There is no rule that says a teller must meet the eye of each listener during the course of a story, but if you look mostly at the floor or ceiling, the audience could get the idea that you are afraid of them or not interested in them. I look around a lot at different faces, because I feel that looking at just a few people puts a burden on them to look interested.
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When I tell a story, I usually try to sound not like somebody else, but like me at my best, without the “uhs” and “you knows” that spatter everyday conversation, and without the bright cheerfulness that comes over even the most sensible people when they talk to the very young.