Every man can tell how many goats or sheep he possesses, but not how many friends.
~ Marcus Tullius Cicero
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When Elizabeth got her "pillow pet," she said, "Ooooh... It's like sleeping on a lamb."
Now, I'm not an expert on sheep (or goats or car maintenance or much of anything else), but I would imagine that it is not a pleasant experience to sleep on a lamb. However, I decided a long time ago that Elizabeth is probably wiser than I am.
And maybe that's where "counting sheep" comes from. I don't really know how "counting" and "sleeping on" sheep equate, but maybe they do. Or maybe the word "sleep" is derived from the word "sheep." They have a lot of the same letters.