Seems to me there was an article a few months back on how the use of GPS in cars was handicapping drivers -- damaging their ability to form and manipulate abstr

Seems to me there was an article a few months back on how the use of GPS in cars was handicapping drivers -- damaging their ability to form and manipulate abstract mental maps. I'm of the opinion that you should always learn the thing at about two levels down in automation from where you normally use it. So, for programming, I'm all for assembler, compiler, and C programming skills, even though those might never be used in the real world. By the same principle, if you're learning navigation in an airplane, you should learn dead reckoning and a wet compass. If you're learning to driver and shoot a tank you should have pretty good concepts of how rifle combat works, etc. In math and economics, however, I'm not sure what "2 levels down" means. Is math the rote memorization and repetition of stuff? Most definitely not. But does it depend on it? Maybe. Is it the application of pre-existing patterns in any fashion -- such as punching numbers into a calculator? I don't think so. I think it's much more about the ability to teach yourself to find and exploit patterns through trial and error. That's one of the reasons I've always thought so highly of High School Geometry classes -- when done well, they begin to teach how to think, not just what to think. Food for thought.