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]

## Contents

* 1 See also
* 2 Notes
* 3 Bibliography
* 4 External links

## See also

* Carl Friedrich von Weizsäcker
* Clive W. Kilmister
* Combinatorics
* Combinatorics and physics
* David McGoveran
* Digital physics
* Distinction
* Double Mersenne number
* H. Pierre Noyes
* Ted Bastin

## Notes

1. ↑ 1.0 1.1 Ted Bastin and C.W. Kilmister, Combinatorial Physics, World Scientific 1995, ISBN 981-02-2212-2
2. ↑ H. Pierre Noyes (2001). J. C. van den Berg. ed. Bit-String Physics: A Finite and Discrete Approach to Natural Philosophy. World Scientific. ISBN 978-981-02-4611-2. https://books.google.com/books?id=DI5qEz4RpLQC.
3. ↑ Bastin, T.; Noyes, H. Pierre; Amson, John; Kilmister, Clive W. (1979). "On the physical interpretation and the mathematical structure of the combinatorial hierarchy". Int. J. Theor. Phys. 18 (7): 445–488.
4. ↑ H. Pierre Noyes (March 23, 2001). "Observational Evidence for Two Cosmological Predictions Made by Bit-String Physics". Publication 8779. Stanford Linear Accelerator Center. http://www.slac.stanford.edu/cgi-wrap/getdoc/slac-pub-8779.pdf. Retrieved June 22, 2011.

## Bibliography

* A formal development of the combinatorial hierarchy in terms of group theory appears in the appendix to "On the physical interpretation and the mathematical structure of the combinatorial hierarchy," Int. J. Theor. Phys. 18, 7 (1979) 445.
* Theory of Indistinguishables, A.F. Parker-Rhodes, Reidel, 1981.
* Journal of the Western Regional Chapter of the Alternative Natural Philosophy Association
* H. Pierre Noyes. Bit-String Physics: a Novel “Theory of Everything”. SLAGPUB-6509, August 1994.
* H. Pierre Noyes. A Short Introduction to BIT-STRING PHYSICS. SLAC–PUB-7205, June 1997.

## External links

* "Journal of the Western Regional Chapter of the Alternative Natural Philosophy Association". Stanford University. http://www.stanford.edu/~pnoyes.

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