Couple of years back we spotted a whale (humback) tail slapping fairly close by. We headed on a course that would take us behind the whale and then parallel but at a safe distance. Next thing we know the whale disappears, only to reappear right on our stern. She sat there for five or ten minutes following us and then disappears again and returns with her calf. They then proceeded to dance around the boat, diving under and reemerging the other side sometimes so close one could almost touch them, the mother quite happy for the calf to be right alongside us while she loitered slightly further away.
After half an hour or so they waved a cheery goodbye and put many boat lengths on us in a matter of a few moments. We could not have outpaced them if we tried.
“Give a man a fire and he's warm for a day, but set fire to him and he's warm for the rest of his life.” Terry Pratchett