Chairman’s Report - The 5th BCSCMsG International Symposium
The Fundamental Semantic Foundation of the Sciences
Computational Rewrite Systems at CASYS 05

Introduction
At CASYS 03 in the 4th BCSCMsG International Symposium, ‘The Universe, the Nothing that is?’, Diaz & Rowlands (D&R) presented their paper ‘A Computational path to the Nilpotent Dirac Equation’. It unveiled a remarkable new discovery. There exists a nilpotent universal computational rewrite system (NUCRS) with an infinite universal alphabet, see inset below. It defines the semantics of quantum mechanics in terms of a universal grammar, such that the nipotent generalization of Dirac’s famous quantum mechanical equation is the computational machine order code.

Further in a companion paper ‘Symmetry Breaking and the Nilpotent Dirac Equation’ Rowlands shows that the symmetry breaking of this nilpotent Dirac equation, describes the spontaneous emergence of both 3+1 relativistic space time and the experimentally validated strong, weak and electromagnetic quantizations (including spin) of Standard Model elementary particle physics, from their empty set. That is to say, these fundamental physical quantum mechanical structures not only define level one of the ontological hierarchy corresponding to the NUCRS semantics, but are those from which all subsequent levels of this hierarchy will be reconstituted in 3+1space-time due to the action of the strong, weak, electromagnetic and gravitational forces.

This discovery of the NUCRS thus provides a sound scientific basis, able to turn the Group’s Premise and Mission Statement below into an actual Evolutionary ‘Anthropic’ Semantic Principle, by means of which the Group’s search for the fundamental physical foundations of computing as used in brains, can be realized.

For there can be little doubt in view of natural language that the human brain is a universal computational semantic machine and that the NUCRS provides a natural model and modes by means of which human speech, writing and the hearing of natural language, could actually be realized (through a neural NUCRS semantic ontology) so as to allow the human race, as is actually happening in science, to comprehend the evolutionary cosmos in which it lives. For example, the above hypothesis immediately raises the question “Is the DNA/RNA genetic code itself, a NUCRS?” for this would explain all living systems (including, of course, the biological human brain) as the product of further intermediate level NUCRS hierarchical semantic ontologies. It would also answer the grand unsolved problem of the genetic code, as to how the 3+1space-time structure of its organisms is encoded within it.

It was therefore decided to dedicate the 5th BCSCMsG International Symposium at CASYS 05 to the concept of computational rewrite systems and to this remarkable quantum mechanical discovery, which defines Nature’s rules, in the Premise below, as those of the Nilpotent Dirac Equation.

Premise and Mission Statement - now the Evolutionary ‘Anthropic’ Semantic Principle
In science, Nature sets the rules, but it must never be forgotten, that it is only because life has exploited these rules successfully for billions of years to our evolutionary advantage, that human brains are able to understand them. The mission, at the (physical) foundations of computing/information processing if one accepts the premise, is therefore to identify how these rules were exploited to achieve this end.

The CASYS05 BCSCMsG International Symposium, which comprised some 15 presented papers, see sidebar abstracts’05, including those of two invited full conference speakers, John Horton Conway FRS, the John Von Neumann professor of mathematics at Princeton, and Brian Josephson, FRS, Nobel Laureate in Physics, was again a very highly successful meeting, attracting good audiences of some 10 to 30+ delegates at each symposium session. I should like to thank all the speakers for their most valuable and exciting contributions, and Daniel Dubois, the Director of CHAOS, on behalf of his conference organization, for all his & their hard work in making CASYS05 once again a conference not to be missed. A full set of conference abstracts, 150 plus, appears in the CASYS 05 abstracts volume issued to all delegates, and full symposium papers, hopefully including all of those of the abstracts’05 sidebar, will appear in the CASYS05 Proceedings to be published next year. It is also of mention that Anticipatory Computation, the subject of the whole conference, can now be recognized with hindsight as a computational rewrite process; a fact which says much for the prescience of Professor Dubois in ‘anticipating’ this new branch of the computer science which concerns semantic computation, which he has now championed for many years, through the concepts of chaotic computation, incursion, hyperincursion and of course computing anticipatory systems. And the concept of semantic computation would provide an alternative explanation of why Dubois’s concepts above are so successful in arriving rapidly at sound computational solutions to difficult problems, and as to why recursion in the form of ordinary digital computation may fail to do this.

Other prescient work on semantic computation can thus now be recognized to concern the ‘New Computing Principle’ of Fatmi & Resconi (in which the description of the optimal design for the physical machine already incorporates a Lagrangian) and the ‘Theory of the Cybernetic and Intelligent Machine based Lie Commutators’(in which computer input/output is represented by a categorical arrow). Both follow from Dennis Gabor’s 1960 paper ‘A Universal Non-linear filter, Predictor and Simulator which optimizes itself by a Learning Process’, which is generalized by using Resconi & Jessels’ 1986 categorical formulation of ‘General System Logical Theory’ based on Jessel’s 1954 formalization of Huygens’ principle of secondary sources. These might now be more appropriately named respectively:- as the New Semantic Computing Principle, the Theory of the Semantic and Intelligent Machine …. , and General System Semantic Theory (references to these papers are below and in the appendix of A Remarkable Quantum Mechanical Discovery paper^a discussed later)

