Over the years, I have read and heard many stories of dogs seemingly supernatural ability to sense when their master is coming home, or when the mail truck is on its way, etc. I believe there is some tendency among humans to treat this as a magical "sixth sense". Or to over-credit the sense of hearing: "dogs can differentiate the sound of their owner's car/school bus from 5 miles away"--I'm definitely calling bs on that one.
But as so often is the case, there is a known or posited scientific explanation. This article focuses on the time-decay of smell, in combination with other cues, as the explanation. E.g., the family children, in this case, arrive home from school on a school bus. The departure and arrival times of school buses are pretty predictable, I bet +- 5 minutes 95% of the time. The rate at which the children's scent decays is the main clue. This signals to the dog that arrival is imminent, prompting it to lurk in anticipation near the door.
The final part of the magic trick is delivered by the acute--but not magically powerful--sense of hearing. The dog lurks near the door, and they do hear the vehicle far sooner than any human would. They react in anticipation, completing the illusion that they have a magical superpower.
Encountering scientific explanations is ultimately much more rewarding than crediting far-fetched or magical explanations of phenomena.
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