Ultimate Freedom, 2

Imagination is not an empirical or superadded power of consciousness, it is the whole of consciousness as it realizes its freedom.

— Jean-Paul Sartre

.

Your mental world/software world lies your ultimate freedom.

It is where anything not forbidden can happen.

It is where anything logically consistent can happen.

— Me@2016-11-20 09:14:06 AM

— Me@2021-09-26 09:22:54 PM

.

.

2021.09.26 Sunday (c) All rights reserved by ACHK

改變因果鏈起點

這段改編自 2010 年 4 月 24 日的對話。

.

所以,我們先企圖進攻那些大題目,無論它們長遠是否,對你直接有用;因為,過程之中,自然會引發很多技術細節。而那些技術細節,很多是你直接可用的。

原初辛苦上山的目標是,傳說中,山頂上的寶藏。但是,上到山頂後,才發現最珍貴的寶藏,反而是沿途找到的那些。

(安:我覺得你對我最大的價值,反而是:

因為你鼓勵我,先企圖進攻的那些大題目中,很多也是你自己,曾經進攻過的,所以,你從它們之中篩選出來,提議我去研究的,必定是你覺得對我來說,最有價值的那些。

如果不是那樣的話,我可能要麼就是,開始研究某個大題目時,就覺得徬徨,而無心機繼續;要麼就是,真的花了一年半載,研究某個大題目後,發覺原來事倍功半,或者價值不大。)

那其實正正就是,「教育」的精髓,「學習」的意思。

.

為何不事事親身去經歷呢? 

因為人生苦短。

透過吸收他人的經歷,可以改變因果鏈的起點。

.

人在某個意思之下,其實已經有了永生。個別的人會死亡,但人類整體而然,可存在很久。只要不絶種,就是得永生。對於任何物種,都可以這樣說。

但是,只有人類這個物種,有大規模的知識傳授。而大規模的知識傳授,則自然需要大量時間。

幸而,雖然人生苦短,但仍剛剛足夠長,去行一個「學習、發掘和傳授」循環。在進化接力賽中,人類每一代剛好有足夠時間,去完成交收接力棒的工序。在知識上,每一代人也可以,以上一代人的終點,作為自己的起點。

— Me@2021-09-22 10:24:46 PM

.

.

2021.09.23 Thursday (c) All rights reserved by ACHK

Ex 1.21 The dumbbell, 3.3

Structure and Interpretation of Classical Mechanics

.

