Author Archives: rpflee

Maths | Physics

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Maths \in Physics, Physics \in Maths

“Mathematics is a part of physics. Physics is an experimental science, a part of natural science. Mathematics is the part of physics where experiments are cheap.

…

In the middle of the twentieth century it was attempted to divide physics and mathematics. The consequences turned out to be catastrophic. Whole generations of mathematicians grew up without knowing half of their science and, of course, in total ignorance of any other sciences. ”

— On teaching mathematics, by V.I. Arnold
 
 
 
2007.08.26, Sunday, CHK2

Microscope

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2.1 Knowledge map: a Geography of Knowledge

Language Logic Symbolic Logic Mathematical Logic Mathematics Mathematical Physics Theoretical Physics Physics Experimental Physics Chemical Physics Physical Chemistry Chemistry Biochemistry Molecular Biology Biology

Language Logic Mathematics Physics Engineering

August 25, 2007, Saturday, (c) CHK2

以專攻博: 第四階段(博): 例子四

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以你的專長來掌握其他任何科目。

…

例子四: 以物理攻英文

When I was young, I read a lot of Physics books in order to upgrade my English. I did that because I thought English itself was boring but I was interested in Physics. So I would not find an English Physics book boring. Also, the English in a Physics book would be easy. Reading English Physics book is a way to get used to reading English.

When I had found that, with the power of English, I was able to learn a lot of advanced physics, I started to like English. It is as interesting as my Physics. English is part of my Physics. 

August 23, 2007 (c) CHK2

有用的人

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曲:李毅/梁智強 詞:梁智強 主唱: 陳國榮

《小孩不笨》主題曲

誰不希望自己是聰明的人
誰不希望什麼都能一百分
誰能希望自己又呆又傻又愚蠢
誰會願意聽到你真的好笨

有些事情就是這樣的殘忍
有些道路沒有直通那扇門
有些遊戲結果不一定要獲勝
有些收穫不在終點只在過程

我們不會心灰意冷
我們會給自己掌聲
我不是你想像的笨
我也有我自己的門
其實你不是不能
只是你肯不肯
給自己多一個機會
因為我們都是有用的人

2007.08.18 CHK2

Applied Mathematics vs Chemistry

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Chemistry wins!

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

A. Physical Chemistry

B. Organic Chemistry

C. Inorganic Chemistry

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

1. Atoms, Molecules and Stoichiometry

2. The Electronic Structure of Atoms and the Periodic Table

3. Energetics

4. Bonding and Structure

5. Chemical Kinetics

6. Chemical Equilibrium

7. Periodic Properties of the Elements in the Periodic Table

8. The s-Block Elements

9. The p-Block Elements

10. The d-Block Elements

11. Fundamentals of Organic Chemistry

12. Chemistry of Organic Compounds

13. Chemistry in Action

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

2007.08.13 CHK2

以專攻博

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1.31 對策一

那應該取專還是取博呢?

以專攻博(不同的階段可以平行運作)

第一階段(專),

要有一樣專長。即使那一個專長仍未達到世界第一也不是太大問題。

重要的是你要選擇哪一科是你的最最愛。因為當一科是你的最愛的話, 你一定會很有心機研究。無論花多少時間, 你也不覺得是浪費, 你也覺得是值得的。所以你在該科的功力一定不會大差(即使暫時不是世界第一)。

第二階段(專),

在不太差的基礎上, 不斷提昇自己已選擇要發展的專長, 令到那個可能的專長變為真正專長。

第三階段(專),

再提昇你的專長 直至 以下任何一種情況發生

一. 你已是世界第一。

二. 已到了你智力的極限。

(思考題: 怎麼知道自己已到了自己智力的極限呢?)

第四階段(博),

以你的專長在掌握其他任何科目。

例子一: 以數學攻物理

你的專長學問是數學, 解決物理問題時, 你往往會用數學的進路。

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方法一: 以物理攻物理

…

方法二: 以數學攻物理

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例子二: 以程式攻物理

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例子三: 以物理攻數學

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例子四: 以物理攻英文

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例子五: 以光學攻量子力學

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例子六: 以幾何攻幾何

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例子七: 以代數攻代數

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例子八: 以代數攻幾何

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例子九: 以幾何攻代數

…

August 01, 2007 (c) CHK2

Chapter A: StoryArc

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1.1 專博之爭

究竟應該做一個專家還是一個博士呢?

無論做專家或者是做博士都會引起很大的問題:

 

做專家的問題是假若有某幾年你的專業沒有需求時, 你將失業.

做博士則沒有這個問題

但是做博士會遇到另一個大問題.

