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

Intelligence and Wisdom

A few days ago I finally figured out something I’ve wondered about for 25 years: the relationship between wisdom and intelligence. Anyone can see they’re not the same by the number of people who are smart, but not very wise. And yet intelligence and wisdom do seem related. How?

What is wisdom? I’d say it’s knowing what to do in a lot of situations. I’m not trying to make a deep point here about the true nature of wisdom, just to figure out how we use the word. A wise person is someone who usually knows the right thing to do.

If wisdom and intelligence are the average and peaks of the same curve, then they converge as the number of points on the curve decreases. If there’s just one point, they’re identical: the average and maximum are the same. But as the number of points increases, wisdom and intelligence diverge. And historically the number of points on the curve seems to have been increasing: our ability is tested in an ever wider range of situations.

The wise are all much alike in their wisdom, but very smart people tend to be smart in distinctive ways.

— Is It Worth Being Wise?

— Paul Graham

2015.07.03 Friday ACHK

Interest

1. The price paid for obtaining, or price received for providing, money or goods in a credit transaction, calculated as a fraction of the amount or value of what was borrowed

2. A great attention and concern from someone or something; intellectual curiosity

— Wiktionary

interest 2 ~ interest 1  

興趣 ~ 利息 

X is interesting

~ X can generate a lot of interest

~ X can generate a lot of automatic profits

~ X can generate a lot of next steps

— Me@2015-02-19 08:02:49 PM

2015.02.21 Saturday (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

長頸豹 3

尋找時間的定義 1.2

SICM, 3.2 | SICP, 2.2

這段改編自 2010 年 4 月 10 日的對話。

涉獵多門知識,即使對於「本行」的發展,也會有意想不到的幫助。

例如,我對「什麼是時間」這個物理問題,有極之大的興趣。我想像,如果我只閱讀和研究物理,可能窮一身的時間,也沒有寸進。

估不到,在大概 2006 年,我從一本電腦界的神作中,得到了靈感,開始對「時間定義」有一點理解。然後在今年(2010),再加上我在大學時代時,長期訓練得來的「語理分析」功力,我破解了,「時間」的大部分意思。

(安:你上星期也有提及過,那本電腦界的神作。)

又例如,如果一個人過身後,仍然以某種形式存在的話,究竟確實是以哪一種,或者怎麼樣的形式來存在呢?

從物理和電腦知識中,我得到了一些關鍵靈感。

「靈感」中的「靈」,其實就是解「靈活」、「靈通」,即是有大量和多類型的資料或消息來源。

— Me@2014.06.03

2014.06.03 Tuesday (c) All rights reserved by ACHK

化學科背誦 1.3

無足夠資料 10.3

這段改編自 2010 年 7 月 29 日的對話。

至於,另一半需要背誦的資料之中,可避則避,不可避則背。必須「死背」的,就唯有「死背」,不宜顧慮太多,始終考試成績要緊。

去年有一位學生,她說有很多次,在閱讀化學考試卷題目時,都有一頭霧水的感覺,連答案的第一步,都未必寫得出來。然後,我告訴她,如果沒有足夠資料,一個人多聰明也沒有用。正如,即使你是烹飪天才,如果沒有足夠的食物材料,也沒有辦法煮到美味的菜色。所以,我估計她「一頭霧水」的原因是,在化學科之中,沒有作足夠的背誦,導致作答題目時,「原材料」不足。

她不會知道,她不肯背誦化學的真正原因,所以我告訴她。她的性格是,從來不肯做「不合理」的事。雖然她的顯意識不知道,但是潛意識感覺到,化學科需要背誦的東西之中,有一半是無謂的東西。「無謂」的意思是,我剛才所講,沒有道理、不能合體的零碎資料。所以她的潛意識會自動反抗:「即使我用功背誦,長遠來說,那堆無謂的資料,一來不是有趣,二來沒有用處,三來會高速忘記。那我背來有什麼意義呢?」

接著,我跟她(的顯意識)解釋:

你的潛意識雖然沒有錯,化學科需要背誦的東西之中,真的有一半是『不合理』的東西;但是,如果你因為不肯背誦『不合理』的東西,而導致入不到大學,那就更加『不合理』。

兩害取其輕,兩利取其大。入大學前,在化學科之中,你要用你的『顯意識』,凌駕你的『潛意識』。

可以避免的東西,就盡量避免。但是,對於一些考試必須、不能避免的『原材料』,無論『有意義』還是『不合理』,你也要背誦。

我為什麼知道,她有這個性格特質呢?

那是因為我年輕時,也是那樣的。那時,我雖然喜歡聽生物課,但是不太肯溫習。我還以為,那純粹因為我「懶惰」。直到去年才領悟發現,背後真正的原因是,依我的性格,我不肯做「不合理」的事情。

每個人的腦海之中,都有一個「機會成本評價系統」。當我這個「評價系統」發覺,那些零碎資料不能合體,只能「死背」時,它就會知道,有很大的機會,那些東西對我來說,並沒有什麼長遠的價值。那樣,它就會自動大大降低,我的背誦動機。

那樣,當你遇到一些不能避免、必須「死背」的東西時,應該如何安撫,你潛意識之中的「機會成本評價系統」,避免它阻止你的背誦呢?

