Latest post

Nov 2, 2026, 10:14:19

I recently just realized that "sure" and "of course" are different in #English in a daily conversation. My friend said, "You going home?" I mindlessly replied, "Sure." Then I just thought, oh I should've said "of course" instead. It feels so strange: I was taught in school that "sure" and "of course" are the same, and no one told me otherwise, but I just knew it without even knowing I knew it -- it was after I misused the phrase myself once that I realized I knew it.

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Articles

  • Feb 9, 2020

    Monkey-patching graciously

    Article cover image with no practical usageMonkey-patching is a powerful tool in programming. In this article, I used techniques of Ruby metaprogramming to define a series of methods def_after, def_before, etc. to help monkey-patching. They look graciously in that we can use it to shorten the codes for monkey-patching (avoiding aliasing and repeating codes).

    /programming #ruby #meta programming #long paper
  • Jan 26, 2020

    Amazing Siteleaf

    Article cover image with no practical usageI have been using Siteleaf to manage my blog. It is just convenient and amazing.

    /update #update #jekyll
  • Jan 25, 2020

    Hyperellipsoids in barycentric coordinates

    Article cover image with no practical usageIn this article, I introduce the barycentric coordinates: it is an elegant way to represent geometric shapes related to a simplex. By using it, given a simplex, we can construct a hyperellipsoid with the properties: its surface passes every vertex of the simplex, and its tangent hyperplane at each vertex is parallel to the hyperplane containing all other vertices.

    /math #linear algebra #long paper
  • Jan 6, 2020

    Use complex numbers as canonical variables

    Article cover image with no practical usageIn this article, I try exploring an idea: using complex numbers to combine pairs of canonical variables into complex variables: c≔αq+iβp\mathbf c\coloneqq\alpha\mathbf q+\mathrm i\beta\mathbf p. It turns out that we can write canonical equations dcdt=−2iαβ∂H∂c∗\frac{\mathrm d\mathbf c}{\mathrm dt}=-2\mathrm i\alpha\beta\frac{\partial\mathcal H}{\partial\mathbf c^*}, Poisson brackets {f,g}=−2iαβ(∂f∂c⋅∂g∂c∗−∂f∂c∗⋅∂g∂c)\left\{f,g\right\}=-2\mathrm i\alpha\beta \left(\frac{\partial f}{\partial\mathbf c}\cdot \frac{\partial g}{\partial\mathbf c^*}- \frac{\partial f}{\partial\mathbf c^*}\cdot \frac{\partial g}{\partial\mathbf c}\right), and canonical transformations ∂c∗∂c′∗=∂c′∂c,∂c∂c′∗=−∂c′∂c∗\frac{\partial\mathbf c^*}{\partial\mathbf c'^*}= \frac{\partial\mathbf c'}{\partial\mathbf c}, \frac{\partial\mathbf c}{\partial\mathbf c'^*}= -\frac{\partial\mathbf c'}{\partial\mathbf c^*} in these complex numbers. Finally, I show two examples of using them in real problems: a free particle, and a harmonic oscillator.

    /physics #classical mechanics #canonical transformation #hamiltonian #complex #long paper
  • Jan 1, 2020

    Giving birth to my own blog

    Article cover image with no practical usageThis is my first blog! I will share interesting things in my life here.

    /update #update

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