Author Archives: rpflee

Transcender

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One of the most useful mental habits I know I learned from Michael Rabin: that the best way to solve a problem is often to redefine it.

The way to kill it is to redefine the problem as a superset of the current one. The problem is not, what operating system should people use on desktop computers? but how should people use applications? There are answers to that question that don’t even involve desktop computers.

Everyone thinks Google is going to solve this problem, but it is a very subtle one, so subtle that a company as big as Google might well get it wrong. I think the odds are better than 50-50 that the Windows killer– or more accurately, Windows transcender— will come from some little startup.

— Paul Graham

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2010.03.15 Monday ACHK

Sage (mathematics software)

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Design Philosophy of Sage

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William Stein realized several important facts when designing Sage.

* To create viable alternatives to Magma, Maple, Mathematica, and MATLAB, would take hundreds, or thousands of man-years if one started from the beginning.
* There was a large collection of open-source mathematics software already written, but which was written in different languages (C, C++, Fortran and Python being the most common).

So rather than start from the beginning, Sage which is written in Python and Cython integrates all their specialized mathematics software into a common interface. A user needs to know only Python.

Where no open-source option exists for a particular class of problem, then this would be written in Sage. But Sage does not reinvent the wheel. The same design philosophy is used in commercial mathematics program such as Mathematica, but Sage can use a much wider range of open source software solutions than nonfree software, since some open source licensing imposes restrictions on commercial use of code.

— Wikipedia on Sage (mathematics software)

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2010.03.14 Sunday ACHK

Demand transparency

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The problem here is not wealth, but corruption. So why not go after corruption?

We don’t need to prevent people from being rich if we can prevent wealth from translating into power.

How do you break the connection between wealth and power? Demand transparency. Watch closely how power is exercised, and demand an account of how decisions are made.

— Paul Graham

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2010.03.14 Sunday ACHK

多次元宇宙 2

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（安：「因果」是一個比喻空泛的一個概念 … 除了它有一個元素，就是「原因先於結果」。但是，除此之外，什麼是「因果」 呢？其實意思是迷迷糊糊的。）

其實可以這樣說：「不會無 A 而有 B」，那樣，A 就為之 B 的「因」。

（安：你的意思是將「原因」介定為「先決條件」？）

是。

（安：但是，你這個架構，和「原因」這個詞在日常生活的用法不相符。例如，有一件事件 B，它有十個先決條件：A1, A2, …, A10。要 A1, A2 … 到 A10 都發生了，B 才會發生。那樣，哪一個才算是 B 的原因呢？）

簡化起見，假設要 A, B, C 都發生了，D 才會發生。那我可以說「A, B, C 都是 D 的原因」。如果我說「A 是 D 的原因」的話，我都沒有錯，因為我不是說「A 是 D 的唯一原因」。

（安：如果根據你這個講法，「原因」這個詞就更加空泛：幾乎發生於 D 之前的任何事，都可以稱為 D 的原因。）

正正是這樣。所有在事件 D 的過去的事，都是事件 D 的原因。

（安：這樣用的話，會令到「原因」這個詞空泛到完全沒有意義。）

這裡，「原因」這個詞，其實已化成「時間」的意思。「原因」就即是「過去」。當我們說事件 A 是事件 D 的「原因」，其實即是話 A 在 D 的過去。

（安：這個講法很奇怪，而且遺反了日常生活中「原因」這個詞的用法。例如，我說「我有好成績的原因是我有努力讀書。」意思並不只是 「『努力讀書』是在『拿到好成績』的過去。」）

所以要非常小心。我們現在討論的「原因」是取其廣義，意思是「眾多先決條件之一」。而日常生活中的所講的「原因」，是取其狹義，意思是 「眾多先決條件中，最重要的一個」。

— Me@2010.03.13

2010.03.13 Saturday (c) All rights reserved by ACHK

Eric E. Schmidt

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Apple

Schmidt was elected to Apple’s board of directors on August 28, 2006. On August 3, 2009 it was announced that Schmidt would resign his board member position at Apple due to conflict of interests and the growing competition between Google and Apple.

— Wikipedia on Eric E. Schmidt

2010.03.13 Saturday ACHK

Good runners

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Good runners still get tired; they just get tired at higher speeds.

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If you feel exhausted, it’s not necessarily because there’s something wrong with you. Maybe you’re just running fast.

— Paul Graham

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2010.03.13 Saturday ACHK

知己知彼

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Past papers 7

“Past papers” means “past HKCEE/HKAL examination papers”. The topic is for Hong Kong students who are facing HKCEE or HKAL. But the general principles can also be used for tackling other public examinations.

