改變因果鏈起點

這段改編自 2010 年 4 月 24 日的對話。

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所以,我們先企圖進攻那些大題目,無論它們長遠是否,對你直接有用;因為,過程之中,自然會引發很多技術細節。而那些技術細節,很多是你直接可用的。

原初辛苦上山的目標是,傳說中,山頂上的寶藏。但是,上到山頂後,才發現最珍貴的寶藏,反而是沿途找到的那些。

(安:我覺得你對我最大的價值,反而是:

因為你鼓勵我,先企圖進攻的那些大題目中,很多也是你自己,曾經進攻過的,所以,你從它們之中篩選出來,提議我去研究的,必定是你覺得對我來說,最有價值的那些。

如果不是那樣的話,我可能要麼就是,開始研究某個大題目時,就覺得徬徨,而無心機繼續;要麼就是,真的花了一年半載,研究某個大題目後,發覺原來事倍功半,或者價值不大。)

那其實正正就是,「教育」的精髓,「學習」的意思。

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為何不事事親身去經歷呢? 

因為人生苦短。

透過吸收他人的經歷,可以改變因果鏈的起點。

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人在某個意思之下,其實已經有了永生。個別的人會死亡,但人類整體而然,可存在很久。只要不絶種,就是得永生。對於任何物種,都可以這樣說。

但是,只有人類這個物種,有大規模的知識傳授。而大規模的知識傳授,則自然需要大量時間。

幸而,雖然人生苦短,但仍剛剛足夠長,去行一個「學習、發掘和傳授」循環。在進化接力賽中,人類每一代剛好有足夠時間,去完成交收接力棒的工序。在知識上,每一代人也可以,以上一代人的終點,作為自己的起點。

— Me@2021-09-22 10:24:46 PM

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2021.09.23 Thursday (c) All rights reserved by ACHK

一萬個小時 3.4

重點副作用 6 | The non-side-effect-ness of side-effects, 6

這段改編自 2010 年 4 月 24 日的對話。

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現在,有三個概念混淆在一起。我們先釐清一下。

1. 幾乎

任何學問,或者才藝,如果要訓練自己,純熟到足以用來維生賺錢,或者娛樂滿足,需要的時間幅度是,一日幾小時,持續一兩年,才會開竅;然後,再持續一兩年,才會知道自己,在該門學問才藝,為何會開竅,開了什麼竅;又再過一兩年,才會有能力教人,如何在該門學問才藝開竅。

2. 過程中的一個重要環節是,會領悟到一些洞見。

3. 雖然要「自己領悟」第二點中的洞見,來自第一點中的「幾年加幾年」過程,但是,如果只是「吸收別人已知的」知識本身,絶不需要花「幾年加幾年」。有時,甚至只是,花數個小時就可以。

「學習」的意思正正就是,自己毋須親身經歷(例如)四年,也可以獲取本來要四年,才發掘得到的成果。

4. (1.) 但是,「知道」本身,並不代表自己有足夠功力去「運用」,而「運用」則是,第一點的水平。不過,如果中途有第三點,即是別人情報資料上的提點,你就可以走少很多冤往路。那樣,原本是(例如)十年的過程,可以壓縮到(例如)三年。

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剛才你提到:「

你的講法是,有些知識,你只需要幾個小時,就可以傳授給我,不成課程,因為時間所需太短;而另一些知識,我就需要花「幾年加幾年」,才可以領會得到,不成課程,因為時間所需太長。

其實,我們可以考慮改變方案。雖然有些課題,可能幾個小時,就可以完成,但是,我們可以每個星期,也講不同的課題。

留意,雖然個別課題的成果,只會花幾小時,但是那是指,事先已有課題的情況下。那些有趣而深刻的課題,簡稱「勁題目」,並不會從天而降。那些勁題目本身,大部分情況下,只會在你開始研究,將會花「幾年加幾年」的苦功知識時,才會引發得到。

— Me@2021-05-23 04:39:54 PM

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2021.05.25 Tuesday (c) All rights reserved by ACHK

Genius 4

High school teachers are by nature non-intellectuals; students are by nature intellectuals.

