Chairman's Report 2007 on the
6th BCSCMsG International Symposium at CASYS 07 Liege in August
Introduction
At a highly successful and well attended 6th BCSCMsG International Symposium “Rewrite Science - the Universal Semantic Calculus and Grammatical Cosmos” and CASYS'07 the 8th International Conference, 6th-11th August, Liege, Belgium, see Abstracts'07 sidebar, the thesis 'How Intelligence Evolved?', of a Grammatical Cosmos in which the NUCRS universal grammar specifies the staircase of increasing evolutionary complexity of all matter, was significantly substantiated by a new series of major papers.
This staircase, obtained from the spontaneous symmetry breaking of the empty state taken as the Grammatical Cosmos' initial boundary condition (essential to the proper solution of any physical problem), begins by predicting the quantizations of Standard Model elementary particle matter as experimentally validated. It describes these (particles) as the sources and sinks of the 3+1 relativistic space time field, in such a way that the field and its sources and sinks operationally constitute the quantum computational 'machine order code' for all further (universal rewrite) computation corresponding to the staircase of NUCRS infinite universal alphabet, which Rowlands' subsequent presentation showed concerns relativistic quantum mechanics derived from a single operator.
The Symposium Report
Peter Marcer introduced the Symposium with an investigation of 'the symmetries of 3D space' as a central feature of the NUCRS quantum mechanical machine order code and grammar.
Consideration of the set of radial vectors to the surface of a unit sphere centre P, as defining each neighbourhood in 3D space, shows that any such vector through the centre P of the sphere and the plane perpendicular to it, are unique and correspond to the symmetries, U(1), SU(2), in relation to the symmetry of the sphere SU(3). P thus defines a ray space diagram A, where the fundamental quantum mechanical spectral theorem of Hilbert and Von Neumann applies, such that U(1), SU(2) and SU(3) are respectively the symmetry groups, now known to determine the quantizations of the elementary particles of the electromagnetic, weak and strong forces, and U(1).SU(2) is the symmetry of the electroweak force (the photon with its vector bosons) combined in just the right way. Thus (subject to the proviso that every P can indeed be considered as a Lie topological neighbourhood, where the symmetries are those of Lie groups together with their Lie algebras, as defined by their smooth tangent spaces of lines and planes) the NUCRS grammatical sub-alphabet of P, which must differentiate lexicographically between the three axes of space in order to describe three distinct orthogonal spatial axes, may be labelled 'electron', 'muon' and 'tau', in good accord with the Pauli exclusion principle for spin ½ (fermion) anti-commutative states, which applies to each and every unique unit vector and its two perpendicular plane axes at P.
That is to say, in NUCRS where the elementary particles predicted are exclusively those of the Standard Model (and so exclude gravitons!) and 3D space is, as described above, a quantum field, the particles with spin ½ known as the neutrinos take on, as a new testable hypothesis of their behaviour, in an unexplored role in respect to the axes of 3D space. And remarkably, in respect of this '3D spatial quantum field', there exists a Lie symmetry, that of the 3D Heisenberg Lie Group G, in the form of its nilpotent Lie algebra g, as was known to Weyl in 1928, which defines its Heisenberg uncertainty, in terms known as a Robertson relation. However as both g and G have Lie duals, there exist corresponding (Lie) exponential differentiable mappings with differentiable inverses, so that Heisenberg uncertainty can, in this case, be used as the actual means to compute geometrically. As, for example, the description of
U(1,C)
signal processing in the form of quantum holographic encoding/decoding in Magnetic Resonance Imaging (MRI) machines proves and was described in much more detail later in Schempp's invited paper.