這段改篇自 2010年 1 月 3 日的對話。

LKF：我覺得現在的溫習進度不行…

Me：”不行” 是什麼意思？ “不行” 可以是指不合格，又可以指拿不到最好成績（A 級）。

LKF：不知呀 … 我現在只有 chemistry （化學）一科行。

Me：”行” 是什麼意思？

LKF：都應該可以取到 B （B級成績）。

…

Me：哪這一科是不是十分穩陣（安全）？

LKF：應該好穩陣。

Me：你有沒有試過計時計分做歷屆試題（pastpaper）？

LKF：還沒有。

Me：那就不太安全。因為你現在只是憑感覺，認為自己行，沒有客觀的成績做參考。萬一你的感覺錯了，哪怎麼辦呢？

最好是每一次也 限時間 計分數 按年份 做 pastpaper。那樣你就可以知道自己在考試的指定時間內，可以拿到什麼分數，達到什麼水平。還有，你未必每一次也有時間做整整一年的 pastpaper。例如 2006 年的 pastpaper 包括 paper 1 和 paper 2（卷一和卷二），共要六小時完成。但是你某一日只有三小時，不能完成 2006 年整份 pastpaper。那也沒有所謂。你可以一日用三小時做 paper 1，下一日用三小時做 paper 2。重點是要 限時間 和 計分數。

你知不知多少分對應什麼 grade（等級）？

LKF：不是太清楚。

Me：我認為現在你們最大的問題是 不知己又不知彼。知彼的意思是 知道什麼分拿什麼 grade；知己的意思是 知道自己可以拿到多少分數。這些都是一定要問清楚、搞清楚的資料。還有，要得到這些資料是簡單容易的事情。要知彼，你可以問老師，他們一定會知道什麼分拿什麼 grade；要知己，你限時間做 pastpaper，完成後立刻為自己批改，就可以知道自己的水平。

自信不是建基於才華出眾；自信不是建基於沒有困難；自信來自於對自己的了解；自信來自於對客觀環境的了解。

— Me@2010.03.12

2010.03.12 Friday (c) All rights reserved by ACHK

Universal Grammar

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Avram Noam Chomsky (born December 7, 1928) is an American linguist, philosopher, cognitive scientist, political activist, author, and lecturer.

Influence in other fields

Chomskyan models have been used as a theoretical basis in several other fields. The Chomsky hierarchy is often taught in fundamental computer science courses as it confers insight into the various types of formal languages. This hierarchy can also be discussed in mathematical terms and has generated interest among mathematicians, particularly combinatorialists. Some arguments in evolutionary psychology are derived from his research results.

The 1984 Nobel Prize laureate in Medicine and Physiology, Niels K. Jerne, used Chomsky’s generative model to explain the human immune system, equating “components of a generative grammar … with various features of protein structures”. The title of Jerne’s Stockholm Nobel lecture was “The Generative Grammar of the Immune System”.

— Wikipedia on Noam Chomsky

2010.03.11 Thursday ACHK

天使與傻瓜

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If you begin by sacrificing yourself to those you love, you will end by hating those to whom you have sacrificed yourself.

* Self-Sacrifice

— George Bernard Shaw

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天使, 犧牲自己的利益來追求自己的理想.

魔鬼, 犧牲別人的利益來追求自己的理想.

傻瓜, 犧牲自己的理想來追求別人的利益.

智者, 透過實現自己的理想來追求別人的利益.

— Me@2009.09.14, 2010.03.11

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2010.03.11 Thursday copyright ACHK

多次元宇宙

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Multi-dimensional universe

上次你說有關 multi-dimensional 的問題。你可不可以由第一句開始講？

（安：Multi-dimensional … 時間 … 其實我不太記得上次我們說了什麼 …）

我們說有關 points of view 的問題。有時候我的講法和你的講法不同。然後我說，”看法不同” 這個現象可以比喻成，我們其實看著同一個 object（物件），只不過我們各自 由不同的角度去觀察它。

（安：哪和時間有什麼關係呢？）

你上次問，雖然我用了 multi-dimensional universe（多次元宇宙）來比喻 “本體”，但是我這個比喻沒有處理到宇宙萬物的 “因果關係”。接著，我就說，multi-dimension 的其中一個次元就是 ”時間”。而 ”時間”，就是 ”因果網絡”。所以，我這個比喻，已經包括了 “因果關係”。

…

（安：”因果” 是一個比喻空泛的一個概念 … 除了它有一個元素，就是 ”原因 先於 結果”。但是，除此之外，什麼是 ”因果” 呢？其實意思是迷迷糊糊的。）

其實可以這樣說： “不會無 A 而有 B ” ，那樣，A 就為之 B 的 “因”。

（安：你的意思是將 ”原因” 介定為 ”先決條件”？）

是。

— Me@2010.02.10

2010.03.10 Wednesday (c) All rights reserved by ACHK

Publish! 2

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Anything you do not publish,

will disappear with with you.

