SICM, 4.2

Posted on December 31, 2021 by rpflee

This was a virtual machine running the installation of MS-DOS 6.22 in the program VMware Player.

VMware Player was able to run virtual machines, but not to create one. Luckily, there was a website that helped me create virtual machine files. A virtual machine file is just a VMware-formatted text file. It defines the specifications of that virtual machine.

Running MS-DOS 6.22 was just for nostalgia. The real reason for learning virtual machines was to use the mechanics software library of the textbook “Structure and Interpretation of Classical Mechanics”. That library was available only for Linux.

— Me@2021-12-31 01:29:46 PM

Ex 1.22. Driven pendulum

Posted on December 31, 2021 by rpflee

Structure and Interpretation of Classical Mechanics

Show that the Lagrangian (1.89) can be used to describe the driven pendulum, where the position of the pivot is a specified function of time: Derive the equations of motion using the Newtonian constraint force prescription, …

~~~

[guess]

$\displaystyle{ \begin{aligned} m \ddot{y} &= F \cos \theta - mg \\ m \ddot{x} &= - F \sin \theta \\ \end{aligned}}$

$\displaystyle{ \begin{aligned} m \ddot{y} &= F \frac{y_s - y}{l} - mg \\ m \ddot{x} &= - F \frac{x - x_s}{l} \\ \sqrt{(x_s - x)^2 + (y_s - y)^2} &= l \\ \end{aligned}}$

[guess]

— Me@2021-12-30 09:25:17 AM

Shutting Down Google+ for Consumers

Posted on December 29, 2021 by rpflee

pjmorris 4 hours ago [-]

Seems to me like PM’s would think in the most positive terms about the same issue, e.g. what is the maximum amount of ad space that we can use before users lose interest?

No one would directly attempt to be evil, it’d just turn out that way.

“The truly terrible thing is that everybody has their reasons.” ― Jean Renoir

rytis 1 hour ago [-]

Socrates agrees: “no one ever knowingly does wrong”. :)

— Hacker News

2021.12.29 Wednesday ACHK

魔間傳奇 16

Posted on December 29, 2021 by rpflee

相聚零刻 1.3 | 光速飛行 1.2.2.3 | 尋覓 2.2.3.2.3

地獄空蕩蕩　魔鬼在人間

2021.12.29 Wednesday ACHK

無拍之拖

Posted on December 28, 2021 by rpflee

原來是你, 2 | 相聚零刻 2.3 | 尋覓 2.2.3.6.3

電影通常「無中生有」；現實通常「有中生情」。你所追求的東西，可能一直在你身邊，只是你沒有留意。

— Me@2009.04.05

— Me@2012.01.01

所以，你現在毋須太緊張。

現在的你不用，急於找到對象。或者，到你 25 歲時，才遇到 28 歲的他，會好一點。那時，那個他已經是，思想成熟和人格完整的男士。

那不是指，你可以控制。那只是指，理想的劇情怎麼樣。

（CPK: 廿五歲的我，才認識 28 歲的他？會不會太遲？）

其實會。理想劇情，應該這樣說：

你倆可能自小，已經認識對方。到你 25 歲時，才開始有劇情，才與他發展成戀人。那樣，如果加上，你懂得閱人讀心術的話，那些劇情可以是，你由拍拖發展至結婚，只需要一個月時間；因為，你並不是只，認識了他一個月，而是在互相表白，確認成情侶前，就已經相識了十幾年，知道對方什麼性格。亦即是話，戀人之前，你倆就已了解對方是，如何對待身邊，尤其是那些，和自己沒有利益關係的人。

性格上，心靈下，戀愛中，俊男美女，人工合成，都是假的；

性格左，心靈右，戀愛外，義男俠女，原裝正版，才是真的。

— Me@2021-12-28 04:30:02 PM

Silly Dogs

Posted on December 27, 2021 by rpflee

— Me@2021-12-27 05:30:22 PM

2.10 A spacetime orbifold in two dimensions, 5

Posted on December 27, 2021 by rpflee

A First Course in String Theory

$\displaystyle{-ds^2 = -2dx^+ dx^-}$

for the interval to show that any curve in (3) is spacelike.

~~~

$\displaystyle{ \begin{aligned} x^+ x^- &= a^2 \\ x^- &= a^2 \frac{1}{x^+} \\ d x^- &= a^2 \frac{-1}{(x^+)^2} d x^+ \\ \end{aligned}}$

$\displaystyle{ \begin{aligned} -ds^2 &= -2dx^+ dx^- \\ &= \frac{2 a^2}{(x^+)^2} (d x^+)^2 \\ ds^2 &< 0 \\ \end{aligned}}$

— Me@2021-12-27 12:24:09 PM

Book Underlining Principle

Posted on December 26, 2021 by rpflee

間書原理 0

When you are reading, you would underline key words. At one extreme, you underline nothing. So you wouldn’t know which parts are important. At the opposite extreme, you underline everything. Then you also wouldn’t know which parts are important. So the effect of underlining nothing is exactly the same as underlining everything.

This is an example of the principle that

The extreme of Yin is Yang

The extreme of Yang is Yin

陽之極為陰陰之極為陽

That is why I call the principle the Book Underlining Principle.

