以右攻左

Posted on May 16, 2022 by rpflee

這段改編自 2021 年 12 月 13 日的對話。

The whole notion of being “left wing” or “right wing” is silly.

Almost no one initially agrees with the semi-random collection of policies associated with each wing.

They only support those policies after they join the left or right mind tribe.

— 12:27 AM · May 13, 2022

— Elon Musk

大概而言，美國左派的目標是「兼善天下」，美國右派的目標是「獨善其身」。

「兼善天下」（大乘）這目標固然是好，但就大到執行不到。

「獨善其身」（小乘）這目標則執行得到，但是就小到，其實沒有大用。如果是僅是「小乘」而已，人生沒有多大意義。試想想，假如，你可以「獨善其身」，生活富足，但是沒有愛人，沒有朋友，你會被迫，思考人生的意義。

「被迫思考人生意義」，可以簡稱「抑鬱」。

所以上次說，情況有如行路，要左右腳配合，才會暢順。如果你竟然，堅持只用左腳，或者只用右腳走路的話，你自然會感到，人生悲慘。

而今次多一個細節，就是「以右攻左」。成功「獨善其身」，才有能力「兼善天下」。「兼善天下」是目標，「獨善其身」是執行方法。

「兼善天下」是最終目標，永不達到，但可以不斷走近。「獨善其身」則是起點。千里之行，始於足下。沒有起點，就沒有旅程。

— Me@2022.05.16 06:48:36 PM

Watermelon

Posted on May 14, 2022 by rpflee

1990s, 19

(package-initialize)

(custom-set-variables
 '(cua-mode t nil (cua-base))
 '(custom-enabled-themes (quote (leuven))))
(custom-set-faces
 )

(set-register ?e '(file . "~/.emacs"))

(prefer-coding-system 'utf-8)

;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;

(defun backup-dot-emacs ()
  (interactive)

  (save-buffer)

  (setq backup-path (format "%s%s%s" 
              "/path_to_the_backup_folder/ubuntu_dot_emacs_" 
              (format-time-string "%Y_%m_%d_%I_%M_%S_%p")  
              ".el"))
  
  (write-file backup-path 'confirm)

  (setq original-cursor (point))

  (kill-buffer) 
  (find-file "~/.emacs")

  (goto-char original-cursor)
)

(global-set-key (kbd "C-`") 'backup-dot-emacs)

;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;


(set-register ?d '(file . "/path_to_the_blog_folder/dialogue59.txt"))

;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;

(defun backup-blogging-tray ()
  (interactive)
  (save-buffer)

  (setq return-file-name (buffer-file-name))

  (setq backup-path (format "%s%s%s" 
                "/path_to_the_backup_folder/blogging_tray_" 
                (format-time-string "%Y_%m_%d_%I_%M_%S_%p")  
                ".txt"))

  (write-file backup-path 'confirm)

  (setq original-cursor (point))

  (kill-buffer) 

  (find-file return-file-name)

  (goto-char original-cursor)
 
)

(global-set-key (kbd "C-x C-a") 'backup-blogging-tray)

;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;