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Anything you do not publish,

will disappear in this world after your life.

— Me@2010.03.08

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2010.03.10 Wednesday copyright ACHK

時間定義

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時間 = 因果網絡

all the necessary conditions（所有先決條件）= sufficient condition（充份條件）

（廣義）原因 = one of the necessary conditions（先決條件之一）

（狹義）原因 = 主要原因 = 主要先決條件

先決條件：　不能有 B 而沒有 A 的話，那 A 就是 B 的先決條件。

怎樣判別一個先決條件是不是主要先決條件？

— Me@2010.02.10

2010.03.09 Tuesday (c) All rights reserved by ACHK

A great artist

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Anybody can look at a pretty girl and see a pretty girl. An artist can look at a pretty girl and see the old woman she will become. A better artist can look at an old woman and see the pretty girl that she used to be. But a great artist — a master — and that is what Auguste Rodin was — can look at an old woman, portray her exactly as she is… and force the viewer to see the pretty girl she used to be…. and more than that, he can make anyone with the sensitivity of an armadillo, or even you, see that this lovely young girl is still alive, not old and ugly at all, but simply prisoned inside her ruined body. He can make you feel the quiet, endless tragedy that there was never a girl born who ever grew older than eighteen in her heart…. no matter what the merciless hours have done to her. Look at her, Ben. Growing old doesn’t matter to you and me; we were never meant to be admired — but it does to them. Look at her! (UC)

— Robert A. Heinlein

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2010.03.09 Tuesday ACHK

Past papers 6

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雖然原理你已明白，但是到你執行時，一定受你原本的習慣所影響，未必能妥善貫徹。所以，這些心理技巧和工作方法，一定要在平日溫習時先行練習，養成習慣，化成自然反應。

當年我考 ALevel pure maths （高考純數學）時， section A（短題目）竟然 7 題題目中，有 4 題不懂做。但是，我當時十分鎮定，立刻停止不懂的題目，儲存住那些時間，先去做 section B（長題目）。完成所有 section B 的題目後，我才回頭做剛才不懂的 4 題 section A 短題目，結果 4 題都給我想通了。

那時，我為何可以那麼鎮定呢？現在的我反而沒有那麼鎮定。大部分人亦不會那麼鎮定，去立刻停止當時想不到的題目。通常都會覺得 “只差一點點，就會想通那道題目” ，所以再花一些時間。結果還是想不到。但是已花了額外的時間去想，放棄的話會更加心有不甘，所以會花再多的時間去想。 … … 那樣，就會不知不覺墮進惡性循環，浪費極多的時間。

高考時的我可以那麼鎮定，是因為我平日溫習時，幾乎每日都做按年份的 pastpaper。做 pastpaper 會限時間和計分數。每日都有模擬考試，所以已經習慣了 “有題目想不通” 的情況。”唔識就飛” （想不通就立刻停止原本的題目，去做下一題）已成了我的反射動作。

所以說，我不斷提醒你們的，是一些考試必須的情緒技巧，一定要在平日已經練習好。否則，你在考試時的心理質素差的話，即使知識水平夠，你也不能獲取高分數。

— Me@2010.03.06

2010.03.08 Monday (c) All rights reserved by ACHK

Curry–Howard correspondence 2

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The Curry–Howard correspondence also raised new questions regarding the computational content of proof concepts which were not covered by the original works of Curry and Howard. In particular, classical logic has been shown to correspond to the ability to manipulate the continuation of programs and the symmetry of sequent calculus to express the duality between the two evaluation strategies known as call-by-name and call-by-value.

Speculatively, the Curry–Howard correspondence may be expected to lead to a substantial unification between mathematical logic and foundational computer science: …

— Wikipedia on Curry–Howard correspondence

2010.03.08 Monday ACHK

Curry–Howard correspondence

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If one now abstracts on the peculiarities of this or that formalism, the immediate generalization is the following claim: a proof is a program, the formula it proves is a type for the program. Most informally, this can be seen as an analogy which states that the return type of a function (i.e., the type of values returned by a function) is analogous to a logical theorem, subject to hypotheses corresponding to the types of the argument values passed to the function; and that the program to compute that function is analogous to a proof of that theorem. This sets a form of logic programming on a rigorous foundation: proofs can be represented as programs, and especially as lambda terms, or proofs can be run.

The correspondence has been the starting point of a large spectrum of new research after its discovery, leading in particular to a new class of formal systems designed to act both as a proof system and as a typed functional programming language.

— Wikipedia on Curry–Howard correspondence

2010.03.07 Sunday ACHK