(反對)開夜車 2.5

本文章並(!)不(!)可作為醫學建議。如需醫學意見,請諮詢專業人士。

(問:「只要飛蚊不惡化」?你怎能保證?)

不能。那正正就是,我更大的苦惱。

一日不能知道,我當年開始患飛蚊症的真正原因,我也會不安,擔心症狀加劇。

「飛蚊症」只是某個或某些疾病的一個「症」,而不是「疾病」本身。一日不能知道,我飛蚊症的病因,我也不能有力預防,症狀的加劇。

(問:你不是說,長期夜睡少睡,導致你的飛蚊症嗎?)

那只是估計,不是肯定。

那一段時間,「出事」前的一兩個星期,我剛好時常睡不著,導致睡了很少。所以,長期夜睡少睡,很可能是主要的原因。

當然,如果平日的睡眠充足,並不會因為單一事件,某一晚的夜睡少睡,就立刻有飛蚊。如果人體是那麼沒有彈性,人類這種生物,可能一早就已經絕種了。

但是,如果是長期夜睡少睡,身體自然會越來越虛弱。到達某個臨界點時,意外事件就可以隨時發生。從相反的角度來講,如果平日睡眠適量,就等於刪除了,飛蚊症的其中一個主要誘因,從而大大減低了,其發生的機會率。

本文章並(!)不(!)可作為醫學建議。如需醫學意見,請諮詢專業人士。

— Me@2019-04-13 03:34:33 PM

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2019.04.15 Monday (c) All rights reserved by ACHK

Physical laws are low-energy approximations to reality, 1.3.1

d_2019_04_07__22_39_01_PM_

Symmetry breaking is important.

When there is symmetry-breaking, the system goes to a low-energy state.

Each possible low-energy state can be regarded as a new “physical world”.

One “physical world” cannot jump to another, unless through quantum tunnelling. But the probability of quantum tunnelling happening is low.

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Low-energy physics theories, such as harmonic oscillator, are often simple and beautiful.

— Professor Renbao Liu

— Me@2019-04-08 10:46:32 PM

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2019.04.09 Tuesday (c) All rights reserved by ACHK

scmutils

In order to run the SICM code, you need to install the scmutils library. Just go to the official page to download the library and follow the official instructions to install it in a Linux operating system.

When you try to run it, your system may give the following error message:

/usr/local/bin/mechanics: line 16: exec: xterm: not found

If so, you should install the program xterm first.

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Also, in case you like to use Emacs as editor, you can:

Just include the following in your .emacs file:

(defun mechanics ()
  (interactive)
  (run-scheme
    "ROOT/mit-scheme/bin/scheme --library ROOT/mit-scheme/lib"
  ))

Replace ROOT with the directory in which you installed the scmutils software. (Remember to replace it in both places. If it is installed differently on your system, just make sure the string has the form “/path/to/mit-scheme --library /path/to/scmutils-library“.) Restart emacs (or use C-x C-e to evaluate the mechanics defun), and launch the environment with the command M-x mechanics.

— Using GNU Emacs With SCMUtils

— Aaron Maxwell

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In my Ubuntu 18.04, the paths are:

(defun mechanics()
  (interactive)
  (run-scheme
   "/usr/local/scmutils/mit-scheme/bin/scheme --library 
/usr/local/scmutils/mit-scheme/lib"
  ))

— Me@2019-04-07 02:52:50 PM

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2019.04.07 Sunday (c) All rights reserved by ACHK

Confirmation principle

Verification principle, 2.2 | The problem of induction 4

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The statements “statements are meaningless unless they can be empirically verified” and “statements are meaningless unless they can be empirically falsified” are both claimed to be self-refuting on the basis that they can neither be empirically verified nor falsified.

— Wikipedia on Self-refuting idea

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In 1936, Carnap sought a switch from verification to confirmation. Carnap’s confirmability criterion (confirmationism) would not require conclusive verification (thus accommodating for universal generalizations) but allow for partial testability to establish “degrees of confirmation” on a probabilistic basis.

— Wikipedia on Verificationism

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Confirmation principle should not be applied to itself because it is an analytic statement which defines synthetic statements.

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Even if it does, it is not self-defeating, because confirmation principle, unlike verification principle, does not requires a statement to be proven with 100% certainty.