— Me@2022.05.14 05:10:49 PM

Ex 1.25 Properties of Dt, 2

Posted on May 14, 2022 by rpflee

Structure and Interpretation of Classical Mechanics

Demonstrate that …

b. $\displaystyle{D_t (c F) = c D_t F}$

c. $\displaystyle{D_t (F G) = F D_t G + (D_t F) G}$

~~~

$\displaystyle{ \begin{aligned} &D_t (c F) \circ \Gamma[q] (t) \\ \end{aligned} }$

$\displaystyle{ \begin{aligned} &= \partial_0 \left[c F(t, q, v, a, ...) \right] + \partial_1 \left[c F(t, q, v, a, ...) \right] v(t) + \partial_2 \left[c F(t, q, v, a, ...) \right] a(t) + ... \end{aligned} }$

$\displaystyle{ \begin{aligned} &= c \partial_0 F(t, q, v, a, ...) + c \partial_1 F(t, q, v, a, ...) v(t) + c \partial_2 F(t, q, v, a, ...) a(t) + ... \end{aligned} }$

$\displaystyle{ \begin{aligned} &= c \left[ \partial_0 F(t, q, v, a, ...) + \partial_1 F(t, q, v, a, ...) v(t) + \partial_2 F(t, q, v, a, ...) a(t) + ... \right] \end{aligned} }$

$\displaystyle{ \begin{aligned} &= c D_t F \circ \Gamma[q] (t) \\ \end{aligned} }$

$\displaystyle{ \begin{aligned} &D_t (FG) \circ \Gamma[q] (t) \\ \end{aligned} }$

$\displaystyle{ \begin{aligned} &= \partial_0 \left[ F(t, q, v, a, ...) G(t, q, v, a, ...) \right] \\ &+ \partial_1 \left[ F(t, q, v, a, ...) G(t, q, v, a, ...) \right] v(t) \\ &+ \partial_2 \left[ F(t, q, v, a, ...) G(t, q, v, a, ...) \right] a(t) + ... \\ \end{aligned} }$

$\displaystyle{ \begin{aligned} &= \left[ \partial_0 F(t, q, v, a, ...) \right] G(t, q, v, a, ...) + F(t, q, v, a, ...) \partial_0 G(t, q, v, a, ...) \\ &+ \left\{ \left[ \partial_1 F(t, q, v, a, ...) \right] G(t, q, v, a, ...) + F(t, q, v, a, ...) \partial_1 G(t, q, v, a, ...) \right\} v(t) \\ &+ \left\{ \left[ \partial_2 F(t, q, v, a, ...) \right] G(t, q, v, a, ...) + F(t, q, v, a, ...) \partial_2 G(t, q, v, a, ...) \right\} a(t) + ... \\ \end{aligned} }$

$\displaystyle{ \begin{aligned} &= \left[ \partial_0 F(t, q, v, a, ...) \right] G(t, q, v, a, ...) \\ &+ \left[ \partial_1 F(t, q, v, a, ...) \right] G(t, q, v, a, ...) v(t) \\ &+ \left[ \partial_2 F(t, q, v, a, ...) \right] G(t, q, v, a, ...) a(t) + ... \\ \\ &+ F(t, q, v, a, ...) \partial_0 G(t, q, v, a, ...) \\ &+ F(t, q, v, a, ...) \partial_1 G(t, q, v, a, ...) v(t) \\ &+ F(t, q, v, a, ...) \partial_2 G(t, q, v, a, ...) a(t) + ... \\ \end{aligned} }$

$\displaystyle{ \begin{aligned} &= \left[ \partial_0 F(t, q, v, a, ...) + \partial_1 F(t, q, v, a, ...) v(t) + \partial_2 F(t, q, v, a, ...) a(t) + ... \right] G(t, q, v, a, ...) \\ &+ F(t, q, v, a, ...) \left[ \partial_0 G(t, q, v, a, ...) + \partial_1 G(t, q, v, a, ...) v(t) + \partial_2 G(t, q, v, a, ...) a(t) + ... \right] \\ \end{aligned} }$

$\displaystyle{ \begin{aligned} &= \left\{ D_t F \circ \Gamma[q] (t) \right\} G(t, q, v, a, ...) + F(t, q, v, a, ...) D_t G \circ \Gamma[q] (t) \\ \end{aligned} }$

$\displaystyle{ \begin{aligned} &= \left\{ D_t F \circ \Gamma[q] (t) \right\} G \circ \Gamma[q] (t) + F \circ \Gamma[q] (t) D_t G \circ \Gamma[q] (t) \\ \end{aligned} }$

The meaning of $\displaystyle{\delta_\eta (fg)[q]}$ is

$\displaystyle{\delta_\eta (f[q]g[q])}$

$\displaystyle{ \begin{aligned} &D_t (FG) \circ \Gamma[q] (t) \\ \end{aligned} }$

$\displaystyle{ \begin{aligned} &= \left\{ D_t F \circ \Gamma[q] (t) \right\} G \circ \Gamma[q] (t) + F \circ \Gamma[q] (t) D_t G \circ \Gamma[q] (t) \\ \end{aligned} }$

