Monthly Archives: October 2012

原因 2.3

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這段改編自 2010 年 4 月 3 日的對話。

（安：這個問題有趣的地方在於，科學家可以透過收集不斷收集，不同的「個別事件」，歸納到一些「科學通則」。換句話說，科學家可以連繫起「現象」和「自然規律」。由「現象」走到「規律」，叫做「科學法度」，即是科學研究之方法；由「規律」走到「現象」，叫做「科學解釋」和「科學預測」，即是科學研究成果之應用。）

無錯。如何由「現象」走到「規律」，是整個話題的核心所在。剛才沒有提及這一點，其實是犯了「偷換話題」的毛病。

根據我的講法，「原因」無論是在廣義、中義，還是狹義，都有「先決條件」的意思。剛才你的案例中，可以把「原因」講到不是「先決條件」，正正是因為不自覺地，偷換了話題：

「

例如，禮堂甲火警的原因是，有一位講者亂拋煙蒂（煙頭）。而那個還未熄滅的煙蒂，剛跌落一堆舊報紙之中。

在這個案例中，「亂拋煙蒂」既不是「禮堂甲火警」的「先決條件」，因為還有其他情況，例如電線短路，可以導致「禮堂甲火警」；亦不是「充份條件」，因為如果沒有那堆舊報紙的「配合」，「亂拋煙蒂」就不會引起火災。

」

原本想討論的是，「『亂拋煙蒂』是否『今次禮堂甲火警』的原因？」但是，話題突然間轉換成，「『亂拋煙蒂』是否『禮堂甲火警』的原因？」

— Me@2012.10.16

2012.10.16 Tuesday (c) All rights reserved by ACHK

Paradox 4.3

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According to the definition/usage of the word “true”:

A = “A” is true

“A” is true = A

e.g. The sentence “Snow is white” is true = Snow is white

Not-A = “A” is false

“A” is false = Not-A

e.g. The sentence “Snow is white” is false = Snow is not white

Paradox is due to the mixing of para-level (meta-level) and original level. As long as we do not allow mixing levels, there are no paradoxes. Every sentence should only be allowed to describe sentences which have lower levels. So the sentence “this sentence is false” should not be allowed.

this sentence is false = “this sentence is false” is (in ordinary level) true

this sentence is false = “this sentence is false” is (in meta level) false

In detail, according to the definition of the word “true”:

this sentence is false = “this sentence is false” is true

But according to the meaning of the sentence itself:

this sentence is false = “this sentence is false” is false

So there is a contradiction. 

— Me@2012.04.01

— Me@2012.10.05

— Me@2012.10.15

2012.10.15 Monday (c) All rights reserved by ACHK

原因 2.2

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這段改編自 2010 年 4 月 3 日的對話。

我覺得我對「原因」意思的講法，比李生的講法好一點，假設你沒有錯誤轉述他的意思。他講法的問題在於「任大任小」—— 範圍既不是小到，講單一特定事件（今次禮堂火警），亦不是大到，講一般事件（有關火災的自然規律、科學通則）。

如果小到講單一特定事件，「亂拋煙蒂」是「今次禮堂甲火警」的「先決條件」。如果大到講一般事件，「亂拋煙蒂」不是「火警」的「先決條件」。如果範圍在兩者之間，但又沒有講明在兩者之間的哪裡，那「『亂拋煙蒂』是不是『先決條件』？」就沒有所謂「答案」。如果範圍在兩者之間，而你又已經釐清問題的話，答案就會顯而易見：

「亂拋煙蒂」是「今次禮堂甲火警」的「先決條件」。

「亂拋煙蒂」不是「禮堂甲火警」的「先決條件」。

「亂拋煙蒂」不是「火警」的「先決條件」。

— Me@2012.10.14

2012.10.15 Monday (c) All rights reserved by ACHK

Curry’s paradox 1.2

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Paradox 4.2

The resolution of Curry’s paradox is a contentious issue because resolutions (apart from trivial ones such as disallowing X directly) are difficult and not intuitive. Logicians are undecided whether such sentences are somehow impermissible (and if so, how to banish them), or meaningless, or whether they are correct and reveal problems with the concept of truth itself (and if so, whether we should reject the concept of truth, or change it), or whether they can be rendered benign by a suitable account of their meanings.

