<1984, 4

Posted on March 17, 2021 by rpflee

— Photomyne colorization

— Me@2021-03-17 07:29:18 PM

Problem 2.8

Posted on March 17, 2021 by rpflee

A First Course in String Theory

2.8 Spacetime diagrams and Lorentz transformations

Show that the $\displaystyle{{x'}^0}$ and $\displaystyle{{x'}^1}$ axes … appear in the original spacetime diagram as oblique axes.

~~~

The Lorentz transform:

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

The inverse Lorentz transform:

$\displaystyle{ \begin{aligned} x^0 &= \gamma ((x')^0 + \beta (x')^1) \\ x^1 &= \gamma (\beta (x')^0 + (x')^1) \\ \end{aligned}}$

The $\displaystyle{(x')^0}$ -direction unit vector is $\displaystyle{((x')^0, (x')^1) = (1, 0)}$ .

When $\displaystyle{((x')^0, (x')^1) = (1,0)}$ ,

$\displaystyle{(x^0, x^1) = (\gamma, \gamma \beta)}$

When $\displaystyle{\beta > 0}$ ,

$\displaystyle{ \begin{aligned} \tan \phi &= \frac{\gamma \beta}{\gamma} \\ &= \beta \\ \end{aligned}}$

where $\displaystyle{\phi}$ is the angle between $\displaystyle{x^0}$ -axis and $\displaystyle{(x')^0}$ -axis.

…

— Me@2021-03-17 03:42:23 PM

Single-world interpretation, 11

Posted on March 16, 2021 by rpflee

Brian T. Johnston

All well and fine, but tunnel diodes work and they can’t unless there is MW

Luboš Motl

LOL, such a connection is at most a fairy-tale for kindergarten-age children

You need multiple worlds to explain one single world?

Are you stupid?

— Me@2017-07-17 02:58:25 PM

2021.03.16 Tuesday ACHK

情理

Posted on March 16, 2021 by rpflee

Arts | Science, 4

情

~ context

~ special case

理

~ general case

— Me@2017-05-09 10:09:38 AM

大種子論, 2.5

Posted on March 15, 2021 by rpflee

機遇創生論, 2.5

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
專家博士

心靈作業系統

多重自我
專家博士
虛擬機器

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。

「大種子論」包含了「種子論」、「多種自我論」和「心靈作業系統」等等。而「種子論」，就已經包含了時間元素，因為，它探討了「因果」、「決定論」和「副作用」等，講述如何處理未來。例如，我們於以前討論過，尋找另一半的最佳方法，可能是什麼。

（安：你還發表了「專博論」。）

「專家博士論」可以視為，身處於「多重自我論」之中。各門專業或博業，可以視為不同的自我。它們其實先天處於，競爭的狀態，正在搶奪你的時間。

「專家博士論」講述，自己的眾多各種專博自我，如何融洽相處，繼而更上一層樓，合體成一個「大自我」。

（安：即是你所謂的「變形金剛」。眾多小機械人，合體成一隻大機械人。）

「專家博士論」，亦可以講成「心靈作業系統」的一員，因為它就是一個，特別精心設計的「作業系統」。

有好一點的講法。

「專家博士論」，應視為「心靈作業系統」的前傳，教你如何以最有效率的方法，去建立一個，有「完備知識」的「心靈作業系統」，簡稱「完備知識體（系）」。

「專家博士論」，就是那個疑似的「最有效率方法」。

— Me@2021-03-15 04:31:34 PM

2019

Posted on March 14, 2021 by rpflee

— Me@2021-03-14 07:54:40 PM

Ex 1.19 A two-bar linkage

Posted on March 14, 2021 by rpflee

Structure and Interpretation of Classical Mechanics

The two-bar linkage shown in figure 1.3 is constrained to move in the plane. It is composed of three small massive bodies interconnected by two massless rigid rods in a uniform gravitational field with vertical acceleration $\displaystyle{g}$ . The rods are pinned to the central body by a hinge that allows the linkage to fold. The system is arranged so that the hinge is completely free: the members can go through all configurations without collision. Formulate a Lagrangian that describes the system and find the Lagrange equations of motion. Use the computer to do this, because the equations are rather big.