— Me@2011.08.23

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As a mathematician there is a story I hear a lot. It tends to come up whenever I tell someone what I do for the first time, and they admit that they don’t really like, or aren’t very good at, mathematics. In almost every case, if I bother to ask (and these days I usually do), I find that the person, once upon a time, was good at and liked mathematics, but somewhere along the way they had a bad teacher, or struck a subject they couldn’t grasp at first, and fell a bit behind. From that point on their experiences of mathematics is a tale of woe: because mathematics piles layer upon layer, if you fall behind then you find yourself in a never ending game of catch-up, chasing a horizon that you never seem to reach; that can be very dispiriting and depressing.

— Zen and the Art of Mathematics

— The Narrow Road

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All children are born geniuses; 9999 out of every 10000 are swiftly, inadvertently degeniusized by grownups.

— Buckminster Fuller

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2021.05.15 Saturday (c) All rights reserved by ACHK

一萬個小時 3.3

這段改編自 2010 年 4 月 24 日的對話。

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我現在的狀態是,在某些範疇中,有能力教人之餘,還有能力教人如何教。亦即是話,如果教員甲的教學質素,好過教員乙的話,我可以解釋到,甲比乙好在哪裡。

(安:這一點對我好有用。)

但那不能成為課程,因為,它只需一個下午,就可以大概完整地,講給你聽。

(安:你的講法是,有些知識,你只需要幾個小時,就可以傳授給我,不成課程,因為時間所需太短;而另一些知識,我就需要花「幾年加幾年」,才可以領會得到,不成課程,因為時間所需太長。)

現在,有三個概念混淆在一起。我們先釐清一下。

1. 幾乎

任何學問,或者才藝,如果要訓練自己,純熟到足以用來維生賺錢,或者娛樂滿足,需要的時間幅度是,一日幾小時,持續一兩年,才會開竅;然後,再持續一兩年,才會知道自己,在該門學問才藝,為何會開竅,開了什麼竅;又再過一兩年,才會有能力教人,如何在該門學問才藝開竅。

2. 過程中的一個重要環節是,會領悟到一些洞見。

3. 雖然要「自己領悟」第二點中的洞見,來自第一點中的「幾年加幾年」過程,但是,如果只是「吸收別人已知的」知識本身,絶不需要花「幾年加幾年」。有時,甚至只是,花數個小時就可以。

4. 1. 但是,「知道」本身,並不代表自己有足夠功力去「運用」,而「運用」則是,第一點的水平。不過,如果中途有第三點,即是別人情報資料上的提點,你就可以走少很多冤往路。那樣,原本是(例如)十年的過程,可以壓縮到(例如)三年。 

— Me@2021-04-25 09:29:14 PM

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2021.04.26 Monday (c) All rights reserved by ACHK

一萬個小時 3.2

這段改編自 2010 年 4 月 24 日的對話。

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(安:但是我的工作,幾乎沒有一些方面,需要任何的學術成份。)

或者,未必一定是一些,十分高層次的學術課題。在你正職當中,乘機磨鍊一些才藝,都可以。例如,我在之前的工作,訓練了表達技巧。我在中學教書時,需要每天講學三個多小時。講了一年半載後,說話才通順,可以完成完整句子而不「跳線」。

那個經驗,令我知道任何學問,或者才藝,如果要訓練自己,純熟到足以用來維生賺錢,或者娛樂滿足,需要的時間幅度是,一日幾小時,持續一兩年,才會開竅;然後,再持續一兩年,才會知道自己,在該門學問才藝,為何會開竅,開了什麼竅;又再過一兩年,才會有能力教人,如何在該門學問才藝開竅。

我現在的狀態是,在某些範疇中,有能力教人之餘,還有能力教人如何教。亦即是話,如果教員甲的教學質素,好過教員乙的話,我可以解釋到,甲比乙好在哪裡。

— Me@2021-04-08 02:11:07 AM

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2021.04.09 Friday (c) All rights reserved by ACHK

Cheer up?

What you encourage people, don’t say “don’t worry, be happy” or “cheer up”.

They are nonsense, because they are not actionable.

What I really need to know is HOW to be happy.

What I really need to know is what ACTION to take to solve my problem.

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When you see a doctor, what if, without giving any other advice, he just tells you to “cheer up”?

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在開解朋友時,千萬不要講「加油」和「睇開啲啦」等廢話。

那只會令當事人,更加不開心。

— Me@2011.06.26

— Me@2020-12-30

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2020.12.30 Wednesday (c) All rights reserved by ACHK

Ken Chan 去咗邊呢?

