The joint Norwegian University of Science and Technology (previously the University of Trondheim)/ BCSCMsG Symposium ' Science and Philosophy Engaged' 31st March-2nd April, 2006
Organized by Professor Stein Johansen, NTNU and held at Saga Trollheimen conference center in Norway
A short perspective, Peter Marcer, BCSCMsG chair.
The symposium’s theme “How close are we to a fundamental theory” was set by its first speaker Peter Rowlands [1] following the general welcome address in the same spirit by Stein Johansen. Johansen was sure the presentations at cutting edge natural science and philosophy, would inspire delegates to the collaborative effort needed for a successful conclusion to this quest for a fundamental theory, which this preliminary joint meeting was initiated by him to explore, together with the BCS Cybernetic Machine specialist Group.
In Peter’s own words in his opening presentation on the State-of-the-art at the cutting edge. “Since we are aiming at providing a fundamental theory which explains as much as possible with as few assumptions as possible, and are in my opinion already a long way down the road, one of the first things I would like to do is an audit of how far this has been achieved, which in the first instance would necessarily be mostly from, my own perspective, though I would then like to extend it as much as possible to find links with the work of others. I want to distinguish between what is certain, what is probable, and what is tentative, and where the gaps are, and where there are opportunities to extend, etc. The normal conference procedure doesn't allow this, but I think we have the opportunity (after Stein’s welcome) to go directly for the jugular”.
Both Johansen and Rowlands’ confidence was not misplaced. Each succeeding presentation did indeed contribute not only to the success of the meeting, but to filling of ‘Rowlands’ gaps and a significant increase in what the proposed fundamental theory would explain, under the headings of certain, probable and tentative.
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The starting point for the fundamental theory was, by general agreement, the Rowlands/Diaz universal computation rewrite system [2], the language semantics and universal grammar of which predicts the current foundations of Standard Model elementary particle quantum physics, as experimentally validated. The success of this prediction, which also includes the simultaneous emergence of 3+1 relativistic space time as the result of the spontaneous symmetry breaking of the nilpotent vacuum (supported by other significant predictions presented during the meeting summarized briefly below or cited in references), invokes the leading questions :- “ Is it the semantic correctness of the universal rewrite language descriptions in addition to the usual syntactic correctness, which give them, their predictive power?” ; “Is this power to capture physics as experimentally validated, universal as the nature of its grammar implies, so that, for example, it also applies to living systems, too?” ; and “Is the DNA/RNA genetic code itself a rewrite** of this universal computational rewrite mechanism?”
** Rewrites of the universal rewrite system are possible, because any symbol of the system’s potentially infinite alphabet of symbols, can stand for itself, a sub-alphabet, or the entire infinite alphabet.
To sum up; all the presentations added to the delegates’ confidence that Rowlands’ opening remarks (in quotation marks above), were a correct assessment, and that the answer to these leading questions was almost certainly “yes”.
For example, a gap in Rowland’s own current predictions, is a general means, which Erik Trell supplied (the next day) to calculate the Standard Model elementary particle masses. The premise of Trell’s successful 1998 calculations is that these are based on 3D geometric space as the rewrite approach also predicts must indeed be the case. Remarkably, Trell’s calculations [3], again in excellent agreement with those obtained by experiment, follow from Marius Sophus Lie’s 1871 doctoral thesis [4] (which is the essential mathematical germ for his now famous transformation group methodology, published with Engel in 3 volumes in 1888-93, in Leipzig). For here, for the first time, Lie formulates this germ of his novel mathematical thinking linking metric and projective ‘abstract’ geometries, in terms of 3D geometric space! Lie shows that the properties of the coordinate origin of 3D Euclidean space with its eight fold signatures (dubbed by Trell, the ‘cubit’) can be reciprocally (i.e. doubly) projected onto a sphere. This seminal work of Lie, in line with the successful predictive use of Lie algebras in elementary particle theory already well established, thus says, as can now be recognized with hindsight :-
i) that 3D geometric space must be encodable in quantum mechanics by means of phase (where there are, as Berry first found, quantum observables that are the gauge invariant (geometric) phases of the quantum mechanical system state vector [5]);
ii) that the double/reciprocal mapping in quantum mechanical language is, see quantum holography described below, most probably phase conjugate adaptive resonance, and,
iii) that, as Trell shows, “this cubit eightfold/eightfold way reciprocal mapping onto the sphere ” allows the calculation of the elementary particle masses.
