Mythbusters actually tested if this was true by trying to train a fish to swim through a maze. They decided that they do have better memories than 3 seconds. A video showing this can be found here:
The behaviour often expressed by fish, including goldfish, suggest they can have long-term memory….certainly more than 3 seconds. My Grandfather would tap his foot at the edge of his pond and the fish would come to the side where he was stood to be fed. He fed them every other day, indicating at least a 48 hour memory of a signal that indicated feeding time.
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