I am a proggrammer and have been for some time. For me, it is difficult to compare then and now, but here is some situation I run into from time to time:
Currently I am working on getting my pilot's license. So I have to go sit inside a plane and fly. As a programmer, I want to do everything exactly as my flight instructor tells me. So when he says "increase the height at a constant speed of 70mph", I look at the dashboard and make sure to keep that speed. The problem is that, especially when landing, you have to keep so many factors in mind, that observation becomes very stressfull and the landing unstable. So my instructor told me this: "stop looking at the measurement equipment. Start looking outside! Feel the plain!". That was a good hint for me. But then my brain started thinking: "So, how will I know the speed?", because for landing, speed is very crucial. My brain came up with a number of ideas, then evaluated them and now I use my ears to deduce the speed from the sound of the engine, which takes a lot of stress away... though I am very sure that's not what my instructor meant. It's still not a feel for the speed, but it's easier and my landings became a lot more stable in just minutes!
As a result I think, a programmer is a lot more problem->solution oriented than your average person, so while an average person will try to get the feel (and take another few hours, but have a better long-term solution), a programmer goes about a logical course, like using unused capabilites.