Diagram B illustrates how in actual 3D space, the encoding/decoding Fourier transform action (in accord with the Heisenberg uncertainty principle defined by g the Lie algebra of G) actual happens in MRI. It shows the 'frequency induced signal' U(1,C) described by the Heisenberg helix of G off resonance losing amplitude (z axis) i.e. thermodynamically decaying due to a transverse relaxation effect, but remarkably simultaneously regaining energy due to longitudinal relaxation, so as to embed the U(1) signal in the complex plane C = (x+iy), where it can be described as a phase difference. For, with respect to G and g, G represented as
is such that (x - path difference, y – phase difference) form
a Fourier duality encoding pair (x,y) = (x + iy) so embedding the complex plane C in G, and
g the infinitesimal Lie generators {P,Q,Z} where [P,Q] = Z; [P,Z] = 0;[Q,Z] = 0, are represented by
having Lie exponential diffeomorphisms
are the components of the automorphism of G, able to describe the inverse Fourier transform action of decoding, i.e. they give rise to the identity exp (xP + yQ + (z - ½ xy)Z) = G and where the conformal complex mode coordinates T= ½(P + iQ and T* = ½(P- iQ) permit through the linear Schrodinger representation U of G, a quantum mechanical description at the photon level in terms of the creation/ annihilation operators a = U(T) and a* = U(T*) of an emitter/absorber model.
However Rowlands and Diaz CASYS 05, have shown that the NUCRS infinite alphabet determined by the nilpotents Xn2 = 0, Xn ≠ 0 corresponds to the infinite square roots of -1, n = 1,2 ,...... . Thus the symbol i (i.e.'√-1') in NUCRS stands for the whole infinite alphabet, embedding it in a particular complex plane C on a line i = √-1, where each letter of the alphabet located on this line denotes a (fermion) anti-commutative state and is unique, so locating this line at a point of an x axis in a particular complex plane at x = spin ½..
This immediately suggests, that the Riemann Zeta function in relation to the famous Riemann Hypothesis represents this NUCRS mapping in the complex plane, so that through the NUCRS alphabet, it describes the wholly entangled nature of Grammatical Cosmos, in terms of the Zeta function's zeros, where by the Riemann Hypothesis, these are non trivial i.e. nilpotent and are all located on the line x = ½ . This is in line with Berry's hypothesis, that the imaginary parts of the non trivial zeros of the Riemann Zeta function are the eigenvalues of some still unknown self adjoint Hamiltonian operator with time reversal asymmetry (a property of the NUCRS ) of which phase space trajectories are chaotic.
It is in agreement with the fact the each letter of NUCRS infinite alphabet has the same 'nilpotent' formulation Xn2 = 0 at all levels of its rewrite structure and so is self similar of fractal dimension 2 and therefore embeddable in the complex plane C ; i.e. can be mapped in a conformal fashion onto the open unit disc (which is the geometry of i = √-1). It thus corresponds to the universal fractal attractor of the Golden number see Diagram C and relates to the wave in behaviour seen at the boundary of the Mandelbrot set.
As the harmonic analysis on the 3D Heisenberg Lie group G discovered and applied by Schempp to the description and control of MRI and Synthetic Aperture Radars, proves is indeed be the case. As do - the field symmetry U(1, C) in terms of the polarization wave property of electromagnetic signals in relation, for example, to the quantum mechanical Aharonov Bohm effect; the helices of RNA/DNA (see Hill& Rowlands below) and the representation the Riemann sphere of the complex plane by stereographic projection, where the pole is the point at infinity called in perspective the 'vanishing point', which in art is a very late discovery of the nature of human perception Diagram D below.
All were cited in this presentation authored by Marcer and Rowlands, in support of the hypothesized testable nilpotent nature of the Zeta's zeros, as the precise means of describing quantum entanglement in NUCRS.
There later followed, in further support of this NUCRS hypothesis, Trell's invited paper (based on Lie's 1871 Norwegian language thesis concerning real 3D space, foundational to his more general famous transformation methodology), where Trell uses the 'cubit' symmetry structure of the eight cubes about the point P of the neighbourhood with its eightfold way cubit metric scaling of signature +++, -++, +-+,++-, +--,-+-, --+, --- to calculate the relative masses of all the families of the elementary particles, in good accord with their experimentally determined values, and their quantizations as previously calculated by Rowlands.
