Author Archives: rpflee

Khan Academy

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The Khan Academy is a non-profit educational organization created in 2006, by Salman Khan. With the stated mission of “providing a high quality education to anyone, anywhere”, the website supplies a free online collection of more than 2,300 micro lectures via video tutorials stored on YouTube teaching mathematics, history, finance, physics, chemistry, biology, astronomy, and economics.

— Wikipedia on Khan Academy

With so little effort on my own part, I can empower an unlimited amount of people for all time. I can’t imagine a better use of my time.

— Salman Khan (educator)

2011.06.10 Friday ACHK

電流電壓

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這段改編自 2010 年 5 月 9 日的對話。

「電流」（current）的意思是，通過某一個橫切面，每一秒有多少電荷（charge）。

「電壓」（voltage）是「電動勢」和「電位差」的統稱。「電動勢」（electromotive force）的意思是，由電路（electric circuit）中的一點去另一點，每一個單位的電荷，可以賺取多少能量（energy）。「電位差」（potential difference）的意思是，由電路中的一點去另一點，每一個單位的電荷，需要付出多少能量。

有一批車輛要使用海底隧道。簡便起見，假設該條海底隧道只有一個收費站。如果將「車輛」比喻成「電荷」的話，「電流」（車流）的意思是，每一秒有多少輛車，通過那個收費站。而「電壓」的意思是，通過那個收費站，每一輛車要付出多少錢。

還有，海底隧道收費站的「賺錢能力」（earning power），可以用作比喻「電功率」（electric power）。「賺錢能力」的意思是，那個收費站，每一秒可以收到多少錢。

那樣，你能理解為什麼「電功率 ＝ 電流 X 電壓」嗎？

— Me@2011.06.09

2011.06.09 Thursday (c) All rights reserved by ACHK

Density matrix

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The difference between the classical and quantum dynamical equations is just hidden in the fact that rho,x,p are operators in quantum theory and they generally don’t commute with each other. But otherwise, the interpretation from classical physics may be pretty much directly extended to the quantum theory!

— Density matrix and its classical counterpart

— Lubos Motl

2011.06.09 Thursday ACHK

discipline | boring

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One of the most dangerous illusions you get from school is the idea that doing great things requires a lot of discipline. Most subjects are taught in such a boring way that it’s only by discipline that you can flog yourself through them. So I was surprised when, early in college, I read a quote by Wittgenstein saying that he had no self-discipline and had never been able to deny himself anything, not even a cup of coffee.

I’m not saying you can get away with zero self-discipline. You probably need about the amount you need to go running. I’m often reluctant to go running, but once I do, I enjoy it. And if I don’t run for several days, I feel ill. It’s the same with people who do great things. They know they’ll feel bad if they don’t work, and they have enough discipline to get themselves to their desks to start working. But once they get started, interest takes over, and discipline is no longer necessary.

— Paul Graham

2011.06.07 Tuesday ACHK

Delta encoding

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diff 4

The version history is paired with the use of delta encoding technology. To conserve bandwidth and time, if a file in a user’s Dropbox folder is changed, Dropbox only uploads the pieces of the file that are changed when syncing.

— Wikipedia on Dropbox (service)

2011.06.07 Tuesday ACHK

Principle of Least Action, 3.3

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Instead, the energy is universally defined in such a way that it is conserved as a result of the time-translational symmetry; and the action is defined in such a way that the condition δS=0 (stationarity of the action) is equivalent to the equations of motion. These are the general conditions that define the concepts in general and that make them important; particular formulae for the energy or action are just particular applications of the general rules.

— Lubos Motl

2011.06.06 Monday ACHK

瘋人新世紀

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（安：對我來說，這個是一個嶄新的想法。）

哪個想法？

（安：你那個「地球人大部分是『瘋子』」的比喻。）

如果你覺得這個只是一個「比喻」的話，即是你未完全領會它的意思。

（安：這個牽涉到語意問題。如果「地球人大部分是『瘋子』」中的「瘋子」不是比喻的話，你就扭曲了「瘋子」這個字眼的意思。）

如果「瘋子」是指「瘋人院內的病人」的話，那當然不是每一個人也是「瘋子」。但是，如果「瘋子」是指「不理性的人」的話，地球人中，「瘋子」佔了大多數。

還有，即使假設，對於「個人」而然，「理性的人」比「不理性的人」多；對於「群體」來說，「瘋狂的機構」遠比「理性的機構」多。

— Me@2011.06.04

2011.06.04 Saturday (c) All rights reserved by ACHK

Principle of Least Action, 3.2.2

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Fermat’s principle is the main principle of quantum electrodynamics where it states that any particle (e.g. a photon or an electron) propagates over all available (unobstructed) paths and the interference (sum, or superposition) of its wavefunction over all those paths (at the point of observer or detector) gives the correct probability of detection of this particle (at this point). Thus the extremal (shortest, longest or stationary) paths contribute into this interference most as they can not be completely canceled out.

