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It was a night like any other night, except here I was climbing the platonic peaks like Romeo on a second date.
这是一个再寻常不过的夜晚，只不过，我在攀登一座想像中的高峰，如同罗密欧的第二次赴约。
I was there for the dame. She had eyes like imaginary numbers and curves that went on forever.
我去那是为了那位夫人。她有着虚数般难以刻画的眼睛和一头长长的卷发。
Said she wanted to go home. Said I could help. Said the pay was good.
她说她要回家，而我可以帮忙，她说会给我很好的报酬。
Didn't say anything about climbing a... 'Who's there?'
并没有提到爬上……“谁？”
'Manny Brot, private eye.'
“曼尼·勃罗特，私家侦探。”
'What are you doing here?'
“你来干什么？”
'A pretty number sent me to find a stolen dingus.'
“一个漂亮的数字差我来找一个失窃的东西。”
'Well, to enter the cave, you must answer my riddles three.'
“想要进入这个洞穴，你必须解出我的三则谜语。”
What was it with riddles, and why do they always come in threes?
谜语是什么，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？”
'It's not an egg!'
“不是蛋！”
I took out the rock that had nearly brained me before and gave it a hard ponder.
我拿出了那块差点把我开瓢的石头，开始仔细思考。
The size of the rising bump on my conk said to me that this thing had area, and a lot of it.
石头突起的部分有大小，这告诉我这个东西有面积，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, this triangle had a quarter of the area of the full triangle.
谁都能看出，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. And I just kept going.
又一次，剩下面积的四分之一被拿走了。我就这样一直操作。
After an infinite number of cuts, I was satisfied that my triangle had zero area.
在无穷次操作之后，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, but my own two mitts had created something crazy, and new.
确实，我不经常惊到我自己，但我自己创造了神奇的、新颖的东西。
'Very good. Now, show me a shape with finite area, but an infinitely long perimeter.'
“很好。现在，给我一个面积有限的图形，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, smooth it out, and lay it on the ground...'
如果我在这个图形的边界上去掉一点，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. It would go on forever.'
“等我说完，你才能说话。它就会一直延伸下去。”
'Are you through?' 'Yeah.' 'So show me that shape then.'
“你说完了？”“说完了。”“那就给我看看这个图形。”
Mmm ... I hadn't been this stuck since the Rubik's Cube fiasco of '58.
嗯...我在1958年的魔方难题之后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. What's this?
圆的周长是2π乘上半径。三角形的周长是三边的和。这是什么？
An angle. An angle from heaven. What if I were to pinch each side, like so.
一个角。天使般的一个角。我如果把每条边向外拉，像这样。
A third of the way through, just so. And do it again, and again, and again.
把边的三分之一拉起来，就像这样。再做一次，再做一次，第三次。
After each pinch, the perimeter got a third longer because where there had been three line segments, now there were four.
每次拉，周长都增长三分之一。因为原来有三个线段，现在变成了四个。
As for the area, every pinch made more triangles, that's true.
对于面积，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, approaching a fixed number,
可以说面积是收敛的，面积会接近一个固定值。
while the perimeter was just getting bigger and bigger, uncontrollably ballooning like an overindulgent birthday clown.
可是周长的确在变得越来越大，无法控制，就像小丑一样向外膨胀。
After infinity pinches, flimflam, there it was: Finite area, but infinite perimeter. Now that is a piece of work.
在无限次向外拉以后，看：有限的面积，无限的周长。这就是成果。
'Oh, you're good. Riddle three: Show me a picture that if I magnify it under my microscope,
“哦，你很强。第三条谜语：给我一张图片，如果我用望远镜观察它，
I'll keep seeing the original picture, no matter how much I zoom in.'
我仍然能看到原始的图像，不论我把它放大多少倍。”
'You're a strange little man.' 'Thank you.'
“你真是个怪人。”“谢谢。”
I was out of ideas, so I looked at my muse, my complex Dora.
我没主意了，所以我看向我的小本，那位朵拉女士。
'Who's the dame?' And then it hit me.
“这位女士是谁？”我突然有了主意。
'She's a heart breaker, my fractal femme fatale. Will she do?'
“她能让你心碎，我的分形的致命小姐。她符合吗？”
'Yes, she'll do just fine.'
“没错，她正好。”
It was dark, and at first I thought the cave was empty, but then I noticed: the box.
天很暗，刚开始我以为山洞是空的，但我马上注意到了那个盒子。
The dame had played me like a triangle. She had told me she wanted to go home.
女士像玩弄三角形一样玩了我。她告诉过我她想回家。
What she really wanted was to bring her home here. The fractals spread everywhere.
她想的其实是把她家带来这里。分形散到了各处。
Most of them the same no matter how deep you looked at them, like Dora's mugshot.
他们大多长得一样，无论你多么细看它们，就像朵拉女士的照片。
Some had infinitely long perimeters, others were objects with no area or volume,
有的图形有无限长的周长，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。
