Author Archives: rpflee

多重網誌 1.1

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這段改編自 2010 年 4 月 3 日的對話。

（安：你可以考慮一下，開一個新的 blog（網誌），用來輯錄你一些很有意思的文章。）

那就即是我原本的那一個網誌。為什麼我要另外，開一個新的呢？

（安：你原本的網誌，夾雜了很多各種主題、不同類型的文章，閱讀起來十分不連貫。有時，我有無所適從的感覺。）

你沒有必要閱讀我「整個」網誌。其實，你只要點擊任何一個 label（標籤），你就會只看到，那一個主題的系列文章。例如，如果你在我的網誌上，點擊「Earth」標籤，你就會閱讀到我同你的對話紀錄，主要研究「地球事務」。又例如，如果你點擊「study」，你就會閱讀到我的教學過程，主要有關「讀書心得」。

— Me@2013.05.18

2013.05.19 Sunday　(c) All rights reserved by ACHK

Identical particles 4

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Indeed, if certain objects could move infinitely fast, we might expect to find the universe populated with large sets of indistinguishable particles, all of which are really instances of a small number of prototypes moving infinitely fast from place to place, so that they each occupy numerous locations at all times. This may sound implausible until we recall that the universe actually is populated by apparently indistinguishable electrons and protons, and in fact according to quantum mechanics the individual identities of those particles are ambiguous in many circumstances. John Wheeler once seriously toyed with the idea that there is only a single electron in the universe, weaving its way back and forth through time. Admittedly there are problems with such theories, but the point is that causality and the directionality of time are far from being straightforward principles.

— 1.7  Staircase Wit

— Reflections on Relativity

— mathpages

2013.05.17 Friday ACHK

微積分 1.2

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這段改編自 2010 年 6 月 29 日的對話。

「微積分」其實只是一個「高級一點的乘數表」。　

「微積分」沒有什麼好怕；只要你把「微積分公式表」當成「乘數表」般詳加背誦，在日常應用時，就不會有什麼大困難。

— Me@2013.05.16

2013.05.16 Thursday (c) All rights reserved by ACHK

受難曲 1.5

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The Dark Knight

這段改編自 2010 年 4 月 3 日的對話。

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又再例如，在電影《The Dark Knight》（黑夜之神）中，Bruce Wayne 化身成「蝙蝠俠」，去打擊罪案，導致傷痕累累，身心受創。他的女朋友 Rachel Dawes 明知他為 Gotham City 的市民犧牲了很多，但是，Rachel 卻不會因為那樣，而更加欣賞和支持他。反而，Rachel 因為 Bruce 的「蝙蝠俠」善行，而離開了他。

有很多時，「企圖改善世界」的後果是，自己被遺棄。

— Me@2013.05.14

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Don’t talk like you’re one of them! You’re not… even if you’d like to be. To them you’re just a freak, like me. They need you right now, but when they don’t, they’ll cast you out. Like a leper.

— The Joker

— The Dark Knight

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2013.05.15 Wednesday (c) All rights reserved by ACHK

Force

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Any particle can be exchanged in some context or another. So every kind of particle in one way or another produces a force.

In molecular physics, it’s the exchange of electrons which creates force [in covalent bond]. In electrodynamics, it’s the exchange of photons back and forth which creates force.

So [every] particle is connected with a force when that particle can be exchanged or jump back and forth between two something else.

There are people say that there are [only] four forces of nature.

No.

There is a force of every possible kind of particle.

— Lecture 1 | New Revolutions in Particle Physics: Standard Model 

— Leonard Susskind

2013.05.13 Monday ACHK

受難曲 1.4

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Nikola Tesla 2

這段改編自 2010 年 4 月 3 日的對話。

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public domain image

再例如，「電磁王」Nikola Tesla 是一位物理學家和工程師，一生中有無數發明。最重要的發明之一，是「交流電」。你和我每天的生活，都享受著他這個創作成果。

他對人類的貢獻，無可限量。「所以」，他遭到「天讉」。他破了產，晚年過著貧困的生活。最終，他在所住的酒店房間，孤獨地過身。臨終時，身邊一個親人朋友也沒有。

— Me@2013.05.12

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Tesla never married, claiming that his chastity was very helpful to his scientific abilities. However, towards the end of his life, he told a reporter, “Sometimes I feel that by not marrying, I made too great a sacrifice to my work….”