— Wikipedia on Curry’s paradox

Regarding Curry’s paradox is an unresolved important question is silly.

Paradox is due to the mixing of para-level (meta-level) and original level. As long as we do not allow mixing levels, there are no paradoxes. Every sentence should only be allowed to describe sentences which have lower levels.

— Me@2012-10-13 02:41:50 PM

2012.10.14 Sunday (c) All rights reserved by ACHK

Mirror selves, 2

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說到底，愛情就是一個人的自我價值，在別人身上的反映。

– 愛默生

.

After all, the desire for love is the desire for a lifelong intellectual partner.

— Me@2012-10-11 12:29:17 AM

.

.

2012.10.14 Sunday (c) All rights reserved by ACHK

原因 2.1

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這段改編自 2010 年 4 月 3 日的對話。

（安：以前我們討論過，「原因」這個詞，有三種可能意思。廣義是指「先決條件之一」。狹義是指「最主要的先決條件」。然後，還有一個不廣不狹，你戲稱為「中義」的用法，是指「充份條件」，即是「所有先決條件」。

最近，我重新再聽李生的《心通識六講》。當中，李生說「原因」在日常生活中，還可能有其他用法 —— 既不是指「先決條件」，亦不是指「充份條件」。

例如，禮堂甲火警的原因是，有一位講者亂拋煙蒂（煙頭）。而那個還未熄滅的煙蒂，剛跌落一堆舊報紙之中。

在這個案例中，「亂拋煙蒂」既不是「禮堂甲火警」的「先決條件」，因為還有其他情況，例如電線短路，可以導致「禮堂甲火警」；亦不是「充份條件」，因為如果沒有那堆舊報紙的「配合」，「亂拋煙蒂」就不會引起火災。

你的講法和李生的講法的分歧在於，你是講某一件特定事件，而李生講的，是一般事件。）

無錯。我所講的，是個別事件；而李生講的，非個別事件。「亂拋煙蒂」是「今次禮堂甲火警」的「先決條件」，但不是「禮堂甲火警」的「先決條件」。

如果警方要追究，他們會調查個別事件，即是「今次禮堂甲火警」的「先決條件」是什麼。換句話說，那個亂拋煙蒂的講者，將會被起訴。但是，如果消防要建議學校，如何防範再發生「禮堂甲火警」，研究這一次個別事件的先決條件，並不足夠。消防和學校，還要「搜羅」所有會引起「禮堂甲火警」的因素，逐一「刪除」。

— Me@2012.10.14

2012.10.14 Sunday (c) All rights reserved by ACHK

Curry’s paradox 1.1

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Paradox 4.1

When you equal the meta sentence level and the sentence level, it is nothing special about the paradox, for it is just a contradiction between the sentence and the meta-sentence.

In Curry’s paradox, “X -> Y” is what you want to prove. So you try “if X”, to see if you can get Y.

But by letting “X = X -> Y” and if X, and X = X -> Y, then Y. You are actually doing circular proof. 

Effectively you use X to prove X, which is a useless proof.

Paradox is due to the mixing of para-level (meta-level) and original level. As long as we do not allow mixing levels, there are no paradoxes. Every sentence should only be allowed to describe sentences which have lower levels.

— Me@2012.04.01

— Me@2012.10.05

— Me@2012.10.13

2012.10.13 Saturday (c) All rights reserved by ACHK

Scalable

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next ~ scalable

— Me@2011.12.02

Anything not scalable cannot make sure its own long-term survival.

— Me@2012-10-13 11:26:12 AM

Information survives by people copying it.

– John Baez, mathematical physicist

2012.10.13 Saturday (c) All rights reserved by ACHK

Independent vs Mutually Exclusive

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這段改編自 2010 年 6 月 8 日的對話。

大部分 probability（機會率）的初學者，都會混淆「independent events」（獨立事件）和「mutually exclusive events」（互斥事件）。只要記住以下兩個重點，就不會再混淆兩者。

第一個重點是，「兩件事」和「一件事」之別。「Independent」通常是指，兩件事件互不相干。「Mutually exclusive」通常是指，同一件事件的兩個可能結果，不會同時發生。例如，骰子甲和骰子乙是 independent 的話，即是甲乙的結果不會影響對方。而骰子甲不會在同一次，同時「擲到 2」和「擲到 3」。所以，「甲 2」和「甲 3」是 mutually exclusive 事件。

第二個重點是，「沒有關係」和「有關係」之別。「Independent」是指，兩個結果互不相干。「Mutually exclusive」是指，兩個結果十分相干；它們是敵人關係。

— Me@2012.10.13

2012.10.13 Saturday (c) All rights reserved by ACHK

Existence, 2

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Existence is not a property of an object. It is a property of properties.

