Category Archives: Translation | 文字學

Random variable

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Random variable X represents a single-valued result of a random event. Its value is unknown to us, not because of our ignorance, but because of its non-existence. The value exists only after the happening of that random event.

Symbol x represents a particular value of X. It is an existing value that can be substituted to X. We use symbol x instead of a number because we have not yet known what that particular number is.

— Me@2016-04-08 05:24:45 PM

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X ~ random variable

It is a variable due to the fact that the “identical” random process can result differently at different times.

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x ~ a value of X

Since it is a particular value of X, it is not a variable. However, it may seem to be a variable because it may still be unknown to us.

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Symbol P(X) is meaningless because inside, it must be a statement (representing an event). Symbol X is a random variable, not a statement.

Instead, “X=x” is a statement. So expression P(X=x) is meaningful, such as

P(X=x) = {\begin{cases}{\frac {1}{2}},&x=0,\\{\frac {1}{2}},&x=1,\\0,&x\notin \{0,1\} \end{cases}}

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From another point of view, X is a noun phrase, such as “my monthly salary”, not a number. Symbol x is a number, although maybe not known yet. That’s why whatever the formula, it contains no X‘s, but x‘s. For example,

\cdots = {\begin{cases}{\frac {1}{2}},&x=0,\\{\frac {1}{2}},&x=1,\\0,&x\notin \{0,1\} \end{cases}}

— Me@2016-05-04 06:32:24 PM

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2023.05.16 Tuesday (c) All rights reserved by ACHK

權力來源 1.4

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這段改編自 2010 年 4 月 24 日的對話。

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勢

~ environmental default

— Me@2021-11-16 07:59:12 PM

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勢

~ potential

~ 未來事件s對現在的影響

— Me@2023-03-12 09:14:50 AM

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potential energy

~ energy of potential motion

~ energy of future motion

— Me@2023-04-16 12:08:08 PM

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權力

~ 勢力

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大概而言，「權」即是「勢」。但是，兩詞給人的感覺不同。根本的原因是，它們的用法，不大相同。

「權力」著重個人，例如：「甲擁有很大的權力。」「勢」則著重外在。甲身處環境的人事心理結構，形成了一個「勢」。如果當時的那個「勢」對甲有利，就簡稱為：「甲擁有很大的勢力。」

— Me@2023-04-17 12:56:11 AM

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2023.04.17 Monday (c) All rights reserved by ACHK

Why does the universe exist? 7.2

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“There is nothing in that region of space”

and

“there is nothing outside the universe”

have different meanings.

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there is nothing except quantum fluctuations in that region of space

= the best detector detects nothing but quantum fluctuations

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there is nothing outside the universe

= whatever detected, label the whole collection as “the universe”

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“There is nothing outside the universe” does not (!!!) mean that “we go outside the universe to keep searching, but find nothing”.

— Me@2012-10-15 08:33:01 AM

— Me@2022-11-27 09:09:53 PM

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2022.11.28 Monday (c) All rights reserved by ACHK

天助自助者，自助人恆助之

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這段改編自 2021 年 12 月 15 日的對話。

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Don’t spend your time making other people happy. Other people being happy is their problem. It’s not your problem. If you are happy, it makes other people happy.

— @naval

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你在人生中，有一大部分問題，都是來自於，你以為你有責任，去解決其他人的問題。

在那愚善的年代，我不明白這一句。直到近年，我才深切體會到，它的意思。另一個版本是：

每人都有對自己的最先責任，和最終責任。其他人對你，則沒有必然責任。你對其他人，亦沒有。

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當你覺得你一定、必須、任何時候，也有責任要，幫助任何他人時，那就是你摧毁自己（和他人）的人生之始。合理的版本是，

你先獨善其身；然後，行有餘力的話，就在有些時候，幫助有些應該幫助的人，如果當事人同意的話。

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記住，起點是，你有責任，去解決你自己的問題，但是，你並沒有責任，去解決其他人的問題。有時，間中幫助人，並不是因為責任，而是基於愛心或情義。而「有時候，在你沒有責任幫時，仍然選擇幫」，正正是人性光輝之處。

精確一點用字的話：必須做的工作，為之「責任」；可做可不做的，為之「愛心」或「情義」。

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既然可幫可不幫，那樣，什麼時候應該幫呢？

— Me@2022-11-05 12:54:58 PM

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2022.11.06 Sunday (c) All rights reserved by ACHK

Presentation 基本原理 1.2.2.5

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這段改編自 2010 年 4 月 24 日的對話。

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然後第三點會，補充第一點。剛才第一點說，一課應只有一個重點。定義何謂「一點」和何謂「一課」，正正是講者的職責。

