I could be 0 km from home,

也可能是0公里
or I could be -10, if I'd gone two steps to the left.

也可能是 -10 如果我两次都是向左的话
You can deal with this by saying not just 5 km,

你不能只说5公里
but plus or minus 5 km.

而应该是+5或者-5公里
If you give a sign, on top of the number,

如果你在数字前加一个符号
that takes care of all ambiguity in one dimension.

就把一维运动的所有的歧义解决了
So the sign of the number is adequate to keep track of my motion.

所以数字的符号对于记录运动足够了
But, you know, in 2D,

但在二维空间中
the options are not just left and right or north and south,

不仅可以向左向右或者向南向北
but infinity of possible directions in which I could go those 5 km.

我在走那5公里的时候可以有无数个方向
What I could do on the first day is to come here.

我可以第一天到这里
On the second day, could be to go there.

第二天可以到那里