R Hansen: >>It is the process that takes place after the rules have been set. The rules of chess are quite finite and simple but figuring out and organizing the resultant complexity is abstraction.
Joe N reterts: >Perhaps reading the dictionary definition or even the Wikipedia article of abstract and abstraction would help clue you in on how the rest of the English speaking public uses the term.
I shouldn't be so glib. I apologize. Certainly anyone skilled at thinking through chess strategies and puzzles would be called an abstract thinker. That's one sense of the term in common usage, and I think I more or less gave some credence to that use. Any symbolic operation or mode of thinking might be called abstract. Any *difficult* mental operation is called abstract by some.
But thinking through a math problem in terms of mental imagery is no less abstract, and in the same sense. But how can I say that, when I've already agreed with Parnas the "more abstract than" is a less than useful concept?
I remember how I solved the old chestnut "what is greater, e^pi or pi^e?" I did it "in my head" without paper while walking my dog. Basically through examining curves in my imagination, plus a few elementary facts.