So in a sense, replacing verification principle by confirmation principle can avoid infinite regress.

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Accepting confirmation principle is equivalent to accepting induction.

“This is everything to win but nothing to lose.”

— Me@2012.04.17

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2019.04.06 Saturday (c) All rights reserved by ACHK

PhD, 3.5

碩士 4.5 | On Keeping Your Soul, 2.2.5

這段改編自 2010 年 4 月 18 日的對話。

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要完成一個「研究式碩士」課程,上課考試雖然必須,但只是次要的劇情。你「正職」要做的是,做研究。你雖然需要交學費,但大學會有資助給你。一般而言,大學給你的資助,會大於你給大學的學費。

理論上,你可以視那個差額,為你的「薪金」,或者「生活費」。有了這個「薪金」,你就可全職做研究。

(問:實際上呢?)

實際上,就當然沒有那麼理想。

讀研究式碩士或博士課程,因為有資助,你需要做本科課程的助教;職責包括,批改大學本科生的功課、開導修課等。所以,作為一位研究生,你做研究以外,既要上課考試,亦要做助教。

(問:三重身份,哪有那麼多的時間?)

無錯。你真正可以做研究的時間,不多於半職。

即使是研究部分,大部分情況下,你也只可以研究,你上司有興趣的課題。而那課題,往往也未必是,你自己最想研究的東西。

(問:你上司?)

即是你碩士或博士的論文導師。那教授有雙重角色。他既是指導你的老師,亦是指示你的上司。

那兩個角色,本來就不應由,同一個人飾演。

(問:為什麼呢?)

如果甲是你的老師,他做決定時,主要會由誰的利益出發?

如是甲是你的上司,他做決定時,又主要會由誰的利益出發?

(問:你的意思是,「誰是主角」和「誰是助手」?)

如果甲是你的老師,甲你二人,誰是僱主?誰是僱員?

如果甲是你的上司,甲你二人,那誰是僱主?誰是僱員?

— Me@2019-04-05 12:00:42 PM

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2019.04.05 Friday (c) All rights reserved by ACHK

Finding trajectories that minimize the action

We have used the variational principle to determine if a given trajectory is realizable. We can also use the variational principle to find trajectories. Given a set of trajectories that are specified by a finite number of parameters, we can search the parameter space looking for the trajectory in the set that best approximates the real trajectory by finding one that minimizes the action. By choosing a good set of approximating functions we can get arbitrarily close to the real trajectory.

— Structure and Interpretation of Classical Mechanics

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We have used the variational principle to determine if a given trajectory is realizable.

How?

— Me@2019-03-29 04:23:36 PM

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Check if the action of that given trajectory is stationary or not.

— Me@2019-03-29 04:25:45 PM

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2019.03.29 Friday (c) All rights reserved by ACHK

Quantum classical logic

Mixed states, 2 | Eigenstates 4

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— This is my guess. —

If the position is indefinite, you can express it in terms of a pure quantum state[1] (of a superposition of position eigenstates);

if the quantum state is indefinite, you can express it in terms of a mixed state;

if the mixed state is indefinite, you can express it in terms of a “mixed mixed state”[2]; etc. until definite.

At that level, you can start to use classical logic.

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If you cannot get certainty, you can get certain uncertainty.

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[1]: Me@2019-03-21 11:08:59 PM: This line of not correct. The uncertainty may not be quantum uncertainty. It may be classical.

[2]: Me@2019-03-22 02:56:21 PM: This concept may be useless, because a so-called “mixed mixed state” is just another mixed state.

For example, the mixture of mixed states

\displaystyle{p |\psi_1 \rangle \langle \psi_1 | + (1-p) |\psi_2 \rangle \langle \psi_2 |}

and

\displaystyle{q |\phi_1 \rangle \langle \phi_1 | + (1-q) |\phi_2 \rangle \langle \phi_2 |}

is

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\displaystyle{\begin{aligned}  &w \bigg[ p |\psi_1 \rangle \langle \psi_1 |+ (1-p) |\psi_2 \rangle \langle \psi_2 | \bigg] +  (1-w) \bigg[ q |\phi_1 \rangle \langle \phi_1 | + (1-q) |\phi_2 \rangle \langle \phi_1 | \bigg] \\  &= w p |\psi_1 \rangle \langle \psi_1 | + w (1-p) |\psi_2 \rangle \langle \psi_2 | +  (1-w) q |\phi_1 \rangle \langle \phi_1 | + (1-w) (1-q) |\phi_2 \rangle \langle \phi_1 | \\  \end{aligned}}

