Emacs, 2

Posted on March 4, 2013 by rpflee

Nice to see Emacs getting a bit of press recently. I’ve used it for almost 20 years now and it dominates my time at the keyboard. It isn’t perfect and I’m reluctant to recommend it but I wouldn’t want to be without it. Let me explain.

The best thing about Emacs is that it can do everything (including the things it can’t do yet). The worst thing about Emacs is finding out how it does anything. I wouldn’t call it discoverable. In fact, on several occasions, I’ve learned about Emacs by accident: you press the wrong key combination (easy to do when you’re holding down a couple of keys and stretching for a third) and, look, something interesting happens!

— Accidental Emacs

— 2008-05-06

— Thomas Guest

2013.03.04 Monday ACHK

Overprolific Alpha Geeks

Posted on March 4, 2013 by rpflee

Everyone, including Alpha Geeks, use only one app:

People complain about how their work wants them to use organizers…

Joel Splosky uses Excel for everything.

HR person sends website designs in PPT.

Don Lancaster sees the world in Postscript.

— Running notes from

Life Hacks: Tech Secrets of Overprolific Alpha Geeks

— Danny O’Brien

— 11 February, 2004

— by Cory Doctorow

2013.03.03 Sunday ACHK

微積分 6.2

Posted on March 3, 2013 by rpflee

無限年 3.2

這段改編自 2010 年 4 月 3 日的對話。

「爺爺」=「爸爸的爸爸」

「 $\left( \lim_{x \to \infty} \frac{1}{x} \right) = 0$ 」 = 「如果 x 越來越大，1/x 會越來越接近零。」

「\left( \lim_{x \to \infty} \frac{1}{x} \right) = 0」 = 「如果 x 越來越大，1/x 會越來越接近零。」

還有，這一句仍然只是「簡稱」，還未精確到可以視為數學句子。完整的版本詳盡很多。

詳細一點的版本是，

「 $\left( \lim_{x \to \infty} \frac{1}{x} \right) = 0$ 」 = 「只要 x 足夠大，1/x 就會足夠接近零。」

只要具體釐清，在這個上文下理中，何謂「足夠大」和「足夠接近」，你就可以得到「 $\left( \lim_{x \to \infty} \frac{1}{x} \right) = 0$ 」的正式數學意思。

「 $\left( \lim_{x \to \infty} \frac{1}{x} \right) = 0$ 」 = 「無論 a 的數值是多麼小，你都可以令 1/x 和零的相差小於 a，只要你設定 x 的數值大於 1/a 。」

— Me@2013.03.03

Learning physics online?

Posted on March 2, 2013 by rpflee

事業愛情觀 3

It always makes me laugh when people hope they can learn physics online. Yeah, sure you can, just as you can learn languages online but you’re not going to be articulate compared to someone that is on a full time course. They live physics for years with like minded people, day in, day out. If you want to learn physics the same way someone learns a foreign language by carrying around a translation dictionary because they lack the effort required, then go right ahead. Just don’t delude yourself in believing you can know what a graduate physicist knows.

Let me put it another way:

A physicist on a full time course might spend at least 50 hours a week learning about physics. How much time do you have to spare?

— answered May 25 ’11 at 22:16

— Larry Harson

2013.03.02 Saturday ACHK

Marriage

Posted on March 2, 2013 by rpflee

Process, not a state, 8

Marriage is not a single event. Marriage is a lifelong process.

“Married” is not a state, but a process.

— Me@2010.12.24

微積分 6.1

Posted on March 2, 2013 by rpflee

無限年 3.1

這段改編自 2010 年 4 月 3 日的對話。

簡便起見，你可以視「無限份之一」等如「零」。

$\frac{1}{\infty} = 0$

1/infinity = 0

不過，那只是輔助記憶的密碼，而不是正確合法的數學符號，因為，「無限」並不是一個數字，你不可以用「無限」來運算，或者表達任何數量。正確的寫法是，

$\left( \lim_{x \to \infty} \frac{1}{x} \right) = 0$

\left( \lim_{x \to \infty} \frac{1}{x} \right) = 0

而它的真正意思是：

如果 x 越來越大，1/x 會越來越接近零。

（安：那為什麼不直接那樣說，而要用複雜的數學符號來誤導人？）

因為那句說話冗長，但在數學中又要時常使用。沒有「簡稱」的話，會十分不便。正如，當我們教一個小朋友，「爺爺」是「爸爸的爸爸」的簡稱時，他同樣可以質疑，為什麼不直接說「爸爸的爸爸」，而要用複雜難寫的文字來誤導人？

「爺爺」=「爸爸的爸爸」

「 $\left( \lim_{x \to \infty} \frac{1}{x} \right) = 0$ 」= 「如果 x 越來越大，1/x 會越來越接近零。」

還有，這一句仍然只是「簡稱」，還未精確到可以視為數學句子。完整的版本詳盡很多。

— Me@2013.03.01

Backward compatibility, 5

Posted on March 1, 2013 by rpflee

To enjoy the past without limiting your life progress, install the past as virtual machines in the present.