[Another extraordinary possible link in this saga, is then that Euclid (Book XIII proposition 17) deduced that the dodecahedron can be derived from a cube in such a way that each of the twelve edges of the cube is a diagonal of the faces of the dodecahedron. It follows, each face having five diagonals, that five cubes can thus be inscribed and that any rotation of the dodecahedron into itself induces a permutation of the five cubes, in such a way that different rotations give rise to the different permutations. The dodecahedral group is therefore, as can be proved, isomorphic with the alternating A5 subgroup of order 12x5 = 60 of the permutation group P5, where now one can tentatively identify the five elements of the group with the five composite operations of Rowlands’ nilpotent universal rewrite system.
It may also provide a link to Wilson’s [6] renormalization group approach to the calculation of material phase transitions (for example, that of ice to water to steam) in 3D geometric space. For Wilson borrowed from mathematicians the key idea of mapping a space (usually the Hamiltonian (metric) space H) onto itself so as to yield the stable and unstable fixed points/attractors, where the latter define these (material phase transitions). The key concept is that of universality and of a universality class, where these depend only on the symmetry of an order parameter and a parameter 
= 4 - d where d is the dimensionality. This says that in a world with more than four dimensions, microscopic quantum fluctuations would cancel out so that one would conclude that the equations of classical dynamics must apply, but in & below four dimensions, quantum fluctuations on all scales up to a correlation length continue to be significant.]
All these almost certainly provide further confirmation, as per Marcer’s presentation, that the Clifford/fermionic partition of the nilpotent quantum mechanical state space (NQM) from which the universal rewrite system is derived, is the dual of the Lie/bosonic partition as governed by the nilpotent 3D Heisenberg Lie group G [7]. For G’s nilpotent Lie algebra Y 
0, Y2 = 0 is the simplest Lie algebra and, as was already known to Weyl, defines its Heisenberg uncertainty. In other words the three dimensions of space are inseparable. Marcer then illustrated, with examples:- Schempp’s quantum holography [7] based on G as applied by Schempp to the parameterization and control of Magnetic (nuclear spin) Resonance 2D/3D Imaging and microscopy (MRI) in worldwide use in medical diagnosis and research (see http://www.civm.duke.edu for example). The illustrations show: actual quantum holograms demonstrating their holographic property; the principles of holographic/holophonic transduction across a media interface as achieved in the laboratory; the nature of phase conjugate active mirrors; etc (see http://www.bcs.org.uk/cybergroup.htm (see quantumholography sidebar). Thus Heisenberg uncertainty in MRI, for example, is the actual means to compute (also used by Trell in his mass calculations in the form 
px = h) because it has the 3D geometric reciprocity that Lie discovered in his 1871 thesis. For all Lie groups concern differentiable exponential mappings with a differentiable inverses(i.e. Lie diffeomorphisms), so that G (and Heisenberg uncertainty!) has a dual. Thus as MRI proves experimentally, quantum holographic measurement i.e. the encoding and decoding of 2D/3D imagery, where the images are extracted by phase conjugate adaptive resonance, is the result of “ the collapse of the wave function” followed by “its re-expansion”. See final illustration sidebar above – it shows a sphere wherein the G Heisenberg helix off resonance loses amplitude due to a transverse relaxation effect, but gains energy due to the corresponding longitudinal relaxation effect. That is, one sees, in this frequency induced thermodynamic quantum decay of the energy of nuclear spins, the dual/reciprocal mappings of G, appropriate to Lie’s 1871 thesis, as it applies in 3D geometric image production. The thermodynamic entropy produced is thus both a measure of disorder and an information metric for the 3D images, where its quantum phase nature, shows the MRI measurement mechanism, to be that of a Quantum Carnot Engine (QCE).