— This is my guess. —

— Me@2012.04.15

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2019.03.22 Friday (c) All rights reserved by ACHK

Find one, organize two

Technical debt

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dna113 1 day ago [-]

I recently needed an HDMI cord for a monitor and realized that my cord drawer was accruing technical debt.

Whenever I am done with a cord I just throw it in there… it gets all tangled up with all the others. When I inevitably need one of those cords I impatiently pull it out and it makes all the other cords more tangled.

Here I am needing an HDMI cable that won’t just come out easily, I have to pay off my past laziness. But I have choices/tradeoffs/opportunities here.

I can just hurry up and get the minimum untangled and get back to watching TV.

I could untangle all of them since untangling one of them will help me untangle the others and wrap and label them.

I could just untangle the minimum, but also throw a roll of tape and a marker in there and wrap and label all future cords that go into that drawer, eventually they’ll all be nicely wrapped up and well documented.

¯\_(ツ)_/¯

jolmg 1 day ago [-]

Wow. I never thought of clutter in the home as technical debt, but it’s as similar as you describe. That really makes me see home organization in a whole new light.

— Technical Debt Is Like Tetris

— Hacker News

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Whenever you have to search for something, once you have found it, organize an additional thing.

— Me@2019-03-12 11:12:28 AM

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2019.03.13 Wednesday (c) All rights reserved by ACHK

(反對)開夜車 2.4

本文章並(!)不(!)可作為醫學建議。如需專業意見,請諮詢專業人士。

至於,我自己的案例,則幸好是良性的,不會致盲;只要飛蚊不惡化,視力不會減弱。

(問:但你剛才說,飛蚊症「會帶來精神困擾」?)

無錯。可以說是心靈創傷。

(問:為什麼呢?)

如果你買了一個電腦熒光幕,發現有死點,你會怎樣做?

(問:立刻要求商戶更換。新買的電器,必定在保養期內,可以更換。)

假設不可更換呢?

(問:如果只是一兩點的話,應該不會太明顯。我會先用它,直到幾年後才再換。

但是,如果不只是一兩點的話,我可能會忍受不到;如果我負擔得起,我會立刻買過另一部。)

再假設,你永久不能更換熒光幕呢?

(問:永久有死點?)

無錯。

(問:那又真的,十分不自在。

你的意思是,「熒光幕永久有死點」就是患飛蚊症的感受?)

無錯。

所以,患了飛蚊症以後,我一聽到「不可逆轉」這四個字,就有一點兒緊張;患了飛蚊症以後,我以為,我人生不可能再快樂。

幸好,一年之後,我竟然習慣了——只要飛蚊不惡化,我就不會因為那些「死點」,而明顯不開心。

(問:「只要飛蚊不惡化」?你怎能保證?)

不能。那正正就是,我更大的苦惱。

一日不能知道,我當年開始患飛蚊症的真正原因,我也會不安,擔心症狀加劇。

「飛蚊症」只是某個或某些疾病的一個「症」,而不是「疾病」本身。一日不能知道,我的飛蚊症的病因,我也不能有力預防,症狀的加劇。

(問:你不是說,長期夜睡少睡,導致你的飛蚊症嗎?)

本文章並(!)不(!)可作為醫學建議。如需專業意見,請諮詢專業人士。

— Me@2019-03-18 04:47:58 PM

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2019.03.18 Monday (c) All rights reserved by ACHK

Physical laws are low-energy approximations to reality, 1.2

d_2019_01_31__23_12_26_PM_

When the temperature \displaystyle{T} is higher than the critical temperature \displaystyle{T_c}, point \displaystyle{O} is a local minimum. So when a particle is trapped at \displaystyle{O}, it is in static equilibrium.

However, when the temperature is lowered, the system changes to the lowest curve in the figure shown. As we can see, at the new state, the location \displaystyle{O} is no longer a minimum. Instead, it is a maximum.

