# Entropy at the Beginning of Time, 1.2

Logical arrow of time, 10.2.2

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If at the beginning, the universe had a high entropy, it was at a macrostate corresponding to many indistinguishable microstates.

That description is self-contradictory, because “two macroscopically-indistinguishable microstates” is meaningful only if they were once macroscopically distinguishable before.

That is not possible for the state(s) at the beginning of the universe, because at that moment, there was no “before”.

So it is meaningless to label the universe’s beginning macrostate as “a state corresponding to many indistinguishable microstates”.

Instead, we should label the universe’s beginning state as “a state corresponding to one single microstate”.

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For example, assume that the universe was at the macrostate $\displaystyle{A}$ at the beginning; and the $\displaystyle{A}$ is corresponding to two macroscopically-indistinguishable microstates $\displaystyle{a_1}$ and $\displaystyle{a_2}$.

Although microstates $\displaystyle{a_1}$ and $\displaystyle{a_2}$ are macroscopically-indistinguishable, we can still label them as “two” microstates, because they have 2 different histories — history paths that are macroscopically distinguishable.

However, for the beginning of the universe, there was no history. So it is meaningless to label the state as “a macrostate with two (or more) possible microstates”.

So we should label that state not only as one single macrostate but also as one single microstate.

In other words, that state’s entropy value should be defined to be zero.

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If in some special situation, it is better to label the universe’s beginning state as “a state with non-zero entropy”, that state will still have the smallest possible entropy of the universe throughout history.

So it is not possible for the universe to have “a high entropy” at the beginning.

— Me@2022-01-08 02:38 PM

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# Entropy at the Beginning of Time, 1.1

Logical arrow of time, 10.2.1

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Two distinguishable macrostates can both evolve into one indistinguishable macrostate.

— Me@2013-08-11 11:08 AM

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Note that, tautologically, any system can be at only one single macrostate at any particular time.

So the statement actually means that it is possible for two identical systems at different macrostates evolve into the same later macrostate.

— Me@2022-01-08 03:12 PM

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But the opposite is not possible. Two indistinguishable macrostates is actually, by definition, one macrostate. It cannot evolve into two distinguishable macrostates.

One single macrostate is logically impossible to be corresponding to two different possible later macrostates.

— Me@2022-01-08 01:29 PM

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If the beginning universe state had a high entropy, by definition, it was at a macroscopic state with many possible macroscopically-indistinguishable microstates.

However, if it is really the state of the universe at the beginning, it is, by definition, a single microstate, because “different microstates” is meaningful only if they were once distinguishable.

— Me@2013-08-11 01:42 PM

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a macrostate = a set of macroscopically-indistinguishable microstates

— Me@2022-01-09 07:43 AM

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The meaning of “entropy increases” is that state $\displaystyle{S_1}$ and state $\displaystyle{S_2}$ both evolve into state $\displaystyle{S_3}$.

But for the beginning of the universe, there were no multiple possible macrostates that the beginning state could be evolved from.

— Me@2013-08-11 01:44 PM

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# Eternal return, 2

A “perfect copy” is not a “copy”, because if a copy is perfect, it would be logically indistinguishable from the original.

In other words, we would not be able to determine which one is the “copy” and which one is the “original”, even in principle.

There would be no meaningful difference between the meanings of the labels “copy” and “original”.

— Me@2013-08-11 1:38 PM

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# 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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# Is logic empirical?

Each of the logics is analytic.

Which logic is the best for describing the world” is synthetic.