c. Make a change of coordinates to a coordinate system with center of mass coordinates \displaystyle{x_{cm}}, \displaystyle{y_{cm}}, angle \displaystyle{\theta}, distance between the particles \displaystyle{c}, and tension force \displaystyle{F}. Write the Lagrangian in these coordinates, and write the Lagrange equations.

~~~

[guess]


(define (KE-particle m v)
  (* 1/2 m (square v)))

(define ((L-free-constrained m0 m1 l) local)
  (let* ((extract (extract-particle 2))
     (p0 (extract local 0))
     (q0 (coordinate p0))
     (qdot0 (velocity p0))
  
     (p1 (extract local 1))
     (q1 (coordinate p1))
     (qdot1 (velocity p1))
  
     (F (ref (coordinate local) 4)))
 
    (- (+ (KE-particle m0 qdot0)
          (KE-particle m1 qdot1))
       (U-constraint q0 q1 F l))))

(define ((extract-particle pieces) local i)
  (let* ((indices (apply up (iota pieces (* i pieces))))
         (extract (lambda (tuple)
                    (vector-map (lambda (i)
                                  (ref tuple i))
                                indices))))
    (up (time local)
        (extract (coordinate local))
        (extract (velocity local)))))

(define (U-constraint q0 q1 F l)
  (* (/ F (* 2 l))
     (- (square (- q1 q0))
        (square l))))

(let ((L (L-free-constrained 'm_0 'm_1 'l))
      (q-rect (up (literal-function 'x_0)
                  (literal-function 'y_0)
                  (literal-function 'x_1)
                  (literal-function 'y_1)
                  (literal-function 'F))))
  (show-expression
   ((compose L (Gamma q-rect)) 't)))

\displaystyle{ \frac{1}{2} m_0 \left( \dot x_0^2 + \dot y_0^2 \right) + \frac{1}{2} m_1 \left( \dot x_1^2 + \dot y_1^2 \right) + \frac{F}{2 l} \left( l^2 - y_1^2 + 2 y_0 y_1 - x_1^2 + 2 x_0 x_1 - y_0^2 - x_0^2 \right) }

\displaystyle{ = \frac{1}{2} m_0 \left( \dot x_0^2 + \dot y_0^2 \right) + \frac{1}{2} m_1 \left( \dot x_1^2 + \dot y_1^2 \right) - \frac{F}{2 l} \left[ (y_1 - y_0)^2 + (x_1 - x_0)^2 - l^2 \right] }


(define ((q->r m0 m1) local)
  (let ((q (coordinate local)))
    (let ((x_cm (ref q 0))
          (y_cm (ref q 1))
          (theta (ref q 2)) 
          (c (ref q 3))
	      (F (ref q 4))
	      (M (+ m0 m1)))
      (let ((x0 (- x_cm (* (/ m1 M) c (cos theta))))
            (y0 (- y_cm (* (/ m1 M) c (sin theta))))
            (x1 (+ x_cm (* (/ m0 M) c (cos theta))))
            (y1 (+ y_cm (* (/ m0 M) c (sin theta)))))
        (up x0 y0 x1 y1 F)))))

(let ((q (up (literal-function 'x_cm)
	         (literal-function 'y_cm)
	         (literal-function 'theta)
	         (literal-function 'c)
	         (literal-function 'F))))
  (show-expression (q 't)))

 
(show-expression
 (up 't
     (up 'x_cm 'y_cm 'theta 'c 'F)
     (up 'xdot_cm 'ydot_cm 'thetadot 'cdot 'Fdot)))


(show-expression
  ((q->r 'm_0 'm_1) 
     (up 't
         (up 'x_cm 'y_cm 'theta 'c 'F)
         (up 'xdot_cm 'ydot_cm 'thetadot 'cdot 'Fdot))))


(let ((q (up (literal-function 'x_cm)
             (literal-function 'y_cm)
             (literal-function 'theta)
             (literal-function 'c)
             (literal-function 'F))))
  (show-expression ((q->r 'm_0 'm_1) ((Gamma q) 't))))


(show-expression
  ((F->C (q->r 'm_0 'm_1)) 
     (up 't
         (up 'x_cm 'y_cm 'theta 'c 'F)
         (up 'xdot_cm 'ydot_cm 'thetadot 'cdot 'Fdot))))

(define (L-cm m0 m1 l)
  (compose
   (L-free-constrained m0 m1 l) (F->C (q->r m0 m1))))

(show-expression
 ((L-cm 'm_0 'm_1 'l)
     (up 't
         (up 'x_cm 'y_cm 'theta 'c 'F)
         (up 'xdot_cm 'ydot_cm 'thetadot 'cdot 'Fdot))))

\displaystyle{    \frac{1}{\mu} = \frac{1}{m_0} + \frac{1}{m_1}    }

\displaystyle{    L_{cm}     }

\displaystyle{  = \frac{    ( c^2 \dot \theta^2 + \dot c^2 ) l m_0 m_1                   + (l m_0^2 + 2 l m_0 m_1 + l m_1^2) (\dot x_{cm}^2 + \dot y_{cm}^2)  + F ( l^2 - c^2 )(m_0 + m_1)  }{2 l (m_0 + m_1)}    }

\displaystyle{  = \frac{    ( c^2 \dot \theta^2 + \dot c^2 ) l m_0 m_1                   + l (m_0 + m_1)^2 (\dot x_{cm}^2 + \dot y_{cm}^2)  + F ( l^2 - c^2 )(m_0 + m_1)  }{2 l (m_0 + m_1)}    }

\displaystyle{  =   \frac{1}{2} ( c^2 \dot \theta^2 + \dot c^2 ) \mu                   +  \frac{1}{2} (m_0 + m_1) (\dot x_{cm}^2 + \dot y_{cm}^2)  +  \frac{1}{2l} F ( l^2 - c^2 )   }


(show-expression
 (((Lagrange-equations
    (L-cm 'm_0 'm_1 'l))
   (up (literal-function 'x_cm)
       (literal-function 'y_cm)
       (literal-function 'theta)
       (literal-function 'c)
       (literal-function 'F)))
  't))


(show-expression
 (((Lagrange-equations
    (L-cm 'm_0 'm_1 'l))
   (up (literal-function 'x_cm)
       (literal-function 'y_cm)
       (literal-function 'theta)
       (lambda (t) 'l)
       (literal-function 'F)))
  't))

[guess]

— Me@2021-09-17 06:35:51 AM

.

.

2021.09.18 Saturday (c) All rights reserved by ACHK

Year 2000 Reloaded

These are what I kept reminding myself during my Age of University.

1. I think, therefore I am

A lot of times, something seems to be a deadend.

However, once I have faith that a solution may be possible and start to think, most of the time, that “deadline” is actually resolvable.

2. Nothing Less

A lot of times, an action seems to be insignificant.

However, actually, every action may have infinite consequences, especially when you cultivate it.

3. The Aladdin Factor

A key to get a meaningful life is to dare to ask other people or yourself for answers, advice, or favours, when necessary.

Don’t be afraid to ask, as long as a request is ethical, reasonable, and polite.

— Me@2011.08.17

— Me@2021-09-11

.

.

2021.09.12 Sunday (c) All rights reserved by ACHK

相聚零刻 2.1

尋覓 2.2.3.6.1

.

男士 20 歲時,還找不到女朋友,可能是好事,因為,男士其實要到 28 歲時,思想才帶點成熟,通常。

那是某一個哲學家講的。我當年在 25 歲時,就已經聽到這一點。到 28 歲時,真的明白了一些,以前不明白的東西。(當然,任何年齡也可以這樣說,如果一個人不斷進步的話。)

例如,說話時,為什麼會「食螺絲」(舌頭打結)呢?

是因為,企圖在同一刻講,超過一個字。只要稍為放慢說話速度,就可以化解。

又例如,生活中,為什麼會諸事不順呢?

是因為,企圖在同一格時間中,放多於一件事。

然後,那個哲學家又說… … 千萬不要說出去,以免得罪人。

然後,那個哲學家又說,至於女士,則於 18 歲時,就已經成熟;自此以後,就不再成熟了。

聽不聽得出,他在投訴什麼呢?

他的意思是,女士在思想上,於 18 歲時,就已經成熟;自此以後,就不再成熟。(當然,那只是大概而然;每個人也不同。)

.

女士,就是介乎於,男士與小孩之間的物體。

那個哲學家,覺得那是缺點。但我覺得不一定;那也可以是優點。

例如,善良之女士,可以永久可愛。男士則不可以。男士青春期時,聲線會變。變聲後,不可能再可愛。

女士要可愛。男士要可靠。

無論在外表或性格上,女士的職責是,保持可愛,尋找可靠;男士的職責則是,保持可靠,保護可愛。

— Me@2021-07-26 05:12:55 PM

— Me@2021-09-07 05:15:56 PM

.

.

2021.09.10 Friday (c) All rights reserved by ACHK