How can hope and despair be akin?

[Eomer of the Rohirrim]

Hello, pretties.

So I'm all set to start work on my dissertation (finally). I'm going to be writing about the meaning of life. My general take on this is that life is meaningless. What I'm really interested in discussing in my paper, though, is whether this would be cause for happiness or despair—because there's a long history in philosophy of writers being dismayed by such conclusions.

Now, there's a beautiful line in The Return of the King, spoken by Aragorn. Here it is:

"We come now to the very brink, where hope and despair are akin."

I'd love to work it into the essay if at all possible! But that's secondary. What I really want to ask you lovely people is what you make of the line, because it's meaning doesn't strike me as particularly clear.

What was 'Gorn saying?