In previous article, we introduced various figures with holes in 4D. How to study these holes? This article aims to provide an intuition of homotopy and homology in algebraic topology.

The introduction to 2D surface knots wasn't actually very detailed last time. Today we want to analyze knots from another perspective. Let's try to unknot some knots in 4D space!

Here we introduce a new algebraic system that can "unify" high-dimensional geometry - Geometric Algebra. This encompasses scalars, vectors, n-vectors. It even includes spinors (rotate twice to look th

In our 3D world, one of the most magical things is the electromagnetic field. Various induction phenomena are 3D and require the right-hand rule in space. Can we analogize these things to 4D?

Minecraft4D is a true 4D (hypercube-based) 4-voxel sandbox game. (If you include time, it’s actually in 5D spacetime!) Currently, the game only supports single-player creative mode.

This series has been imagining a fictional 4D world. No matter how we describe its appearance in words, a world lacking physics is static and non-interactive. So today we'll study Newtonian mechanics

We discussed how 2D beings would view photos of our world last time. Today, a mysterious person claiming to live in 4D space has connected with our computer. They say they have 3D retinas that can dir

Many literary works have mentioned fictional 2D flat worlds. We'll experience the first-person perspective of flat beings with computers. This is a pre-excercise for the vision of 4D beings.