Explain the significance in that Paulo Coelho opens The Alchemist with the modified myth of Narcissus: how is it of importance to the plot?
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There are several versions of the story of Narcissus. In each case, he is a handsome and vain youth who spurns the attentions of others, and ultimately falls in love with his own reflection. There are, also, many versions of how Narcissus dies, but all are related to his callous behavior toward others and his love for his own image.
In the "Prologue" of Paulo Coelho's The Alchemist, the author presents a version of this famous tale. In this telling, Narcissus does indeed fall in love with his image. However, here he dies by falling into the lake, while in other versions he commits suicide or simply fades away. As with other stories of Narcissus, some do mourn his passing rather than cursing him. And as with the other tales, a flower blooms where Narcissus passes away.
A striking difference here is that the lake, not a wood nymph, mourns the loss of Narcissus—so much so that she cries an endless stream of tears, and the water becomes salty.
...when Narcissus died, the goddesses of the forest appeared and found the lake, which had been fresh water, transformed into a lake of salty tears.
The goddesses ask the lake why it weeps and it tells them it is for Narcissus. They comment that they can understand this: they had pursued him through the forest, but only the lake could get close enough to see his beauty.
The lake is puzzled, and asks the goddesses if Narcissus was beautiful. The goddesses reply that the lake would know better than anyone, having gazed upon his face so often.
The lake was silent for some time. Finally, it said:
"I weep for Narcissus, but I never noticed that Narcissus was beautiful. I weep because, each time he knelt beside my banks, I could see, in the depths of his eyes, my own beauty reflected."
Coelho's use of this version of Narcissus' story accomplishes two purposes. First, it presents the notion that not everyone agrees on what is valuable in this world. For example, at the end of the novel, when Santiago has been beaten by the robbers, the last robber mocks Santiago's dream, noting that he had had a similar dream. Santiago will take the dream the robber dismisses to his heart, and it will lead him to a treasure. For the robber, only money and/or jewels have any value. However, Santiago has learned that treasure comes in many forms, and the most valuable of them need not literally be found in a chest, buried at the foot of an old tree.
Another thought is that some people realize their own worth by seeing themselves through the loving eyes of another. Fatima knows that she is lovely because Santiago loves her. Whether she is beautiful based upon society's expectations is not relevant. His love for her is what matters. She has no worry about anything that may come along, for with Santiago's love, she is all that she could want to be. His love makes her feel treasured, and she promises to wait for him.