# Small big bang 4

Arthur Schopenhauer claimed that phenomena have no free will, but the will as noumenon is free.

— Wikipedia on Free will

Man can do what he wills but he cannot will what he wills.

On The Freedom Of The Will (1839)

— Arthur Schopenhauer

A will itself cannot be willed because it is the first cause of a causal chain. A first cause is a starting point. Anything can be willed would not be a first cause.

— Me@2012.11.29

# Easy 2

Easy” in Chinese is “容易”, literally meaning “able to change“.

— Me@2012-11-29 10:47:38 AM

# 電流電壓 2

（CPK：那樣，這一點的 voltage 數值是什麼？）

— Me@2012.11.30

# Godel 4.2

Godel’s Incompleteness Theorems are anti-self-reference:

For any formal system strong enough to include the system of arithmetic, to prove its consistency, you need a stronger system.

— Me@2012-04-02 9:35:17 AM

# Publish! 9.3

Life isn’t a support system for art. It’s the other way around.

“C.V.”, 101

On Writing

— Stephen King

2012.11.29 Thursday ACHK

# Monty Hall problem 1.5.2

 Tree showing the probability of every possible outcome if the player initially picks Door 1 — Wikipedia on Monty Hall problem

（安：但是，這個樹形圖，好像都是不太容易明白。可不可以再解釋一下？）

— Me@2012.11.28

# Superdeterminism 2.2

Paradox 9.3 | Bell’s theorem, 4.2

The meaning of the phrase “counterfactual definiteness” in quantum mechanics or Bell’s theorem is not the same as that in the superdeterminism theory. They are two different concepts.

In the superdeterminism theory, no non-local wave function collapse effect is needed, as all are pre-programmed, including the experimenters’ choices of measurement axes. Superdeterminism assumes that the world is classical and classically deterministic.

In such a situation, it is counterfactual definite in a sense that there is no quantum superposition. A system has a definite classical state even before any measurements.

However, it is not counterfactual definite in sense that there are no alternatives. It is not meaningful to ask, “What if the experimenter had chosen another measurement axis?”

Bell’s theorem assumes that the types of measurements performed at each detector can be chosen independently of each other and of the hidden variable being measured. In order for the argument for Bell’s inequality to follow, it is necessary to be able to speak meaningfully of what the result of the experiment would have been, had different choices been made. This assumption is called counterfactual definiteness.

But in a deterministic theory, the measurements the experimenters choose at each detector are predetermined by the laws of physics. It can therefore be argued that it is erroneous to speak of what would have happened had different measurements been chosen; no other measurement choices were physically possible.

— Wikipedia on Superdeterminism

Superdeterminism is cheating.

— Me@2012-11-24 11:21:01 AM

# Lightning

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Thunder is good, thunder is impressive; but it is lightning that does the work.

– Mark Twain, 1908

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2010.01.27 Wednesday ACHK

# Monty Hall problem 1.5.1

「蒙提霍爾問題」（Monty Hall problem）有一個比較平易近人的解答。

 This is a public domain image.
Player’s pick has a 1/3 chance
while the other two doors have 1/3 chance each, for a combined 2/3 chance.
— Wikipedia on Monty Hall problem

 This is a public domain image.
With the usual assumptions player’s pick remains a 1/3 chance,
while the other two doors have a combined 2/3 chance:
2/3 for the still unopened one and 0 for the one the host opened.
— Wikipedia on Monty Hall problem

「蒙提霍爾問題」假設了，在遊戲開始時，三扇門「門後有房車」的機會均等。所以，你選定了一道門後，你中獎的機會就是三分之一，而其他門中獎機會率的總和，有三分之二。那樣，在主持人打開另外的其中一道門後，如果你維持原本的選擇，你中獎的機會就仍然只有三分之一。主持人打開了一道沒有車的門，而又容許你改變選擇，就相當於給予你，一次過選擇其他全部門的機會。因此，如果你肯改變選擇，你中獎的機會率，就會由三分之一，躍升至三分二。

— Me@2012.11.26

# Quantum teleportation

The no-communication theorem thus says shared entanglement alone can not be used to transmit any information. Compare this with the no teleportation theorem, which states a classical information channel can not transmit quantum information. (By transmit, we mean transmission with full fidelity.) However, quantum teleportation schemes utilize both resources to achieve what is impossible for either alone.