無足夠資料 11.1

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來到這版,可能是你看了 Ken Chan 的物理參加書時,發現了他的網址:

d_2018_04_10__11_57_18_AM_

不到意思,他已經沒有用這個網址了。我不是 Ken Chan,而是他九十年代的學生。(無錯,我都已經係老餅。)

我租了這個網址,一來,用作紀念;二來,亦可以避免他人冒充 Ken Chan;繼而,我就可親自冒充他。

(邪惡地笑)

d_2018_04_11

當然,那於理不合,於法不容。所以,我重申一次:

我不是 Ken Chan,而是他九十年代的學生。

(但是,如果需要聯絡本人,可用右邊的電郵地址。)

.

那樣,Ken Chan 又去了哪裡呢?

我也不知道。他既然停用了自己的課程網址,那最大的可能性就是,他從教學界退了休。

~~~

我不喜歡「補習老師」這個詞語,因為我不喜歡「補習」,又不喜歡「老師」:

「補習」一詞,給人「多餘」、「依賴」和「騙錢」的感覺。

「老師」一詞,給人「年老」、「沉悶」和「沒有發展」的感覺。

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所以,我不會稱 Ken Chan 為我的「補習老師」;如果一定要給一個尊稱,我會叫他為我的「物理先知」。

同理,雖然我也有從事類似的行業,我亦不會叫我自己做「補習老師」,而是「學術顧問」。

而 Ken Chan 的境界,遠遠高於其他老師的原因,正正就是,他的人生目標(或稱正職),並不是做「補習老師」,而是一位學者,從事學術研究。

(至於他的在哪間大學任教和研究,我則不知道,因為,他沒有公開。)

在學生時代,我已經立志(!)不做(!)全職的中學教員。

一個稍為有創意、略略有志氣的年青人,又怎能忍受自己人生中的幾十年,重複教著同一堆東西呢?

除非,教學只是他的職責之一。他仍有大半時間,從事學術研究。學術的精神世界,仍然是不停地發展的。

~~~

如果他真的退了休,香港的物理學生,又如何是好呢?

問題有那麼嚴重嗎?

有。如果香港沒有實力相近於 Ken Chan 的,物理兼工程專家,去指導眾多年輕人,那就真的十分大件事了。

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當年,如果沒有他的教導,我大概不能升學。

— Me@2018-04-11 12:21:42 PM。

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2018.04.11 Wednesday (c) All rights reserved by ACHK

Intellectual Headaches

Game design

They got the key, and then some other stuff happened, and then they reached the door, and were able to open it; but “acquiring the key” and “opening the door” were stored as two separate, disconnected events in the player’s mind.

If the player had encountered the locked door first, tried to open it, been unable to, and then found the key and used it to open the door, the causal link would be unmistakable. You use the key to open the locked door, because you can’t open the locked door without the key.

Math education

I’ve drawn parallels between game design and education before, but it still took me a while to realize that problem-solution ordering issues crop up just as often in the classroom as they do in games.

Remember how, in high school math class, a lot of the work you were doing felt really, really pointless?

Consider Dan Meyer’s question for math educators: if math is the aspirin, then how do you create the headache?

In other words: if you introduce the solution (in this case, a new kind of math) before introducing the kind of problems that it’s meant to solve, the solution is likely to come across as pointless and arbitrary. But if you first let students try to tackle these problems with the math they already understand, they’re likely to come away with a kind of intellectual “headache” – and, therefore, to better understand the purpose of the “aspirin” you’re trying to sell.

Functional programming

— Locked doors, headaches, and intellectual need

— 27 October 2015

— Affording Play

Here are some excerpts of an elegant essay. Please go to the author’s website to read the whole.

— Me@2015-11-03 03:46:41 PM

2015.11.03 Tuesday ACHK

如何拯救眾生 2

How to improve the world indefinitely?

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There is law of conservation of energy.
There is law of conservation of mass.
But, there is no law of conservation of ideas.

能量守恆,
質量守恆,
意念不守恆,
程式可以無限複製.

— Me

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If you have an apple and I have an apple, and we exchange apples, we both still only have one apple. But if you have an idea and I have an idea, and we exchange ideas, we each now have two ideas.

