This book is a unique summary of the results of a long research project undertaken by the authors on discreteness in modern physics. In contrast with the usual expectation that discreteness is the result of mathematical tools for insertion into a continuous theory, this more basic treatment builds up the world from the discrimination of discrete entities. This gives an algebraic structure in which certain fixed numbers arise. As such, one agrees with the measured value of the fine-structure constant to one part in 10,000,000 (107). Combinatorial Space The Story of the Particle Concept Dimensionality The Simple Bit-String Picture The Fine Structure Constant Calculated Process and Iteration Pre-Space: High-Energy Particles: Non-Locality Space, Relativity and Classical Space Perception Current Quantum Physics, State/Observer Philosophy: Complementarity Just Six Numbers Quantum or Gravity?