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。)