第三點就是，宏觀而言，

說話要 in series（串聯），不要 in parallel（並聯）。你要說完一句說話，才開始下一句。你要講完一個 point（要點），才講下一個。

千萬不要企圖，在同一刻時間中，講超過一句說話。亦千萬不要企圖，在同一句說話中，包含超過一個要點（point）。

簡言之，說話要有條理。

— Me@2010.09.05

那就正正為什麼是「條理」，而不是「塊理」。思路是一「條」線，不是一「塊」面。

那就正正為什麼是「思路」，而不是「思面」。思路是一條「路」，不是一塊「面」。

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那正正是，「安排」這個詞語的意思，把眾多想法要點，安放成一個排列。

情形就好像打字一樣。打字快的原因是，你打完一個英文字母，才打下一個；而不是在同一刻，打超過一個字母。

如果你企圖在同一刻，打超過一個字母，你會打錯字。字母次序錯了的話，時間得不償失。

— Me@2010.09.05

— Me@2022-10-25 02:58:36 PM

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2022.10.26 Wednesday (c) All rights reserved by ACHK

開心 vs 關心

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Euler problem 2

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The older I get, the less I care about what people think about me. Therefore the older I get, the happier I am.

—

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By considering the terms in the Fibonacci sequence whose values do not exceed four million, find the sum of the even-valued terms.

(defun fib (n)
  (cond ((= n 0) 0)
        ((= n 1) 1)
        ((> n 1) (+ (fib (- n 2)) (fib (- n 1))))))

(time (fib 40))

;; Evaluation took:
;;   2.648 seconds of real time
;;   2.640080 seconds of total run time
;;   99.70% CPU
;;   9,002,590,370 processor cycles
;;   0 bytes consed
;; 

;; tail resursion

(defun fib-t (n)
  (labels ((fib-iter (m a b)
            (if (= m 0)
            a
            (fib-iter (- m 1) b (+ a b)))))
        (fib-iter n 0 1)))

(time (fib-t 40))

;; Evaluation took:
;;   0.000 seconds of real time
;;   0.000002 seconds of total run time
;;   100.00% CPU
;;   2,184 processor cycles
;;   0 bytes consed
;;
  
;; infinite list

(defmacro append-last (lst obj)
  `(append ,lst (list ,obj)))

(defun fib-i (n)
  (labels ((fib-iter (m fib-list a b)
            (if (> m (- n 2))
            fib-list
            (fib-iter (1+ m)
                (append-last fib-list (+ a b))
                b
                (+ a b)))))
    (fib-iter 0 '(0 1) 0 1)))

(time (fib-i 40))

;; Evaluation took:
;;   0.000 seconds of real time
;;   0.000008 seconds of total run time 
;;   100.00% CPU
;;   21,960 processor cycles
;;   32,768 bytes consed


(defun filter (fn lst)
  (let ((acc nil))
    (dolist (x lst)
      (let ((val (funcall fn x)))
    (if val (push val acc))))
    (nreverse acc)))

(defmacro filter-list (fn lst)
  `(filter #'(lambda (x)
                (if (funcall ,fn x) x))
            ,lst))

(defmacro filter-2 (fn1 fn2 lst)
  `(filter-list #'(lambda (x)
                    (if (and
                    (funcall ,fn1 x)
                    (funcall ,fn2 x))
                    x))
                ,lst))

(reduce #'+ (filter-2 #'evenp
              #'(lambda (x) (< x 4000000))
              (fib-i 100)))

; 4613732

— Me@2022-08-07 12:34:19 PM

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2022.08.09 Tuesday (c) All rights reserved by ACHK

難得有情人

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形上情人 2.2 | 冰心鎖 2.2 | 超時空接觸 3.4

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認為愛情是要找到「條件最好的那一位」的人，不會從一而終，因為永遠可能有，亦必定有，條件更好的另一位。

— Me@2022-02-08 11:50:35 PM

你不是找「條件最好」的人，做你的另一半。你是要找「條件最適合你」的人。留意，「她最適合你」並不保證，你最適合她。所以，準確一點的講法是：

「你是要找『條件最適合你』的人，如果你剛巧又，最適合她的話。」

.

你不是找「條件最好」的人，做你的另一半。你是要找「與你感情至深」之人。

留意，「你對她有情」並不保證，她對你有情。「她是與你感情至深的人」並不代表，你是與她感情至深之人。「她是你的蘇眉」並不意味，你也是她的蘇眉。

Today I found my soulmate; she didn’t.