$\displaystyle{ \begin{aligned} &= \left[ (D_t F) G + F D_t G \right] \circ \Gamma[q] (t) \\ \end{aligned} }$

$\displaystyle{ \begin{aligned} D_t (FG) \circ \Gamma[q] (t) &= \left[ (D_t F) G + F D_t G \right] \circ \Gamma[q] (t) \\ \\ D_t (FG) &= (D_t F) G + F D_t G \\ \end{aligned} }$

— Me@2022.05.12 07:02:30 PM

The least of all evils, 9

Posted on May 12, 2022 by rpflee

眾害取其輕 9

Politics allows people to vote for the impossible, which may be one reason why politicians are often more popular than economists, who keep reminding people that there is no free lunch and that there are no “solutions” but only trade-offs.

— Thomas Sowell

2022.05.12 Thursday ACHK

難得有情人

Posted on May 12, 2022 by rpflee

形上情人 2.2 | 冰心鎖 2.2 | 超時空接觸 3.4

認為愛情是要找到「條件最好的那一位」的人，不會從一而終，因為永遠可能有，亦必定有，條件更好的另一位。

— Me@2022-02-08 11:50:35 PM

你不是找「條件最好」的人，做你的另一半。你是要找「條件最適合你」的人。留意，「她最適合你」並不保證，你最適合她。所以，準確一點的講法是：

「你是要找『條件最適合你』的人，如果你剛巧又，最適合她的話。」

你不是找「條件最好」的人，做你的另一半。你是要找「與你感情至深」之人。

留意，「你對她有情」並不保證，她對你有情。「她是與你感情至深的人」並不代表，你是與她感情至深之人。「她是你的蘇眉」並不意味，你也是她的蘇眉。

Today I found my soulmate; she didn’t.

所以，準確一點的講法是：

「你是要找『與你感情最深』之人，如果你剛巧也是，『與她感情最深』之人。」

只有一見鍾愛，沒有一見鍾情。

愛是感覺，只需零時無知、一時誤會、兩時消失。

一見可以生愛，日久才能生情。

情需要時間，情需要空間。情是「超時空接觸」。

愛可以替代；情不可以。

「情人」的重點在於情。

情者，情境也。

情人者，情境之人也。

愛人可以替代；情人不可以，因為情境不可以。

時常有愛人，難得有情人。

感情者，感受到相同之情境也。

情人者，與爾有共同經歷之人也。

你要找的，不是所謂「外在條件最好」的人，而是「感情至深」之人。

你要找的，不是「條件人」，亦不是「有緣人」，而是「有情人」。

— Me@2022.05.11 07:07:43 PM

伏線驅動程式 1.5

Posted on May 11, 2022 by rpflee

冰心鎖 2 ｜形上情人 2

這段改編自 2010 年 10 月 14 日的對話。

我發覺人生，即使愛情以外的範疇，主要的演變都是，身不由己式，依靠伏線來驅動。

既然那樣，你就有心理準備，你的人生目標夢想，例如愛情，最終還有一個可能性是，伏來伏去伏不到。「伏線」的意思正正包括，不受你控制，有時伏到有時伏不到。

即使伏得到的話，伏到什麼，你也不會事前知道。

例如，你可能覺得，因為你的條件好，所以最終會找到，你的另一半。但是，雖然受條件影響，但愛情不是純粹的「條件運算」。正如友情一樣，很多時，和你最要好的朋友，並不是所謂「條件最好」的朋友。

認為愛情是要找到「條件最好的那一位」的人，不會從一而終，因為永遠可能有，亦必定有，條件更好的另一位。

— Me@2022-02-08 11:50:35 PM

你不是找「條件最好」的人，做你的另一半。你是要找「條件最適合你」的人。留意，「她最適合你」並不保證，你最適合她。所以，準確一點的講法是：

「你是要找『條件最適合你』的人，如果你剛巧又最適合她的話。」

我在自己的筆記中寫過，「Find a Metaphysical Lover」（尋找形上的情人）。後來，我發現在李生的著作中，也有類似的想法。他著作中其中一句的大概是，「愛情應該始於外在條件，成於形上。」

— Me@2014.09.07

即使假設，愛情是條件運算——找條件最好的那一位，你亦只能透過自我提升，工作上進，提高「找到另一半」的機會率。但是，那個機會率，永不會是百分之一百。

首先，你沒法保證，你是你心上人的可能對象中，條件最好的一個。

另外，即使是，可能正正是因為你條件太好，沒有人覺得，可以匹配到你。又或者，正正是因為你條件太好，有心人也以為，你已名花有主，不感示好。

— Me@2022.05.10 05:23:26 PM

Junkions

Posted on May 7, 2022 by rpflee

output = system.exec_command("date +%Y.%m.%d")
output += " "
output += system.exec_command("date +%I:%M:%S")
output += " "
output += system.exec_command("date +%p")

clipboard.fill_clipboard(output.upper())
keyboard.send_keys("<ctrl>+v")

output = system.exec_command("date +%Y.%m.%d")
output += " "
output += system.exec_command("date +%A")
output += " (c) All rights reserved by "

clipboard.fill_clipboard(output)
keyboard.send_keys("<ctrl>+v")

output = system.exec_command("date +_%Y_%m_%d_")
output += system.exec_command("date +_%H_%M_%S_%p")

clipboard.fill_clipboard(output.upper())
keyboard.send_keys("<ctrl>+v")

— Me@2022.05.07 11:27:28 AM

Quick Calculation 3.4

Posted on May 6, 2022 by rpflee

A First Course in String Theory

Show that

$\displaystyle{ \begin{aligned} F^{\mu \nu} &= - F^{\nu \mu} \\ F^{0 i} &= - F_{0 i} \\ F^{ij} &= F_{ij} \\ \end{aligned} }$