~~~

[guess]


(define ((F->C F) local)
  (->local (time local)
           (F local)
           (+ (((partial 0) F) local)
              (* (((partial 1) F) local) 
                 (velocity local)))))
 
;

(define ((q->r l1 l2) local)
  (let ((q (coordinate local)))
    (let ((x2 (ref q 0))
	      (y2 (ref q 1))
	      (theta (ref q 2)) 
          (phi (ref q 3)))
      (let ((x1 (+ x2 (* l1 (cos theta))))
	        (y1 (+ y2 (* l1 (sin theta))))
	        (x3 (+ x2 (* l2 (cos phi))))
	        (y3 (+ y2 (* l2 (sin phi)))))
        (up x1 y1 x2 y2 x3 y3)))))

;

(show-expression
  ((q->r 'l_1 'l_2) 
     (up 't
	     (up 'x_2 'y_2 'theta 'phi)
	     (up 'xdot_2 'ydot_2 'thetadot 'phidot))))

;

(define (KE m vx vy)
  (* 1/2 m (+ (square vx) (square vy))))

(define ((T-rect m1 m2 m3) local)
  (let ((q (coordinate local))
        (v (velocity local)))
    (let ((x1dot (ref v 0))
          (y1dot (ref v 1))
	      (x2dot (ref v 2))
	      (y2dot (ref v 3))
	      (x3dot (ref v 4))
	      (y3dot (ref v 5)))
      (+ (KE m1 x1dot y1dot)
  	     (KE m2 x2dot y2dot)
	     (KE m3 x3dot y3dot)))))

(show-expression
 ((T-rect 'm_1 'm_2 'm_3)
    (up 't
	    (up 'x_1 'y_1 'x_2 'y_2 'x_3 'y_3)
	    (up 'xdot_1 'ydot_1 'xdot_2 'ydot_2 'xdot_3 'ydot_3))))

;

[guess]

— Me@2021-03-12 05:37:27 PM

Energy 6

Posted on March 12, 2021 by rpflee

time ~ change

energy ~ the ability of causing change

Each system tends to reach its own lowest potential energy state because “lowest potential energy state” means “least ability to change”.

— Me@2013.06.29

— Me@2021-03-12

The infinite-next

Posted on March 11, 2021 by rpflee

The infinite-next is Now-here-I.

— Me@2012.12.04

或許，無限旅程，就在此刻此處此人。

— Me@2021-03-11 10:08:02 PM

6.4311

Death is not an event of life. Death is not lived through.

If by eternity is understood not endless temporal duration but timelessness, then he lives eternally who lives in the present.

Our life is endless in the way that our visual field is without limit.

— Tractatus Logico-Philosophicus (1922)

— Ludwig Wittgenstein

— translated by Charles Kay Ogden

嶄新的世界 4

Posted on March 10, 2021 by rpflee

這段改編自 2010 年 10 月 14 日的對話。

然後，我們回到「你倆其中一方，要去外國升學」的問題。這個如果發生在我身上，我不會覺得是問題；因為，如果是外星人的愛情，就不太需要一定在一起。反而，我最重視的是，關注對方的短期生活，過得快不快樂；和長期人生，過得有沒有意義。

如果你的「愛情」是純粹為了，追求「愛情的感覺」的話，那你所謂的愛情，就是只是自私的愛情。如果只是自私的愛情，即使不是一方外地升學，即使在一起，也不會維持得到。

所以，如果是真正長久愛情的話，就不會是自私的。真正永久愛情，就是「不需要愛情的愛情」，就是「不需要愛情感覺的愛情」。愛情的核心，並不是感覺，而是兩個心靈的獨有關係。

