Jonny English, 2

A man without hope is a man without fear.

— Daredevil: Born Again

— Frank Miller

— Me@2016-04-09 09:49:28 PM

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2022.04.19 Tuesday ACHK

Posted in OCD

相聚零刻 1.2.2

這段改編自 2021 年 12 月 12 日的對話。

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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,千萬去表白!

— 楚兒戀愛說

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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

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2022.04.18 Monday (c) All rights reserved by ACHK

Logical arrow of time, 11

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

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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

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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}

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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

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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

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2022.04.14 Thursday (c) All rights reserved by ACHK

地獄篇 10

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

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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

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2022.04.13 Wednesday (c) All rights reserved by ACHK

伏線驅動程式 1.4

這段改編自 2010 年 10 月 14 日的對話。

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答覆我一句,聘請還是不聘請,並不是問題。最滋擾人的是,不置可否。

「究竟那間補習社會聘請我,我應該等待那份工作,還是立刻找其他呢?」

記住,大概而然:

需要對方行動的事情,對方「不置可否」這行動本身,就已代表了「否」,即婉拒。婉拒者,婉轉地拒絶也。例如,你向心上人表白,但她很長時間後,例如一星期,仍然沒有回覆。

需要你方主動的項目,對方「不置可否」這行動本身,就已代表了「可」,即默許。默許者,沉默地允許也。例如,你看到一枚戒指很美,問女朋友:「買給你好嗎?」她不出聲的話,就即是「要」。

這大原則未必準確,但亦所差無幾。

當然,最終我也只能,找其他工作。我在報紙中的招聘廣告中,找到這裡的一份數學助教工作。 我其實不是找「中學教師」的工作。我曾經立志,做中學教師。

我在中六預科,一堂純數學課中,覺得老師講得很好,心裡有感而發:「大個千萬不要做中學教師。」否則,在事業上,我將要花數十年的時間,循環同一年。

我當時找助教工作,只視作臨時的唯生措施。只不過到簽約時,校長問如果給三班給我教好不好。薪金高一節,我當然說好。

先教兩年中學,之後我才回去讀物理,都算是可取的人生軌跡。

— Me@2022-04-12 11:34:16 AM

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2022.04.12 Tuesday (c) All rights reserved by ACHK

Ex 1.24 Constraint forces, 1.3

Structure and Interpretation of Classical Mechanics

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Find the tension in an undriven planar pendulum.

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Tangential component:

\displaystyle{\begin{aligned}  \left(F_{\text{net}}\right)_t &= m a_t \\  - mg \sin \theta &= m l \ddot \theta \\  \end{aligned}}

Radial component:

\displaystyle{\begin{aligned}  \left(F_{\text{net}}\right)_r &= m a_r \\  F(t) - mg \cos \theta &= m l \dot \theta^2 \\  \end{aligned}}

— Me@2022-04-10 04:22:27 PM

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2022.04.10 Sunday (c) All rights reserved by ACHK

Remove time from physics

motohagiography on May 14, 2018 | next [–]

I once saw a fridge magnet that said “time is natures way of making sure everything doesn’t happen all at once,” and it’s stuck with me.

The concept of time not being “real,” can be useful as an exercise for modelling problems where to fully explore the problem space, you need to decouple your solutions from needing them to occur in an order or sequence.

From an engineering perspective, “removing” time means you can model problems abstractly by stepping back from a problem and asking, what are all possible states of the mechanism, then which ones are we implementing, and finally, in what order. This is different from the relatively stochastic approach most people take of “given X, what is the necessary next step to get to desired endstate.”

More simply, as a tool, time helps us apprehend the states of a system by reducing the scope of our perception of them to sets of serial, ordered phenomena.

Whether it is “real,” or an artifact of our perception is sort of immaterial when you can choose to reason about things with it, or without it. A friend once joked that math is what you get when you remove time from physics.

I look forward to the author’s new book.

— Hacker News

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2022.04.10 Sunday ACHK

十萬七千里 3.2

數學教育 7.4 | The least of all evils 8.2 | 眾害取其輕 8.2

這段改編自 2010 年 4 月 24 日的對話。

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… began doing just one thing ever which he had control.

