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

注定外傳 1.11

Can it be Otherwise? 1.11

換句話說,某一件事件是否「必然」,不會是絕對的;而是相對於某個「觀測準確度」而言。例如:

甲:這次數學考試我不合格。那是不是必然的呢?

乙:你可以反問:「如果遇到相同的情境,可不可以有不同的結果?」

那樣,你就可以知道,答案是「非必然」,因為,參加這次考試的同學中,有很多也是合格的。

甲:那不算是「相同的情境」。我問的是「我不合格,是不是必然?」

我和其他人不同,所以,即使是面對同一份試題,也不算是「相同的情境」。不同的人有不同的基因,繼而有不同的天資。

乙:那怎樣才算「相同情境」?

甲:應該討論「同一個人」。

乙:那樣,你數學考試不合格,答案都是「不注定」,因為,你在眾多數學考試中,有很多時也是合格的。

甲:那不算是「相同的情境」。我問的是「這次數學考試」。不同的試卷,有不同的難度。

乙:那樣,你試一試再次考同一份試卷。如果合格,那就可以證明,你的數學考試不合格,是偶然,並非必然。

甲:那不算是「相同的情境」。我問的是「這次數學考試」。

相同的試卷,第二次做的時候,已有額外的記憶;例如,已知會出哪幾道題目。那又怎算是「相同的情境」呢?

乙:那怎樣才算是「相同的情境」呢?

依你的講法,你要是「同一個人,同一份試卷,同一次」,才算是「相同的情境」。那樣,你原本的問題「那次數學考試,是否注定不合格」,就會變成了一條「廢問題」。

剛才已經講過,問一件事件是否注定,就相當於問:

下次如果遇到相同的情境,可不可以有不同的結果?

但是,你卻在問了之後,認為那是「下次」,不是「那一次」,所以不算是「相同的情境」。

那樣的話,唯一同「那一次」相同的情境,就真的只有「那一次」。「那次數學考試,是否注定不合格」的唯一可能答案,就是「是」,因為,「那一次」已經發生了。

過去的事不能改變,所以是必然的。

— Me@2015-10-29 03:10:19 PM

Q: Can it be otherwise?

A: What is “it”?

— Me@2015-10-29 03:10:14 PM

2015.11.03 Tuesday (c) All rights reserved by ACHK