~~~

Eq. (3.15):

$\displaystyle{ F_{\mu \nu} \equiv \partial_\mu A_\nu - \partial_\nu A_\mu \\ }$

Eq. (3.29):

$\displaystyle{ F^{\mu \nu} = \eta^{\mu \alpha} \eta^{\nu \beta} F _{\alpha \beta} \\ }$

Eq. (3.16):

$\displaystyle{ F_{\mu \nu} = - F_{\nu \mu} \\ }$

$\displaystyle{ \begin{aligned} F_{\mu \nu} &= - F_{\nu \mu} \\ \eta^{\mu \alpha} \eta^{\nu \beta} F_{\mu \nu} &= - \eta^{\mu \alpha} \eta^{\nu \beta} F_{\nu \mu} \\ \eta^{\mu \alpha} \eta^{\nu \beta} F_{\mu \nu} &= - \eta^{\nu \beta} \eta^{\mu \alpha} F_{\nu \mu} \\ F^{\mu \nu} &= - F^{\nu \mu} \\ \end{aligned} }$

$\displaystyle{ \begin{aligned} F^{\mu \nu} &= \eta^{\mu \alpha} \eta^{\nu \beta} F_{\alpha \beta} \\ F^{0 i} &= \eta^{0 \alpha} \eta^{i \beta} F _{\alpha \beta} \\ &= \eta^{0 0} \eta^{i \beta} F _{0 \beta} + \eta^{0 1} \eta^{i \beta} F _{1 \beta} + \eta^{0 2} \eta^{i \beta} F _{2 \beta} + \eta^{0 3} \eta^{i \beta} F _{3 \beta} \\ &= (-1) \eta^{i \beta} F _{0 \beta} + (0) \eta^{i \beta} F _{1 \beta} + (0) \eta^{i \beta} F _{2 \beta} + (0) \eta^{i \beta} F _{3 \beta} \\ &= (-1) \eta^{i \beta} F _{0 \beta} \\ &= - F _{0 i} \\ \end{aligned} }$

$\displaystyle{ \begin{aligned} F^{\mu \nu} &= \eta^{\mu \alpha} \eta^{\nu \beta} F_{\alpha \beta} \\ F^{i j} &= \eta^{i \alpha} \eta^{j \beta} F_{i j} \\ &= \sum_\alpha \sum_\beta \eta^{i \alpha} \eta^{j \beta} F_{\alpha \beta} \\ &= \sum_\beta \eta^{i i} \eta^{j \beta} F_{i \beta} \\ &= \eta^{i i} \eta^{j j} F_{i j} \\ &= (1) (1) F_{i j} \\ &= F_{i j} \\ \end{aligned} }$

— Me@2022.05.05 07:49 PM

The Lisp debugger

Posted on May 5, 2022 by rpflee

oo101 7 days ago [-]

There are a few ways in which the shared objects method you suggest does not match the full power of Lisp debugging.

First of all, when a C program crashes, it just crashes. There is no REPL. There is only a core dump. So any live-debugging you plan to do is after the fact. After you have seen a crash, you would now begin to prepare for the next crash by launching your process via GDB or restarting your process and attaching a GDB to it. Whether a similar crash would occur again or not or when it would occur again depends on the nature of the bug. Now contrast this with Lisp debugging when your program crashes, it stops there and offers you an REPL to interact with the program right then. There is no need to wait for the next crash.

