1. Fractals and embedding dimensions

2. The dimension of an infinitely “crinkly” line > 1
The dimension of an infinitely “crinkly” line > 1. It’s “embedding space” is 2 dimensions.

3. The same can be done with a 2D sheet: infinitely crinkled it has dimension > 2. It’s “embedding space” is 3 dimensions.
Note that this is complicated by the fact that we are viewing this on a 2D screen.
But you could model it in real life with just a sheet of paper

4. The same can be done with 3D tubes: infinitely branching it has dimension > 3. It’s “embedding space” is 4 dimensions.

5. Since we are 3d creatures, thinking about 4 dimensions is a challenge
Since we are 3d creatures, thinking about 4 dimensions is a challenge. Consider that unfolding a 3D box gives you 6 sides. Unfolding a 4D box gives you 8 cubes

6. In 1954 surrealist painter Salvador Dali painted Corpus Hypercubus
In 1954 surrealist painter Salvador Dali painted Corpus Hypercubus. Why put Christ in relation to a hypercube?