Fourier Transforms

Fourier transforms are a staple of the mathematical diet, finding a place both in the halls of academia and the rugged infoscape of industry application. They represent a special form of function approximation or curve-fitting that is suitable to many types of information distributions.

Most folks wonder how they should live their lives, at least once in a while. Some folks think they've got the answer and try to share it with others. The first and second groups often clash with each other, and one statement that seems to come up more often than most is "Well, that may be right for you but it's not right for me." A lot of times this either ends the conversation or spawns endless rabbit trails about absolute versus relative morality.

So how does this come back to Fourier transforms? One thing that helps me understand how morality can both be "absolute" and "relative" at the same time is the function approximation analogy. Known samples are hard points, and everything else in between is interpolated. For me, things like moral situations directly matching sample points in my moral framework (say maybe the ten commandments) are hard points. Other types of situations represent interpolated points. The interesting thing about this is that you can very clearly say that a fitted curve is wrong at a point if it's at a sample point position and the curve doesn't hit the sample. However, there's a bit more give in the situation the further away from known sample points you go. Even within that, though, it's usually easy to see when a curve is aberrant from the overall pattern for points anywhere even close to a known sample.

Of course, both groups may not agree at all about what the hard points are, but I've found this to be helpful in understanding the rigidity and flexibility of my own beliefs. Knowing that helps me not get caught in conversations that seem to go nowhere.