— Me@2012-04-14 11:32:36 AM

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# 機遇再生論 1.6

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（而這個意思，亦在「機遇再生論」的原文中，用作其理據。）

$P(A) = \frac{1}{N}$

$P(\text{not} A) = 1 - \frac{1}{N}$

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$P(A) = \frac{1}{N}$

$P(\text{not} A) = 1 - \frac{1}{N}$

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(問：那樣，為什麼要問多一次呢？）

「如果洗牌兩次，起碼一次洗到原本排列 A 的機會率是多少？」

$A_2$ = 兩次洗牌的結果，起碼一次洗到原本排列 A

$A_2$ 的互補事件為「不是 $A_2$」：

= 兩次洗牌的結果，不是起碼一次洗到原本排列 A

= 兩次洗牌的結果，都不是排列 A

$P(\text{not} A_2) = (1 - \frac{1}{N})^2$

$P(A_2)$
$= 1 - P(\text{not} A_2)$
$= 1 - (1 - \frac{1}{N})^2$

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$P(A_m)= 1 - (1 - \frac{1}{N})^m$

$P(A_m)$
$= 1 - (1 - \frac{1}{N})^m$
$= 1 - (1 - \frac{1}{52!})^{10,000,000}$

$1.239799930857148592 \times 10^{-61}$

— Me@2018-01-25 12:38:39 PM

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# 機遇再生論 1.5

（請參閱本網誌，有關「重言句」、「經驗句」和「印證原則」的文章。）

「同情地理解」的意思是，有些理論，雖然在第一層次的分析之後，有明顯的漏洞，但是，我們可以試試，代入作者發表該理論時的，心理狀態和時空情境；研究作者發表該理論的，緣起和動機；從而看看，該理論不行的原因，會不會只是因為，作者的語文或思考不夠清晰，表達不佳而已？

（而這個意思，亦在「機遇再生論」的原文中，用作其理據。）

$P(A) = \frac{1}{N}$

$P($not $A) = 1 - \frac{1}{N}$

— Me@2017-12-18 02:51:11 PM

# 注定外傳 2.6

Can it be Otherwise? 2.6 | The Beginning of Time, 7.3

『所有』，就是『場所之有』。

— Me@2016-05-18 11:40:31 AM

# 注定外傳 2.5

Can it be Otherwise? 2.5 | The Beginning of Time, 7.2

4. 即使可以追溯到「時間的起點」（第一因），所謂的「可以」，只是宏觀而言，決不會細節到可以推斷到，你有沒有自由，明天七時起牀。

（問：如果因果環環緊扣，即使細節不完全知道，至少理論上，我們可以知道，如果「第一因」本身有自由，那其他個別事件，就有可能有（來自「第一因」的）自由；如果連「第一因」也沒有自由，那其他個別事件，都一律沒有自由。

「第一因有自由。」

「第一因」根據定義，是沒有原因的。亦即是話，「時間的起點」，再沒有「之前」。而「有自由」，就即是「有其他可能性」。所以，「第一因有自由」的意思是，

「第一因還有其他的可能性。」

（問：如果有「造物主」，祂不就是那個誰，可以從宇宙之初的不同可能性中，選擇一個去實現嗎？）

「因果是否真的『環環緊扣』，有沒有可能，有『同因不同果』的情況？」

— Me@2016-03-15 08:43:58 AM

# 注定外傳 2.3

Can it be Otherwise? 2.3

— Me@2016-01-06 03:17:54 PM

# 注定外傳 2.2

Can it be Otherwise? 2.2

「成績注定」和「主動溫習」，根本沒有矛盾。

— Me@2015-12-29 03:12:39 PM

# 注定外傳 2.1.2

Can it be Otherwise? 2.1.2 | The problem of induction 2.2

1. 當你的「相似事件」和「原本事件」的結果相同時，你只可以知道「原本事件」，可能是注定；你並不可以肯定「原本事件」，一定是注定，因為，你並不能保證，下一件「相似事件」的結果，會不會仍然和「原本事件」相同。

2. 當你的「相似事件」和「原本事件」的結果不同時，你亦不可以肯定「原本事件」，一定是偶然，因為，結果不同，可能只是由於「相似事件」和「原本事件」，不夠相似而已。

— Me@2015-11-17 02:02:03 PM

# 注定外傳 2.1.1

Can it be Otherwise? 2.1.1 | The problem of induction 2.1

（層次一的事件描述：）

（層次一的反證：）

（層次二 —— 準確一點的事件描述：）

（層次二 —— 詳細一點的反證：）

（層次三：）

（層次四：）

— Me@2015-11-17 02:02:03 PM

# 注定外傳 1.11

Can it be Otherwise? 1.11

— Me@2015-10-29 03:10:19 PM

Q: Can it be otherwise?