始於外在條件，而成於形上。

亦即是話，如果我的另一半，有大理想要追求的話，我一定會支持，甚至一同去追求。即使要的分隔（例如）四年，我也不會太介意。（如果是永久的分隔，則是另一個話題，暫且不談。）

那如何維繫感情呢？

首先，你要知道，何謂「感情」。

「感情」者，「感受相同情境」也。

動物間，所能感受的相同情境，可能只有物理世界，即是日常生活。而精靈仙子間，所能感受和創造的相同情境，則不只有物理世界，亦不限於日常生活。只要你倆在分隔期間，持續有超時空搞作，感情方能維持，甚至加深。

例如，你倆可以共同研究，留學那科的學術題目。

又例如，你倆可以共同編寫一個網誌。

再例如，你倆共同經營一個網站。

最好的共同情境，就是共同創作。「共同創作」就是，共同創造一個，嶄新的世界。

— Me@2021-02-27 08:40:29 AM

<1984, 3

Posted on March 9, 2021 by rpflee

— DeepAI colorization

— Me@2021-03-09 08:29:33 PM

Problem 2.7

Posted on March 9, 2021 by rpflee

A First Course in String Theory

2.7 A more general construction for cones?

Consider the $\displaystyle{(x, y)}$ plane and the complex coordinate $\displaystyle{z = x + iy}$ . We have seen that the identification $\displaystyle{z \sim e^{\frac{2 \pi i}{N}} z}$ , with $\displaystyle{N}$ an integer greater than two, can be used to construct a cone.

Examine now the identification

$\displaystyle{z \sim e^{2 \pi i \frac{M}{N}} z, ~~~ N > M \ge 2,}$

where $\displaystyle{M}$ and $\displaystyle{N}$ are relatively prime integers (their greatest common divisor is one).

…

Determine a fundamental domain for identification.

…

Given two relatively prime numbers a and b, there exists integers m and n such that $\displaystyle{m a + n b = 1}$ .

~~~

[guess]

Since M and N are relatively prime numbers, there exists integers m and n such that $\displaystyle{m M + n N = 1}$ .

$\displaystyle{\frac{M}{N} m = \frac{1 - nN}{N}}$ .

Therefore,

$\displaystyle{\left[e^{2 \pi i \frac{M}{N}}\right]^m = e^{2 \pi i \frac{1 - nN}{N}}}$ for some integers m and n.

As a result, a fundamental domain is provided by the points z that satisfy $\displaystyle{0 \le \arg(z) < 2 \pi \frac{1}{N}}$ .

[guess]

— Me@2021-03-09 04:58:02 PM

Single-world interpretation, 10

Posted on March 8, 2021 by rpflee

If the operators corresponding to two observables do not commute, they have no simultaneous eigenstates and they obey the uncertainty principle. A state where one observable has a definite value corresponds to a superposition of many states for [another] observable.

— Wikipedia on Quantum superposition

That is a major mistake of the many-worlds interpretation of quantum mechanics.

— Me@2021-03-07 06:11:22 PM

Interest, 3

Posted on March 6, 2021 by rpflee

1. The price paid for obtaining, or price received for providing, money or goods in a credit transaction, calculated as a fraction of the amount or value of what was borrowed

2. A great attention and concern from someone or something; intellectual curiosity

— Wiktionary

If you have a lot of interests now, you will have a lot of interests.

興趣造就利息。

— Me@2021-03-03 05:23:49 PM

利息

~ 休息時自生之利

~ 自動收入

— Me@2021-03-03 05:25:42 PM

如此仙子 1.4

Posted on March 5, 2021 by rpflee

鐵達尼極限 2.6 | 尋覓 1.9 | 已婚單身 1.5 | Singles 1.5

這段改編自 2010 年 10 月 14 日的對話。

以下不是已知事實，而是一連串的可能性。

可能，人於在生之後，仍然以靈魂的方式存在。

可能，現在的個別靈魂，再不是單獨的，而是一個特超巨大生命體的一分子。個別靈魂不會再感孤獨。

在這佪可能之下，人在那時再毋須人間愛情。

如果再假設，人死了以後不會再死的話，就毋須再繁殖。那樣，就再不會有，大自然製造的愛情陷阱。那人就多了一個原因，不再需要愛情。

分散的靈魂, 必在愛中重合. — Mr Lee

— Me@2021-02-27 08:40:29 AM

To realize is to realize, 1.1

Posted on March 3, 2021 by rpflee

realize

1. (transitive) To become aware of

2. (formal, transitive) To make real

— Wiktionary

Sometimes, just realization itself is already a realization.

Realization has two meanings.

Sometimes, when you realize something, you realize that something at that very moment.

察覺

~ 實現

For example, when you ask “how to be a polite person”, you become a polite person.

In other words, when you realize that you should be a polite person, that polite person is realized at that moment.

— Me@2021-02-19 06:32:05 AM

— Me@2021-03-02 04:39:33 PM

Ex 1.18 Bead on a triaxial surface, 2

Posted on March 2, 2021 by rpflee

Structure and Interpretation of Classical Mechanics

A bead of mass m moves without friction on a triaxial ellipsoidal surface. In rectangular coordinates the surface satisfies

$\displaystyle{\frac{x^2}{a^2} + \frac{y^2}{b^2} + \frac{z^2}{c^2} = 1}$

for some constants a, b, and c. Identify suitable generalized coordinates, formulate a Lagrangian, and find Lagrange’s equations.

