Daily Archives: March 15, 2010

無足夠資料

Posted on by

Past papers 8

“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.

這段改編自 2010年 1 月 3 日的對話。

.

KYH: 我覺得自己在 physics（物理）上沒有天份，因為我花了很多時間在 physics，也沒有什麼成效。

Me: 是不是讀書的方法錯了？

KYH: 不知呢 … 但是將同樣長度的時間放上另一科的話，例如 pure maths（純數學），我會很快上手。

Me: physics 都可以很快上手。

KYH: 真的嗎？　那我讀 physics 的方法可能是錯的。

Me: 你現在的 physics 老師和 pure maths 老師，哪一個教得比較好？

KYH: 兩個都不好，因為我們基本上都是自修的。 physics 老師隨便地將自己的意思講一下，之後就「飛書」，省略了大部分的內容，然後就叫我們自己溫習。

Me: 那就即是話你的 physics 老師根本沒有教到任何東西。那你的 pure maths 老師有教書嗎？

KYH: 有 … 其實都是我們自己讀 …

Me: 我的意思是，你的 pure maths 老師有沒有教實質內容？

KYH: 有 …

Me: 分別就在這裡！　一個有教實質內容，一個沒有教實質內容。根據你的說法，你的 physics 老師根本沒有教內容。

KYH: 我覺得是。他只是跟課文講一講就算。

Me: 所以就是說，即使你的 pure maths 老師都是教得不太好，不夠詳細，但是他起碼有教內容，起碼有教第一層基本功。所以主要問題是這個，而不是你有沒有 physics 天份的問題。當然，我現在講可能會太遲，因為距離考試只有三、四個月。你這麼遲才知道這點，想百分百補救是不可能的。你現在補救的話，大概只能拿到 B 級，拿不到 A 級成績。但是起碼你知道你 physics 讀得不好，不是你自己的問題，而是你的 physics 老師失職。

— Me@2010.03.15

.

.

2010.03.15 Monday (c) All rights reserved by ACHK

Recursion

Posted on by

Recursive humor

A common joke (for example recursion in the Jargon File) is the following “definition” of recursion.

    Recursion

        See “Recursion”.

(Obviously, this recursion lacks the base case, so it will recur indefinitely.)

This is a parody on references in dictionaries, which in some cases may lead to circular definitions among related words. Jokes often have an element of wisdom, and also an element of misunderstanding. This one is also the shortest possible example of an erroneous recursive definition of an object, the error being the absence of the termination condition (or lack of the initial state, if looked at from an opposite point of view). Newcomers to recursion are often bewildered by its apparent circularity, until they learn to appreciate that a termination condition is key.

An example of this can be found by searching Google for the term “Recursion”. Google cleverly puts the searcher in an endless cycle, of suggesting “Recursion” as the word they were trying to spell, even though that's exactly the input they just used.

A variation is:

    Recursion

        If you still don't get it, see: “Recursion”.

which actually does terminate, as soon as the reader “gets it.”

— Wikipedia on Recursion

2010.03.15 Monday ACHK

Transcender

Posted on by

.

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

.

.

.

2010.03.15 Monday ACHK