Note: This post has been automatically imported from my old blog. Formatting may be incorrect.
I'm not exactly sure what made me think of this, but the other day while on a medium-length drive I realized that driving can be thought of as a low-pass filter on speed: The amount of time it will take you to get to the destination is much more affected by the slow but long-lasting changes in speed and not on the quick but oscillatory changes. Pursuing this line of thought further (the drive was pretty long), I realized that car-sickness can be thought of as a high-pass filter on speed: slow, long-lasting changes don't matter, but quick oscillatory ones have a big effect. I spent quite some time turning this over in my head, including recognizing the fact that the speed-time relation involved integrating speed and the speed-sickness relation involved differentiating it, and it was honestly a joy to find such a simple little connection. Really, though, it was a good demonstration for me of the power of integration (philosophical, not mathematical!).
Before making the (quite unexpected) connection between an abstract concept from signal analysis theory and a concrete daily action, I understood what filters were and how they worked, and I had a strong grasp on how changes in my driving speed would affect my overall trip, but now I can use the knowledge I have from both fields and apply it to both. When considering filters, I can concretize problems by relating them back to my very perceptual experiences with driving. On the flip side, if I ever want to take a more intellectual approach to driving (which I doubt will happen, but it might), I will be able to use my experience with signal theory to solve problems like "What's the best way to get to the destination quickly without making Alyssa sick?"
In the scheme of things, this integration was quite unimportant. But it really hammered home to me the fact that integration really is a (the?) vital cognitive tool in a really neat, fun way.