You realize, that looks really miraculous

你们会觉得这看上去十分不可思议
because we just wrote down an arbitrary force

因为我们刚刚随便写了一个力
that we all cooked up together with these exponents,

我们一起写出了这些指数项
and the answer depends on the path.

而该力所做的功与路径有关
And I guarantee you,

而且我跟你保证
if you just arbitrarily write down some force, it won't work.

你如果只是随便写下一些力是不行的
So, maybe there is no Law of Conservation of Energy

所以也许在维数大于一的空间中
in more than one dimension.

能量守恒定律根本不成立
So, how am I going to search for a force that will do the job?

我该如何寻找一个能够完成这项任务的力
Are there at least some forces for which this will be true? Yes?

是否存在一些力符合能量守恒定律请说
No, but see the point is

不对注意关键是
you've got to first write down a force in the xy plane.

你写下的力首先是位于 xy 坐标系内的