Secondly, when you debug with GDB, you would be dealing with syntaxes: The syntax of C that we are so familiar with. The GDB syntax to investigate the problem that we may be less familiar with. When the Lisp debugger offers the REPL to you, you are working with Lisp again. Your compiler, debugger, program, etc. all are part of the same unified environment where you just execute Lisp code to debug your issue.

Finally, putting your code in shared objects and reloading them requires you to go through the complete write-build-test-debug cycle. And then what do you do if your shared object itself crashes? With Lisp you skip the write-build-test part when all you want to do is debug an error. You jump straight to the debug part of the cycle and begin investigating the runtime state. And it works the same in a uniform manner whether your main program crashes or a dependency crashes.

— A Road to Common Lisp

— Hacker News

2022.05.05 Thursday ACHK

數學時間論 4

Posted on May 4, 2022 by rpflee

生物時間論 4

2022.05.04 Wednesday ACHK

數學教育 7.5.1

Posted on May 3, 2022 by rpflee

Genius 4.2.1 | A Fraction of Algebra, 2.1

這段改編自 2010 年 4 月 24 日的對話。

另外，他提的另一個，有關學習數學的要點是，即使假設你在大學中，學到的數學，在日常生活中沒有用，單單是為獲取，那些嶄新的元素概念本身，就已經能夠令你有超能力；令你有一些，常人沒有的思考工具、比喻語言。

（安：但是，這個講法可能有一個問題。

雖然，你剛才列舉了數個例子，來示範如何將高深數學，間接應用到人生處世，但是，一般人未必有那種能力。所以我想問，你又是如何去跨過這個難關呢？）

什麼難關？

（安：去翻譯那些抽象數學概念，到其他範疇，或者日常生活。）

那不是「難關」。你的意思是，一般人也沒有那個能力，而我有。所以，那是超能力；我當年一定是，用了一些秘技，才獲取之。

天才之道，點滴累積。其實並沒有所謂的「秘技」。只要一步一步地，學習數學，就自然建構出，一個相對接近完整的數學思考體系，生成「翻譯抽象數學概念到其他範疇」等能力。

所以，我猜想你的疑問是，其實我所講的「點滴累積」，或者「一步一步地」，雖然理想上是，基本的要求，但是現實中是，大部人也做不到。那就代表著，大部人可能也會遇到，一個共通的「難關」。那個「難關」究竟是什麼？我又是如何克服它，而做到「一步一步地」「點滴累積」的呢？

你問題的最簡化版本是：「如何學習數學，開創人生？」

有起碼以下三個先決條件：

1. 對數學（及其他學問人生），有極大興趣；

2. 遇到合理的老師和書籍：

重點是，數學概念或運算上的主要步驟，亳無違漏。支節可免，但主旨必須。細節可以無師自通，大節必靠前人指點。平地自己行，斜地靠梯級。平地可跳步，梯不可跳級。

3. 極超大量的背誦和練習：

數學是理科，所以其背誦方法，不是「死背」零碎隨機的資料，而是「生背」息息相關的訊息。融匯貫通地背誦的唯一方法是，極超大量的操練。

你所講的「難關」，就是以上的第二點。老師有分好老師和差老師。大部分也是差老師。而差老師再分兩類：不懂數學和不懂教學。

— Me@2022.05.02 11:48 PM

AutoKey

Posted on April 28, 2022 by rpflee

First photo, 3 | 1990, 3


output = system.exec_command("date +%Y.%m.%d")
keyboard.send_keys(output + " ")
output = system.exec_command("date +%I:%M")
keyboard.send_keys(output + " ")
output = system.exec_command("date +%p")
keyboard.send_keys(output)


output = system.exec_command("date +%Y.%m.%d")
keyboard.send_keys(output + " ")
output = system.exec_command("date +%A")
keyboard.send_keys(output)
output = " (c) All rights reserved by "
keyboard.send_keys(output)


output = system.exec_command("date +_%Y_%m_%d_")
keyboard.send_keys(output)
output = system.exec_command("date +_%H_%M_%S_%p")
keyboard.send_keys(output)

— Me@2022.04.28 09:04 AM

Ex 1.25 Properties of Dt

Posted on April 21, 2022 by rpflee

Structure and Interpretation of Classical Mechanics

The total time derivative $\displaystyle{D_t F}$ is not the derivative of the function $\displaystyle{F}$ . Nevertheless, the total time derivative shares many properties with the derivative. Demonstrate that $\displaystyle{D_t}$ has the following properties …

