This book stems from a concept that, from an information-theoretic and computational perspective, e-dimensionality represents optimal information representation. Drawing on the principle that nature consistently chooses optimal solutions, this book demonstrates that noninteger dimensionality provides a unifying framework for understanding diverse phenomena across physics, 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.
Key Features:
• 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 1 to 6 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.
- Analyses algorithms that generate optimal dimensionality fractals of different kinds, ranging from linear structures to three-dimensional ones.
- Useful in simulation of natural phenomena, and they lead to novel methods of optimization.
1. Information and optimal representation.
2. The intrinsic
dimensionality of data.
3. Fractals with optimal information dimension.
4.
Self-similarity, maximum entropy principle, and the genetic code.
5.
Information optimality and the geometry of chromatin.
6. Autonomous cognitive
agents in a neural network.
7. Evolutionary stages in the universe.
8.
Nonlocal noise and self-decoherence.
9. Significance testing in natural and
biological systems.
10. Epilogue.
Subhash Kak is Regents Professor at Oklahoma State University (Stillwater, Oklahoma) and a Distinguished Academic Scholar at Chapman University (Orange, California). He has held academic appointments at Imperial College London, Louisiana State University (Baton Rogue, Louisiana), Indian Institute of Technology Delhi, and Curtin University (Perth, Australia). He has authored several books, of which the most recent one is The Age of Artificial Intelligence. Since 2018, he has been a member of the Indian Prime Ministers Science, Technology, and Innovation Advisory Council.