— Me@2013-02-24 2:50 am

The attraction of virtualizing older operating systems is that it throws off the eternal yoke of backwards compatibility. Instead of bending over backwards to make sure you never break any old APIs, you can build new systems free of the contortions and compromises inherent in guaranteeing that new versions of the operating system never break old applications.

— Has The Virtualization Future Arrived?

— April 26, 2009

— Coding Horror

— by Jeff Atwood

You cannot start a new chapter of your life if you keep re-reading the last one.

—

The past is a good place to visit but a bad place to stay.

—

Factors

Posted on February 28, 2013 by rpflee

因子

factors = independent causes

因素 = 原因元素 = 原因粒子

product = the results of factors multiplying together

產品 = 積 = 因素成果

multiply

乘 = 騎 = 順勢 = 利用

— Me@2013-02-28 8:16 pm

微積分 5

Posted on February 28, 2013 by rpflee

這段改編自 2010 年 6 月 15 日的對話。

導數（derivative）dy/dx 的定義是

$\frac{dy}{dx} = \lim_{\Delta x\rightarrow 0} \frac{f(x + \Delta x)-f(x)}{(x + \Delta x)-x}$

\frac{dy}{dx} = \lim_{\Delta x \rightarrow 0} \frac{f(x + \Delta x) – f(x)}{(x + \Delta x) – x}

但是，你千萬不要直接背誦這個數式，因為它很繁複。你需要記憶的，是淺白一點的版本：　

$\Delta y = f(x + \Delta x)-f(x)$

$\frac{dy}{dx} = \lim_{\Delta x\rightarrow 0} \frac{\Delta y}{\Delta x}$

\Delta y = f(x + \Delta x) – f(x)

\frac{dy}{dx} = \lim_{\Delta x \rightarrow 0} \frac{\Delta y}{\Delta x}

— Me@2013.02.28

Exchange symmetry

Posted on February 28, 2013 by rpflee

Because the exchange of two identical particles is mathematically equivalent to the rotation of each particle by 180 degrees (and so to the rotation of one particle’s frame by 360 degrees), the symmetric nature of the wave function depends on the particle’s spin after the rotation operator is applied to it. Integer spin particles do not change the sign of their wave function upon a 360 degree rotation — therefore the sign of the wave function of the entire system does not change. Semi-integer spin particles change the sign of their wave function upon a 360 degree rotation (see more in spin-statistics theorem).

— Wikipedia on Exchange symmetry

2013.02.27 Wednesday ACHK

Blogging

Posted on February 27, 2013 by rpflee

Writing a blog is an entertainment against loneliness.

— Me@2009.12.18

無限蘋果 1.6

Posted on February 27, 2013 by rpflee

無限年 2.6 | 微積分 4.6 | Process, not a state, 7

大概而言，接受不到「無限」的話，你可以把它看成「超大」。「超大」只是一個模糊的印象，而不是一個明確的數字。　

準確而言，「無限」不是一個數字，而是一個過程。它是「不停地增長」這個過程，的一個簡稱。

— Me@2013.02.27

Elementary particles, 2

Posted on February 27, 2013 by rpflee

Tommaso Dorigo’s comrade Vladimir Lenin believed that an electron was a galaxy with many electrons, and so on, indefinitely. That’s what he meant by the statement that matter was “inexhaustible”. This hierarchical picture of the Matryoshka Universe was clearly indefensible already during Lenin’s life. First, it has to stop at the Planck scale because distances shorter than the Planck scale are unphysical, or at least don’t follow the normal laws of geometry. Second, two electrons must be exactly identical to allow chemistry to work, so they can’t carry any substructure that would be as variable as one of a galaxy (or even a high entropy, which must be zero).

— Composite vs elementary particles

— Lubos Motl

2013.02.27 Wednesday ACHK

Records

Posted on February 26, 2013 by rpflee

No records, no results.