— Wikipedia on Fermat’s principle

2011.06.04 Saturday ACHK

傷逝

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Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation; with no Invariant Sections, no Front-Cover Texts, and no Back-Cover Texts.

2011.06.04 Saturday ACHK

Principle of Least Action, 3.2.1

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How does the particle find the right path?

Does it ‘smell’ the neighboring paths to find out whether or not they have more action?

In the case of light, when we put blocks in the way so that the photons could not test all the paths, we found that they couldn’t figure out which way to go, and we had the phenomenon of diffraction.

— Chapter 19. The principle of least action

— Volume 2. Mainly electromagnetism and matter

— The Feynman Lectures on Physics

2011.06.02 Thursday ACHK

十萬七千里 1.2

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（安：我同意這個講法。如果我真的要在日常生活過得快樂的話，我一定要改變工作環境，轉換上司。但是，我現在沒有可能做到這一點。那我應該怎麼辦呢？）

即是話，現在不是理論問題，而是「如何在實際環境，恰當執行這個理論」的問題。

（安：無錯。）

第一，最重要的是，你知道最理想的情況是什麼；如果沒有任何形式的限制的話，你想你的世界是怎麼樣。

第二，原則上的目標知道了後，並未足夠，因為現實會有很多技術細節和外在限制，阻礙你走到最終理想。但是，即使你現在的現實和理想相差「十萬八千里」，你總會有方法把它們的距離減至「十萬七千里」。

（安：如果真的是沒有方法呢？）

那就先試試把現實拉近至，和理想只相差「十萬七千九百九十九里」；完成以後，再試試把現實拉近至，和理想至只相差「十萬七千九百九十八里」；如此類推。

一步也走不到的話，就走 0.1 步； 0.1 步都走不到的話，就走 0.01 步；如此類推。

— Me@2011.06.01

2011.06.01 Sunday (c) All rights reserved by ACHK

Curiosity

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Curiosity turns work into play. For Einstein, relativity wasn’t a book full of hard stuff he had to learn for an exam. It was a mystery he was trying to solve. So it probably felt like less work to him to invent it than it would seem to someone now to learn it in a class.

–- Paul Graham

2011.06.01 Wednesday ACHK

Write your own

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Still, I don’t claim to be the exclusive authority on this topic; if you don’t like what you read here, write your own.

— How To Become A Hacker

— Eric Steven Raymond

— Me@2010.11.22

“Hacker” here means a highly skilled programmer, not a computer criminal. — Me

The basic difference is this: hackers build things, crackers break them. — Eric S. Raymond

2011.05.31 Tuesday ACHK

運算三部曲 1.2

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這段改編自 2010 年 5 月 1 日的對話。

第二，沒有驗算的題目，即使最終答案真的錯了，通常也會有一定程度的步驟分。所以，作答時一定要寫清楚運算步驟，千萬不要一步就跳到最後答案。

記住，答題的結構應該是，

1. 寫公式

2. 代數字

3. 出答案

很多時，這三步各有一分。例如：

F = ma

= (5kg) (10 m/s^2)

= 50 N

— Me@2011.05.31

2011.05.31 Tuesday (c) All rights reserved by ACHK

Principle of Least Action, 3.1

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Moreover, in the usual formulation of classical action principles, the initial and final states of the system are fixed, e.g.,

    Given that the particle begins at position x1 at time t1 and ends at position x2 at time t2, the physical trajectory that connects these two endpoints is an extremum of the action integral.

In particular, the fixing of the final state appears to give the action principle a teleological character which has been controversial historically. However, this apparent teleology occurs only because of the way in which the question was asked. By specifying some but not all aspects of both the initial and final conditions (the positions but not the velocities) we are making some inferences about the initial conditions from the final conditions, and it is this “backward” inference that can be mistaken for a teleological causal influence.

— Wikipedia on Principle of least action

2011.05.30 Monday ACHK