Traditionally, computers define logical operators on real values: AND 0 0 | 0 1 0 | 0 0 1 | 0 1 1 | 1 OR 0 0 | 0 1 0 | 1 0 1 | 1 1 1 | 1 XOR 0 0 | 0 1 0 | 1 0 1 | 1 1 1 | 0 I believe a similar construct can be made for complex values except that logical equivalency could maybe have two interpretations: either the magnitude is the core comparison value or the frequency (radian representation of the complex value in the unit circle) is the core comparison value. From a magnitude perspective, we could say that X AND Y for two complex values X and Y is itself if and only if both X and Y lie on the same circle. In a sense, this is establishing a primitive group structure because the value of the operator depends on whether or not an item belongs in a set. Likewise, we could define an XOR operator the same way, just in the inverse, that both X and Y do not belong to the same circle. From a frequency perspective, we could say that X AND Y for two complex values X and Y is itself if and only
Handwritten notes about computer science, artificial intelligence, and mathematics. Essays about philosophy, psychology, and society.