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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2022.01.09 Sunday (c) All rights reserved by ACHK

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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2022.01.09 Sunday (c) All rights reserved by ACHK

魚目混珠 1.2

Pure evil does no harm, because if someone is purely evil, everyone will know that and avoid him.

It is the evilness of a good man that creates big harm.

The evilness of great man creates the biggest harm.

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An organization cannot be purely evil.

Anything purely evil cannot be big, because being big requires consistency, which requires good.

— Me@2011.10.11

— Me@2022-01-08

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2022.01.08 Saturday (c) All rights reserved by ACHK

Book Underlining Principle

間書原理 0

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When you are reading, you would underline key words. At one extreme, you underline nothing. So you wouldn’t know which parts are important. At the opposite extreme, you underline everything. Then you also wouldn’t know which parts are important. So the effect of underlining nothing is exactly the same as underlining everything.

This is an example of the principle that

The extreme of Yin is Yang

The extreme of Yang is Yin

陽之極為陰 陰之極為陽

That is why I call the principle the Book Underlining Principle.

The source of this principle is that when you push something to one extreme at the object level, that action may also push it to the opposite extreme at the meta level.

For example, when you underlining all the words, at the object level, it means that everything is important. However, at the meta level, “being important” must be relative to something else. You need to distinguish the important words from the unimportant ones. When you underlining all the words, there is no such distinction. So “being important” has become meaningless.

— Me@2021-12-13 11:08 AM

— Me@2021-12-26 03:39 PM

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2021.12.26 Sunday (c) All rights reserved by ACHK

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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2021.12.21 Tuesday (c) All rights reserved by ACHK

Alfred Tarski 4

Godel 20

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[guess]

A system can be both complete and consistent because in that system, a metatheorem cannot be translated into a theorem, so a paradox cannot be made.

[guess]

— Me@2017-04-10 10:40:38 AM

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2021.04.27 Tuesday (c) All rights reserved by ACHK

大腦物理性損毀不是比喻, 2

權力來源 2.1

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大多數人相信沒用,苟且偷生,什麼都不做,少數人去做,就真的沒用,而且還要被大多數人背叛出賣。大多數人相信有用,去做一點點,就真的有用。所以有用沒用不是獨立於人的行為的客觀事實,而純粹是人選擇的結果,這是典型的博弈問題。您國命運就是您國人選擇的結果,也就是所謂報應,不能怪任何別人[。]

— 李穎

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2020.08.04 Tuesday ACHK

Omnipotence 4.2

When responding to the question “can X create a stone that it cannot lift”, another flawed argument is

X can create the stone that it cannot lift but it chooses not to create it. So there is no stone it cannot lift yet. So X has not failed the omnipotence test.

This argument is wrong.

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When we ask “can X choose to create a stone that it cannot lift”, we are discussing whether X has an ability. When we discuss ability, it is always about a potential, a possibility.

Y is able to do action B

always means that

“Y does B” is possible,

which is equivalent to

“Y does B” is not contradictory to any logical laws nor physical laws.

“Whether Y has already done B or will do B” is not the point.

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If we allow such “Y can do B but it chooses not to” argument, then anyone is omnipotent. For example,

Can you fly?

I can fly but I choose not to. So even though you have never seen me flying and will never see me flying, it is not because I cannot fly; it is just because I choose not to.

Can you choose to fly?

I can choose to fly but I choose not to choose to fly.

This type of arguments make the word “can“ meaningless.

— Me@2020-03-30 06:52:58 AM

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2020.04.19 Sunday (c) All rights reserved by ACHK

太極滅世戰

機遇創生論 1.5

這段改編自 2010 年 4 月 18 日的對話。

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這個大統一理論的成員,包括(但不止於):

精簡圖:

種子論
反白論
間書原理
完備知識論

自由決定論

它們可以大統一的成因,在於它們除了各個自成一國外,還可以合體理解和應用。

下一個定律,就是「間書原理」。

「間書原理」的意思,其實是「陽之極為陰;陰之極為陽」。但那不易理解,所以,我在十多年前,舉了「間書」的例子:

我們平日看書時會間書:用紅筆間低重要的句子。

間書的一個極端是一句也不間。那我們就不知哪些是重要句子。

間書的另一個極端是句句間。那我們也不知哪些是重要句子。

— Me@2003-2004

其他例子有:

順其自然:在生活中百分百地「順其自然」,是一件十分不自然的事。

不要執著:要求自己在任何情況下也「不要執著」,本身是一個執著。

— 改編自李天命先生

知道這個原理後,你在生活處世,凡事就自然不會走得太盡,因為你知道,企圖走得太盡的後果是,輕則過猶不及,重則物極必反。

間書原理 水清則無魚

另外,運氣太好時,你會格外小心,因為,好事可以引發壞事,而大好事可以引發大壞事。運氣太差時,你亦不要過份擔心,因為,只要保命,運氣比「太差」更差的話,隨事引發大好事。

我一直以為,尋尋覓覓,兩把年紀,仍然未找到另一半,不幸也。但是,在 2019 滅世戰開始後,我發覺仍然單身,是極大的福份。

或許,到 2021 時,地球和我都仍然存在的話,宇宙會把我一切的夢想,化身成人,和我一同去創造,無限個嶄新的世界。

好事可以變好事

壞事可以變壞事

好事可以變壞事

壞事可以變好事

不要奢望,你可以控制到事情,向這四個方向中的哪一個去發展。你只可以引導,你只可以鼓勵,你不可以控制。

這正正呼應我剛剛講的「種子論」。你可以控制起點,卻不可以控制結果。

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當你對「間中原理」深刻心領神會後,你不會輕易羨慕別人的「運氣」或者「天份」,因為通常,凡事有代價。看到別人好時,你反而會問:「他付出了什麼代價,作出了什麼犧牲?」

當你對「間中原理」深刻心領神會後,有時,你更可以主動使用。

例如,以前的眾多考試中,有時,有溫習的那一次,成績反而比沒有溫習的那一次低。

其實,原因並不是「有沒有溫習」本身,而是你「是不是太過刻意」,去奪取成績。

不如,你試試積極溫習,然後,不理成績地,盡情發揮。或許,你有意想不到的收穫。

(問:「不理成績」而又要「盡情發揮」?自相矛盾也?)

你只能提升獲得佳績的機會率,所以,要試前積極溫習,試試盡情發揮;但是,你卻不能直接控制,將要奪得什麼成績,所以,要「不理成績」。

又例如,你下次失眠時,你試試躺下,然後張開雙眼,嘗試迫自己清醒。或者,不知不覺間,你會睡著了。

再例如,如果你由於怕做得不好,而遲遲拖延著一些必須事務的話,你不妨反轉心態,試試在你的能力範圍內,把該事做到最差。或許那樣,你不會再拖延,反而會極早基本完成了該事,剩下了時間,給你改善那「草稿」。

間書原理 置之於死地而後生

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主動版的「間中原理」,其實就是「種子論」。

把手緊握 什麼都沒有
把手放開 你得到一切

主動版的「間中原理」,可以戲稱為「耍太極」。

1171e-yin_and_yang

Wikipedia
public domain image
陽之極為陰 陰之極為陽

— Me@2020-04-13 06:58:18 PM

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2020.04.16 Thursday (c) All rights reserved by ACHK

Omnipotence 4.1

Please read these 2 posts first:

For all, 3 | Omnipotence

For all, 3.2 | Omnipotence 2

You can find them by searching “omnipotence” using this blog’s search box.

— Me@2020-04-08 03:17:34 PM

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If X is omnipotent, X can create a stone that it cannot lift. Then X is not omnipotent, because there is a stone it cannot lift. So omnipotence is a self-contradictory concept.

What if we define omnipotence not as “being able to do anything” but as “being able to do anything except logical self-contradictory ones“?

In order words, omnipotence means that being able to do anything logically possible. Omnipotence does not mean that being able to do also logically impossible things.

This re-definition is not useful, because the original meaning of “being omnipotent” already is “being able to do anything except logical self-contradictory ones“.

There is no re-definition needed. You can only say that the re-definition clarifies the original meaning of “being omnipotent”. However, this clarification cannot eliminate the self-contradictory nature of the meaning of “omnipotence” itself. For example, the following argument is wrong.

If X is omnipotent, “X can create a stone that it cannot lift” is self-contradictory because it is contradictory to “X is omnipotent”.

Since “X can create a stone that it cannot lift” is logically impossible, it should not be a requirement of being omnipotent.

This argument is wrong because:

1. “X can create a stone that it cannot lift” is not SELF-contradictory.