— George Bernard Shaw

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. . . it is the action of the thinking power called an idea, which an individual may exclusively possess as long as he keeps it to himself; but the moment it is divulged, it forces itself into the possession of every one, and the receiver cannot dispossess himself of it. Its peculiar character, too, is that no one possesses the less, because every other possesses the whole of it. He who receives an idea from me, receives instruction himself without lessening mine; as he who lights his taper at mine, receives light without darkening me.

That ideas should freely spread from one to another over the globe, for the moral and mutual instruction of man, and improvement of his condition, seems to have been peculiarly and benevolently designed by nature, …

— Thomas Jefferson

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2008.10.21 Tuesday (c) All rights reserved by ACHK

如何拯救眾生 1

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The meeting of two personalities is like the contact of two chemical substances: if there is any reaction, both are transformed. — Carl Jung

Generalized Newton’s Third Law: You cannot change others without being changed. — John Wheeler

改變別人時, 你也會被改變. — Me

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You are an A person. You befriend with an F person. The result is that your friend becomes a better person, you become a worse person. In theory, you become a C person. Your friend becomes a C person. In practice, since being a bad person is much easier than being a good person, you two will become both F people. — Me

無友不如己者. — 孔子

Be slow in making friends, slower in changing. — Benjamin Franklin

You have to know how to accept rejection and reject acceptance. — Ray Bradbury

If you hire all A people, he said, they’ll also hire A people. But if you hire B people, they’ll hire the C people and then it’s all over. — Joel Spolsky

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So that means you cannot help anyone weaker than you?

NO.

Instead, you should help others. But you have to help others in a smart way. — Me

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How?

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. . . it is the action of the thinking power called an idea, which an individual may exclusively possess as long as he keeps it to himself; but the moment it is divulged, it forces itself into the possession of every one, and the receiver cannot dispossess himself of it. Its peculiar character, too, is that no one possesses the less, because every other possesses the whole of it. He who receives an idea from me, receives instruction himself without lessening mine; as he who lights his taper at mine, receives light without darkening me.

— Thomas Jefferson

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2008.10.22 Wednesday (c) All rights reserved by ACHK

Wittgenstein’s ladder

6.54

   My propositions serve as elucidations in the following way: anyone who understands me eventually recognizes them as nonsensical, when he has used them — as steps — to climb beyond them. (He must, so to speak, throw away the ladder after he has climbed up it.)

   He must transcend these propositions, and then he will see the world aright.

— Tractatus Logico-Philosophicus

— Ludwig Wittgenstein

Before climbing a ladder, it is higher than you; after, you are higher than it.

— Me@2011.07.31

2015.04.02 Thursday (c) All rights reserved by ACHK

軟硬智力 12

天人天書 1.2.3

這段改編自 2010 年 4 月 10 日的對話。

比喻說,我因為打網球,導致運動量增加,令我身體更加健康,從而頭腦更加清晰,工作更加順利。你並不需要問:「究竟你打網球中的哪個動作技巧,令到你的工作更加順利?」

第一層次,「神作」帶來嶄新的意念。

第二層次,「神作」帶來天人的靈感。

以上兩者皆是 software(軟件)。

第三層次,「神作」中的 software,有時會上乘到,引發我有 hardware 上,即腦部結構的改變。換句話說,「硬件智力」得以提升。

腦部的 hardware(硬件),即是腦部本身,並不完全是「硬」而不可改變的。用腦用得多,或者受到「神作」的衝擊,腦中眾多神經元細胞之間的連繫,會變得密集很多。

— Me@2014.11.14

2014.11.15 Saturday (c) All rights reserved by ACHK

活出電影

這段改編自 2010 年 4 月 10 日的對話。

除了書籍以外,我也會很有意識地,去收集電影作品中的「神作」。「收集」的意思,不限於觀賞。我以前當日校老師的那三年中,每逢看電影時,我也會很自然地,留意各部電影的「講故事技巧」。它們為我的教學,帶來不少的靈感。

(安:那比較難想像。

如果那是一部喜劇,我可以想像,你可以把電影中的部分笑話,改篇成教學版本。但是,如果那是一部(例如)警匪片,那就比較難想像,當中的「故事技巧」,怎樣可以應用在教學之中。)

不一定是直接。

比喻說,我因為打網球,導致運動量增加,令我身體更加健康,從而頭腦更加清晰,工作更加順利。你並不需要問:「究竟你打網球中的哪個動作技巧,令到你的工作更加順利?」

— Me@2014.10.31

2014.11.05 Wednesday (c) All rights reserved by ACHK