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"I had plenty of time for meditation, and now and then I would give some thought to Kurtz. I wasn't very interested in him. No. Still, I was curious to see whether this man, who had come out equipped with moral ideas of some sort, would climb to the top after all and how he would set about his work when there." (1.74)
Despite himself, Marlow becomes more and more curious about this faceless figure of Kurtz. From the brickmaker's description of him, Marlow assumes that Kurtz came out "equipped with moral ideas of some sort," probably the sort that try to justify imperialism. When compared to the godlessness of the crew surrounding Marlow, Kurtz seems like a good alternative.
"Where the pilgrims imagined it crawled to I don't know. To some place where they expected to get something. I bet! For me it crawled towards Kurtz—exclusively […]." (2.7)
This has quickly stopped being curiosity and become obsession: Marlow doesn't see the wilderness as his destination anymore, but just Kurtz. (Or are they really that different?)
"'And by the way, I suppose Mr. Kurtz is dead as well by this time.'
"For the moment that was the dominant thought. There was a sense of extreme disappointment, as though I had found out I had been striving after something altogether without a substance. I couldn't have been more disgusted if I had travelled all this way for the sole purpose of talking with Mr. Kurtz." (2.23-24)
Marlow just can't leave it alone: Kurtz is dead, but he's still obsessed with the man—so obsessed that he visits the Intended. We hope he got what he was looking for.