The QCE [8] is a recently discovered quantum mechanical extension to the standard thermo- dynamic Carnot Engine, where the required quantum preparation necessary prior to any quantum measurement, ensures that the Second Law of Thermodynamics continues to hold. This extension, specified in terms of the single parameter phase of the quantum coherence, thus has measurable consequences, even in the totally empty quantum vacuum state (as the condition of nilpotence has already lead us to believe must be the case, from Rowlands’ work) showing that quantum coherence is a form of “dark energy”. Further it follows, that this initial empty state of relativistic 3+1 space-time and elementary particle matter :-
i) has the 3D spatial and the temporal quantum coherence necessary for holography, and
ii) is such that there will be spontaneous phase conjugate adaptive resonance, which means not just a Big Bang, but, as can be shown, an optimally organized process having more in common with the birth of ‘an organism’.
This latter is an assertion that can be made with increasing confidence following the very impressive presentation of Rowlands and his colleague Vanessa Hill [9]. They applied the universal rewrite system to a detailed prediction of the 3D geometric structure of nucleotide base-pairings inside the double helix of DNA, and to the codons of the genetic code for the proteins; and found these as they are known to exist in nature.
This provides very significant new supporting evidence, to that already published, that the DNA/RNA genetic code is indeed a rewrite** of the universal rewrite system based on the semantic language of the codons/base pairings. For example, the Gariaev group [10] has already shown that the statistical properties of this ‘codon’ language for actual living system DNA sequences, have much in common with those of human natural language, where both are quite different from random sequences of symbols; thus showing, based on experiment and computer simulations, that DNA is a almost certainly a biowavecomputer capable of the holographic processing and storage (i.e. a QCE) of 3D information concerning the morphology of its organism, as also predicted independently by Marcer and Schempp using quantum holography.
Further there is already a significant body of published work, in support of the brain working by quantum holography see other sidebars, that would flow from this hypothesis that DNA/RNA is a universal rewrite system & implying that the human brain is also universal semantic machine/QCE. This would not only account for the semantic/semiotic functioning of human natural languages, saying that these are an example of a further rewrite** of the universal rewrite mechanism, but it would explain the distinction between human/biological intelligence and artificial intelligence based on digital computation and their totally different information processing architectures.
Scheldrup [10] set out experimental evidence, from his own extensive experience of complementary medicine, of why the above cited extensions to existing models of physics and biology, would, he was convinced, provide a science of healing, largely missing from Western medicine.
Purcell [11] gave an ‘Jungian/Pauli’ perspective by means of artifacts and symbols across the ages, as extensively researched by her. These expressed, she felt deeply, as an avant-garde painter and philosopher, mankind’s largely unconsciously arrived at, experiential understanding of the forces and geometry at work in the physical world. In particular she emphasized the historically recognized significance of the shape, now known as the Klein bottle. This raised the question, are these artifacts and symbols perhaps, evidence of the seeds of thought from which the semiotics of mathematics and modern science were conceived?
Johansen’s masterly exposition[12] of the Fibonacci sequence and the possibility and significance of its recursive development in relation to number 5, lead several members of the audience to ask if there was a relationship here with scales in music and of universality of music & with Penrose tiling?
References
1. Rowland’s audit (to appear in proceedings)
2. Rowlands, Peter and Diaz Bernard, 2003, A Computational Path to the Nilpotent Dirac Equation, Symposium 10, International Conference for Computing Anticipatory Systems, HEC Liege, Belgium, August 11-16, 2003, International Journal of Computing Anticipatory Systems, editor Daniel Dubois, 203-218. also at arXiv.cs.OH/0209026
3. Trell E. 1998, The Eightfold Eightfold Way, Algebras Groups and Geometries 15,447-471.
4. Marius Sophus Lie’s Doctoral Thesis, English Translation by Trell E. Commentary by Trell & Santilli, 1998 Algebras Groups and Geometries 15, 395-445
