# Burkhard Heim

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“The accident left him without hands and mostly deaf and blind when he was 19.”

“Heim had to undergo a series of operations after the explosion which resulted in the loss of his arms. He found that intense concentration on the study of Einstein’s relativity theory helped him control the pain in his arms mentally and physically.”

— Wikipedia

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Me: Physics 能醫百病
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2008.05.31 Saturday $copyright CHK^2$

# Doctor

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Bachelor: someone has general knowledge

Master: someone has the ability to practice a particular field of knowledge

Doctor: someone has the ability to teach a particular field of knowledge

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— How to Get a PhD (book), by Estelle Phillips and Derek.S. Pugh
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harry 2007-02-26 19:30

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2008.05.29 Thursday $copyright CHK^2$

# Microscope 2

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Chapter 2

Applied Mathematics

2.11 Knowledge map

Language, Logic, Maths, Physics, Chemistry, Biology

Logic, Pure Maths, Applied Maths, Mathematical Physics, Theoretical Physics, Experimental Physics

Logic, Pure Maths, Applied Maths, Pure Physics, Applied Physics, Engineering

Logic, Maths, Physics, Chemical Physics, Physical Chemistry

2.12 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
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2008.05.27 Tuesday $copyright CHK^2$

# The Machine 2

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Palmer Joss: By doing this, you’re willing to give your life, you’re willing to die for it. Why?

Ellie Arroway: For as long as I can remember, I’ve been searching for something, some reason why we’re here. What are we doing here? Who are we? If this is a chance to find out even just a little part of that answer… I don’t know, I think it’s worth a human life. Don’t you?

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— Contact (The Movie)
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2008.05.26 Monday $CHK_2$

# 前傳 9

Emerson I

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If I have lost confidence in myself, I have the universe against me.

–Ralph Waldo Emerson

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2008.05.25 Sunday $CHK_2$

# Contents Chapter 1

Contents

Preface 緣起

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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 Constrast
1.1.6 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

2 Applied Mathematics
3 Storyline
4 Master
5 Writing
6 Doctor
7 Painting

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A Storyarc
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2008.05.24 Saturday $copyright CHK^2$

# Lightning 2

If you want to build a ship, don’t drum up the men to gather wood, divide the work and give orders. Instead, teach them to yearn for the vast and endless sea.

— Antoine de Saint-Exupéry

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2008.05.22 Thursday $CHK_2$

# Collections

Maths is not Science. Maths is the language of Science.

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Chinese + English + Maths = Language

G.Maths + A.Maths + Computer = Logic

G.Maths + A.Maths + Physics = Mathematics

Physics + Chemistry + Biology = Science

Biology + Art = Arts

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I studied them all 10 years ago.

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2007.02.12 2007.08.30 $copyright CHK^2$

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harry 2007-02-13 20:50

# 1.1.6 What is Mathematics?

As long as you can realize the difference between analytic statements and synthetic statements, you can know what pure mathematics is.

Pure Mathematics is a system of useful analytic statements.10

Pure Mathematics is a system of useful tautologies, whether obvious or unobvious.

In Physics, every generation of physicists have to update the previous theories. For example, Einstein’s theory of gravity has updated Newton’s, explaining what Newton’s gravitation could not explain. But for Pure Maths, although every generation of mathematicians also create new mathematics, the new theories do not and cannot contradict the old ones. For example, “1+1=2” is always true, even in thousands of years later.11

1.1.7 Why maths is always true but physics is not?12

Pure Maths is a system of analytics statements. Analytic statements say nothing about the world. When you say nothing, you cannot be wrong.

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10 In Philosophy of Mathematics, this is called the Formalist’s theory of Mathematics. There is a bug in the formalist’s system. It is about the status of the axiom of infinity. For reference, see Bertrand Russell’s Introduction to Mathematical Philosophy.

11 Mathematics is eternal, as it is timeless, or outside time.
12 Mr. Lee

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2008.05.20 Tuesday $copyright CHK^2$

# Postscript

I have lived in the pursuit of a vision, both personal and social.

Personal: to care for what is noble, for what is beautiful, for what is gentle; to allow moments of insight to give wisdom at more mundane times.

Social: to see in imagination the society that is to be created, where individuals grow freely, and where hate and greed and envy die because there is nothing to nourish them.

These things I believe, and the world, for all its horrors, has left me unshaken.

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— Russell’s Autobiography

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2008.05.19 Monday $CHK_2$

# 三一萬能俠

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State 1:

Physics

Pure Maths, Applied Maths

State 2:

Pure Maths

Physics, Applied Maths

State 3:

Applied Maths

Pure Maths, Physics

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This is about my A-level period. That period is the most amazing moments of my life. I still cannot get that time back.

