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I will be the first to admit that math was not my favorite subject in school, and in fact it made me HELLA anxious.
我将是第一个承认数学不是我的菜的人，事实上，数学对我来说还挺让人抓狂的。
But I've definitely warmed to it, especially since I heard about the Ham Sandwich theorem--
但我的确开始喜欢上数学了，尤其是当我知道了“火腿三明治定理”以后——
what, a girl loves to eat!--
怎么了，女孩子是吃货怎么了！——
oh, and also the fact that it might help us better understand our universe, but whatever.
哦，对了，这个定理还能帮助我们更好地理解我们的宇宙，不过，那又怎样。
Let's take a step back and start with pancakes.
我们还是先退回来从煎饼开始说起吧。
A bit of a departure from the universe and ham sandwiches,
听着和宇宙，火腿三明治定理不怎么沾边儿哈，
but this smorgasboard will eventually all make sense, I promise.
但我保证，这个北欧美食我绝对不是来说着玩儿的。
The pancake theorem states that if I have a pancake on a plate, there's at least one cut that I can make to divide that pancake in half. Simple.
煎饼定理指出，如果我在盘子里放了个煎饼，至少要切一刀才能将煎饼分成两半。手到擒来。
If I add another pancake on the plate, no matter where it is,
如果往盘子里再放一个煎饼，不管放在哪里，
there's going to be at least one cut that I can make through both of them that will allow me to divide both pancakes in half.
要想把两个煎饼都分成两半，至少也要切一刀。
Again, simple enough, right?
还是很简单对吧？
But, that's because the pancake theorem technically only deals in 2-dimensional space,
问题是，这是因为严格来讲，煎饼定理针对的只是二维空间的问题，
like these pancakes that we're talking about are perfectly flat as if they were pancakes that we've drawn on a piece of paper.
比如我们刚刚谈到的煎饼是理想状态下的平面，就如同是画在纸上的煎饼一样。
The Ham Sandwich theorem takes the concept and moves it into 3-dimensions, the world we actually live in.
火腿三明治定理借鉴了这个概念并将其引入了三维空间，即我们实际生活的世界。
Ok, I'm about to drop a math formula on you here, but I want you to stay calm and stay with me, ok, here we go.
好了，现在，我要搬一个数学公式出来了，但我希望大家保持冷静，不要走开，好吗？大家准备好哈。
Given n measurable objects in n-dimensional Euclidean space,
假设在n维欧氏空间中有n个可测量物体，
it is possible to divide all of the objects in half (with respect to their volume) with a single (n-1)-dimensional hyperplane .
则可以用一个（n-1）维超平面将所有物体分成两半（相对于它们的体积）。
Yeah, I know. I read that sentence when I was first researching this video and was just like, "No. there's no way."
嗯，我懂。准备拍这个视频的时候，第一次读到这句话我也是你们这个反应，“不可能。绝壁不可能。”
BUT it turns out this convoluted statement actually expresses something remarkably simple and useful,
但事实证明，这个复杂的陈述实际上表达的概念非常简单而且实用，
so I want you to come on an imaginary adventure with me.
所以我希望大家能和我来一次想象力的冒险之旅。
Say we have a ham sandwich.
假设我们有一个火腿三明治。
That's our n-measurable objects, our 3 measurable things: 2 slices of bread and 1 slice of ham.
它就是我们的n个可测量的物体，这里我们有3个可测量的物体：2片面包，1片火腿。
(We're being stingy with the ham, ok.)
（我们这个火腿很小气啊，就这样吧。）
In 3-dimensional space, it's possible to use a single cut to divide the sandwich in half, no matter where the 3 items are.
在三维空间里，无论3个物体在哪里，都可以一次性将三明治切成两半。
Now, this doesn't JUST mean that a sandwich AS A WHOLE can be halved.
