Author's Note on Hidden Scope: The "Ximending pedestrians" presented in this paper serve as a macroscopic metaphor for a deeper subject: the electron. The true ambition of this work is to demonstrate that discrete mathematics—rather than continuous analysis—may provide the natural language for deriving the mysterious constants of fundamental physics. As a preliminary indication: the fine-structure constant's inverse, long suspected by Arthur Eddington to be exactly 137, admits the structurally elegant decomposition 137 = 2⁷ + 3². Eddington was ridiculed by the physics community for insisting that 137 must be an integer derivable from first principles. He lacked, however, the discrete-algebraic framework to justify his intuition. This paper represents a first step toward such a framework. Classical probability theory asserts that the probability of two specific individuals encountering each other in an unbounded spatial domain converges to zero. We resolve this paradox by introducing the Yu Model of Discrete Intentional State-Space, which posits that human spatial cognition operates on a finite-dimensional binary decision lattice rather than a continuous manifold. By axiomatizing directional intent as a 6-bit state vector, we derive the Yu Constant Pₘₔ = 1/64, representing the invariant probability of a successful spatial encounter. We further introduce the Origin Paradox, distinguishing between the Static Origin (0, 0) and the Struggling Origin (1, 1). Applications include urban navigation theory, behavioral economics, and the epistemology of chance encounters.
Yu et al. (Mon,) studied this question.