你可以試試,化「死背」為「生背」。

「死背」的意思是,沒有天然的道理,去整合眾多零碎的資料;各項資料都要各自為政,獨立記憶。但是,沒有先天自然的故事和上文下理,不代表不可以後天創作故事,潛建一些上文下理,去減輕背誦的難度。

有部分的記憶法,就是利用這個原理,把原本要「死背」的東西,喬裝成可以「生背」的材料。

— Me@2014.02.03

2014.02.04 Tuesday (c) All rights reserved by ACHK

化學科背誦 1.2

無足夠資料 10.2

這段改編自 2010 年 7 月 29 日的對話。

所以我猜想,你們真正需要投訴的是,在化學科,要背誦的東西之中,有很多都要「死背」—— 沒有明顯的意思,令到你們可以,把那些零碎資料合體,導致一來背起來格外辛苦,二來背完以後,又很快會不記得。

我中五時有讀化學,中六時則沒有。但是,根據常理推測,化學科需要背誦的東西之中,起碼有一半是有道理的,或者有上文下理可依,例如「物理化學」部分。換句話說,即是可以「生背」,毋須「死背」。那樣的話,化學科的這一半,你就應該沒有困難。

至於,另一半需要背誦的資料之中,可避則避,不可避則背。必須「死背」的,就唯有「死背」,不宜顧慮太多,始終考試成績要緊。

「死背」的意思是,沒有天然的道理,去整合眾多零碎的資料;各項資料都要各自為政,獨立記憶。但是,沒有先天自然的故事和上文下理,不代表不可以後天創作故事,潛建一些上文下理,去減輕背誦的難度。

有部分的記憶法,就是利用這個原理,把原本要「死背」的東西,喬裝成可以「生背」的材料。

— Me@2014.01.31

2014.01.31 Friday (c) All rights reserved by ACHK

化學科背誦 1.1

無足夠資料 10.1

這段改編自 2010 年 7 月 29 日的對話。

你們的化學科,主要有什麼困難?

(CSY:所要花的時間,好像遠多於其他科。)

(LMC:需要背誦的東西實在太多。)

其實即使是數學科和物理科,都有很多東西要背。分別就在於,數學和物理之中,要背的東西有道理。因為各項零碎資料之間,有著千絲萬縷的關係,所以最終可以合體,化成一個知識大結構。

所以我猜想,你們真正需要投訴的是,在化學科,要背誦的東西,有很多都要「死背」—— 沒有明顯的意思,令到你們可以,把那些零碎資料合體,導致一來背起來格外辛苦,二來背完以後,又很快會不記得。

— Me@2014.01.28

2014.01.28 Tuesday (c) All rights reserved by ACHK

Snowball

Flywheel 2

Learning anything is like learning language — you cannot learn a language by just reading books or dictionaries.

— Me@2013-02-11 06:28:56 PM

天才之道

點滴累積

— Me@2007.09.19

Language courses are an anomaly. I think they’re better considered as extracurricular activities, like pottery classes. They’d be far more useful when combined with some time living in a country where the language is spoken. On a whim I studied Arabic as a freshman. It was a lot of work, and the only lasting benefits were a weird ability to identify semitic roots and some insights into how people recognize words.

– Paul Graham

Learning math and physics takes a whole lifetime. Luckily, it’s a lot of fun… if you have a reasonably patient attitude.

— How to Learn Math and Physics

— John Baez

Life is like a snowball. The important thing is finding wet snow and a really long hill.

— Warren Buffett

2013.02.13 Wednesday (c) All rights reserved by ACHK

Teaching is useless

無足夠資料 9 | 數學教育 4 | What is statistics? 2 | 軟硬智力 10

Intellect is invisible to those have none.

– Arthur Schopenhauer

Teaching is useless. Information is useful. Although intelligence can seldom be increased, giving relevant information to a GOOD person so that he can fully realize his existing intelligence potential is always useful.

The intelligence-absorption principle should actually be called the information-absorption principle, because intelligence cannot be increased directly.

「智攝原則」應該改稱為「資攝原則」,因為你沒有可能,直接增加別人的智力。你可以做到的,就只有透過給予相關資料,去加快別人智力潛能的發展。換句話說,你只可以破除無知,而不可刪減愚蠢。

Information is just like technology: Intellectually challenging to create doesn’t mean intellectually challenging to use.

— Me@2011.11.10

You cannot teach a man anything, you can only help him to find it for himself.

– Galileo

2012.09.23 Sunday (c) All rights reserved by ACHK

背公式

這段改編自 2010 年 6 月 9 日的對話。

背誦公式時,不能單靠直接的背誦。你還要透過做大量的題目練習,才能有長久的記憶,因為題目有上文下理,你會知道什麼時候,應該用什麼公式。只是憑空背誦公式,是沒有用的。

— Me@2012.09.18

2012.09.18 Tuesday (c) All rights reserved by ACHK

Meaningful 5

X is meaningful

= You can keep developing X

= X always has next steps

1. If you have a lot of good intellectual and social connections, you can keep having the next steps.

2. Action is a good way to create the next steps and decrease uncertainties. 

— Me@2012.05.14

2012.07.10 Tuesday (c) All rights reserved by ACHK