The source of this principle is that when you push something to one extreme at the object level, that action may also push it to the opposite extreme at the meta level.

For example, when you underlining all the words, at the object level, it means that everything is important. However, at the meta level, “being important” must be relative to something else. You need to distinguish the important words from the unimportant ones. When you underlining all the words, there is no such distinction. So “being important” has become meaningless.

— Me@2021-12-13 11:08 AM

— Me@2021-12-26 03:39 PM

相聚零刻 1.2

Posted on December 26, 2021 by rpflee

光速飛行 1.2.2.2 | 尋覓 2.2.3.2.2

2021.12.26 Sunday ACHK

因果鏈捷徑

Posted on December 25, 2021 by rpflee

改變因果鏈起點, 1.3

這段改編自 2010 年 4 月 24 日的對話。

幸而，現實不是那樣。現實是，人有足夠的生命，去累積有用的人生經驗；而且，傳授所花的年期，遠少於親身經歷所花。

簡單來說，發掘知識時間極長；複製知識時間極短。

經濟學家張五常，在一篇文章中解釋到，為何社會科學進展不大，不如科學科學。科學需要觀測和實驗，簡稱「測驗」。科學科學測驗的時段不長。而社會科學測驗的時段，則往往橫跨數十年。

例如，一個社會學家研究社會學，可能需要花足足幾十年，臨到退休時，才有一些有意義的見解。那樣，他的人生剩下的年期，就未必足夠，去著書立說，傳授那些真知灼見。

又例如，要找到哪種經濟制度，對個人對社會最為有利，測驗所需的時間，起碼以十年為單位。但是，物理學中的牛頓定律，是真是假，在一個中學實驗室，花幾天就可以測驗完成。　　

所以，剛才講費曼說的「『接棒接得切』（來得及接棒），所以人類知識容易累積」，大概只適用於科學科學，不及於社會科學。

（安：我從來未試過，從這個角度思考。那可以解釋到，為何物理學可先進到，有相對論和量子力學，但經濟學暫時不能。

科學技術，簡稱科技，在一百年的進展，超乎人類想像。社會技術，在同樣的一百年間，雖未至於沒有進展，但相比起科技，卻顯得微不足道。）

— Me@2021-12-25 11:34:13 AM

Once upon a time

Posted on December 22, 2021 by rpflee

— Me@2021-12-22 09:43:22 PM

2021.12.22 Wednesday ACHK

Ex 1.21 The dumbbell, 3.4.2

Posted on December 22, 2021 by rpflee

Structure and Interpretation of Classical Mechanics

e. Make a Lagrangian ( $\displaystyle{= T - V}$ ) for the system described with the irredundant generalized coordinates $\displaystyle{x_{cm}}$ , $\displaystyle{y_{cm}}$ , $\displaystyle{\theta}$ and compute the Lagrange equations from this Lagrangian. They should be the same equations as you derived for the same coordinates in part d.

~~~

[guess]


(define ((L-cm m0 m1 l) local)
  (let* ((q (coordinate local))
	 (v (velocity local))
	 (x_cm (ref q 0))
	 (y_cm (ref q 1))
	 (theta (ref q 2))

	 (x_cm_dot (ref v 0))
	 (y_cm_dot (ref v 1))
	 (theta_dot (ref v 2))
	 
	 (M (+ m0 m1))
	 (mu (/ 1 (+ (/ 1 m0) (/ 1 m1)))))

    (+ (* (/ 1 2) M (+ (square x_cm_dot) (square y_cm_dot)))
       (* (/ 1 2) mu (square l) (square theta_dot)))))

$\displaystyle{ L_{cm} = \frac{1}{2} (m_0 + m_1) (\dot x_{CM}^2 + \dot y_{CM}^2 ) + \frac{1}{2} \mu l^2 \dot \theta^2 }$


(show-expression
 (((Lagrange-equations
    (L-cm 'm_0 'm_1 'l))

   (up (literal-function 'x_cm)
       (literal-function 'y_cm)
       (literal-function 'theta)))
  't))

[guess]

— Me@2021-12-22 01:20:55 PM

Eternal return, 2

Posted on December 21, 2021 by rpflee

A “perfect copy” is not a “copy”, because if a copy is perfect, it would be logically indistinguishable from the original.

In other words, we would not be able to determine which one is the “copy” and which one is the “original”, even in principle.

There would be no meaningful difference between the meanings of the labels “copy” and “original”.

— Me@2013-08-11 1:38 PM

Prayer 5.2

Posted on December 20, 2021 by rpflee

Praying is not for asking, but for holding your thoughts, so that you can listen.

— Me@2011.08.30

To realize is to realize, 1.4

Posted on December 20, 2021 by rpflee

The Buddha attacked all attempts to conceive of a fixed self, while stating that holding the view “I have no self” is also mistaken. This is an example of the middle way charted by the Buddha.

— Wikipedia on Philosophy of self

The ultimate self-fulfilling prophecies:

1. free will or not

2. god or no god

3. afterlife or not

4. future spouse exists or not

Why self-fulfilling?

3. afterlife or not

Whether “afterlife” exists or not depends on your definitions of “self” and “afterlife”.

At one extreme, the definition of “afterlife exists” is that, after death, the same fixed self will continue to exist; “you” will exist in exactly the same way as before. In this definition, afterlife does not exist.

Note that even before death, during your normal lifetime, there is actually no “same fixed self”, “you” keeps changing every day and every second.

At the opposite extreme, the definition of “afterlife exists” is that, some aspects of you continue to exist in some way. In this definition, afterlife exists.

For example, if some of your writings still exist after your death, they will preserve some of your mind.

This question is like, when your old computer is dead and has got replaced, does it still exist?

The old computer hardware does not exist anymore. However, some of the software and the data do. But just some, not all.

Continue to exist?

All of you?

Some of you?

YES

— Me@2021-12-18 07:24:32 PM

He attributes his lifelong habit of writing every day to an incident in 1932 when a carnival entertainer, Mr. Electrico, touched him on the nose with an electrified sword, made his hair stand on end, and shouted, “Live forever!” It was from then that Bradbury wanted to live forever and decided his career as an author in order to do what he was told: live forever.

— Wikipedia on Ray Bradbury

1990s, 10

Posted on December 16, 2021 by rpflee

— Me@2021-12-16 09:56:07 PM

2.10 A spacetime orbifold in two dimensions, 4

Posted on December 16, 2021 by rpflee

A First Course in String Theory

(b) … the family of curves

$\displaystyle{x^+ x^- = a^2}$ ,

where $\displaystyle{a > 0}$ …

…

Show that the identification (2) relates points on each separate curve.