— Wikipedia on No-communication theorem

2012.11.26 Monday ACHK

# Fixed stars

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* Writers may be classified as meteors, planets, and fixed stars. A meteor makes a striking effect for a moment. You look up and cry “There!” and it is gone forever. Planets and wandering stars last a much longer time. They often outshine the fixed stars and are confounded by them by the inexperienced; but this only because they are near. It is not long before they must yield their place; nay, the light they give is reflected only, and the sphere of their influence is confined to their orbit — their contemporaries. Their path is one of change and movement, and with the circuit of a few years their tale is told. Fixed stars are the only ones that are constant; their position in the firmament is secure; they shine with a light of their own; their effect today is the same as it was yesterday, because, having no parallax, their appearance does not alter with a difference in our standpoint. They belong not to one system, one nation only, but to the universe. And just because they are so very far away, it is usually many years before their light is visible to the inhabitants of this earth.

o Vol. 2 “The Art of Literature” as translated in Essays and Aphorisms (1970), as translated by R. J. Hollingdale

– Arthur Schopenhauer

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2010.06.06 Sunday ACHK

# Monty Hall problem 1.4.3

Frequency probability and Bayesian probability, 3.2.3

（安：「頻率機會率」和「貝葉斯機會率」的分別作於，「頻率學派」認為，機會率的數值是客觀的，反映著被觀察系統的物理性質；而「貝葉斯學派」則認為，機會率的數值是主觀的，反映著觀察者對一個物理系統的知識多寡。

「頻率機會率」和「貝葉斯機會率」衝突的來源，在於雙方也假設了，對於一個機會率問題，我們可以有把「觀察者」和「被觀察者」，百分百地截然分開。在這裡，「觀察者」即是「機會率使用者」；「被觀察者」即是「外在物理系統」。

「觀察者」加「被觀察者」作為一個整體，作為一個單一系統的話，「機會率」就是那個大系統的性質。

 This work is in the public domain in the United States, and those countries with a copyright term of life of the author plus 100 years or less.

（安：假設梵高（Van Gogh）的一幅名畫，給一位有錢人甲，用一億元買下來。然後我們問，究竟那幅名畫的「價值」，是那幅畫本身的性質，還是有錢人甲的性質？

— Me@2012.11.25

# Superdeterminism 2.1

Paradox 9.2 | Bell’s theorem, 4.1

Bell’s theorem states that if Bell’s inequality is violated by experimental results, then the original quantum mechanics is correct in a sense that no local hidden variable theory is possible to replace it. Nature is either non-local or non-counterfactual-definite (or both).

1. The principle of locality:

There are two possible meanings of “locality” here.

1.1 The principle is correct in a sense that no causal influence can be faster than light.

1.2 The principle is incorrect in a sense that distant particles can be entangled. Correlation without causation can be instantaneous.

Assume that a pair of particles are entangled. Measuring one particle will collapse the wave function, which governs both particles, instantaneously.

2. Counterfactual definiteness:

2.1 It is correct in a sense that an object has a definite quantum state.

2.2 It is incorrect in a sense that, more often than not, the definite quantum state is not corresponding to a definite classical state (aka eigenstate). Instead, that quantum state is a superposition of different eigenstates.

The meaning of the phrase “counterfactual definiteness” in quantum mechanics or Bell’s theorem is not the same as that in the superdeterminism theory. They are two different concepts.

— Me@2012-11-24 11:21:01 AM

# A Word to the Wise

It turns out there is, and the key to the mystery is the old adage “a word to the wise is sufficient.” Because this phrase is not only overused, but overused in an indirect way (by prepending the subject to some advice), most people who’ve heard it don’t know what it means. What it means is that if someone is wise, all you have to do is say one word to them, and they’ll understand immediately. You don’t have to explain in detail; they’ll chase down all the implications.