这并不仅仅意味着整个三明治可以被切成两半。
If we're defining the sandwich as our 3 items (bread, bread, and ham),
也即如果我们将三明治定义为三个事物（面包，面包和火腿），
even if we dropped our sandwich on the floor and the three items were all over the place,
即便我们把三明治掉到了地上，掉得到处都是，
yeah, we could draw one plane that would divide the entire volume of the sandwich in two.
我们也还是可以用某个平面将整个三明治分成两份。
But it ALSO means, and this is where it gets real cool, that each individual item in the sandwich,
但它也意味着，这也是这个公式最酷的地方，三明治中的每个单独物体，
no matter where they are in space, can be divided perfectly in two with one plane.
无论它们处于空间中的哪个位置，也可以被完美地分为两份。
This part is easier to picture if we get rid of gravity and picture the pieces of our ham sandwich floating in the air.
如果不考虑重力，想象我们的火腿三明治是漂浮在空中的，这一点会更容易想象出来。
Doesn't matter where, they could be right next to each other or on opposite ends of the universe
无论它们在哪里，无论是紧挨着彼此，还是分别位于宇宙的两端，
and there is still at least one magic plane that could bisect all of the ingredients perfectly, with one cut.
都还是存在一个神奇的平面可以将它们一次性完美地对半切开。
Ok, so this is cool and made us do some fun mental gymnastics,
好了，这很酷，我们也跟着做了一些有趣的心理体操，
but I'm never going to drop my ham sandwich on the floor
但我绝对不会把三明治掉到地上
and then whip out my calculator like, "let me find the magic line that divides all these in two".
然后把计算器掏出来，说“我来找找那条能够将所有这些东西分成两半的神奇线条”。
So exactly how is this important or useful?
话说回来，这个定理到底重要在哪里呢？又有何用处呢？
Well, a paper that came out a few years ago wanted to explore exactly that, and came to some cool conclusions,
几年前发表的一篇论文就探讨了这个问题，也得出了一些很好的结论，
stating that "At any given instant of time,
结论就是“在任何给定的时刻，
there is one planet, one moon and one asteroid in our solar system
我们的太阳系都只有一个地球，一个月球和一个小行星，
with a single plane touching all three that exactly bisects the total planetary mass, the total lunar mass, and the total asteroidal mass of the solar system."
而有一个平面能够将所有三个天体的质量一分为二。”
All of this is to say, theoretical mathematics like this helps us understand the very nature of the way the universe behaves.
所有这一切都是想表明，这样的理论数学有助于我们理解宇宙运动方式的本质。
We can use things like the ham sandwich theorem, along with our understanding of physics and the natural sciences,
我们可以用火腿三明治定理，以及我们对物理学和自然科学的理解，
to help us make computer simulations of everything from atomic phenomena to the movement of celestial bodies.
来帮助我们对从原子现象到天体运动的各种事物进行计算机模拟。
Man, the world is crazy and beautiful.
天了噜，这个世界真是又疯狂又美丽啊。
And who knew that talking about ham sandwiches could turn this former math-phobe into, dare I say, a math enthusiast.
谁又知道聊聊火腿三明治也能让我这个数学恐惧症患者变成，说句不中听的，数学粉呢。
You like our videos but you haven't subscribed? Something doesn't add up!
喜欢我们的视频又还没有订阅？怪不得有个数据没涨！
Subscribe to Seeker to keep understanding more about our universe,
赶紧订阅我们的频道，加深对宇宙的了解吧，
and check out this video about how a universe could've bumped into ours.
而这个视频就讲述了其他宇宙和我们的宇宙发生碰撞时的情形。
And just FYI, the original creator of the ham sandwich theorem was named Hugo Steinhaus,
最后，还有一点仅供大家参考，提出火腿三明治定理的那个哥们儿叫Hugo Steinhaus，
and worked out this problem while hiding from the Nazis in a Polish farmhouse during WWII.
这个定理是第二次世界大战期间他在波兰一家农舍躲避纳粹时想出来的。
BADASS. I'm Maren, thanks for watching Seeker.
杂皮。我是Maren，感谢大家收看我们的节目。
