Now, Callie loves to play fetch. So, I got a stick and threw it for her several times. My own dog, Buck, was there also, but Buck never learned to play fetch. I tried to teach him more than once over the years, but he would just watch the stick fly through the air and then look at me. "Oh, well," I thought, "I guess he's just not interested."
Callie sure was interested, though. She was running after the stick, biting the stick, and growling fiercely when I'd try to take the stick back from her.
Then one time I threw the stick through the air and Buck went chasing after it! I'd never been able to convey to him what I wanted him to do, but watching Callie he had suddenly worked out the rules of the game. Once he understood, he played with the same enthusiasm she has always shown.
There's the Order of Reason at work for you.
I never know that anyone is "thinking," except insofar as they can communicate something to me that reminds me of the internal process I identify by the work "thinking."The lower animals are limited by the lack of language, and so they have a lesser access to the order than we have. Yet to see one observe a game and learn its rules, across species?