# Complex plane as a connection between differentiation and integration

The coefficients in a Taylor series may be calculated by differentiation, while those in a Fourier Series may be calculated by integration. Since these two types of series are really the same in the complex plane, this suggests that there exists some hidden connection between differentiation and integration that the only complex number can reveal.

— Visual Complex Analysis p.79, by Tristan Needham

2009.12.31 Thursday ACHK

# The less of two evils

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The less of two evils

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2009.12.31 Thursday $ACHK$

# Twistor string theory

In 2003, Edward Witten proposed to marry twistor and string theory by embedding the topological B model of string theory in twistor space. His objective was to model certain Yang-Mills amplitudes. The resulting model has come to be known as twistor string theory.

Witten (2004) built on this insight to propose a way to do string theory in twistor space, whose dimensionality is necessarily the same as that of 3+1 Minkowski spacetime. Hence twistor string theory is a possible way to eliminate the need for more than 3 spatial dimensions when doing (super)string theory.

— Wikipedia on Twistor theory

2009.12.30 Wednesday ACHK

# 超能力千里馬

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* 世有伯樂，然後有千里馬．千里馬常有，而伯樂不常有。

–《馬說》, 韓愈

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–Me@2009.12.29

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2009.12.30 Wednesday $copyright ACHK$

# PLT Scheme

There is also PLT Scheme, which uses an incompatible branch of wxWindows (version 1), created in 1995. The toolkit is deeply integrated with the language run-time (garbage collection, resource administration) unlike in other languages, which simply provide a library binding.

— Wikipedia on wxWidgets

2009.12.29 Tuesday ACHK

# Trigger an idea

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That’s what triggered the idea. Sometimes ideas are born out of necessity: you solve a problem for yourself, and you hopefully solve it for a number of other people too.

— Bhatia, Founders at Work

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2009.12.29 Tuesday $ACHK$

# Connection between Taylor series and Fourier series

Taylor series and Fourier series of real functions are merely two different ways of viewing complex power series.

— Visual Complex Analysis p.77, by Tristan Needham

One is by setting $r$ to be constant, another is by setting $\theta$ to be constant.

— Me@2007

2009.12.28 Monday (c) ACHK

# Twistor theory

In theoretical and mathematical physics, twistor theory is a mathematical theory mapping the geometric objects of conventional 3+1 space-time (Minkowski space) into geometric objects in a 4 dimensional space with metric signature (2,2). This space is called twistor space, and its complex valued coordinates are called “twistors.”

— Wikipedia on Twistor theory

2009.12.27 Sunday ACHK

# Mysterious duality

In theoretical physics, mysterious duality is a set of mathematical similarities between some objects and laws describing M-theory on k-dimensional tori on one side, and geometry of del Pezzo surfaces on the other side.

In theoretical physics, mysterious duality is a set of mathematical similarities between some objects and laws (and perhaps all of them, if the conjecture is extended appropriately) describing M-theory on k-dimensional tori (i.e. type II superstring theory on T^{k-1} if k is positive) on one side, and geometry of del Pezzo surfaces (for example, the cubic surfaces) on the other side.

— Wikipedia on Mysterious duality

2009.12.26 Saturday ACHK

# Perseverance

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Perseverance is important because, in a startup, nothing goes according to plan. Founders live day to day with a sense of uncertainty, isolation, and sometimes lack of progress. Plus, startups, by their nature, are doing new things — and when you do new things, people often reject you.

— Founders at Work, Jessica Livingston

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2009.12.26 Saturday $ACHK$

# Spacetime foam

Quantum foam is the source of quantum randomness.

— Me@2009.09.06

2009.12.25 Friday (c) ACHK

# 聖誕誡命

Sentence 1 is achieved by sentence 2.

— based on Mr Lee@philosophical analysis lecture@2002

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The greatest commandment, Jesus:

1. One should love Yahweh with one’s entire heart, soul, mind, and strength.

2. One should love one’s neighbour as one would love oneself.

— the Gospels of Mark[12:28–34] and of Matthew[22:34-40]

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Not many people have realized that the two are actually the same sentence.

Sentence 2 is the ONLY method to achieve sentence 1.

— Me@2009.12.04 2009.12.25

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2009.12.25 Friday $copyright ACHK$

# Fans

First, organize 1,000

I think the ability to find and organize 1,000 people is a breakthrough opportunity. One thousand people coordinating their actions is enough to change your world (and make a living.)

You don’t find customers for your products. You find products for your customers.

— Seth Godin

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2009.12.24 Thursday $ACHK$

# Illusion 2

Dedicated to the memory of Mr Shields …

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The first time I saw him, he asked me to help to print several pages of notes. The general office computer could not print his file. So I used my computer in the Staff Room 4 to print the pages. (I do not remember clearly. Maybe it was that my computer could not print it. We went to the general office to print it.)

He said he had been Hong Kong, teaching English for over a decade. I wanted to know which of the staff rooms would be his office. But I did not know how to say it in English,

“Where do you sit?”

He replied, “What do you mean?”

— Me@2009.12.23

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* Now he has departed from this strange world a little ahead of me. That means nothing. People like us, who believe in physics, know that the distinction between past, present, and future is only a stubbornly persistent illusion.

–- Einstein

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2009.12.23 Wednesday $copyright ACHK$

# Presentation 2

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For presentation, I do not feel nervous anymore.

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Whenever I do not feel nervous, I feel bored.

— Me@2009.12.21

2009.12.22 Tuesday $copyright ACHK$

# Hubbard-Stratonovich transformation 2

The Hubbard-Stratonovich (HS) transformation is an exact mathematical transformation invented by Russian physicist Ruslan L. Stratonovich and popularized by British physicist John Hubbard.

— Wikipedia on Hubbard-Stratonovich transformation

2009.12.21 Monday ACHK

# The Magic City

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The second theme is concerned explicitly with technology. It is a law of life in the magic city that if you wish for anything you can have it. But with this law goes a special rule about machines. If anyone wishes for a piece of machinery, he is compelled to keep it and go on using it for the rest of his life.

— Disturbing the Universe, p.4

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2009.12.21 Monday $ACHK$

# Hubbard-Stratonovich transformation

It is used to convert a particle theory into its respective field theory by linearizing the density operator in the many-body interaction term of the Hamiltonian and introducing a scalar auxiliary field. It is defined as (Baeurle 2002, Baeurle 2003)

where the real constant a > 0. The basic idea of the HS transformation is to reformulate a system of particles interacting through two-body potentials into a system of independent particles interacting with a fluctuating field.

— Wikipedia on Hubbard-Stratonovich transformation

2009.12.20 Sunday ACHK