So the particle is not in static equilibrium. Instead, it is in unstable equilibrium. In other words, even if the particle is displaced just a little bit, no matter how little, it falls to a state with a lower energy.

This process can be called symmetry-breaking.

This mechanical example is an analogy for illustrating the concepts of symmetry-breaking and phase transition.

— Me@2019-03-02 04:25:23 PM

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2019.03.02 Saturday (c) All rights reserved by ACHK

Computing Actions

Lagrangians in generalized coordinates

The function \displaystyle{S_\chi} takes a coordinate path; the function \displaystyle{\mathcal{S}} takes a configuration path.

\displaystyle{\begin{aligned}  \mathcal{S} [\gamma] (t_1, t_2) &= \int_{t_1}^{t_2} \mathcal{L} \circ \mathcal{T} [\gamma]  \\   S_\chi [q] (t_1, t_2) &= \int_{t_1}^{t_2} L_\chi \circ \Gamma [q]  \\   \end{aligned}}

\displaystyle{\begin{aligned}  \mathcal{S} [\gamma] (t_1, t_2)  &= S_\chi [\chi \circ \gamma] (t_1, t_2) \\  \end{aligned}}

Computing Actions

\displaystyle{\texttt{literal-function}} makes a procedure that represents a function of one argument that has no known properties other than the given symbolic name.

The method of computing the action from the coordinate representation of a Lagrangian and a coordinate path does not depend on the coordinate system.

Exercise 1.4. Lagrangian actions

For a free particle an appropriate Lagrangian is

\displaystyle{\begin{aligned}  L(t,x,v) &= \frac{1}{2} m v^2  \\   \end{aligned}}

Suppose that x is the constant-velocity straight-line path of a free particle, such that x_a = x(t_a) and x_b = x(t_b). Show that the action on the solution path is

\displaystyle{\begin{aligned}  \frac{m}{2} \frac{(x_b - x_a)^2}{t_b - t_a} \\   \end{aligned}}

— Structure and Interpretation of Classical Mechanics

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\displaystyle{\begin{aligned}  L(t,x,v) &= \frac{1}{2} m v^2  \\   \end{aligned}}

\displaystyle{\begin{aligned}  S_\chi [\gamma] (t_1, t_2) &= \int_{t_1}^{t_2} L_\chi (t, q(t), Dq(t)) dt \\  &= \int_{t_2}^{t_1} \frac{1}{2} m v^2 dt \\  &= \frac{1}{2} m v^2 \int_{t_2}^{t_1} dt \\  &= \frac{1}{2} m v^2 (t_2 - t_1)  \\  &= \frac{1}{2} m (\frac{x_2 - x_1}{t_2 - t_1})^2 (t_2 - t_1)  \\  &= \frac{1}{2} m \frac{(x_2 - x_1)^2}{t_2 - t_1}   \\   \end{aligned}}

— Me@2006-2008

— Me@2019-03-10 11:08:29 PM

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2019.03.10 Sunday (c) All rights reserved by ACHK

PhD, 3.4

碩士 4.4 | On Keeping Your Soul, 2.2.4 | Release early. Release often, 3.4

這段改編自 2010 年 4 月 18 日的對話。

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(問:他們大概毋須,任何博士學位吧?

根本,「愛因斯坦」這名字,遠遠重要過,「博士」這銜頭。)

無錯。所以,我以上是說「理想而言」。實際而言,在你不是研究生的情況下,要「不斷做研究」,近乎沒有可能;除非,你是金庸小說中的主要角色。

(問:什麼意思?)

他們彷彿都是,既不用上班,亦毋須維生。

那樣,他們才可以全天候地,鑽研武功。

(問:那即是應該攻讀研究院?

但是,你剛才又說:

如果不是為了做研究,而是純粹為了穫得,碩士或博士學位的話,攻讀研究院是,十分浪費時間的。

你的意思是,應該為了「做研究」而讀研究院,而不應為了「得學位」?)

差不多。

這兩個目標不一定有衝突,可以並存。

但是,「做研究」應為主要目標,「得學位」應為「副作用」,或「錦上添花」。

詳細一點來說,「讀研究院」是為了獲得資源,令你有全職的時間,去研究學問。

(問:什麼「資源」?)