如果你在多方面都學識充裕的話. 通常來說, 你不會是某一方面的第一, 因為你把時間分散了.

 

1.2 第二是沒有意思的

做不到第一的話有什麼問題呢?

做第二名通常是沒有什麼意思的.

 

例子一

有不少人也記得第一個踏足月球的人是岩士唐.

哪第二位是誰呢? 大概不會有人記得…

 

例子二

假設你是一個單身男士, 很想娶某位女士為妻.

但是你只是該位女士眾多可能對象中第二喜歡的.

那是完全沒有用的

因為她一定不會嫁給你.

 

1.31 對策一

那應該取專還是取博呢?

 

1.32 對策二

哪怎樣保證可以做到第一?

2. 軟硬智力

3.1 洗衣機與電飯煲

3.2 鱷魚與長頸鹿

July 31, 2007 (c) CHK2

Contents Chapter 2

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Contents
Preface 緣起

1 Additional Mathematics
2 Applied Mathematics

2.1 Knowledge map: a Geography of Knowledge
2.1.1 Mathematical Physics and Theoretical Physics
2.1.2 Chemical Physics and Physical Chemistry
2.1.3 Collections and recollections

2.2 Dispersion
2.2.1 Why is there dispersion
2.2.2 Guided reading

2.3 Statistics
2.3.1 Statistics
2.3.2 Statistics extra
2.3.3 Statistics bonus
2.3.4 Statistics extra bonus

2.4 Pure Definition
2.4.1 Time
2.4.2 Newton, Leibniz, Einstein
2.4.3 Lee’s Pure Definition of Time
2.4.4 Guided reading

2.4.5 Time in a Machine
2.4.6 Chronon: Zeno paradox
2.4.7 What time is it

2.5 Physicists’ Time Travel
2.5.1 Feynman’s Antiparticle
2.5.2 Feynman Diagrams
2.5.3 A particle that travels back in time
2.5.4 Blackhole Radiation
2.5.5 What will you see when a spaceship travels back in time

2.6 Writers’ Time Travel

2.7 Space Travel

2.8 Quantum Gravity

3 Storyline
4 Master
5 Writing
6 Doctor
7 Painting

A Storyarc

Bibliography 參考書目

July 24, 2007 (c) CHK2

Contents

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Contents
Preface 緣起

1 Additional Mathematics
1.1 General Mathematics
1.1.1 Analytic and Synthetic
1.1.2 Logic and Pure Mathematics
1.1.3 Scene One
1.1.4 Scene Two
1.1.5 Contrast
1.1.6 What is Mathematics

1.2 Additional Additional Mathematics
1.2.1 Deduction and Induction
1.2.2 Mathematical Induction
1.2.3 數學歸納法
1.2.4 數學感應法

1.13 Newton’s Binomial Theorem
1.13.1 \displaystyle{(1 + x)^{-1}}

1.13.2 \displaystyle{(1 + x)^{\frac{1}{2}}}

1.16 Exercises

2 Applied Mathematics
3 Storyline
4 Master (On career planning)
5 Writing
6 Doctor (On studying skills)
A Storyarc 

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July 21, 2007 (c) CHK2

應數頌讚

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In praise of Applied Mathematics:

.

Paper 1:

I: Theoretical Mechanics

  1. Vectors in 2D and 3D
  2. Statics
  3. Kinematics
  4. Newton’s laws of motion
  5. Impact
  6. Friction
  7. Motion of a rigid body

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Paper 2:

II. Differential Equations

III. Numerical Methods

IV. Probability and Statistics

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2007.07.05 CHK2

Spinoza

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Wikipedia:

在倫理學上，斯賓諾莎認為，一個人只要受制於外在的影響，他就是處於奴役狀態，而只要和上帝達成一致，人們就不再受制於這種影響，而能獲得相對的自由，也因此擺脫恐懼。

斯賓諾莎還主張無知是一切罪惡的根源。

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Wikipedia:

斯賓諾莎還認為上帝是每件事的「內在因」，上帝通過自然法則來主宰世界，所以物質世界中發生的每一件事都有其必然性；世界上只有上帝是擁有完全自由的，而人雖可以試圖去除外在的束縛，卻永遠無法獲得自由意志。如果我們能夠將事情看作是必然的，那麼我們就愈容易與上帝合為一體。因此，斯賓諾莎提出我們應該「在永恆的相下」（sub specie aeternitatis）看事情。

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Russell’s History of Western Philosophy, on Spinoza:

Only ignorance makes us think that we can alter the future;

what will be will be,

and the future is as unalterably fixed as the past.

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2007.07.05 CHK2