How geometry is fundamental for chess

Summary

Understanding Geometrical Concepts Humans are the only animals that we know that understand geometrical concepts. Humans are the only animals that we know that understand geometrical concepts. Things like lines and shapes (triangles, squares, circles etc.). Not only do we understand these concepts, we can also combine them in a infinite, recursive way to form new geometrical forms. We can also transform them through rotation. This is important for chess. Chess relies on geometrical concepts fundamentally. The concept of a line of varying discrete lengths (a line distance of 1 for a pawn, 2 on the first move). A vertical line rotated by 45 degrees for the length of a bishop. A knight is an example of a recursive transformation, combining 1 and 2 length lines at 90 degree angles. Same with the queen (diagonal and straight). Numerosity is also fundamental. The piece involves an understanding of numerosity to move a certain amount of squares. This may seem obvious, but it needs to pointed out because everyday experience disguises the miracle. These geometrical concepts do not exist in nature. There are no lines and squares. If it's obvious then why did it take 4.5 billion years since the development of life to emerge? Animals do not possess a sense of discrete numbers. Animals don't possess a sense of discrete numbers. Chimpanzees, instead of seeing 6 and 7, they feel 6ish-7ish. This is shown when they have to pick a plate with the most food. The further the difference between the amount of chocolate chips, the easier it is for them (e.g. choosing between 2 and 10 chocolate chips). They get it right when it's between 1 and 2 chocolate chips. But if it's between 6 and 7, then it's difficult, the performance decreases when the ratio between the amount of chips decreases. This is represented by Weber's Law which states that the threshold needed to detect a stimulus grows in proportion with the initial stimulus (e.g. to have an equal performance for comparing 1 vs 2 chips m...