Multiverse

A physics statement is meaningful only if it is with respect to an observer. So the many-world theory is meaningless.

— Me@2018-08-31 12:55:54 PM

— Me@2019-05-11 09:41:55 PM

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Answer me the following yes/no question:

In your multi-universe theory, is it possible, at least in principle, for an observer in one universe to interact with any of the other universes?

If no, then it is equivalent to say that those other universes do not exist.

If yes, then those other universes are not “other” universes at all, but actually just other parts of the same universe.

— Me@2019-05-11 09:43:40 PM

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2019.05.11 Saturday (c) All rights reserved by ACHK

追憶逝水年華, 3

In Search of Lost Time, 3 | (反對)開夜車 3.1 | 止蝕 4

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其實,我中五那年,試過企圖「開夜車」。詳細過程怎樣,已不太記得。但是,總體的感受,仍然是深刻。

那時,我有很多天真的想法,例如:

1. 只要每晚睡少四小時,就每晚可以多四小時溫習。

2. 只要每晚可以多四小時溫習,就可以追回之前,落後了的進度。

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實情是,「貪心」帶來「貧窮」:

很多時,我也是覺得自己,溫習的進度落後了,來不及準備那年的公開試。所以,想透過凌晨(例如)三時起牀,來追回之前,落後了的進度。但是,我卻幾乎每天凌晨,也起不到牀,導致溫習大計失敗,遺撼非常。繼而,因為失落了,更多的時間,我就覺得,更加需要在下一天,凌晨起牀。

惡性循環,持續了很久,浪費了我大量的時間。其實,只要我睡眠適量,作息定時,反而有不少機會,有上佳的成績。

現在回想起來,仍然驚嘆著,為何年輕時,可以那麼愚蠢。

只可以說,人在惶恐時,多麼糊塗的事,都可以發生。

— Me@2019-05-09 10:04:55 PM

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2019.05.10 Friday (c) All rights reserved by ACHK

Ex 1.8 Implementation of $\delta$

\displaystyle{ \begin{aligned} \delta_\eta f[q] &= \lim_{\epsilon \to 0} \left( \frac{f[q+\epsilon \eta]-f[q]}{\epsilon} \right) \\ \end{aligned}}

The variation may be represented in terms of a derivative.

— Structure and Interpretation of Classical Mechanics

\displaystyle{ \begin{aligned} g( \epsilon ) &= f[q + \epsilon \eta] \\ \delta_\eta f[q] &= \lim_{\epsilon \to 0} \left( \frac{g(\epsilon) - g(0)}{\epsilon} \right) \\ &= D g(0) \\ \end{aligned}}

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A lambda expression evaluates to a procedure. The environment in effect when the lambda expression is evaluated is remembered as part of the procedure; it is called the closing environment.

— Structure and Interpretation of Classical Mechanics

(define (((delta eta) f) q)
  (let ((g (lambda (epsilon) (f (+ q (* epsilon eta))))))
    ((D g) 0))) 

— Me@2019-05-05 10:47:46 PM

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2019.05.05 Sunday (c) All rights reserved by ACHK

Classical probability, 7

Classical probability is macroscopic superposition.

— Me@2012.04.23

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That is not correct, except in some special senses.

— Me@2019-05-02

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That is not correct, if the “superposition” means quantum superposition.

— Me@2019-05-03 08:44:11 PM

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The difference of the classical probability and quantum probability is the difference of a mixed state and a pure superposition state.

In classical probability, the relationship between mutually exclusive possible measurement results, before measurement, is OR.

In quantum probability, if the quantum system is in quantum superposition, the relationship between mutually exclusive possible measurement results, before measurement, is neither OR nor AND.

— Me@2019-05-03 06:04:27 PM

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2019.05.03 Friday (c) All rights reserved by ACHK

PhD, 3.6

碩士 4.6 | On Keeping Your Soul, 2.2.6

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有生以來,你遇過的教師有多少個?

而值得尊重的,又有多少個?

— Me@2019-04-30 11:22:05 PM

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2019.04.30 Tuesday (c) All rights reserved by ACHK

Varying a path

Suppose that we have a function \displaystyle{f[q]} that depends on a path \displaystyle{q}. How does the function vary as the path is varied? Let \displaystyle{q} be a coordinate path and \displaystyle{q + \epsilon \eta} be a varied path, where the function \displaystyle{\eta} is a path-like function that can be added to the path \displaystyle{q}, and the factor \displaystyle{\epsilon} is a scale factor. We define the variation \displaystyle{ \delta_\eta f[q]} of the function \displaystyle{f} on the path \displaystyle{q} by

\displaystyle{\delta_\eta f [q] = \lim_{\epsilon \to 0} \left( \frac{f[q + \epsilon \eta] - f[q]}{\epsilon} \right)}

The variation of \displaystyle{f} is a linear approximation to the change in the function \displaystyle{f} for small variations in the path. The variation of \displaystyle{f} depends on \displaystyle{\eta}.

— 1.5.1 Varying a path

— Structure and Interpretation of Classical Mechanics

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Exercise 1.7. Properties of \displaystyle{\delta}

The meaning of \displaystyle{\delta_\eta (fg)[q]} is

\displaystyle{\delta_\eta (f[q]g[q])}

— Me@2019-04-27 07:02:38 PM

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2019.04.27 Saturday ACHK

Mixed states, 4

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How is quantum superposition different from mixed state?

The state

\displaystyle{|\Psi \rangle = \frac{1}{\sqrt{2}}\left(|\psi_1\rangle +|\psi_2\rangle \right)}

is a pure state. Meaning, there’s not a 50% chance the system is in the state \displaystyle{|\psi_1 \rangle } and a 50% it is in the state \displaystyle{|\psi_2 \rangle}. There is a 0% chance that the system is in either of those states, and a 100% chance the system is in the state \displaystyle{|\Psi \rangle}.

The point is that these statements are all made before I make any measurements.

— edited Jan 20 ’15 at 9:54

— Mehrdad

— answered Oct 12 ’13 at 1:42

— Andrew

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Given a state, mixed or pure, you can compute the probability distribution \displaystyle{P(\lambda_n)} for measuring eigenvalues \displaystyle{\lambda_n}, for any observable you want. The difference is the way you combine probabilities, in a quantum superposition you have complex numbers that can interfere. In a classical probability distribution things only add positively.

— Andrew Oct 12 ’13 at 14:41

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— How is quantum superposition different from mixed state?

— Physics StackExchange

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2019.04.23 Tuesday ACHK

(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