2008.05.18 Sunday $copyright CHK^2$

# 1.1.5 Contrast

Table 1.1: Contrasting

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Analytic

Synthetic

Logic
Pure Mathematics

Applied Mathematics

Physics

Relations of ideas

Matter of fact6

Deduction

Induction

Say nothing

Say something7

Always correct

Maybe wrong

Theory

Experiment

Software

Hardware

Computer Science

Computer Engineering

Mathematical Geometry

Physical Geometry

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6 David Hume

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2008.05.17 Saturday $copyright CHK^2$

# 四川緬甸

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2008.05.15 Thursday $\copyright CHK^2$

# Life Goal

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2008.05.14 Wednesday $copyright CHK^2$

# 前傳 7

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……..欣悉二月八日為 永遠榮譽主席 陳達明 之壽辰，特此來函敬賀。冀 達明主席 閣下，身體安康，生活愉快! 更望 主席閣下 福壽連綿，繼續春風化風，桃李滿門!
……..謹代表 達明國際同盟會 各同窗致意。

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………………….此致

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2008.05.14 Wednesday $copyright CHK^2$

# 1.1.2 Logic and Pure Mathematics

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Pure Mathematics is a system of (nontrivial) tautology. Roughly speaking, a tautology2 is an analytic statement.

For example, consider this mathematics statement:

2 + 2 = 4

You do not have to do any kind of real world experiments in order to verify the statement. As long as you know the meanings of the symbols “2”, “+”, “=”, and “4”, you know that the statement is correct, and always. Of course, it says nothing about the physical world.

In pure mathematics, since you cannot and do not have to say anything about the real physical world, you can do3 anything you like. Just like what you do when designing the rules of chess.4 You can do anything as long as they are

consistent and

interesting.5
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Is a tautology just a nonsense?

Maybe, maybe not. It depends on context:

When you present an analytic statement as an analytic statement, it is not a nonsense.

When you present an analytic statement as a synthetic statement, it is a nonsense.

2 重言句, 恆真式
3 define
4 or when programming a software
5 i.e. useful
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Imagine the following scenes.

1.1.3 Scene One

A primary school student wrote 2 + 2 = 5 in his homework. His mathematics teacher told him that 2 + 2 = 5 was incorrect, “Two plus two should equal Four.” In such context, the statement is, although analytic, not a nonsense.

1.1.4 Scene Two

After 30 years of research, a physicist declared his research result, “Two plus Two equals Four!!!” In such context, the statement is, although true, a nonsense.

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2008.05.12 Monday $copyright CHK^2$

# K

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My answer is that you would be a truly free person. You would be forever liberated from the tyranny of others’ opinions, from self-doubt, from the fear of life and the fear of death, and from the demands of time.

Instead, you would be free to enjoy life as it is and to find fulfillment and joy in helping others.
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— Kenneth Ring’s Lessons from the Light

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2008.05.11 Sunday $CHK_2$

# 前傳 6

World’s funniest joke

“A couple of New Jersey hunters are out in the woods when one of them falls to the ground. He doesn’t seem to be breathing, his eyes are rolled back in his head. The other guy whips out his cell phone and calls the emergency services. He gasps to the operator: “My friend is dead! What can I do?” The operator, in a calm soothing voice says: “Just take it easy. I can help. First, let’s make sure he’s dead.” There is a silence, then a shot is heard. The guy’s voice comes back on the line. He says: “OK, now what?” ”

— Wikipedia
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harry 2007-01-25 20:41

=.=” 我覺得唔好笑喎
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— Cantonese by Me
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2008.05.10 Saturday $copyright CHK^2$

# 1.1.1 Analytic and Synthetic

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1.1.1 Analytic and Synthetic

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To know what mathematics itself is, we have to realize that there are two kinds of statements: analytic statements and synthetic statements.

For an analytic statement, there is no information about the objective world. Whether an analytic statement is true or not depends on only the meanings of the component words. No real world experience is needed.

For a synthetic statement, there is some information about the objective world. Whether a synthetic statement is true or not depends on not only the meaning of the component words, but also the objective facts of the world.

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For example, consider this statement

I have passed the exam or I have not.
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It is an analytic statement … because you do not have to check my examination result to verify the statement. As long as you know the meanings of “or” and “not”, you know that the statement is always true. But it says nothing about the world.
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Consider another statement:

I have passed the exam.

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It is a synthetic statement … because you have to check my examination result to verify the statement. Even if you know the meanings of “or” and “not”, you do not know whether the statement is true or not. But the statement says something about the world.

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2008.05.08 Thursday $copyright CHK^2$