~~~

Identification (2):

$\displaystyle{(x^+, x^-) \sim \left( e^{-\lambda} x^+, e^{\lambda} x^- \right)}$ , where $\displaystyle{e^\lambda \equiv \sqrt{\frac{1+\beta}{1-\beta}}}$ .

$\displaystyle{ \begin{aligned} (x^+)' &= e^{- \lambda} x^+ \\ (x^-)' &= e^{\lambda} x^- \\ \end{aligned} }$

$\displaystyle{ \begin{aligned} (x^+)' (x^-)' &= e^{- \lambda} x^+ e^{\lambda} x^- \\ &= a^2 \\ \end{aligned} }$

— Me@2021-12-15 04:18:27 PM

Minority Report

Posted on December 14, 2021 by rpflee

未來報告

Minority Report is a 2002 American science fiction action film directed by Steven Spielberg, starring Tom Cruise, and loosely based on the 1956 short story “The Minority Report” by Philip K. Dick. The picture is set in Washington, D.C. and Northern Virginia in the year 2054, where Precrime, a specialized police department, apprehends criminals based on foreknowledge provided by three psychics called “precogs”.

— Wikipedia on Minority Report

2021.12.14 Tuesday ACHK

Ordinary

Posted on December 14, 2021 by rpflee

The power of a man’s virtue should not be measured by his special efforts, but by his ordinary doing.

— Blaise Pascal

2021.12.14 Tuesday ACHK

改變因果鏈起點, 1.2

Posted on December 12, 2021 by rpflee

這段改編自 2010 年 4 月 24 日的對話。

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。

簡單而言，即是「接棒接得切」。

（安：何謂「接棒接得切」呢？）

意思是，人類整體之知識，可以累積。例如，你現在 30 歲。雖然有 30 年的人生經驗，但是那毋須用，三十年去傳授。你的後輩，可能只需花一年，就可以學到，那 30 年的所有重點。

你可以想像，如果人類的生命太短，例如平均得 3 年的話，那就既沒有足夠時間，去累積人生經驗，更沒有足夠時間，去傳授下一代。那樣，人類整體之知識，就不可累積。

第二種假想情況是，你現時 30 年的人生經歷，要花足足 20 年，才傳授得到。那樣，人類的整體智力，就會累積得超慢。

（安：第二種情況，我不太明白。）

我改一改那些數字。如果你 80 年的人生經歷，要花足足 79 年，才傳授得到的話，你是否會有，那額外附加的 79 年壽命呢？

你相當於要有，起碼 159 年的壽命，才能完成整個，知識交棒的工序。

幸而，現實不是那樣。現實是，人有足夠的生命，去累積有用的人生經驗；而且，傳授所花的年期，遠少於親身經歷所花。

簡單來說，發掘知識時間極長；複製知識時間極短。

— Me@2021-12-11 07:18:17 PM

Physics Town

continues

Monthly Archives: December 2021

SICM, 4.2

Ex 1.22. Driven pendulum

Shutting Down Google+ for Consumers

魔間傳奇 16

無拍之拖

Silly Dogs

2.10 A spacetime orbifold in two dimensions, 5

Book Underlining Principle

相聚零刻 1.2

因果鏈捷徑

Once upon a time

Ex 1.21 The dumbbell, 3.4.2

Eternal return, 2

Prayer 5.2

To realize is to realize, 1.4

1990s, 10

2.10 A spacetime orbifold in two dimensions, 4

Minority Report

Ordinary

改變因果鏈起點, 1.2