Once you go to multidimensional vector spaces, you don't need order. For example, the classic rock-paper-scissors can be modeled with 3 points in 2d. This has

Once you go to multidimensional vector spaces, you don't need order. For example, the classic rock-paper-scissors can be modeled with 3 points in 2d. This has fundamental implications, as many activities do have this cyclical parts (see also such decomposition for vector fields, https://en.wikipedia.org/wiki/Helmholtz_decomposition https://en.wikipedia.org/wiki/Helmholtz_decomposition). Vide Reinforcement Learning for StarCraft 2: https://deepmind.com/blog/article/AlphaStar-Grandmaster-level-in-StarCraft-II-using-multi-agent-reinforcement-learning https://deepmind.com/blog/article/AlphaStar-Grandmaster-leve...