$\displaystyle{D_t (F + G) = D_t F + D_t G}$

~~~

Eq. (1.108):

$\displaystyle{ D(F \circ \Gamma[q]) = (DF\circ\Gamma[q])D\Gamma[q] }$

Eq. (1.109):

$\displaystyle{ DF \circ \Gamma[q] = \left[ \partial_0 F \circ \Gamma[q], \partial_1 F \circ \Gamma[q], \partial_2 F \circ \Gamma[q], ... \right] }$

Eq. (1.110):

$\displaystyle{ \left(D \Gamma[q] \right)(t) = \left( 1, Dq(t), D^2 q(t), ... \right) = \begin{bmatrix} 1 \\ Dq(t) \\ D^2 q(t) \\ ... \\ \end{bmatrix} \\ }$

$\displaystyle{ \begin{aligned} D(F \circ \Gamma[q])(t) &= (DF\circ\Gamma[q])D\Gamma[q](t) \\ &= \left[ \partial_0 F \circ \Gamma[q], \partial_1 F \circ \Gamma[q], \partial_2 F \circ \Gamma[q], ... \right] \begin{bmatrix} 1 \\ Dq(t) \\ D^2 q(t) \\ ... \\ \end{bmatrix} \\ &= \partial_0 F \circ \Gamma[q] + \partial_1 F \circ \Gamma[q] D q(t) + \partial_2 F \circ \Gamma[q] D^2 q(t) + ... \\ &= \partial_0 F \circ \Gamma[q] u(t) + \partial_1 F \circ \Gamma[q] D q(t) + \partial_2 F \circ \Gamma[q] D^2 q(t) + ... \\ \end{aligned} }$ ,

where $\displaystyle{u(t) \equiv 1}$ .

$\displaystyle{ \begin{aligned} D(F \circ \Gamma[q]) &= \partial_0 F \circ \Gamma[q] u + \partial_1 F \circ \Gamma[q] D q + \partial_2 F \circ \Gamma[q] D^2 q + ... \\ &= \partial_0 F \circ \Gamma[q] J_0 \circ \Gamma[q] + \partial_1 F \circ \Gamma[q] J_1 \circ \Gamma[q] + \partial_2 F \circ \Gamma[q] J_2 \circ \Gamma[q] + ... \\ \end{aligned} }$

where

$\displaystyle{ \begin{aligned} I_0 \circ \Gamma[q] &= t \\ \\ I_{n>0} \circ \Gamma[q] &= I_{n>0} (t, q, v, a, ...) \\ &= I_{n>0} (t, q, Dq, D^2 q, ...) \\ &= D^{(n-1)} q \\ \\ J_{n} \circ \Gamma[q] &= D(I_n (t, q, v, a, ...)) \\ \end{aligned} }$

The meaning of $\displaystyle{\delta_\eta (fg)[q]}$ is

$\displaystyle{\delta_\eta (f[q]g[q])}$

— Me@2019-04-27 07:02:38 PM

$\displaystyle{ \begin{aligned} D(F \circ \Gamma[q]) &= \partial_0 F \circ \Gamma[q] J_0 \circ \Gamma[q] + \partial_1 F \circ \Gamma[q] J_1 \circ \Gamma[q] + \partial_2 F \circ \Gamma[q] J_2 \circ \Gamma[q] + ... \\ &= \left[(\partial_0 F) J_0 + (\partial_1 F) J_1 + (\partial_2 F) J_2 + ... \right] \circ \Gamma[q] \\ \end{aligned} }$

.
Eq. (1.113):

$\displaystyle{ D_t F \circ \Gamma[q] = D(F \circ \Gamma[q]) }$

$\displaystyle{ \begin{aligned} D_t F \circ \Gamma[q] &= \left[(\partial_0 F) J_0 + (\partial_1 F) J_1 + (\partial_2 F) J_2 + ... \right] \circ \Gamma[q] \\ \\ D_t F &= (\partial_0 F) J_0 + (\partial_1 F) J_1 + (\partial_2 F) J_2 + ... \\ \end{aligned} }$

Eq. (1.114):

$\displaystyle{ \begin{aligned} D_t F (t, q, v, a, ...) &= \partial_0 F(t, q, v, a, ...) + \partial_1 F(t, q, v, a, ...) v + \partial_2 F(t, q, v, a, ...) a + ... \\ \end{aligned} }$

$\displaystyle{ \begin{aligned} D_t F \circ \Gamma[q] (t) &= \partial_0 F(t, q, v, a, ...) + \partial_1 F(t, q, v, a, ...) v(t) + \partial_2 F(t, q, v, a, ...) a(t) + ... \\ \end{aligned} }$

$\displaystyle{ \begin{aligned} &D_t (F + G) \circ \Gamma[q] (t) \\ \end{aligned} }$

