# 原因非理由

— Me@2016-03-31 08:35:43 PM

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# Random variable

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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# 權力來源 1.4

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~ environmental default

— Me@2021-11-16 07:59:12 PM

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~ 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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~ 勢力

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「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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# Copyleft 7

What stands in the way becomes the way.

— Marcus Aurelius

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capitalize on

~ 用之以謀利

~ 利用

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copyleft

~ 敵為己用

~ 幽默利用

~ 反利用

~ 草船借箭

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— Me@2023-03-01 01:22:15 PM

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# Why does the universe exist? 7.2

“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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# 天助自助者，自助人恆助之

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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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— Me@2022-11-05 12:54:58 PM

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# Presentation 基本原理 1.2.2.5

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— Me@2010.09.05

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— Me@2010.09.05

— Me@2022-10-25 02:58:36 PM

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# 開心 vs 關心

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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# Inception 18

~ 潛移默化

— Me@2016-04-02 08:40:30 PM

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# Visualize

visualize ~ feel all at once

— Me@2016-09-28 08:20:18 PM

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visual ~ same-time representation ~ spatial representation

— Me@2016-06-30 07:38:28 AM

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# 難得有情人

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— Me@2022-02-08 11:50:35 PM

「你是要找『條件最適合你』的人，如果你剛巧又，最適合她的話。」

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Today I found my soulmate; she didn’t.

「你是要找『與感情最深』之人，如果你剛巧也是，『與她感情最深』之人。」

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「情人」的重點在於情。

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— Me@2022.05.11 07:07:43 PM

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Someone who causes people to do that which they ought to do but which they would not do in his absence.

— John T. Reed

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2022.03.21 Monday ACHK

# The 4 bugs of quantum mechanics popular, 1.3

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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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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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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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.

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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?`

— Me@2022-02-11 12:47:14 AM

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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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