— Stephen Covey

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這個原理用作,人生哲學的比喻的話,就是指,即使「目標不可能」,也不代表「要完全放棄」。亦即是話,即使你的一些人生目標,不可能實現,那也不代表你,完全沒有東西可以做。那「不可能的目標」或許可以,轉化為一個「可能的近似版本」。

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即使有些情況下,現實和理想,還相差十萬八千里,你總可以嘗試,把理實拉近理想一點點。你由 108,000 里,行到 107,999 里之處,才再想下一步,如何行近再一點點。見步行步,行步見步。

達到或接近理想,不是每人都做到。但是,減少理實和理想的距離,那怕只是一點點,則是大部人都,可以執行的任務。

追尋快樂,要機緣巧合。但減輕痛苦,則能力可及。

— Me@2022-04-09 04:20:42 PM

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2022.04.09 Saturday (c) All rights reserved by ACHK

Quick Calculation 3.2

A First Course in String Theory

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Verify that the gauge transformation (3.10) are correctly summarized by (3.21).

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Eq. (3.21):

\displaystyle{ \begin{aligned}   A_\nu' &= A_\nu + \partial_\nu \epsilon \\   \end{aligned} }

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\displaystyle{ \begin{aligned}   \left( A_0', A_1', ... \right) &= \left( - \Phi + \frac{\partial \epsilon}{\partial x^0}, A^1 + \frac{\partial \epsilon}{\partial x^1}, ... \right)  \\   \left( -\Phi', {A^1}', ... \right) &= \left( - \Phi + \frac{1}{c} \frac{\partial \epsilon}{\partial t}, A^1 + \frac{\partial \epsilon}{\partial x^1}, ... \right)  \\   \end{aligned} }

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\displaystyle{ \begin{aligned}   \Phi' &= \Phi - \frac{1}{c} \frac{\partial \epsilon}{\partial t}  \\     \left( {A^1}', {A^2}', {A^3}' \right) &= \left( {A^1}, {A^2}, {A^3} \right) + \left( \frac{\partial}{\partial x^1}, \frac{\partial}{\partial x^2}, \frac{\partial}{\partial x^3} \right) \epsilon \\     \end{aligned} }

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Eq. (3.10):

\displaystyle{ \begin{aligned} \Phi' &= \Phi - \frac{1}{c} \frac{\partial \epsilon}{\partial t} \\ \vec A' &= \vec A + \nabla \epsilon \\ \end{aligned} }

— Me@2022-04-07 07:05:29 PM

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2022.04.07 Thursday (c) All rights reserved by ACHK

C and Lisp

numeromancer on Jan 25, 2010 [-]

In every art there is a dichotomy between the practical and the theoretical, and each has their fundamentals. In Comp. Sci., those two sets of fundamentals are these: sets of machine instructions, which come in several varieties; and lambda calculus, or one of the equivalent (by Church’s Thesis) formal systems. C and Lisp are similar in that they represent the first steps in each case to reach the other: C is a level above machine code, providing some abstraction and portability to the use of machine code, the fundamental elements of practical computing; lisp is a level above lambda calculus, providing a practical system for using functions, the fundamental elements of theoretical computing.

In short, mastery of C is concomitant with the ability to measure the cost of computation (sometimes, regardless of the value of it); mastery of Lisp is concomitant with the ability to measure the value of computation (sometimes, regardless of the cost).

Since C and Lisp lie on opposite borders of the universe of computation, knowing both will allow you to better measure the scope of that universe.

— Ask HN: Why does learning lisp make you a better C-programmer?

— Hacker News

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2022.04.07 Thursday ACHK

Circus

drblast on Oct 27, 2010 | next [–]

Living with one child is like living with a demanding, but mostly reasonable, roommate who really likes spending time with you until she goes to bed early.

Having two or more children is like living in a circus where all the performers are deaf.

— Ask HN: How does having a baby change your life?

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2022.04.07 Thursday ACHK

伏線驅動程式 1.3

這段改編自 2010 年 10 月 14 日的對話。

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為何我在幾年前,會在這裡教書呢?

因為之前我找到工作的那間補習社,言而無信。我應徵面試完時,面試職員說會聘請我,叫我等消息。一段時間後,還未有消息。

一般而言,面試職員只會,叫人「等消息」。想聘請的話,自然會聯絡我。沒有消息的話,就代表不聘用。所以,在通常的情況下,沒有消息時,並不需要再,打電話去詢問。

但是,那次的面試職員是說「會聘請」,稍後再聯絡。所以,長久沒有消息時,我致電詢問。但是,接線人員的答覆是,會再聯絡;即是模稄兩可。隔了數天之後,我又再問多一次,究竟是聘不聘用。

