Monthly Archives: September 2011

Think Different

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Here’s to the Crazy Ones.

The misfits.
The rebels.
The troublemakers.
The round pegs in the square holes.

The ones who see things differently.
They’re not fond of rules.
And they have no respect for the status quo.
You can quote them, disagree with them,
disbelieve them, glorify or vilify them.

About the only thing that you can’t do, is ignore them.
Because they change things.
They invent. They imagine. They heal.
They explore. They create. They inspire.
They push the human race forward.

Maybe they have to be crazy.

How else can you stare at an empty canvas and see a work of art?
Or, sit in silence and hear a song that hasn’t been written?
Or, gaze at a red planet and see a laboratory on wheels?

We make tools for these kinds of people.

While some may see them as the crazy ones, we see genius.
Because the ones who are crazy enough to think that they can change the world,
are the ones who do.

— Think Different

— Apple

2011.09.07 Wednesday ACHK

Number, Time, Money, 2

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Ideal clock 3 | 時間定義 13

這段改編自 2010 年 3 月 6 日的對話。

「理想時鐘」的恰當定義是，讀數和最多其他時鐘吻合的鐘。「快慢」可以相對於「理想時鐘」的讀數來描述。

（安：但是，這到頭來也要用「時間」這個概念來定義「快慢」。

你對「時間」的講法，最有趣的地方是，彷彿可以完全刪除「時間」這個詞語，而又可以完全描述，平時要用「時間」才能講到的東西。「速度」和「時間」有關，所以我在想，有沒有可能不用「時間」，也可以定義到「快慢」呢？）

我剛才並沒有用「時間」來定義「快慢」。我用具體的「理想時鐘讀數」來定義「快慢」，其實已避開了「時間」這個抽象概念。

（安：但是，我又可以追問，你的「理想時鐘」究竟在量度什麼？）

我不一定要答「時間」。我有其他恰當的答法。

— Me@2011.09.07

2011.09.07 Wednesday (c) All rights reserved by ACHK

Time in physics

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1.    Time is just another, imaginary dimension of space
2.    The question about the existence of the past depends on our definition of existence
3.    The future doesn’t exist at the present regardless of any definitions
4.    Some units of time are better than others
5.    Among conserved quantities, time has a special relationship with energy
6.    All physical systems with many degrees of freedom inevitably possess a future-time asymmetry, the so-called logical arrow of time
7.    The logical arrow of time implies the asymmetry of all macroscopic processes, i.e. the thermodynamic arrow of time and other arrows of time
8.    An exact time-reversing symmetry which holds in Nature is called CPT and only applies to the microscopic laws
9.    To properly understand the psychological perception of time, one needs to analyze the functions of the brain
10.   When times become as short as the Planck time, \(10^{-43}\) seconds, time develops some wholly unfamiliar properties

— Ten new things modern physics has learned about time

— Lubos Motl

2011.09.06 Tuesday ACHK

新亞書院

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節錄二

新亞書院學規 –錢穆

■你須在尋求偉大的學業與事業中來完成你自己的人格。

■一個活的完整的人，應該具有多方面的智識，但多方面的智識，不能成為一個的完整的人。你須在尋求智識中來完成你自己的人格，你莫忘失了自己的人格來專為智識而求智識。

2007.06.16 CHK2

— Me@2011.09.05

2011.09.05 Monday ACHK

迷宮筆記

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這段改編自 2010 年 5 月 18 日的對話。

哪些地方不明白、有問題？

（CYW：老師解答過之後，大部分題目我都明白。但是，之後要我自己做的話，大部分題目我也做不到。）

那就即是不明白。「聽別人解答題目」和「自己做題目」的分別，就好像「看著別人行迷宮」和「自己行迷宮」的分別。你看著別人行迷宮時明白，不代表你在迷宮之中時，可以自己走出來。

所以，你要在平時做大量的題目，以作練習之用。還有，練習題目時，你要習慣儲存重點。

— Me@2011.09.05

2011.09.05 Monday (c) All rights reserved by ACHK

Class projects

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1. The programs you write in classes differ in three critical ways from the ones you’ll write in the real world: they’re small; you get to start from scratch; and the problem is usually artificial and predetermined. In the real world, programs are bigger, tend to involve existing code, and often require you to figure out what the problem is before you can solve it.

2. That leads to our second difference: the way class projects are measured. Professors will tend to judge you by the distance between the starting point and where you are now. If someone has achieved a lot, they should get a good grade. But customers will judge you from the other direction: the distance remaining between where you are now and the features they need. The market doesn’t [care] how hard you worked. Users just want your software to do what they need, and you get a zero otherwise.

3. There seem to be two big things missing in class projects: (1) an iterative definition of a real problem and (2) intensity.

– Paul Graham

2011.09.04 Sunday ACHK

Time PageRank

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PageRank 6 | Ideal clock 2.2 | 時間定義 12.2

（安：如果不容許提及「時間」這個概念呢？那如何描述「快慢」？）

「快慢」可以相對於「理想時鐘」的讀數來描述。你問這個問題，其實就相當於問，何謂「理想時鐘」？

麻煩的地方是，如果我答「『理想時鐘』就是宇宙中最『準確』的計時器」的話，你可以追問，你怎樣知道，哪一個時鐘比較準確呢？

假設，我有兩個計時器，時鐘 A 和 時鐘 B。想知哪一個較準的話，你可以用一個比它們都更加準的「時鐘 C」，來跟它們比較。A 和 B 之中，哪一個的讀數比較接近 C，就是較為準確的時鐘。但是，你又可以追問，你怎樣可以事先知道，時鐘 C 比 A 或者 B，都較為準確？

你可以用一個比 ABC 都更加準的「時鐘 D」，來跟它們比較。然後，你再可以追問，你怎樣可以事先知道，時鐘 D 比 A、B 或者 C，都較為準確？

— Me@2011.09.03

2011.09.03 Saturday (c) All rights reserved by ACHK

Renormalization 3

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The infinite intermediate results are needed because these “infinities” arise from the extrapolation of the low-energy physics to the insanely high energies. However, they have no impact on the low-energy observables. That’s why they’re not a source of problems even in the limit where you treat them as strictly infinite numbers – e.g. when you set \( \epsilon = 0 \) in the dimensional regularization.

— Regularization and renormalization

— Lubos Motl

2011.09.02 Friday ACHK