~~~

[guess]

The generalized coordinates:

$\displaystyle{\begin{aligned} x &= a \sin(\theta )\cos(\varphi),\\ y &= b \sin(\theta )\sin(\varphi),\\ z &= c \cos(\theta), \end{aligned}}$

where

$0\leq \theta \leq \pi ,\qquad 0\leq \varphi <2\pi .$

${\begin{aligned} \dot x &= a \dot \theta \cos(\theta) \cos(\varphi) - a \dot \varphi\sin(\theta ) \sin(\varphi) \\ \dot y &= b \dot \theta \cos(\theta) \sin(\varphi) + b \dot \varphi \sin(\theta) \cos(\varphi) \\ \dot z &= - c \dot \theta \sin(\theta) \end{aligned}}$


(define ((F->C F) local)
  (->local (time local)
           (F local)
           (+ (((partial 0) F) local)
              (* (((partial 1) F) local) 
                 (velocity local)))))

;

(define ((e->r a b c) local)
  (let ((q (coordinate local)))
    (let ((theta (ref q 0)) 
          (phi (ref q 1)))
      (let ((x (* a (sin theta) (cos phi)))
	    (y (* b (sin theta) (sin phi)))
	    (z (* c (cos theta))))
        (up x y z)))))

;

(define ((L-rect m) local)
  (let ((q (coordinate local))
        (v (velocity local)))
    (* 1/2 m (square v))))

(define (L-e m a b c)
  (compose (L-rect m) (F->C (e->r a b c))))

;

(show-expression
  ((L-e 'm 'a 'b 'c)
   (->local 't
             (up 'theta 'phi) 
             (up 'thetadot 'phidot))))

;

(show-expression
 (((Lagrange-equations
    (L-e 'm 'a 'b 'c))
   (up (literal-function 'theta) (literal-function 'phi)))
  't))

[guess]

— Me@2021-03-01 06:22:50 PM

Physics Town

continues

Monthly Archives: March 2021

<1984, 4

Problem 2.8

Single-world interpretation, 11

情理

大種子論, 2.5

2019

Ex 1.19 A two-bar linkage

Energy 6

The infinite-next

嶄新的世界 4

<1984, 3

Problem 2.7

Single-world interpretation, 10

Interest, 3

如此仙子 1.4

To realize is to realize, 1.1

Ex 1.18 Bead on a triaxial surface, 2