「我可不可以與,當天的面試人員,傾一傾談?」

「不可以。」

仍然沒有答覆。

答覆我一句,聘請還是不聘請,並不是問題。最滋擾人的是,不置可否。

「究竟那間補習社會聘請我,我應該等待那份工作,還是立刻找其他呢?」

當然,當年還年輕,才會犯這類低級錯誤。

愛情上,找到男/女朋友前,要不斷結識新的朋友,尤其異性。

事業上,莫講話我當時,未有固定工作,即使正職在職,亦即是話,任何情況下,本應不斷去面試,尋找新機遇。那樣,才可以為我的未來太太和子女,提供到基本生活的經濟保障。

記住,你可以對,你的金錢和工作有感情,但千萬不要對,你的公司和職位有感情。我年青就,就是犯了「對公司和職位有感情」這重大錯失,導致自己和家人,受了一些不必要之苦;亦導致自己可能不會有,未來的家人。

— Me@2022-03-08 12:06:18 PM

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2022.04.06 Wednesday (c) All rights reserved by ACHK

Ex 1.24 Constraint forces, 1.2

Ex 1.22 Driven pendulum, 3.2

Structure and Interpretation of Classical Mechanics

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Find the tension in an undriven planar pendulum.

~~~

[guess]


(define ((q->r x_s y_s l) local)
  (let* ((q (coordinate local))
         (t (time local))
         (theta (ref q 0))
         (c (ref q 1))
         (F (ref q 2)))
    (up (+ (x_s t) (* c (sin theta)))
        (- (y_s t) (* c (cos theta)))
        F)))

(let* ((xs (literal-function 'x_s))
       (ys (literal-function 'y_s))
       (q (up (literal-function 'theta)
              (literal-function 'c)
              (literal-function 'F))))
  (show-expression ((compose (q->r xs ys 'l) (Gamma q)) 't)))


(define (L-theta m l x_s y_s U)
  (compose
   (L-driven-free m l x_s y_s U) (F->C (q->r x_s y_s l))))

(let* ((U (U-gravity 'g 'm))
       (xs (literal-function 'x_s))
       (ys (literal-function 'y_s))
       (q (up (literal-function 'theta)
              (literal-function 'c)             
              (literal-function 'F)))
       (L (L-theta 'm 'l xs ys U)))
  (show-expression (L ((Gamma q) 't))))
(/
 (+ (* l m ((D x_s) t) (c t) ((D theta) t) (cos (theta t)))
    (* 1/2 l m (expt (c t) 2) (expt ((D theta) t) 2))
    (* l m (c t) ((D theta) t) (sin (theta t)) ((D y_s) t))
    (* g l m (c t) (cos (theta t)))
    (* l m ((D x_s) t) ((D c) t) (sin (theta t)))
    (* -1 l m ((D c) t) (cos (theta t)) ((D y_s) t))
    (* -1 g l m (y_s t))
    (* 1/2 l m (expt ((D x_s) t) 2))
    (* 1/2 l m (expt ((D c) t) 2))
    (* 1/2 l m (expt ((D y_s) t) 2))
    (* 1/2 (expt l 2) (F t))
    (* -1/2 (expt (c t) 2) (F t)))
 l)

(let* ((U (U-gravity 'g 'm))
       (xs (literal-function 'x_s))
       (ys (literal-function 'y_s))
       (q (up (literal-function 'theta)
              (literal-function 'c)
              (literal-function 'F)))
       (L (L-theta 'm 'l xs ys U)))
  (show-expression (((Lagrange-equations L) q) 't)))

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(let* ((U (U-gravity 'g 'm))
       (xs (lambda (t) 0))
       (ys (lambda (t) 'l))
       (q (up (literal-function 'theta)
              (lambda (t) 'l)
              (literal-function 'F)))
       (L (L-theta 'm 'l xs ys U)))
  (show-expression (((Lagrange-equations L) q) 't)))

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\displaystyle{F(t) = l m \left[D \theta(t)\right]^2 + g m \cos \theta(t)}

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[guess]

— Me@2022-04-05 04:16:51 PM

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2022.04.05 Tuesday (c) All rights reserved by ACHK

Dynamical pictures

Comparison of pictures

The Heisenberg picture is closest to classical Hamiltonian mechanics (for example, the commutators appearing in the above equations directly correspond to classical Poisson brackets). The Schrödinger picture, the preferred formulation in introductory texts, is easy to visualize in terms of Hilbert space rotations of state vectors, although it lacks natural generalization to Lorentz invariant systems. The Dirac picture is most useful in nonstationary and covariant perturbation theory, so it is suited to quantum field theory and many-body physics.

Summary comparison of evolutions

— Wikipedia on Dynamical pictures

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2022.04.05 Tuesday ACHK