鑽石棉花 1.1

這段改編自 2010 年 5 月 9 日的對話。

Resistance(電阻)正比於物件的長度,反比於橫切面面積:

化成等式的話,我們需要一個「比例常數」,

在物理上,這個「比例常數」,叫做 「resistivity」(電阻率)。

倒轉寫的話,resistivity 可以透過 運算得到,如果你知道 resistance 的數值的話。

Resistivity 可愛過 resistance,因為 resistivity 可以真正講出某樣物質的特性,而 resistance 則不可以。那是什麼意思呢?你可以這樣去理解:例如,我問你,

鑽石值錢一點,還是棉花值錢一點?

— Me@2011.06.19

2011.06.19 Sunday (c) All rights reserved by ACHK

Theory of Invariants

… relativity isn’t theory of relativity at all, it’s a theory of invariants (already Einstein made this observation, but it was too late, the current name had caught on). Some (and actually many) things in relativity are absolute.

– Marek

2011.06.19 Sunday ACHK

Loop Quantum Gravity 3

Choice in General Relativity: Metric, . Directly determines

Riemannian geometry; Geometrodynamics.

In all other interactions, by contrast, the basic variable is a Connection, i.e., a matrix valued vector potential .

Gauge theories: Connection-dynamics

Connections: Vehicles for parallel transport.

Classical singularities are gates to Physics Beyond Einstein.

— Introduction to Loop Quantum Gravity

— Abhay Ashtekar

2011.06.17 Friday ACHK

Bugs

Only useful programs can have “bugs”.

If a program doesn’t work at all, we won’t be able to see its “bugs”.

— Me@2010.01.22

2011.06.17 Friday (c) All rights reserved by ACHK

Make the world interesting

When a friend of mine used to grumble because he had to write a paper for school, his mother would tell him: find a way to make it interesting. That’s what you need to do: find a question that makes the world interesting. People who do great things look at the same world everyone else does, but notice some odd detail that’s compellingly mysterious.

And not only in intellectual matters. Henry Ford’s great question was, why do cars have to be a luxury item? What would happen if you treated them as a commodity? Franz Beckenbauer’s was, in effect, why does everyone have to stay in his position? Why can’t defenders score goals too?

— Paul Graham

2011.06.16 Thursday ACHK

超時空接觸

The Machine 3

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David Drumlin: I know you must think this is all very unfair. Maybe that’s an understatement. What you don’t know is I agree. I wish the world was a place where fair was the bottom line, where the kind of idealism you showed at the hearing was rewarded, not taken advantage of. Unfortunately, we don’t live in that world.

Ellie Arroway: Funny, I’ve always believed that the world is what we make of it.

– Contact (1997 film)

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2010.01.11 Monday ACHK

防止愚善系統

即使一個人企圖做好人,他也未必是好人。他可能因為人格有嚴重的缺失,導致他時常好心做壞事。而那個「人格缺失」,通常是「愚蠢」。

「好心做壞事」的殺傷力,往往同「壞心做壞事」不相伯仲。

而更麻煩的地方是,你勸諫一個「好心做壞事」的人不要再做壞事時,他會因為愚蠢,而不明白你在說什麼。他心目中以為,出於善意的,就一定是善行。

那是大錯特錯的。

— Me@2011.06.15

Many disasters in the world are due to dumb people trying to save the world.

2011.06.15 Wednesday (c) All rights reserved by ACHK

人海淘金術

對於大部分人來說,你越對他們好,他們就會對你越差。只有小部分人,你對他們好的話,他們會反過來對你好。

(安:我同意你的講法。但是,如果你為了防範別人忘恩負義,而對其他人不好的話,那就會損失了一些潛在的好朋友。)

我沒有講過我會對人不好。

面對一個原本不相識的人,我第一步會對他好。然後,我會視乎他的回應,來決定下一步應該怎樣。如果對方都對我好的話,我會對他更好。如果對方對我不好的話,我不會再對他好。但是,我亦不會對他不好,因為,我會直情不再跟他相處。

人生苦短,不應花任何一秒在壞人身上。

— Me@2011.06.13

2011.06.13 Monday (c) All rights reserved by ACHK

Idea babies

Ideas, he explained, were like babies — everything about their environment said they shouldn’t exist.

But they do. You can’t dwell on problems too early, or they will swamp the virtues and you will decide not to do the project.

— In The Plex: How Google Thinks, Works, and Shapes Our Lives, p.342

2011.06.13 Monday ACHK

二百萬

機械人 2

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戀愛,只可以令到兩個人快樂。

沒有戀愛,卻有時間為一百萬人帶來快樂。

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如果我的戀愛對象,有共同理想的話,我們就可以為,二百萬人帶來快樂。

— Me@2010.06.13

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2011.06.11 Saturday (c) All rights reserved by ACHK

人狗之辨 2

我以前是對任何人都好的。我以前覺得,如果我對一個人好,即使他未必會對我好,至少他不會加害於我。但是,後來我發現,這個想法是錯的。

對於一部分人來說,你對他們好,他們的第一個意識就是,你可以被欺負。

馬克吐溫(Mark Twain)說過,人和狗的最大分別是,如果你對一隻狗好,給牠溫飽,牠很少會咬你。

這類現象可以用「機會成本」來解釋。

你對一個好人好的話,他會覺得是難能可貴,他會珍惜眼前人。因為不想失去你這個好朋友,他會千方百計對你好。

你對一個壞人好的話,他會覺得,既然任何情況下你都會對我好,即是欺負你也不會有任何代價,那我為什麼要對你好呢?

大部分情況下,以上的兩種思想,不會有意識地進行,而會由「潛意識」直接化成「外在表現」。

— Me@2011.06.11

2011.06.11 Saturday (c) All rights reserved by ACHK

Octonions 2

After all, G2 is the automorphism group of the octonions, and it has a 7-dimensional irreducible representation on the imaginary octonions; as explained in “week104” by Robert Helling, the octonions are secretly what let you write down the superstring Lagrangian in 10d spacetime.

— John Baez

2011.06.10 Friday ACHK

Khan Academy

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

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