$\displaystyle{ \begin{aligned} &= \partial_0 \left[F(t, q, v, a, ...) + G(t, q, v, a, ...)\right] \\ &+ \partial_1 \left[F(t, q, v, a, ...) + G(t, q, v, a, ...)\right] v(t) \\ &+ \partial_2 \left[F(t, q, v, a, ...) + G(t, q, v, a, ...)\right] a(t) + ... \\ \end{aligned} }$

$\displaystyle{ \begin{aligned} &= \left[ \partial_0 F(t, q, v, a, ...) + \partial_0 G(t, q, v, a, ...)\right] \\ &+ \left[ \partial_1 F(t, q, v, a, ...) + \partial_1 G(t, q, v, a, ...)\right] v(t) \\ &+ \left[ \partial_2 F(t, q, v, a, ...) + \partial_2 G(t, q, v, a, ...)\right] a(t) + ... \\ \end{aligned} }$

$\displaystyle{ \begin{aligned} &= \partial_0 F(t, q, v, a, ...) + \partial_1 F(t, q, v, a, ...) v(t) + \partial_2 F(t, q, v, a, ...) a(t) + ... \\ &+ \partial_0 G(t, q, v, a, ...) + \partial_1 G(t, q, v, a, ...) v(t) + \partial_2 G(t, q, v, a, ...) a(t) + ... \\ \end{aligned} }$

$\displaystyle{ \begin{aligned} &= D_t F \circ \Gamma[q] (t) + D_t G \circ \Gamma[q] (t) \\ \end{aligned} }$

In short,

$\displaystyle{ \begin{aligned} D_t (F + G) \circ \Gamma[q] (t) &= D_t F \circ \Gamma[q] (t) + D_t G \circ \Gamma[q] (t) \\ \end{aligned} }$

$\displaystyle{ \begin{aligned} D_t (F + G) \circ \Gamma[q] (t) &= (D_t F + D_t G) \circ \Gamma[q] (t) \\ \\ D_t (F + G) \circ \Gamma[q] &= (D_t F + D_t G) \circ \Gamma[q] \\ \\ D_t (F + G) &= D_t F + D_t G \\ \end{aligned} }$

— Me@2022-04-20 11:42:52 AM

Y Combinator, 2

Posted on April 19, 2022 by rpflee

arethuza 7 hours ago [-]

It’s over 30 years since I was taught about the Y combinator and I still find it amazing – it allows you to define recursion in a language which has no concept of recursion or named functions – such as λ-calculus.

The fact that you then define this in terms of amazingly simple functions like the S and K combinators just, in my opinion, adds to how wonderful it is.

— Why Y? Deriving the Y Combinator in JavaScript

— Hacker News

2022.04.19 Tuesday ACHK

Jonny English, 2

Posted on April 19, 2022 by rpflee

A man without hope is a man without fear.

— Daredevil: Born Again

— Frank Miller

— Me@2016-04-09 09:49:28 PM

2022.04.19 Tuesday ACHK

相聚零刻 1.2.2

Posted on April 18, 2022 by rpflee

這段改編自 2021 年 12 月 12 日的對話。

你需要的，不是一個口頭的承諾，而是一個關係［中］，實質的進展。在朋友的外殼下，關係慢慢的，向情侶靠近。明修棧道，暗度陳倉。

當你們的關係，越來越像情侶的時候，你們自然就是情侶。表白呢，只是給這段關係，一個正式的名份。

不單是表白，在建立起吸引之前，暴露需求感，都會降低你的吸引力。 …　而表白呢，其實就是「暴露需求感」的最高形式。

如果愛情是一個朴實的話，那你就一定要，在成熟的時候，［才］去採摘。如果在此之前採摘，那這個果子採下來之後呢，它就不會再成長了；直接爛掉。

— 為什麽遇到喜歡的女生，千萬別去表白！

— 楚兒戀愛說

朋友之道，在乎平等，無所顧忌地聊天。

市面上，有一個害人不淺的思想，就是：「我向一個女仔表白，被拒絶後，我倆仍然可像之前，正常朋友般相處。」

那有可能，但機會極微，因為表白後，我倆再也不是平等的交往了。除非，雙方也很大方，性格異於常人地高級。但是，那樣的話，原本她就大概，不會拒絶我。

— Me@2022-04-18 12:29:00 PM

All men are born free.

Posted on April 17, 2022 by rpflee

Then some get married.

—

2022.04.17 Sunday ACHK

Quick Calculation 3.3

Posted on April 16, 2022 by rpflee

A First Course in String Theory

Verify the equations in (3.26).