— A Word to the Resourceful

— January 2012

— Paul Graham

2012.11.24 Saturday ACHK

# Monty Hall problem 1.4.2

Frequency probability and Bayesian probability, 3.2.2

「頻率學派」和「貝葉斯學派」之中，究竟哪一個正確呢？又或者說，哪一個較為有用呢？

「機會率」既有客觀的成份，又有主觀的成份。留意，這裡「主觀」的意思，並不代表「不正確」。一方面，我們真的使用「機會率」，來描述外在事件；另一方面，「機會率」又真的會反映，一個人對一件外在事件的結果，無知程度的深淺。

「機會率」處理「未知」，但不一定處理「未來」，因為「未知」不一定代表「未來」。例如，剛才的例子中，骰子已擲，而我亦知道了結果，所以不是「未來」。但是，因為你還未看結果，所以相對你來說，那仍然是「未知」。你仍然需要使用「機會率」，來估計結果。大概而言，所有人也不知的，為之「未來」；精確而言，尚未發生的，才為之「未來」。

— Me@2012.11.23

# Superdeterminism

In the context of quantum mechanics, superdeterminism is a term that has been used to describe a hypothetical class of theories which evade Bell’s theorem by virtue of being completely deterministic. Bell’s theorem depends on the assumption of [non-] counterfactual definiteness, which technically does not apply to deterministic theories. It is conceivable, but arguably unlikely, that someone could exploit this loophole to construct a local hidden variable theory that reproduces the predictions of quantum mechanics.

… in a deterministic theory, the measurements the experimenters choose at each detector are predetermined by the laws of physics. It can therefore be argued that it is erroneous to speak of what would have happened had different measurements been chosen; no other measurement choices were physically possible. Since the chosen measurements can be determined in advance, the results at one detector can be affected by the type of measurement done at the other without any need for information to travel faster than the speed of light.

— Wikipedia on Superdeterminism

Even if there are no other physical possibilities for a measurement choice, there are other logical possibilities. The goal of quantum mechanics, or science in general, is to consider, for an identical system, what input results what output.

The problem of superdeterminism in quantum mechanics is not “claiming the observers’ action are deterministic”, but by claiming so, claiming also that there is no decoherence (wave function collapse).

When we say that the observer cannot be separated from the observed, we mean that we have to consider the whole (observed + observer), instead of shifting the system from the observed to the observer, and then ignoring the original observed itself.

— Me@2012-11-20 02:11:06 PM

# Prayer, 4

Praying is for slowing down your thinking, for most monsters are generated by your own mind.

— Me@2012.01.15

# Monty Hall problem 1.4.1

Frequency probability and Bayesian probability, 3.2.1

「機會率」這門學問，有兩個主要的學派：「頻率學派」（frequentist probability）和「貝葉斯學派」（Bayesian probability）。兩派對「機會率」的詮釋，有相反的意見。

「頻率學派」認為，機會率的數值是客觀的，反映著被觀察系統的物理性質。例如，你把某一粒骰子擲了六千次。如果每一個數字出現的次數，都大概是一千次的話，你就可以宣稱，那一粒骰子是正常的。對於該粒骰子，你擲到任何一面的機會率，都是六分之一。「頻率學派」認為，「擲到任何一面機會都是六分之一」這句本身，其實間接地描述了，該粒骰子的物理性質，例如「骰子有六面」和「質量均勻分佈，沒有偏袒」等。

「貝葉斯學派」則認為，機會率的數值是主觀的，反映著觀察者對一個物理系統的知識多寡。即使是同一個系統的同一件事件的同一個可能結果，不同觀察者可以運算到，截然不同的機會率，而他們彼此都沒有錯。例如，我擲了一粒公平骰子後，立刻檢查一下結果，但又不給你看。我發現我擲到「三」。然後，我要你估一估計，結果是什麼。相對於我來說，我擲到「三」的機會率是 100%，而其他數字的機會則是 0%，因為我已經知道結果。但是，你卻仍然不知道結果。所以，相對於你來說，我擲到「三」的機會率只是六分之一，而不是 100%。

「頻率學派」和「貝葉斯學派」之中，究竟哪一個正確呢？又或者說，哪一個較為有用呢？

— Me@2012.11.22

# Godel 4

Any formal system strong enough to include arithmetic unavoidably has self-references.

— Me@2012-04-02 9:32:06 AM