A: What is “it”?

— Me@2015-10-29 03:10:14 PM

# 注定外傳 1.10

Can it be Otherwise? 1.10

（問：如果只是「類似」，當然可以有不同結果。你應該直接問：

』）

（問：不是呀。在量子力學中，即使有兩組百分百一樣的物理系統，即使它們獲得完全相同的輸入，都可能有不同的輸出。）

「相同」的意思，並不是指「沒有可能找到任何分別」。

「相同」的意思是「分別小到不易察覺」。

」，

— Me@2015-10-29 10:12:16 PM

# 注定外傳 1.9

Can it be Otherwise? 1.9

（這裡的「東西」，是指宏觀的物理系統。至於兩粒微觀粒子，則有可能「全同」。但那是另一個話題，容後再談。）

（問：那如果連位置都相同呢？）

— Me@2015-10-07 02:52:21 PM

# 注定外傳 1.8

Can it be Otherwise? 1.8

（問：那如果是數數目（使用整體）的情況呢？

（問：那為什麼不可以說「絕對相同」？）

「絕對」，應該用作「相對」的相反。而「近似」的相反，則應該用「確切」。

（這裡的「東西」，是指宏觀的物理系統。至於兩粒微觀粒子，則有可能「全同」。但那是另一個話題，不宜在這裡詳述。）

— Me@2015-10-04 07:32:32 AM

# 注定外傳 1.7

Can it be Otherwise? 1.7

3.1415926

3.1415927

（問：如果 3.1 和 3.1 呢？它們不是完全（絕對）相同嗎？）

（問：怎樣為之「有實際因素考慮，真的要應用」？）

3.1 厘米 和

3.1 厘米。

（問：那如果是數數目（使用整體）的情況呢？

— Me@2015-09-30 04:26:45 AM

# Can it be Otherwise?

–　Me@2015-09-22 07:41:07 AM

# Quantum Indeterminacy

Quantum indeterminacy is the apparent necessary incompleteness in the description of a physical system, that has become one of the characteristics of the standard description of quantum physics.

Indeterminacy in measurement was not an innovation of quantum mechanics, since it had been established early on by experimentalists that errors in measurement may lead to indeterminate outcomes. However, by the later half of the eighteenth century, measurement errors were well understood and it was known that they could either be reduced by better equipment or accounted for by statistical error models. In quantum mechanics, however, indeterminacy is of a much more fundamental nature, having nothing to do with errors or disturbance.

— Wikipedia on Quantum indeterminacy

Quantum indeterminacy is the inability to predict the behaviour of the system with 100% accuracy, even in principle.

If everything is connected , quantum indeterminacy is due to the logical fact that, by definition, a “part” cannot contain (all the information of) the “whole”.

An observer (A) cannot separate itself from the system (B) that it wants to observe, because an observation is an interaction between the observer and the observed .

In order to get a perfect prediction of a measurement result, observer (A) must have all the information of the present state of the whole system (A+B). However, there are two logical difficulties.

First, observer A cannot have all the information about (A+B).

Second, observer A cannot observe itself to get (all of) its present state information, since an observation is an interaction between two entities. Logically, it is impossible for something to interact with itself directly. Just as logically, it is impossible for your right hand to hold your right hand itself.

So the information observer A can get (to the greatest extent) is all the information about B, which is only part of the system (A+B) it (A) needs to know in order to get a prefect prediction for the evolution of the system B.

— Me@2015-09-14 08:12:32 PM