所以，準確一點的講法是：

「你是要找『與你感情最深』之人，如果你剛巧也是，『與她感情最深』之人。」

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只有一見鍾愛，沒有一見鍾情。

愛是感覺，只需零時無知、一時誤會、兩時消失。

一見可以生愛，日久才能生情。

情需要時間，情需要空間。情是「超時空接觸」。

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愛可以替代；情不可以。

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「情人」的重點在於情。

情者，情境也。

情人者，情境之人也。

愛人可以替代；情人不可以，因為情境不可以。

時常有愛人，難得有情人。

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感情者，感受到相同之情境也。

情人者，與爾有共同經歷之人也。

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你要找的，不是所謂「外在條件最好」的人，而是「感情至深」之人。

你要找的，不是「條件人」，亦不是「有緣人」，而是「有情人」。

— Me@2022.05.11 07:07:43 PM

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2022.05.12 Thursday (c) All rights reserved by ACHK

The 4 bugs of quantum mechanics popular, 1.3

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The common quantum mechanics “paradoxes” are induced by 4 main misunderstandings.

1.  A wave function is of a particle. Wrong.

…

2.1  A system's wave function exists in physical spacetime. Wrong.

…

physical definition

~ define the microscopic events in terms of observable physical phenomena such as the change of readings of the measuring device

~ define unobservable events in terms of observable events

— Me@2022-01-31 08:33:01 AM

superposition

~ lack of the existence of measuring device to provide the physical definitions for the (difference between) microscopic events

— Me@2022-02-12 10:22:09 AM

a physical variable X is in a superposition state

~ X has no physical definition

~ in the experiment-setup design, no measurement device is allowed to exist to provide a definition of different possible values of X

— Me@2022-02-18 02:04:45 PM

2.2   A superposition state is a physical superposition of a physical state. Wrong.

“Quantum state” is a misnomer. It is not a (physical) state. It is a (mathematical) property. It is a system property (of a physical variable) of an experimental-setup design.

“State” and “property” have identical meanings except that:

State is physical. It exists in physical time. In other words, a system's state changes with time.

Property is mathematical. It is timeless. In other words, a system's property does not change. (If you insist on changing a system's property, that system will become, actually, another system.)

For example, “having two wheels” is a bicycle’s property; but the speed is a state, not a property of that bicycle.

superposition state

~ physically-undefined property

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In the phrase “superposition state”, the word “superposition” is also a misnomer.

A superposition state is not of physical waves, nor of physical states. Instead, it is a superposition of physical meanings of some variables in a physical system.

a physical variable X is in a superposition state

~ X is a physically-undefined property (of the physical system)

— Me@2022-02-18 02:04:45 PM

— Me@2022-02-20 06:44:32 AM

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2022.02.21 Monday (c) All rights reserved by ACHK

EPR paradox, 11.6

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What is more difficult to understand is the non-classical part:

What if, instead of turning on a detector before the time of emitting, we turn it on after the pair is emitted but before either of them has reached its destination?

…

In the common (but inaccurate) language, the action of activating a detector has collapsed the wave function of the system.

Would the pair of (such as) spin values be correlated?

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(Me@2022-02-16 12:07:25 AM: I think I have the answer now. I plan to publish it soon. But I keep the following as a record of thoughts.)

There are 2 possibilities.

(I do not know which of them is true, because I have not yet found an actual experiment that has tested against them.)

[guess]

1.

They are correlated only in the statistical sense.

…

2.

Every pair is correlated.

This is stranger than the first case, because if the two detectors are several light-years apart, the whole system exists across those light-years. The strangeness is the fact that even for a system-across-light-years, operations at one end can influence the probability of an event at the other end.

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For the time being, I guess that the second case is the true one.

Even if the first case is the true one, it is still strange because it implies that an action at one part of the system influences the statistical properties of another part, which may be several light-years away.

[guess]

Even in this stranger case, all experimental results are still consistent with special relativity (aka causality), because wave functions are not physical quantities. Instead, they are mathematical quantities for calculating probabilities, which themselves are also mathematical quantities, for predicting experimental results.

— Me@2022-02-11 12:47:14 AM

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Bug fixes:

1.1  It is not the particle’s state that is in a superposition or not, but the system’s state.

2.1  We need to specify which observer that the wave function is with respect to.

A wave function is for an observer to calculate the probabilities of different possible results in an experiment.

2.2  There is no “god’s eye view” in physics.

Every physical event must be described with respect to an observer. Every physical event, even if the event is “to compare observation results”, must be described with respect to an observer. — Me@2017-05-10 07:45:36 AM

2.3  A wave function is mathematical, not physical.

It is a mathematical function for an observer to calculate the probabilities. It is not something existing in physical spacetime. Thus superposition is also not something existing in physical spacetime. So it is meaningless to ask if the system state is in a superposition at a particular time.