— Me@2013-02-25 5:35 pm

無理數 2.2

Posted on February 26, 2013 by rpflee

乘法意思 5.2

這段改編自 2010 年 4 月 3 日的對話。

「有理數」（rational number）的意思是，兩個整數的比例。亦即是話，它是一個分數，而分子和分母都是整數。如果表達成小數，它會是一個「有盡小數」或者「循環小數」。

「有理數」英文「rational number」中的「rational」，在日常生活的意思是「合理的」。但是，在這個數學的情境下，應該解讀成「ratio-nal」。「ratio」即為「比例」。根據現在的上文下理，「rational number」應該翻譯成「比例數」。「比例數」這個詞，比「有理數」直接易明。

— Me@2013.02.26

Hiring

Posted on February 25, 2013 by rpflee

We rely on the Lake Wobegon Strategy, which says only hire candidates who are above the mean of your current employees.

— Hiring: The Lake Wobegon Strategy

— Peter Norvig, Director, Google Research

— 12th March 2006

2013.02.25 Monday ACHK

Consultant

Posted on February 25, 2013 by rpflee

Be a consultant, not a teacher.

Being a teacher makes me old; being a consultant makes me young.

— Me@2009.12.11

無限蘋果 1.5

Posted on February 24, 2013 by rpflee

無限年 2.5 | 微積分 4.5

這段改編自 2010 年 6 月 15 日的對話。

換句話說，這個高速心算方法，其實就是由 x 次方的大小，來比較眾多「超大」的級數。有了這個「比較次方法」，你在作正式的運算前，就可以直接知道答案。所以，除了剛才提及，「用計數機代 x = 100,000」的方法外，你還可以用這個方法，來驗算牽涉「無限」的極限題目。

而你得到的答案，有三種可能。

第一種情況是，因為分母中 x 的最大次方，大過分子中 x 的最大次方，所以當 x 趨向「無限大」時，整個分數會趨向「無限小」，即是零。例如，

$\left( \lim_{x \to \infty} \frac{x^2}{x^3 + 6} \right) = \hspace{5mm} \dots \hspace{5mm} = 0$

lim_{x -> infinity} x^2/(x^3 + 6)

= …

= 0

第二種情況是，由於分母中 x 的最大次方，小過分子中 x 的最大次方，導致當 x 趨向「無限大」時，整個分數都趨向「無限大」，即是「沒有極限」。例如，

$\left( \lim_{x \to \infty} \frac{x^3}{x^2 + 6} \right) = \hspace{5mm} \dots \hspace{5mm} \to \infty$

lim_{x -> infinity} x^3/(x^2 + 6)

= …

-> infinity

最後一種情況是，分母中 x 的最大次方，和分子中 x 的最大次方相同。那樣，當 x 趨向「無限大」時，整個分數都趨向一個「有限數」。至於那個「有限數」是什麼，你只要看看分子和分母中， x 最大次方的係數（coefficients），就可以判斷到。例如，

$\lim_{x \to \infty} \frac{2 x^3 + 3 x + 7}{5 x^3 + 3 x^2 + 6}$

$= \lim_{x \to \infty} \frac{2 x^3 + \hspace{5mm} \dots}{5 x^3 + \hspace{5mm} \dots}$

$= \hspace{5mm} \dots$

$= \frac{2}{5}$

lim_{x -> infinity} (2 x^3 + 3 x + 7)/(5 x^3 + 3 x^2 + 6)

= lim_{x -> infinity} (2 x^3 + …)/(5 x^3 + …)

= …

= 2/5

— Me@2013.02.24

Anger 4

Posted on February 22, 2013 by rpflee

gbog 15 hours ago | link

“Brilliant marketing play”

Maybe, but where the idealism gone? Both on HN, in tech circles, and, yes, at Google, there was some healthy dose of idealism. You know, this thing that make people do thing for something else than money, for the better good of humanity for example.

Idealism (and anger) brought us Linux, Vim, the Web, etc.

…

— Google has killed Android (the brand)

— Hacker News

2013.02.22 Friday ACHK

Always

Posted on February 22, 2013 by rpflee

For all, 2

“Always” means “all the time“, not “an infinite length of time“, for “infinity” is not a number.

— Me@2013-02-21 11:14:53 AM

Physics Town

continues

Author Archives: rpflee

Emacs, 2

Overprolific Alpha Geeks

微積分 6.2

Learning physics online?

Marriage

微積分 6.1

Backward compatibility, 5

Factors

微積分 5

Exchange symmetry

Blogging

無限蘋果 1.6

Elementary particles, 2

Records

無理數 2.2

Hiring

Consultant

無限蘋果 1.5

Anger 4

Always