錢,又名「生活費」。

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碩士有分兩種:「修課式碩士」和「研究式碩士」。 

要完成一個「修課式碩士」課程,你只需讀一些,深過大學本科程度的科目,考試合格就可以。你需要交學費,沒有大學資助。它適合一些工作職位上,需要碩士學歷,而毋需博士學歷的人士。換句話說,報讀「修課式碩士」的人士,通常也沒打算,繼續攻讀博士。

要完成一個「研究式碩士」課程,上課考試雖然必須,但只是次要的劇情。你「正職」要做的是,做研究。你雖然需要交學費,但大學會有資助給你。一般而言,大學給你的資助,會大於你給大學的學費。

理論上,你可以視那個差額,為你的「薪金」,或者「生活費」。有了這個「薪金」,你就可全職做研究。

(問:實際上呢?)

實際上,就當然沒有那麼理想。

— Me@2019-03-06 12:11:31 AM

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2019.03.06 Wednesday (c) All rights reserved by ACHK

Generalized Coordinates

Configuration Spaces

The set of all configurations of the system that can be assumed is called the configuration space of the system.

Generalized Coordinates

  1. In order to be able to talk about specific configurations we need to have a set of parameters that label the configurations. The parameters used to specify the configuration of the system are called the generalized coordinates.

  2. The \displaystyle{n}-dimensional configuration space can be parameterized by choosing a coordinate function \displaystyle{\chi} that maps elements of the configuration space to n-tuples of real numbers.

  3. The motion of the system can be described by a configuration path \displaystyle{\gamma} mapping time to configuration-space points.

  4. Corresponding to the configuration path is a coordinate path \displaystyle{q = \chi \circ \gamma} mapping time to tuples of generalized coordinates.

The function \displaystyle{\Xi \chi} takes the coordinate-free local tuple \displaystyle{( t, \gamma (t), \mathcal{D} \gamma (t), ... )} and gives a coordinate representation as a tuple of the time, the value of the coordinate path function at that time, and the values of as many derivatives of the coordinate path function as are needed.

\displaystyle{ \begin{aligned} \text{generalized coordinate representation} &= \Xi (\text{local tuple})    \\  (t, q(t), Dq(t), ...) &= \Xi_\chi (t, \gamma(t), \mathcal{D} \gamma(t), ...)    \\  \end{aligned} }

\displaystyle{ \begin{aligned}  \text{generalized coordinates} &= q \\   &= \chi \circ \gamma \\   \\  q(t) &= \chi(\gamma(t)) \\   \end{aligned} }

\displaystyle{ \begin{aligned}    t &\to \gamma: \text{configuration path}    \to \chi: \text{generalized coordinates} = q \\     \end{aligned} }

\displaystyle{ \begin{aligned}  (t, q(t), Dq(t), ...) &= \Xi_\chi (t, \gamma(t), \mathcal{D} \gamma(t), ...)     \\  \\  \Gamma[q](t) &= (t, q(t), Dq(t), ...) \\  \Gamma[q] &= \Xi_\chi \circ \mathcal{T}[\gamma] \\   \end{aligned} }

— 1.2 Configuration Spaces

— Structure and Interpretation of Classical Mechanics

— Me@2019-03-01 03:09:25 PM

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2019.03.01 Friday ACHK

The Door 1.1

The following contains spoilers on a fictional work.

In Westworld season 2, last episode, when a person/host X passed through “the door”, he got copied, almost perfectly, into a virtual world. Since the door was adjacent to a cliff, just after passing through it, the original copy (the physical body) fell off the cliff and then died.

Did X still exist after passing through the door?

Existence or non-existence of X is not a property of X itself. So in order for the question “does X exist” to be meaningful, we have to specify “with respect to whom”.

In other words, instead of “does X exist”, we should ask

With respect to the observer Y, does X exist?

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There are 3 categories of possible observers (who were observing X passing through the door):

  1. the original person (X1)
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    X_1 == X

  2. the copied person (X2) in the virtual world
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    For simplicity, assume that X2 is a perfect copy of X.

  3. other people (Y)

— Me@2019-02-09 1:09 PM

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2019.02.28 Thursday (c) All rights reserved by ACHK