Instead, whether a system is in superposition or not (with respect to a particular variable) is an intrinsic property of your experimental setup design, which includes not just objects and devices, but also operations.

“Wave function collapse” is not a physical event that happens during the operation of the experiment. Instead, it “happens” when you replace one experiment design with another.

— Me@2022-02-16 10:45:01 AM

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2022.02.16 Wednesday (c) All rights reserved by ACHK

EPR paradox, 11.5

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Black hole information paradox, 2.2.5

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What is more difficult to understand is the non-classical part:

What if, instead of turning on a detector before the time of emitting, we turn it on after the pair is emitted but before either of them has reached its destination?

Since neither of the detectors at the two end destinations is activated in the beginning, the entangle variables are still physically-undefined (i.e. in a superposition) at that moment the pair is emitted.

However, while the particles are still on the way, at the moment one of two detectors is first activated, the entangled variables get their physical definitions. The system state is no longer in a superposition state. Instead, it becomes a mixed state. In other words, the system has become a classical system (with respect to those entangled variables).

In the common (but inaccurate) language, the action of activating a detector has collapsed the wave function of the system.

Would the pair of (such as) spin values be correlated?

.

(Me@2022-02-16 12:07:25 AM: I think I have the answer now. I plan to publish it soon. But I keep the following as a record of thoughts.)

There are 2 possibilities.

(I do not know which of them is true, because I have not yet found an actual experiment that has tested against them.)

[guess]

1.

They are correlated only in the statistical sense.

Individual pair of values may be not correlated, but a lot of pairs that have the same superposition (at time of emitting) will form that statistical pattern that is indistinguishable from the one that predicted with the assumption that every pair is correlated.

In analogy, in the double-slit experiment, an individual dot on the final screen cannot tell whether the particle was in a superposition. It is only after a lot of dots forming on the final screen, we can check whether there is an interference pattern. When the interference appears (and we assume that the wave function that governs every particle is the same), we say that every particle is in a superposition state. Or put it more accurately, the system is in the same superposition state before each particle has reached the screen.

2.

Every pair is correlated.

[guess]

— Me@2022-02-11 12:47:14 AM

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2022.02.16 Wednesday (c) All rights reserved by ACHK

EPR paradox, 11.4

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Black hole information paradox, 2.2.4

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physical definition

~ define the microscopic events in terms of observable physical phenomena such as the change of readings of the measuring device

~ define unobservable events in terms of observable events

— Me@2022-01-31 08:33:01 AM

In the EPR experiment, if at least one of the detectors at the two end destinations is already turned on at the time of emitting, then (the system that contains) the pair is NOT in a superposition since the beginning.

The entangled variables (that the detector measures) are already physically defined by the detector’s potential behaviors. The system state is already a mixed state, not a superposition.

superposition

~ lack of the existence of measuring device to provide the physical definitions for the (difference between) microscopic events

— Me@2022-01-31 08:33:01 AM

— Me@2022-02-12 10:22:09 AM

With respect to that pair of entangled variables, the experiment setup is just a classical one, which directly follows Aristotle’s 3 laws of logic.

For any proposition \displaystyle{A}, either \displaystyle{A} is true or \displaystyle{\text{NOT}~A} is true, but not both.

There is nothing non-classical about the correlation between the (such as) spin values of the pair.

.

What is more difficult to understand is the non-classical part:

What if, instead of turning on a detector before the time of emitting, we turn it on after the pair is emitted but before either of them has reached its destination?

— Me@2022-02-11 12:47:14 AM

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2022.02.14 Monday (c) All rights reserved by ACHK

EPR paradox, 11.3

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Black hole information paradox, 2.2.3

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It shouldn’t be so surprising that unitarity survives completely while causality doesn’t. After all, the basic postulates of quantum mechanics, including unitarity, the probabilistic interpretation of the amplitudes, and the linearity of the operators representing observables, seem to be universally necessary to describe physics of any system that agrees with the basic insights of the quantum revolution.

On the other hand, geometry has been downgraded into an effective, approximate, emergent aspect of reality. The metric tensor is just one among many fields in our effective field theories including gravity.

— Black hole information puzzle

— Lubos Motl

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identical particles

~ some particles are identical, except having different positions

~ some particle trajectories are indistinguishable

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trajectory indistinguishability

~ particle identity is an approximate concept

~ causality is an approximation

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spacetime is defined by causality

~ so spacetime is also an approximation

— Me@2022-02-11 12:47:14 AM

— Me@2022-02-13 03:38:35 PM

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2022.02.13 Sunday (c) All rights reserved by ACHK