Part Time Scholar

I am getting to the age when my son is studying calculus under the tutilege of  a tutor.  Although he is a few years ahead at math in school, I have to admit the very thought of him doing derivatives makes me feel old.  There is also nostalgia however, as I rekindled my interested in calculus by writing this piece -- and yes, I needed a memory jog from the Internet to complete the formulas.   Most people meet calculus as a set of rules.  Differentiate this.  Integrate that. Memorize formulas. Apply them until the answers come out correctly.  It feels almost mechanical, like a toolkit you learn to use without ever opening it to see how it was built.    But calculus is not really about formulas. At its core, it is about something much more fundamental: how change actually works when you zoom in close enough. The idea of first principles is simple. Instead of accepting shortcuts or memorized rules, you rebuild the concept from the most ba...

I used to pay little attention on boarding at the airport because of my elite status with various airlines. But retirement has kept me grounded and almost swiped my record clean in recent years. Recent trips, including one to Colombia with an infamous American airline, had me thinking more about the science behind plane boarding.   Anyone who has boarded an airplane enough times has likely experienced the strange choreography that unfolds before takeoff. Passengers stand up almost immediately when boarding begins, lines begin forming long before their assigned group is called, and eventually a slow procession starts moving toward the aircraft. For a few moments the line appears to flow smoothly. Then everything stops. Someone is lifting luggage into an overhead compartment. Another passenger realizes they are seated twenty rows further back. A family begins negotiating seating arrangements while the rest of the line quietly waits. Movement resumes briefly before another i...