What is a nilpotent computational rewrite system? See also at arXiv.cs.OH/020906 It differs from traditional rewrite systems (of computational semantic language description with a fixed or finite alphabet) in that the rewrite rules allow new symbols to be added to the initial alphabet. In fact D&R start with just one symbol representing "nothing" and two fundamental rules; create a process which adds new symbols and conserve a process that examines the effect of any new symbol on those that currently exist to ensure “a zero sum” again. In this way at each step a new sub-alphabet of an infinite universal alphabet is created. However the system may also be implemented in an iterative way, so that a sequence of mathematical properties is required of the emerging sub-alphabets. D&R show that one such sequential iterative path proceeds from nothing (corresponding to the mathematical condition nilpotent) through conjugation, complexification, and dimensionalization to a stage in which no fundamentally new symbol is needed. At this point the alphabet is congruent with the Nilpotent generalization of Dirac’s famous quantum mechanical Equation showing that it defines the quantum mechanical “machine order code” for all further (universal) computation corresponding to the infinite universal alphabet++. This rewrite system with its nilpotent bootstrap methodology from “nothing/the empty set” thus defines the requirement for universal quantum computation to constitute a semantic model of computation with a universal grammar. ++ since a new symbol can stand for itself, a sub-alphabet or the infinite universal alphabet, the universal nilpotent rewrite system may thus rewrite itself, ontologically at a higher (hierarchical) level of quantum physical structure.

The 5th BCSCMsG International Symposium Rowland’s paper “Fermion Interactions and Mass Generation in the Nilpotent Formalism” was awarded a CASYS05 best paper award. It continued the theoretical exploration of the properties the nilpotent formalism, so as to explain the existence of nonzero mass in relation to elementary particles of the Standard Model as predicted by the nilpotent Dirac equation. This is one of the Clay Mathematical Institute’s required criteria, for a sound model of elementary particle physics. Another Clay requirement is that of a solid mathematical foundation, which we believe, Diaz and Rowlands’ process of discovery of the universal computational rewrite system provides, not only for the language descriptions of quantum physics, but also for mathematical language itself; see Conway’s paper^b discussed below. A further step towards explaining these was their paper given by Diaz entitled “D: the infinite square roots of –1”. This explains the role of in relation to the universal infinite alphabet, which provides the computational path to the nilpotent Dirac equation. Another relevant paper here was that of Heather and Rossiter, entitled “Anticipation is nowhere and its Logic is Nothing” which discusses, in a category theory context, the mathematical premises behind concepts like ‘nothing’, ‘the null set’, ‘zero’, etc. For as you may have guessed, a nilpotent computational system could loosely be thought of as computation using zero (i.e. topological computation) rather than bits in the binary system 0,1 and it is more general than binary computation as Deutsch’s theory of universal quantum computation shows.

In “Remarkable Quantum Mechanical Discovery”^a, Marcer and Rowlands rework their CASYS03 paper with Schempp, entitled “Zenergy: The ‘Phaseonium’ of Dark Energy That Fuels the Natural Structures of the Universe” in terms of the concept of the nilpotent computational rewrite system:-
i) to verify the previous reached conclusions, which is the case, and
ii) because this new concept is a new and powerful means of presenting these conclusions so as to simplify and facilitate their understanding.

And while Schempp could not be with us, this year, he sent us his update on “Quantum State Tomography of Nanostructures and the Heisenberg Nilpotent Lie Group Model of Quantum Information Processing”. This concerns his latest research in the directly related Lie/boson partition of nilpotent quantum mechanical state space to that of the Nilpotent Dirac Equation which concerns its complementary Clifford/Fermion partition.

The remaining papers presented can then be loosely divided into two areas, concerning:-
a) unresolved problems in fundamental physics, ie “Is time multidimensional?” Fidelman, and the nature of its physical constants, one paper by Malet and the other by Pitkanen, and
b) others, in related problems also of great interest to the group, on the biological sciences from logics defining its chemical structures, Chandler; cortical synchronization, Kaempf; consciousness and health, Van Nieuwenhuijze (2 papers); and quantum coherence in water and its logics, Smith. And also (but in the main conference session) Josephson’s latest and always simulating ideas, this time on the general principles for brain design, using natural linguistics as the model. This is excitingly close to those arising from the computational rewrite system semantic approach, where hierarchy is governed by means of a symbol such that this can stand for itself, a sub-alphabet or the infinite universal alphabet.

It is also possible to identify other examples of computational rewrite systems, namely:-
i) Spenser-Brown’s controversial Laws of Form,
ii) J.H.Conway’s highly prescient 1976 generation of the Surreal Numbers^b, on which he talked at the full CASYS05 conference session. It provides a possible NUCRS foundation for mathematics, as an alternative to that of the more usual Zermelo-Fraenkel set theory, in the form of a non-standard mathematical analysis over the surreal number fields. It is a ‘process’ definition of the numbers as a restricted nilpotent infinite universal alphabet^b, where significantly the symbol has to be added arbitrarily to ensure that this generation process is that of a universally embedding totally ordered (mathematical) Field.
iii) the Alternative Natural Philosophy Association’s discrete model of quantum physics, called the Combinatorial Hierarchy,
iv) the Dirac formalization of quantum mechanics in terms of bra and ket vectors, and
v) examples of conventional rewrite systems are to be found at http://algorithmicbotany.org/papers/#abop, where the more usual finite alphabet semantics corresponding to geometric rules is used to give very lifelike pictures matching those in botany i.e. a sunflower.
Peter Marcer, chair, 30.09.2005

Additional References
1. On Numbers and Games, Conway J.H. Academic Press, London, 1976.
2. Hyperincursivity: A new mathematical theory, Dubois D.& Resconi G. Presses Universitaires de Liege, 1992.
3. General System’ Logical Theory (GSLT) Jessel M.& Resconi G. International Journal of General Systems 1986, 12, 155-182
4. A New Computing Principle Fatmi & Resconi, Il Nuovo Cimento, 101B, no.2, February 1988, 239-242
5. Theory of the Cybernetic and Intelligent Machine based on Lie Commutators, Fatmi H.A, Jessel M., Marcer P.J.& Resconi G. International Journal of General Systems, 16, 1990, 123-164.