May 31, 2020
We may generalize Euler–Lagrange equation to higher dimensional optimization problems: find a function defined inside a region to extremize a functional defined as an integral over that region, with the constraint that the value of the function is fixed on the boundary of the region.
May 14, 2020
The view of the world… Physically! In this article, I tried to use mathematical language to describe models of the physical world. A view of the world should include: a space (actually spacetime) with some mathematical structure on it (whose points are events in the world), a symmetry principle describing the symmetry of the world, and a motion law to describe the physics and dynamics of the world. This article proposed models for Galilean, Einsteinian, and even Aristotelian worlds. Can you come up with even other worlds?
May 14, 2020
Continuing my last work of simulating a mechanical system using RGSS3, I made a new version using rpg_core.js, the game scripting system shipped with RPG Maker MV. This version is live on web!