# 大地之韻律 2

Maths ~ Physics

Maths is the language; physics is the content.

— Me@2009.01.16

— Me@2008.10.20

# 測不準原理 1.6

 \sqrt{\frac{1}{3}} | A \rangle + \sqrt{\frac{2}{3}} | B \rangle

 \frac{400000(1J) + 800000(3J)}{1200000}

= 2.333J

 \sqrt{\frac{400000(1-2.333)^2 + 800000(3-2.333)^2}{1200000}}

= 0.9428J

 \sqrt{\frac{1}{3}} | A \rangle + \sqrt{\frac{2}{3}} | B \rangle

 \sqrt{\frac{1}{3}} | A \rangle + \sqrt{\frac{2}{3}} | B \rangle

— Me@2014.01.14

# First versus Second Order Logic

Conclusion

So, which logic is superior? It depends to some extent on what we need it for. Anything provable in first order logic can be proved in second order logic, so if we have a choice of proofs, picking the first order one is the better option. First order logic has more pleasing internal properties, such as the completeness theorem, and one can preserve this in second order via Henkin semantics without losing the ability to formally express certain properties. Finally, one needs to make use of set theory and semantics to define full second order logic, while first order logic (and Henkin semantics) get away with pure syntax.

On the other hand, first order logic is completely incapable of controlling its infinite models, as they multiply, uncountable and generally incomprehensible. If rather that looking at the logic internally, we have a particular model in mind, we have to use second order logic for that. If we’d prefer not to use infinitely many axioms to express a simple idea, second-order logic is for us. And if we really want to properly express ideas like “every set has a least element”, “every analytic function is uniquely defined by its power series” – and not just express them, but have them mean what we want them to mean – then full second order logic is essential.

— Completeness, incompleteness, and what it all means: first versus second order logic

— Stuart Armstrong

2014.01.11 Saturday ACHK

# 靈界

e.g. 逝者可以透過，過去留下來的文字和錄像等檔案，繼續傳送訊息予生者。

— Me@2014.01.08 16.28.24

# Past Tense vs Present Perfect Tense

1. Past Tense 是講現在之前，已知的一點時間，例如：

He ate his breakfast at 8am.

2. Present Perfect Tense 是講 Present 之前的一段時間。至於是現在之前的哪一刻，則沒有提及：

He has eaten his breakfast.

3. Past Perfect Tense 是講 Past 之中，某一點已知的時間，再之前的一段時間。至於是該點時間之前的哪一刻，則沒有提及：

At 9am, he told me that he had already eaten his breakfast.

Tell 用 past tense “told”，因為你知道他在 9am 時跟你說。

— Me@2013-12-18 01:52 AM

# Monoid

A monoid is a set with an associative binary operation that has an identity element. By the same technique as for groups, any monoid “is” a category with exactly one object and any category with exactly one object “is” a monoid.

— Wikibooks on Category Theory/Categories

2014.01.08 Wednesday ACHK

# Release

In recent years, India and China have had economic booms. How? By getting rid of bureaucracy and regulation and letting competition rule.

— John T. Reed

2014.01.08 Wednesday ACHK

# 測不準原理 1.5

（安：什麼意思？

 \sqrt{\frac{1}{3}} | A \rangle + \sqrt{\frac{2}{3}} | B \rangle

— Me@2014.01.07

# Independent vs Mutually Exclusive, 2

Tree diagram 4

Mutual exclusive events are corresponding to two separate branches of the same tree diagram.

Independent events are corresponding to two independent tree diagrams.

— Me@2014-01-01 6:27 PM

# Magic

In my second time teaching (2007-2008), the magic disappeared because the unknowns had disappeared.

To get magic, you have to jump into the unknowns/future.

— Me@2013-12-31 5:34 PM

# V 和 U 的分別

Electric Potential and Electric Potential Energy

~~~~~~~~~~

electric potential = electric potential energy per unit charge

 V=\frac{U}{Q}

~~~~~~~~~~

 \frac{1}{4 \pi \epsilon_0} \frac{Q_1 Q_2}{r}

 \frac{1}{4 \pi \epsilon_0} \frac{Q}{r}

— Me@2014.01.04