Latest post

Jul 25, 2024, 01:46:46

After giving some thoughts, I think something like GitHub issues can be the ultimate form of a #socialmedia platform. One can conveniently refer to other issues using just owner/repo and issue number. One can use issue templates. One can use Markdown as well as inserting multimedia contents in comments. One can react with an emoji. These features easily beat Reddit and Mastodon. It only misses normal social platform features like exploration and tagging.

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Articles

  • Apr 8, 2020

    The structure of a basic RM game

    In this article, I present minimal examples of a RM game. They only illustrate the basic concepts of how a RM game is structured and what is the running logic of it.

  • Mar 27, 2020

    The frequency assignment of musical notes

    This article explores the concept which I call the frequency assignment, which is a mapping from NN (the set of notes) to R+\mathbb R^+ (the set of frequencies). Concepts such as octaves, intervals, and equal temperaments are introduced.

  • Mar 3, 2020

    Normal vectors of a scalar field

    This article gives the formula for the normal vectors of a surface defined by a scalar field on Rn\mathbb R^n. The normal vector of the graph of the function y=f ⁣(x)y=f\!\left(\mathbf x\right) at (x0,f ⁣(x0))\left(\mathbf x_0,f\!\left(\mathbf x_0\right)\right) is (∇f ⁣(x0),−1)\left(\nabla f\!\left(\mathbf x_0\right),-1\right). This also provides us a way to recover a scalar field from the normal vectors of its graph: normalizing the vectors so that the last component is −1-1, and then integrate the rest components.

  • Feb 29, 2020

    It is Feb 29 today!

    It is Feb 29 today. The date appears once for as long as 4 years!

  • Feb 9, 2020

    Monkey-patching graciously

    Monkey-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).

  • Jan 26, 2020

    Amazing Siteleaf

    I have been using Siteleaf to manage my blog. It is just convenient and amazing.

  • Jan 25, 2020

    Hyperellipsoids in barycentric coordinates

    In 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.

  • Jan 6, 2020

    Use complex numbers as canonical variables

    In 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.

  • Jan 1, 2020

    Giving birth to my own blog

    This is my first blog! I will share interesting things in my life here.

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