Chairman's comment What clinches these arguments so far for me, is that the masses and quantizations of the Standard Model elementary particles are not only predicted to be those found experimentally but that they are invariant template of physical properties which hold, as the NUCRS order code requires be the case, throughout all 3D space independent of both time and evolution! Mathematically these properties are, of course, those to be expected from Lie transformational theory, where bi-linearisation takes place via the calculation of invariants. A fact that would be explained if these invariants are all properties of universal standing wave or a soliton.
A very highly detailed paper by Hill and Rowlands in relation to DNA/RNA biological systems and their geometric structures, Nature's Code (see abstract) written from the single nilpotent Dirac operator perspective of Rowlands for the NUCRS universal grammar and infinite alphabet, was presented by Hill. This fully underpinned and extended that from the earlier complementary perspective of the nilpotent Heisenberg Lie group G referred to and referenced in the AAAI paper, which predicts, for example, the structure of DNA as a semantic wave bio-computer where the two Heisenberg helices of G and its dual G' and their base-pairing SU(2) hologram planes are the basis for the U(1,C) holographic helical signal processing taking place and the semiotics of the genetic code. This very comprehensive treatment fully substantiated the NUCRS hypothesis that the DNA/RNA genetic code is indeed a rewrite at a higher level of molecular complexity further extending the NUCRS' universal alphabet. And where the DNA is known to include the encoding of the human brain.
To summarize therefore. 3D space should no longer be considered as just a plenum within which matter moves, but as a quantum field such as Einstein describes in general relativity, where, it has been said, 'matter bends space and space shapes matter'. An example would be changes in scaling resulting from nearby massive objects that can be expected from Trell's research to subject U(1) signals to lensing effects. Indeed as shown in 'Zero to Infinity', this is, in fact, the actual means by which the dichotomy between nilpotent quantum mechanics and general relativity is resolved thermodynamically.
Further support for the universal rewrite nature of NUCRS
At a higher level of complexity, this comes from the three spin ½ particles, the electron, muon and tau, and the composite (nuclear) matter with spin - these matter symmetries would (in addition to the Trell metric signature of 'cubit' scaling) reflect those of SU(3), which concern the quark patterns, where these are, rather than the doublets of SU(2), expressed in the form of triplets conventionally labelled the red, yellow and blue colour forces interactions produced by gluons (colour bosons) between the quarks.
It is also clear that in relation to the 3D spatial field, that there must also exist SU(2) processes able to change the properties of SU(3) matter interior to any nuclear composite. These processes can thus be hypothesized to define, for example, the two very well known phenomena of nuclear fusion and nuclear fission (as the 2 NUCRS create, conserve productions) where the interactions involve the neutrinos and are recognised to produce the composite nuclear matter/elements of the periodic table in the stars, which are seen here to be 'super' quantum mechanical ray spaces composed from neighbourhoods P.
The NUCRS/nilpotent quantum mechanics (NQM) scaling phenomena and relativity -special and general.
These are essentially one and the same and so relate to the fact that the electro-magnetic vector symmetry U(1) and 'gravity'/scaling determines 'mass', can be expected in the first approximation to obey the same inverse square Coulomb law as is indeed in the case. For in the case of gravity masses replace charges, but due to their scalar rather than vector nature only attract one another.
The VIth International Symposium in honor of Jean-Pierre Vigier organized by Richard Amoroso.
In particular the paper on The Role of Black Hole Dynamics (see Abstracts'07)
contains a totally independently derived theory associated with solutions to General Relativity applied to complex plasma systems, which is supported by experimentally collected data. The solutions and in particular those applied to the dynamics of black holes, were illustrated by remarkable dynamical computer graphic illustrations of the black hole behaviour in good agreement with that astronomically observed. It appears to be closely related to that described in Schempp's quantum holography, where it is called the Hopf fibration or Clifford parallels, which is the visualization via stereographic projection of the foliation of the sphere S3 projected from R4 by nested flat tori see Diagram E , the dynamics of which it purports to represent, has already been identified by Schempp as concerning the light echo phenomena of radiation from the care of galaxies.
Peter Marcer 24/10/07
