Do three-dimensional androids dream of four-dimensional sheep?

This Habr article explores the computer as a fundamental mathematical structure, inviting readers to view computational processes through the lens of abstract mathematics. The author proposes a conceptual approach where a computer is viewed not merely as a physical device, but as a mathematical object existing independently of its silicon implementation. The material examines the theoretical possibility and practical implementation of computing systems in various dimensions, ranging from two-dimensional to four-dimensional spaces. The author demonstrates how instructions for such systems can be formalized using mathematical formulas. This approach provides a deeper understanding of the nature of computation and processor architecture, abstracting away from the usual constraints of the three-dimensional world. The article will be of interest to those passionate about theoretical computer science and mathematical modeling who wish to expand their understanding of how computing systems can be structured in non-traditional geometric spaces.