The e-Dimensionality Information Principle: Data, Representation, and Algorithms

This book is based on an information-theoretic result according to which optimal information is associated with e-dimensionality. Drawing on the principle that nature chooses optimal solutions, it demonstrates that noninteger dimensionality provides a unifying framework for understanding diverse phenomena across physics, cosmology, biology, engineering, and data science. The work explores how optimal information representation naturally leads to scale-invariance and self-similarity – characteristics observed throughout natural systems, from fractals and genetic structures to evolutionary processes and neural networks. This book: Reveals why three-way logic is superior to binary logic in natural systems and provides an information-theoretic rationale for the power laws frequently encountered across scientific applications Explains fundamental biological mysteries, including the non-uniform groupings of codons in the genetic code (ranging from one to six per amino acid), and offers novel insights into chromatin geometry and evolutionary dynamics Addresses the reproducibility crisis in biomedical research by proposing new significance testing approaches based on noninteger dimensionality that move beyond traditional binary hypothesis testing methods Written for researchers and graduate students in electrical engineering, computer science, physics, and biology, this work serves as both an advanced textbook for senior-level and graduate courses and a research resource providing fresh perspectives on longstanding problems across multiple disciplines.