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Matthew Litwin

Archive

  1. The Metric Tensor

    At every point of our coordinate space, we can use the tangent space to define the distance in any (infinitesimal) direction. In general the square of the distance will be a quadratic form in the (infinitesimal) coordinate displacements along the basis vectors of the tangent space.

  2. The Skew Tangent Space

    Sphere

  3. The Tangent Space

    Let's set the scene of the things I think I understand, at least to the first approximation. We have a curvilinear coordinate system on a space under some metric. For example, the surface of a sphere. We will start simple, and then mess with it to look at a slightly more complicated variant.

  4. Interlude in the House of SVG

    Making diagrams for coordinate systems proved harder than I thought, and I got sidetracked.

  5. Tensor Calculus

    So I've been getting back into a bit of physics, and decided to take a crack at general relativity and tensor calculus. It's all derivatives, right, so it should be easy? Well, of course, I'm having trouble. One major sticking point is the notion of a dual basis. I understand the definition but couldn't make it click into a substantive understanding. This is my attempt to start working it out.

    Seems to be a rite of long passage.

  6. Terraform is a JSON transformation language with side-effects

    We use Terraform a lot at my work. There's been an interesting learning curve as I've gone from no knowledge of it, to using it in production. I had a bit of trouble figuring out a conceptual model - a way of thinking about what it was doing - that worked for me.

    Eventually I found one.

  7. Web Sketchpad

    I worked a lot in my career on The Geometer's Sketchpad, an educational geometry visualization and interaction desktop application. Sketchpad had a long and useful life, finally retired as a product in 2019. Twenty-five years! It's still in use as an authoring environment for the HTML5 web viewer.

  8. Preliminaries to a Software Testing Manifesto

    I'm not quite ready for a manifesto. Still gathering my own thoughts, and trying to understand software testing terminology and methodologies. But - feels like there is a fair amount of confusion about how it's supposed to work even in the best case.