What is the difference of nuance: "Look about you," and "Look around you."

I have been reading a book about learning English these days. Today I found the book said that the word "about" reminds native speakers some kind of images like being there around something. And there was a example sentence above "Look about you."
But I don't understand the difference of nuance between about and around in this case.

I'd like to know the difference of nuance of these. Could someone explain to me?