5. Resta R. 1997 The Geometric Phase, Europhysics News 28, 19
6. Wilson K. G. The Renormalization Group and Critical Phenomena, Reviews of Modern Physics, 55,3, July, 583-600.
7. Schempp, W. 1986, Harmonic Analysis on the Heisenberg Group with Applications in signal theory, Pitman Notes in Mathematics, Series 14, Longman Scientific and Technical, London (This book discusses the general properties of nilpotent Lie groups and their nilpotent Lie algebras) ; 1992 Quantum Holography and Neurocomputer Architectures, Journal of Mathematical Imaging and Vision, 2, 279-326, see http://www.bcs.org.uk/cybergroup.htm
8. Scully M. O. et al 2003, Extracting Work from a Single Heat Bath via Vanishing Quantum Coherence, Science, 299, 7th February, 862-864. 10.1126/science.1078955.
9. Rowlands P. & Hill V. Fundamental Structures applied to Physics and Biology (to appear)
10. Peter Gariaev, Uwe Kaempf, Peter Marcer, Georg Tertishy, Boris Birshein and Alexander Iarochenko, Fifth (2002) and Fourth (2001) International Conferences on Computing Anticipatory Systems, CASYS, Liege, Journal of Computing Anticipatory Systems, ed. Dubois D. respectively, Symposium 10 (2002) volume 13, Fractal Structure in DNA Code and Human Language: Towards a Semiotics of Biogenetic Information, 255-273 ; and Symposium 4 (2001) volume 10, The DNA-wave biocomputer, 290-310.
10. Scheldrup to appear in proceedings
11. Purcell to appear in proceedings
12. (more detail from the author) Johansen has developed a universal differential ontology (including epistemology) [13]; aspects of this systemic philosophy earlier being crucial for his establishment of an autonomous theory of in-formed, second degree economics, presented in his Norwegian D.Sc. thesis of 1991. In his differential ontology the qualitative concept of information is sought established with more precision than in Bateson's classic notion, and the categories of 'causality' and 'border' are argued as universally implied in the very concept of information. From the fundamental ontological attributes of the abstract category of 'border', determined with vertical ontological differentiation (different from Spencer-Brown's approach), Johansen has recently argued the Fibonacci algorithm being the elementary and universal form of nature's information processing [14]. Rowlands and Hill [9] present some integration of Johansen's ontological Fibonacci argument with(in) the universal rewrite.
In his presentation Johansen argued the general potential for precise micro-philosophy of basic operators of nature and thought to hold potential for catalyzing significant scientific progress, the invention of the universal Turing machine being a classic example. He also stressed the importance of an adequate and non-trivial basic ontological framing compatible with recent breakthroughs from cutting edge natural science, such as Santilli, Rowlands, Trell, Illert and Gariaev.
Johansen presented a sketch of a highly abstract theory of the form of universal evolution as successive unfoldment and multi-layered complexification from a quite simple mathematical skeleton span by the tandem interplay of two intertwined strands following the Fibonacci algorithm, but with different numerical points of departure. To reconstruct some of the constitutional logic of this fraternal twin-helix stranding, Johansen applied a vertical empty set approach on a rotational succession of the first Fibonacci numbers, with a special emphasis of the dynamical intricacies concerning the Fibonacci number of eight holding a certain double split code of 5/3 constituting a knotted spring point for the unfoldment of the source code for universal evolution. Johansen also pointed out some striking correlations to crucial thought operators in creation myths as well as to findings from Rowlands' universal rewrite system. Johansen argued that evolution of different types and order could be understood inside this overall scheme as generated from different configurations of the basic operators traceless vs. reflexive classification, the last operator inducing higher order Fibonacci patterns and being the key to understand higher forms of evolution such as psychological and cultural.
13. Johansen, Stein 2006: Outline of a Differential Epistemology (English translation of Norwegian book in transit)
14. Johansen, Stein 2006: Initiation of 'Hadronic Philosophy', the Philosophy Underlying Hadronic Mechanics and Chemistry, Hadronic Journal, volume 29, number 2, 111-135.
