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

翻译人员: Mingyu Cui 校对人员: Shengwei Cai

It was a night like any other night,

这是一个再寻常不过的夜晚，

except here I was climbing the platonic peaks

只不过，我在攀登一座想像中的高峰，

like Romeo on a second date.

如同罗密欧的第二次赴约。

(ugh)

（啊）

I was there for the dame.

我去那是为了那位夫人。

She had eyes like imaginary numbers

她有着虚数般难以刻画的眼睛

and curves that went on forever.

和一头长长的卷发。

Said she wanted to go home.

她说她要回家，

Said I could help.

而我可以帮忙，

Said the pay was good.

她说会给我很好的报酬，

Didn't say anything about climbing a...

并没有提到爬上……

Voice: "Who's there?"

声音：“谁？”

Manny Brot: "Manny Brot, private eye."

侦探：“曼尼·勃罗特，私家侦探。”

Voice: "What are you doing here?"

声音：“你来干什么？”

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

侦探：“一个漂亮的数字 差我来找一个失窃的东西。”

Voice: "Well, to enter the cave,

声音：“想要进入这个洞穴，

you must answer my riddles three."

你必须解出我的三则谜语。”

What was it with riddles,

谜语是什么，

and why do they always come in threes?

为什么总是三则？我在心里嘀咕。

"Is it an egg?"

“是一只蛋吗？”

"No. Why would it be an egg?"

“不！怎么会是蛋？”

"It's usually an egg."

“答案通常是蛋。”

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

“什么东西没有面积，但我能握在手里？”

"Is it a dodo egg?"

“是渡渡鸟蛋吗？”（渡渡鸟：一种已灭绝不会飞的鸟）

"It's not an egg!"

“不是蛋！”

I took out the rock that had nearly brained me before

我拿出了那块差点把我开瓢的石头，

and gave it a hard ponder.

开始仔细思考。

The size of the rising bump on my conk

石头突起的部分有大小。

said to me that this thing had area,

这告诉我这个东西有面积，

and a lot of it.

还不小。

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

但如果我从这条边上把三角形裁开呢？

As any mook could see,

谁都能看出，

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

这个小三角形的面积是大三角形的四分之一。

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

我再对每个小三角形做同样的操作。

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

又一次，剩下面积的四分之一被拿走了。

And I just kept going.

我就这样一直操作。

After an infinite number of cuts,

在无穷次操作之后，

I was satisfied that my triangle had zero area.

我很满意，我的三角形没有面积了。

A bounded shape with zero area.

一个被包围的图形，却没有面积。

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

确实，我不经常惊到我自己，

but my own two mitts had created something crazy,

但我自己创造了神奇的、

and new.

新颖的东西。

"Very good. (ahem)

“很好。（咳）

Now, show me a shape with finite area,

现在，给我一个面积有限的图形，

but an infinitely long perimeter."

但是周长是无限的。”

"Let me get this straight.

“让我说清楚吧。

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

如果我在这个图形的边界上去掉一点，

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

抹平它，把他拍在地面上...”

"It would go on for ... "

“它就会一直...”

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

“等我说完，你才能说话。

It would go on forever."

它就会一直延伸下去。”

"Are you through?"

“你说完了？”

"Yeah."

“说完了。”

"So show me that shape then."

“那就给我看看这个图形。”

Mmm ... I hadn't been this stuck

嗯...我在1958年的魔方难题之后

since the Rubik's Cube fiasco of '58.

就从来没遇到过这样的困难。

All the shapes I knew had perimeters.

我知道的所有图形都有周长。

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

圆的周长是2π乘上半径。三角形的周长是三边的和。

What's this?

这是什么？

An angle.

一个角。

An angle from heaven.

天使般的一个角。

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

我如果把每条边向外拉，像这样。

A third of the way through, just so.

把边的三分之一拉起来，就像这样。

And do it again,

再做一次，

and again,

再做一次，

and again.

第三次。

After each pinch, the perimeter got a third longer

每次拉，周长都增长三分之一。

because where there had been three line segments,

因为原来有三个线段，

now there were four.

现在变成了四个。

As for the area,

对于面积，

every pinch made more triangles, that's true.

的确每拉一次都产生了更多的三角形，

But those triangles were getting smaller and smaller.

可是这些三角形却越来越小。

You could say that the area was converging,

可以说面积是收敛的。

approaching a fixed number,

面积会接近一个固定值。

while the perimeter was just getting bigger and bigger,

可是周长的确在变得越来越大，

uncontrollably ballooning like an overindulgent birthday clown.

无法控制，就像小丑一样向外膨胀。

After infinity pinches, flimflam, there it was:

在无限次向外拉以后，看：

Finite area, but infinite perimeter.

有限的面积，无限的周长。

Now that is a piece of work.

这就是成果。

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

“哦，你很强。（咳）第三条谜语：

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

给我一张图片，如果我用望远镜观察它，

I'll keep seeing the original picture,

我仍然能看到原始的图像，

no matter how much I zoom in."

不论我把它放大多少倍。”

"You're a strange little man."

“你真是个怪人。”

"Thank you."

“谢谢。”

I was out of ideas,

我没主意了，

so I looked at my muse, my complex Dora.

所以我看向我的小本，那位朵拉女士。

Voice: "Who's the dame?"

声音：“这位女士是谁？”

And then it hit me.

我突然有了主意。

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

“她能让你心碎，我的分形的致命小姐。

Will she do?"

她符合吗？”

"Yes, she'll do just fine."

“没错，她正好。”

(lightning)

（闪电）

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

天很暗，刚开始我以为山洞是空的，

but then I noticed: the box.

但我马上注意到了那个盒子。

The dame had played me like a triangle.

女士像玩弄三角形一样玩了我。

She had told me she wanted to go home.

她告诉过我她想回家。

(Lightning)

（闪电）

What she really wanted was to bring her home here.

她想的其实是把她家带来这里。

The fractals spread everywhere.

分形散到了各处。

Most of them the same

他们大多长得一样，

no matter how deep you looked at them,

无论你多么细看它们，

like Dora's mugshot.

就像朵拉女士的照片。

Some had infinitely long perimeters,

有的图形有无限长的周长，

others were objects with no area or volume,

其他的没有面积或者体积，

all of them created through infinite repetition.

所有图形都是通过无限的重复动作创造的。

So, you wanted to know what fractals are?

所以你想要知道分形是什么吗？

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

孩子，他们是组成梦的东西。

(Music)

（音乐）