2. “X can create a stone that it cannot lift” is not logically impossible, because, for example, even a human being can create an object that he cannot lift. For example, human beings can create a car that no single person can lift.

Then someone might keep arguing that

But if X is omnipotent, “X can create a stone that it cannot lift” means that “X is omnipotent and X can create a stone it cannot lift”, which is logically impossible. So “X cannot create a stone that it cannot lift” does not make X non-omnipotent.

In other words, “whether X can create a stone that it cannot lift” should not be the requirement of the omnipotence test.

The argument is wrong, because what we are questioning is

Can someone X be omnipotent?

or

Is omnipotence logically possible?

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Remember:

“Being logically possible” means “not self-contradictory”.

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If “X is omnipotent” is true,

then “X can create a stone that it cannot lift” is true.

Then “there is a stone that X cannot lift” is true.

Then “X is not omnipotent” is true.

But “X is not omnipotent” is contradictory to the assumption “X is omnipotent“.

So “X is omnipotent” is self-contradictory.

So the question “whether an entity X can be omnipotent and create a stone that it cannot lift” is illegitimate because “an entity X is omnipotent” is logically impossible in the first place. It should not be placed within a question.

Note that our omnipotent test is

“whether an entity X can create a stone that it cannot lift”,

NOT “whether an entity X can be omnipotent and create a stone that it cannot lift”,

NOR “whether an omnipotent entity X can create a stone that it cannot lift”.

— Me@2020-03-30 06:52:58 AM

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2020.04.10 Friday (c) All rights reserved by ACHK

Two dimensional time 5.2.3

The first time direction is uncontrollable; the second is controlled by making choices, traveling through different realities. Future is a set of parallel universes.

— Me@2017-12-15 10:59:49 AM

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The first time direction, which is along the timeline, is uncontrollable, because one can only travel from the past to the future, not the opposite.

The second direction, which is across different timelines, is controlled by making choices, forming different realities.

— Me@2019-12-21 11:03:23 PM

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2019.12.22 Sunday (c) All rights reserved by ACHK

Two dimensional time 5.2.2

time direction ~ direction of change

multiple time directions ~ multiple directions of change

— Me@2019-12-22 04:38:47 PM

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the first dimension of time ~ direction of change

the second dimension of time ~ direction of change of changes

— Me@2019-12-22 04:46:47 PM

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2019.12.22 Sunday (c) All rights reserved by ACHK

Multiple dimensions of time

Two dimensional time 5.2 | 二次元時間 5.2

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What would be the implications of multiple dimensions of time?

That means the (past) history itself can change, as commonly seen in time travel stories.

But wouldn’t that be the case with one dimension also?

In reality, there is only one dimension of time, meaning that the state of a system keeps changing, forming the timeline. But the timeline itself cannot be changed once formed. In other words, (past) history cannot be changed.

— Me@2019-08-11 04:07:48 PM

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2019.08.11 Sunday (c) All rights reserved by ACHK

Alfred Tarski, 3

The undefinability theorem shows that this encoding cannot be done for semantic concepts such as truth. It shows that no sufficiently rich interpreted language can represent its own semantics. A corollary is that any metalanguage capable of expressing the semantics of some object language must have expressive power exceeding that of the object language. The metalanguage includes primitive notions, axioms, and rules absent from the object language, so that there are theorems provable in the metalanguage not provable in the object language.

— Wikipedia on Tarski’s undefinability theorem

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Tarski’s 1969 “Truth and proof” considered both Gödel’s incompleteness theorems and Tarski’s undefinability theorem, and mulled over their consequences for the axiomatic method in mathematics.

— Wikipedia on Alfred Tarski

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2019.07.20 Saturday 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

The problem of induction 3.3

“Everything has no patterns” (or “there are no laws”) creates a paradox.

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If “there are 100% no first order laws”, then it is itself a second order law (the law of no first-order laws), allowing you to use probability theory.

In this sense, probability theory is a second order law: the law of “there are 100% no first order laws”.

In this sense, probability theory is not for a single event, but statistical, for a meta-event: a collection of events.

Using meta-event patterns to predict the next single event, that is induction.

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Induction is a kind of risk minimization.

— Me@2012-11-05 12:23:24 PM

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2018.12.28 Friday (c) All rights reserved by ACHK