One of the things I have found hard in Quantum Mechanics and in the build up to General Relativity has been the multiple indices used in the notation for multiple dimension spaces. I understand 2-dimensional matrices in the Real number space but have trouble intuiting in higher dimensions. So I try to build models that relate back to the ideas I understand to help me to think that the new idea is "like" a simpler idea in some way. So it was that I came to make a model of the 3-dimensional version of the Levi-Civita tensor. Essentially, it acts in some way like a matrix that assigns a 0, a 1 or a -1 to any multiplication. Obviously, if it is a 0, then the total multiplication is a zero. I used i, j and k coordinates. In my model, i goes to the right, j goes away and k goes up. For any coordinate ijk, you get a zero if any two coordinates are the same. If ijk is 123, 231 or 312 you get a 1. For 321, 213 or 132 you get a -1. You get two none zero entries per vertical or horizontal plane - one is 1 and the other is -1 so it is not quite symmetric - we say anti-symmetric. Now I can visualise it, I need to find out where and how it is used. This was my inspiration
https://en.wikipedia.org/wiki/Levi-Civita_symbol#Three_dimensions
