Gemini* and Gopher

• Personal/Opinions

  • sigh of relief

    the forest breathes out a sigh of relief
    I am still here, still here
    home of lichen and moss
    soft and green and full of life
    quiet, but full of life
    watch your step 
    and you'll be welcomed
    

  • It's Cold Out Again

    It's cold out again, and so I'm back to my blog. I hadn't expected to take a break over the warmer months, though I'm glad I had a lively enough summer that documenting random musings took a backseat.

    I'd drafted all kinds of posts, but I kept getting stuck at the point. I guess I struggle with the open-endedness of something that could be anything I want it to be -- something all for me. That's not a new problem in my life, but it's one I'd like to work on.

• Science

  • Differential equations for simple sloped track (Part I)

    I had this idea last week to set up a differential equation that tracks the movement of an object along a function curve, with a gravity force pulling it downwards depending on the slope of the function at the current point. Basically like a car on a roller coaster, with gravity but no friction, air drag, or other propulsion. The idea can be generalized, but I thought it would be helpful to start with a simple fixed function, namely f(x) = x². I'm assuming a fixed acceleration due to gravity g = 1 (distance unit / (time unit)²).

    The way I approached this was to have a point p which is somewhere on the x number line. Then, I determine the slope of the function at f(p). This is the derivative of f(x) at f(p).