For example, when we say “X does not exist”, we do not mean that “there is an X and X has a property of non-existence.” Instead, existence is a property of the collection of other objects.

Existence is a property of the system that X is in. 

X exists

= the system has the component X

= the system has the property of “having X”

X doe not exist

= no systems have the component X

= no systems have the property of “having X”

— Me@2012.10.11

2012.10.12 Friday (c) All rights reserved by ACHK

Memory 5.3

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這段改編自 2010 年 4 月 3 日的對話。

大明比小明聰明。小明在很多時候，處事能力沒有大明那麼高。所以，大部分情況下，大明的考試分數，都會比小明好。小明發覺沒有辦法，單憑智力去戰勝大明，長期心有不甘。於是，有一次，小明想暗算大明。但是，由於大明比小明足智多謀，他在事前就已經可以，化解了小明的詭計。

這篇文章，內廢而外不廢。

這篇文章，其實就好像「變形金剛」中的機械人。首先，原本只有一隻。然後，我把它複製成多四隻。接著，再把那五隻機械人，變成五種不同的形態。那樣，就可以把它們合體，變成一隻「大機械人」。

— Me@2012.10.12

2012.10.12 Friday (c) All rights reserved by ACHK

Muscles work

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Why does holding something up cost energy while no work is being done?

This is about how your muscles work — the’re an ensemble of small elements that, triggered by a signal from nerves, use chemical energy to go from less energetical long state to more energetical short one. Yet, this obviously is not permanent and there is spontaneous come back, that must be compensated by another trigger. This way there are numerous streches and releases that in sum gives small oscillations that create macroscopic work on the weight.

— This work is licensed under a Creative Commons Attribution-ShareAlike 3.0 Unported License.

— Physics Stack Exchange

— answered Dec 16 ’10 at 11:52

— mbq

2012.10.12 Friday ACHK

Memory 5.2

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這段改編自 2010 年 4 月 3 日的對話。

你會發現，我網誌的部分文章，其實只是在不斷重複，同一句說話。

通常，我每篇文章只有一個重點。但是，我會利用不同的句子，去不斷重複那一個重點。你閱讀時是不易察覺的，因為那些句子，雖然是在講同一個重點，但拼砌在一起時，會貌似一篇有上文下理的故事。例如：

大明比小明聰明。小明在很多時候，處事能力沒有大明那麼高。所以，大部分情況下，大明的考試分數，都會比小明好。小明發覺沒有辦法，單憑智力去戰勝大明，長期心有不甘。於是，有一次，小明想暗算大明。但是，由於大明比小明足智多謀，他在事前就已經可以，化解了小明的詭計。

這篇文章，內廢而外不廢。

— Me@2012.10.11

2012.10.11 Thursday (c) All rights reserved by ACHK

Mass–energy equivalence, 2

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The Question (Submitted July 24, 1997)

Why is it impossible, at this point in time, to convert energy into matter?

The Answer

It happens all the time. Particle accelerators convert energy into subatomic particles, for example by colliding electrons and positrons. Some of the kinetic energy in the collision goes into creating new particles.

It’s not possible, however, to collect these newly created particles and assemble them into atoms, molecules and bigger (less microscopic) structures that we associate with ‘matter’ in our daily life. This is partly because in a technical sense, you cannot just create matter out of energy: there are various ‘conservation laws’ of electric charges, the number of leptons (electron-like particles) etc., which means that you can only create matter / anti-matter pairs out of energy. Anti-matter, however, has the unfortunate tendency to combine with matter and turn itself back into energy.

…

— Koji Mukai, with David Palmer, Andy Ptak and Paul Butterworth

— for the Ask an Astrophysicist

— The National Aeronautics and Space Administration (NASA)

2012.10.10 Wednesday ACHK