This is not about how long Santiago has gone without catching a fish.
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I don't think there is an exact time given, we can surmise that it has been many years. The first sentence reads, "He was an old man who fished alone in a skiff in the Gulf Stream." Santiago is seen as a joke by other fishermen. He has gone 84 days without a fish and, much like him, his boat is creaky and old. The younger fishermen have newer boats and motors. Parents often forbid their sons to fish with him.