~~~

Eq. (3.26):

$\displaystyle{ \begin{aligned} T_{\lambda \mu \nu} &= - T_{\mu \lambda \nu} \\ T_{\lambda \mu \nu} &= - T_{\lambda \nu \mu} \\ \end{aligned} }$

$\displaystyle{ \begin{aligned} T_{\lambda \mu \nu} &= \partial_\lambda F_{\mu \nu} + \partial_\mu F_{\nu \lambda} + \partial_\nu F_{\lambda \mu} \\ \end{aligned} }$

$\displaystyle{ \begin{aligned} T_{\mu \lambda \nu} &= \partial_\mu F_{\lambda \nu} + \partial_\lambda F_{\nu \mu} + \partial_\nu F_{\mu \lambda} \\ &= - \partial_\mu F_{\nu \lambda} - \partial_\lambda F_{\mu \nu} - \partial_\nu F_{\lambda \mu} \\ &= - T_{\lambda \mu \nu} \\ \end{aligned} }$

— Me@2022-04-15 05:10:09 PM

Logical arrow of time, 11

Posted on April 15, 2022 by rpflee

The initial microstates should be averaged, because it forms an ensemble for the initial macrostate.

Note that a macrostate is actually one particular microstate, not a collection of microstates; it is just that we don’t know which particular microstate.

But how come the final possible states should be summed over, not be averaged?

— Me@2013-08-13 05:16 PM

a macrostate = (a microstate in) a set of macroscopically-indistinguishable microstates

— Me@2022-01-09 07:43 AM

Note that, by definition, two macroscopically-indistinguishable microstates will never separate into two distinct macrostates.

— Me@2022-04-14 05:55 PM

The initial macrostate is with probability one, because it is already known. So the summation of the probabilities of all possible mutually exclusive initial microstates that are corresponding to that initial macrostate is one, such as

$\displaystyle{P(I_1) + P(I_2) = 1}$

By definition, the final macrostate is not known yet. Each possible final macrostate is not with probability one.

The probability of getting a particular final macrostate from that initial macrostate is the summation of the probabilities of all possible mutually exclusive final microstates that are corresponding to that final macrostate.

$\displaystyle{P(F_1~\text{or}~F_2) = P(F_1) + P(F_2)}$

$\displaystyle{P(I\to F) = \frac{1}{N_{\text{initial}}} \sum_{ij} P(I_i \to F_j)}$

— Me@2022-04-13 01:09 PM

The only assumptions I made are those about the addition of probabilities of assumptions and their effects – and these logical rules are fundamentally asymmetric when it comes to the role of the assumptions and their consequences. This logical arrow of time can’t be removed from any reasoning about a world that depends on time – time only copies the logical relationship of implication. And this logical arrow of time is the source of the thermodynamic arrow of time as well.

— edited Feb 2, 2011 at 15:23

— answered Jan 14, 2011 at 11:42

— Luboš Motl

— Calculation of the cross section

— Physics StackExchange

地獄篇 10

Posted on April 13, 2022 by rpflee

外在世界是地獄，心中宇宙是天堂；把知識和想像化成現實，就是把地獄天堂化。

— Me@2011.10.05

方法一：

創造或發掘有用的資訊，然後發佈。

例如，公佈騙子的身份和行騙方法，就可否定其害處。

又例如，天花的預防方法和醫治方法，否定了其害處之餘，甚至還否定了其存在。

— Me@2011.10.05

— Me@2022-04-13

Physics Town

continues

Author Archives: rpflee