— Wikipedia on Nikola Tesla

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2013.05.12 Sunday (c) All rights reserved by ACHK

速度準確表達

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人格考試 1.2 | 學科用處

這段改編自 2010 年 6 月 29 日的對話。

這些都要靠平日，長年累月的習慣訓練，導致考試時可以條件反射；並沒有任何直接的「溫習」方法，可以「溫習人格」。換而言之，考試是兩分考學問，八分考能力。如果你只是「知識多」但是「能力差」，考試不會有好結果。

「速度」、「準確度」和「語言」這三項性格特點，其實是同一樣東西的三個方面，而不是三樣各自獨立的東西。例如，如果你運算不準確，就即是花了時間，也拿不到分數。得分效率等如零，沒有任何速度可言。又例如，如果你的語言表達欠佳，閱卷員不能明白你的思想，那就等價於你的作答不準確。你亦會損失大量分數。

這三樣處事效能，統稱為「人格」；「人格」就那「同一樣東西」。

有了「人格考試」這個概念後，你不應該再投訴，中學的學術科目，對你沒有用處；你亦不應該再追問，既然數學科中所學的數學，在日常生活中甚少應用，為什麼我們要花那麼多的時間去學呢？

其實，數學科中的數學，只佔整個「數學科」課程目標的兩成。其餘的八成，都是考驗你的人格。你大概不能說，「人格」不會在日常生活中應用到。

— Me@2013.05.11

2013.05.11 Saturday (c) All rights reserved by ACHK

Terence Tao 1

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A powerful way to prove a mathematical result (e.g. an identity of the form A=B) is to introduce a new object or concept (say C) and connect it in two different ways to the original problem. For instance, if one can show that A=C and one can also show that C=B, then one can deduce that A=B. More generally, one can introduce n new objects or concepts, and establish at least n+1 non-trivial connections between these objects and each other, or to the original problem; for instance, if one introduces two new objects C,D and three connections, two of which A=C, D=B are to the original problem, and one of which C=D is between the newly introduced objects, then one has again established A=B.

A typical example of this is the use of complex analysis methods to solve a real analysis problem, as per Hadamard’s famous dictum “The shortest path between two truths in the real domain passes through the complex domain”. For instance, suppose one wants to compute some real integral A and show that it equals some value B. To do this, one can introduce two new concepts (the complex contour integral C, and the notion of a residue of a pole D); write the real integral as a contour integral (establishing a result of the form A=C), invoke the residue theorem (which is a result of the form C=D), and then compute the residues (a result of the form D=B), to obtain the final desired result A=B.

— Terence Tao

2013.05.11 Saturday ACHK

受難曲 1.2

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這段改編自 2010 年 4 月 3 日的對話。

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（安：那會不會是你的錯覺？市面上，有很多你所謂「平庸」的人，都是找不到對象的。）

但是，我持續觀察到的現象是，只要稍為偉大一點，就有較大機會孤獨終老。

例如，歌星梅艷芳無論在歌唱、演戲，還是慈善事業，都有非凡的成就，但就偏偏最終也找不到結婚對象。而她是非常希望成立自己的家庭的。

又例如，填詞人林夕的愛情歌詞，觸動無數心靈。但是，作為愛情專家的他，自己卻找不到對象，暫時。我希望他最終會找到，如果他想找的話。

— Me@2013.05.10

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2013.05.10 Friday (c) All rights reserved by ACHK

Cosmological constant 2

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Now, you have to realize that the cosmological constant is the energy density of the vacuum.

— The enigmatic cosmological constant

— Lubos Motl

2013.05.10 Friday ACHK