The case of the missing fractals - Alex Rosenthal and George Zaidan

譯者: Jacky Wang 審譯者: Christine Fu

It was a night like any other night,

那是個再平常不過的夜晚

except here I was climbing the platonic peaks

唯一不同的是 我爬上了一座柏拉圖式的山峰

like Romeo on a second date.

像極了二度赴約的羅密歐

(ugh)

（哎）

I was there for the dame.

我是為了一個女人而來的

She had eyes like imaginary numbers

她有著虛數般的眼神

and curves that went on forever.

一頭捲髮好似永無止境

Said she wanted to go home.

她說她想回去

Said I could help.

說我幫得上忙

Said the pay was good.

而且報酬還挺豐碩

Didn't say anything about climbing a...

卻沒說我必須先爬上……

Voice: "Who's there?"

聲音：「是誰在那裡？」

Manny Brot: "Manny Brot, private eye."

曼尼博：「曼尼博，私家偵探。」

Voice: "What are you doing here?"

聲音：「你在這裡幹什麼？」

"A pretty number sent me to find a stolen dingus."

「一位女郎託我尋找 一樣失竊的東西。」

Voice: "Well, to enter the cave,

聲音：「想要進入洞穴，

you must answer my riddles three."

你必須先解開三道謎題。」

What was it with riddles,

為什麼又是謎題？

and why do they always come in threes?

而且為什麼總是一次來三題？

"Is it an egg?"

「是蛋嗎？」

"No. Why would it be an egg?"

「錯。為什麼會是蛋？」

"It's usually an egg."

「謎底通常都是蛋。」

"What can I hold in my hand, but has zero area?"

「甚麼東西沒有面積， 卻能拿在手上？」

"Is it a dodo egg?"

「嘟嘟鳥的蛋？」

"It's not an egg!"

「才不是蛋！」

I took out the rock that had nearly brained me before

我掏出剛才砸到我的那塊石頭

and gave it a hard ponder.

仔細思考了一會兒

The size of the rising bump on my conk

頭上的大腫包告訴我

said to me that this thing had area,

這東西不但有面積

and a lot of it.

而且還不小

But what if I carved out a triangle from this side here?

但假如我從這裡 分割出一個三角形呢？

As any mook could see,

顯而易見

this triangle had a quarter of the area of the full triangle.

這個小三角形的面積是 大三角形的四分之一

I did the same thing again with each of the smaller triangles.

對於剩下的三角形重複同樣的過程

Again, a quarter of the remaining area -- gone.

就又有四分之一的面積消失不見

And I just kept going.

於是我繼續下去

After an infinite number of cuts,

經過無限次的分割之後

I was satisfied that my triangle had zero area.

我很肯定這個三角形已經沒有面積

A bounded shape with zero area.

一個有界的形狀，卻沒有面積

Now, it's not often that I surprise myself,

我並不是常常靈光乍現的人

but my own two mitts had created something crazy,

這次我卻親手創造出這瘋狂的東西

and new.

前所未有

"Very good. (ahem)

「非常好。（嗯哼）

Now, show me a shape with finite area,

下一題，甚麼形狀面積有限

but an infinitely long perimeter."

周長卻是無限長？」

"Let me get this straight.

「先讓我搞清楚。

If I want to make a snip in the border of this shape,

如果我把這個形狀的一個邊剪開，

smooth it out, and lay it on the ground ... "

然後攤平放在地上……」

"It would go on for ... "

「它會一直延……」

"Wait 'til I'm through, and then you can talk.

「等我講完你才能說話。

It would go on forever."

它會一直延伸下去。」

"Are you through?"

「說完了嗎？」

"Yeah."

「嗯。」

"So show me that shape then."

「那麼告訴我那是甚麼形狀吧。」

Mmm ... I hadn't been this stuck

嗯……除了 58 年那次 沒有解開魔術方塊之外

since the Rubik's Cube fiasco of '58.

這是我第一次感覺這麼苦惱

All the shapes I knew had perimeters.

所有我知道的形狀都有周長

Circles: 2πr. Triangles: sum of their sides.

圓形：2πr。三角形：三邊總和

What's this?

這是甚麼？

An angle.

一個角度

An angle from heaven.

好似天使下凡

What if I were to pinch each side, like so.

如果我像這樣在邊上一捏呢？

A third of the way through, just so.

像這樣在三分之一處 弄出新的三角形

And do it again,

再一次

and again,

再來一次

and again.

不斷重複

After each pinch, the perimeter got a third longer

每捏一次，這個圖形的 周長就多了三分之一

because where there had been three line segments,

因為原本的三段

now there were four.

變成了四段

As for the area,

至於圖形的面積

every pinch made more triangles, that's true.

它的確不斷地在增加

But those triangles were getting smaller and smaller.

但不斷增加的三角形卻是越來越小

You could say that the area was converging,

因此實際上面積正慢慢在收斂

approaching a fixed number,

趨近於一個固定的值

while the perimeter was just getting bigger and bigger,

而周長則是不斷增加

uncontrollably ballooning like an overindulgent birthday clown.

就像瘋狂的生日派對小丑一樣

After infinity pinches, flimflam, there it was:

重複動作無限多次之後，結果會是：

Finite area, but infinite perimeter.

有限的面積，無限的周長

Now that is a piece of work.

無庸置疑，是個傑作

"Oh, you're good. (ahem) Riddle three:

「不錯嘛。（嗯哼）第三題：

Show me a picture that if I magnify it under my microscope,

給我一張圖，

I'll keep seeing the original picture,

不管我將它放得多大，

no matter how much I zoom in."

我永遠會看到相同的圖案。」

"You're a strange little man."

「你真是個怪咖。」

"Thank you."

「您過獎了。」

I was out of ideas,

我毫無頭緒

so I looked at my muse, my complex Dora.

我看著朵拉，我的謬思

Voice: "Who's the dame?"

聲音：「這位女郎是誰？」

And then it hit me.

忽然之間，我開竅了

"She's a heart breaker, my fractal femme fatale.

她是我的女神，我的碎形小妖姬

Will she do?"

她可以嗎？」

"Yes, she'll do just fine."

「完全符合要求。」

(lightning)

（雷聲）

It was dark, and at first I thought the cave was empty,

起初我以為洞裡甚麼都沒有

but then I noticed: the box.

接著我看到了一個箱子

The dame had played me like a triangle.

她一直玩弄我於股掌之間

She had told me she wanted to go home.

告訴我她想回家

(Lightning)

（雷聲）

What she really wanted was to bring her home here.

她所謂的家原來是這裡

The fractals spread everywhere.

碎形到處蔓延

Most of them the same

有些碎形，無論放的多大

no matter how deep you looked at them,

你永遠會看到相同的圖案，

like Dora's mugshot.

就像那張照片一樣

Some had infinitely long perimeters,

有些有著無限的周長

others were objects with no area or volume,

還有一些沒有面積和體積的東西

all of them created through infinite repetition.

都是由無限次重複得來的

So, you wanted to know what fractals are?

想知道碎形是甚麼？

孩子，它們是創造夢想的原料。

Well, kid, they're the stuff that dreams are made of.

(Music)

（音樂）