給我。我第一次上他的課時，情形如我日校同學所述，真的連桌子之間的行人路，也放了椅子坐了人。好處是，那證明了導師真的很有型。壞處是，萬一有火警的話，一定傷亡慘重。

事後看來，我當年應該要中六開始時，就補 MC Chan 的物理。

理論上，只要花得足夠多時間研習，不補習也可以獲得，補習時獲得的知識。

實際上，這個講法，就有如：「雖然我住在十二樓，但是只有花足夠多的時間，用心行樓梯，我不乘搭升降機，也可以過到快樂的生活。」

（問：那你即是贊成補習？）

你這樣問沒有意思，因為，那就好像問我，贊不贊成看醫生。那要看情況而定，不能一概而論。

需不需要補習的一個指標是，你在日校專心聽課後，懂不懂做以往的公開試試題？

你可先參考本網誌的五篇文章：

無足夠資料

自我實現預言

天人天書

無足夠資料 4

無足夠資料 5.2

這五篇文章的主旨是，

「無知」即是「缺乏足夠資料」；
「無知」不是「愚蠢」。

需不需要補習的一個指標是，你在日校專心聽課後，懂不懂做以往的公開試試題？

記住，如果需要「補習」的話，重點不在於「補習」（額外上課），重點在於，你可以選擇導師。

而「選擇導師」的重點則在於「選擇」，而不在於「導師」。

有補習導師並不代表，你就會懂得做試題。

所以，「選擇導師」的重點在「選擇」，不在「導師」。

選擇對導師，才會有成果。

而「有料到」的導師極少，不易找到。以下是選擇導師的方法：

…

— Me@2020-03-31 04:28:23 PM

Physics Town

continues

Monthly Archives: April 2020

Meaningful 15

反貼士搵笨大行動 1.4

1990s

Problem 2.2c

Omnipotence 4.2

Superpower

太極滅世戰

CSS, 3

Ex 1.8.2.1 Implementation of $\delta$

Omnipotence 4.1

Time Travel OCD

反貼士搵笨大行動 1.3