Musings of an Analyst

Each of our kids is learning things that have stretched my mind. This includes places where I have learned (or relearned) math and philosophy just to keep up.

On the math front, I have had to relearn some calculus and differential equations to keep up and help with homework. That has been more enjoyable than I remember it being many years ago when I learned it the first time. In some cases, like when studying Feynman’s lectures, I have taken away insights from this relearning that I didn’t get the first time around.

On the math front, I am now having to learn types of math that I never properly learned the first time around. I learned Kepler’s laws the first time around in calculus. I didn’t learn how to derive Kepler’s laws the first time around. The first time around, I learned how to use Lagrange’s method to generate the equations of motion for systems, but my ability to use and apply calculus of variations is limited to Lagrange’s methods for equations of motion. It is much more of a stretch to learn the theory and other applications than I had expected. And, I am still in the process of learning why the action that Lagrange defined is the action that needs to be minimized to as part of the principle of least action. How did he figure that out? Similarly, relearning matrix algebra has led to new struggles and new insights for me. In the past, my emphasis has always been on the “row space.” But, Strang advocates strongly that the “column space” is much more important. Struggling with the ideas a second time has caused me to reflect on this idea in a way that I never really considered the first time around.

On the philosophy front, it is amazing to me how deep of an understanding of philosophy, psychology, and society my kids have and are obtaining. They are thinking deeply on a range of societal questions and doing so in a way that is impressive to me. They have set quite a bar for discussions. Whether it is the applicability of the ideas from “One dimensional man” or the applicability of the ideas from “Manufacturing Consent,” they are exploring topics that are new to me and certainly were not things I was thinking about deeply when I was their age.

On both fronts, they have thrown down the proverbial gauntlet. To keep up, I have a lot to learn…