Combinatorial hierarchy

The combinatorial hierarchy is a mathematical structure of hierarchical sets of bit-strings generated from an algorithm based on "discrimination" (or equivalently XOR). Discovered by Frederick Parker-Rhodes, the hierarchy gives the physical coupling constants from a simple aphysical model. This is a key consequence of bit-string physics, which supposes that reality can be represented by a process of operations on finite strings of dichotomous symbols, or bits (1's and 0's).

Bit-string physics has developed from Frederick Parker-Rhodes' 1964 discovery of the combinatorial hierarchy: four numbers produced from a purely mathematical recursive algorithm that correspond to the relative strengths of the four forces. These strengths are characterized by the strong, weak, electromagnetic (fine-structure constant), and gravitational coupling constants.[1] Other leading contributors in the field include H. Pierre Noyes, Ted Bastin, Clive W. Kilmister, John Amson, Mike Manthey, and David McGoveran.[1][2]

As described by Bastin et al.,[3] the hierarchy is generated as the cumulative sum of the sequence 3, 7, 127, 2¹²⁷ − 1. This sequence is generated by starting from 3 and taking the next number to be 2 to the previous number less 1. (These are the four known odd Catalan–Mersenne primes.) The cumulative sum is therefore 3, 10, 137, 2¹²⁷ + 136. The paper claims that the reciprocals of the latter quantities give the relative strengths of the strong, weak, electromagnetic, and gravitational forces, and that the sequence ends there because the next entry would create instability.

In a 2001 paper by Noyes, evidence was presented for predictions made by the theory that were later confirmed.[4]