CASYS'09 Computing Anticipatory Systems

CASYS'09
Ninth International Conference on
Computing
Anticipatory
Systems
HEC-ULg, LIEGE, Belgium, August 3-8, 2009
ABSTRACT BOOK
Editor: Daniel M. Dubois
University of Liège, Belgium
Published by CHAOS
Centre for Hyperincursion and Anticipation in Ordered Systems
Institute of Mathematics, University of Liège, Belgium
CASYS’09 ABSTRACT BOOK
Edited by D. M. Dubois, Published by CHAOS, 2009.
Daniel M. Dubois
Director of CHAOS asbl
Institut de Mathématique, B37, Université de Liège,
Grande Traverse 12, B-4000 Liège 1, Belgique
Tél.: + 32 4 366 94 96 - Fax: + 32 4 366 94 89
E-mail::[email protected]
http://www.ulg.ac.be/mathgen/CHAOS
CHAOS asbl
Centre for Hyperincursion and Anticipation in Ordered Systems
Association Sans But Lucratif
Institute of Mathematics, B37, University of Liège,
Grande Traverse 12, B-4000 Liège 1, Belgium
Copyright © 2009 by CHAOS
Abstracts are reproduced from camera-ready copies prepared by the authors.
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No part of the material protected by this copyright notice may be reproduced or utilised in any
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information storage and retrieval system, without permission from the copyright owners.
Dépôt Légal D/2009/8079/1
ISSN 1373-4903
ISBN 2-930396-10-5
Imprimé en Belgique - Printed in Belgium
TABLE OF CONTENTS
SYMPOSIUM 10
7th BCSCMsG International Symposium
on
Grammatical Cosmos II,
dedicated to the Quantum Hologram - Focus Session - Intelligence,
Consciousness & How The Laws of Physics Become the Laws of Life
organised by Peter J. Marcer
SESSION 10.1.
TUESDAY AUGUST 4, 8:30-12:30, ROOM 138
Chairpersons: Peter Marcer & Cyril Smith
Perplexity I. Logical Structures of Irregular Mathematics
Jerry LR Chandler (USA)
Mathematics and Physics as Emergent Aspects of a Universal Rewrite
System
Peter Rowlands (United Kingdom)
An "Uncertainty Relation" Between Spatial and Temporal Neuronal
Coding as a Possible Reason for Phase Losses in Amblyopia
Uwe Kämpf (Germany), Igor Rabitchev (Russia)
Fractals, Coherence and Brain Dynamics
Giuseppe Vitiello (Italy)
Diffusion Tensor Magnetic Resonance Tomography and Cerebral
White Matter Tractography
Walter Schempp (Germany)
3
5
6
8
9
SESSION 10.2.
THURSDAY AUGUST 6, 14:00-18:00, ROOM 138
Chairpersons: Uwe Kämpf & Garnet Ord
Nature's Fundamental Symmetry-Breaking
Vanessa J. Hill, Peter Rowlands (United Kingdom)
The Numbers of Nature's Code
Vanessa J. Hill, Peter Rowlands (United Kingdom)
Rewriting Anticipatory Systems (RAS) in Chaos Map, Incursive and
Hyperincursive Systems, Self-Replicating Automata, Self-Modifying
Code, and Genetic Code
Daniel M. Dubois (Belgium), Peter J. Marcer, Peter Rowlands (UK)
Anticipating Real-Form Periodical System by Self-Templating
Expansion of Platonic and Archimedean Solids in Original Digital
Universe
Erik Y. Trell (Sweden)
The Science of Life
Otto van Nieuwenhuijze (The Netherlands)
10
11
12
14
16
SESSION 10.3.
FRIDAY AUGUST 7, 14:00-18:00, ROOM 138
Chairpersons: Vanessa Hill & Peter Rowlands
Coherent Frequencies, Consciousness and the Laws of Life
Cyril W. Smith (England, UK)
The Grammatical Universe, and the Laws of Thermodynamics and
Quantum Entanglement
Peter J. Marcer (France), Peter Rowlands (UK)
Riemann Hypothesis and Signal Processing Paradigm
Adrian James Rifat (England, UK)
The Process Semantics of Time and Space as Anticipation
Michael Heather, Nick Rossiter (UK)
Is Special Relativity Logically Prior to Quantum Mechanics?
Garnet N. Ord (Canada)
17
18
19
21
22
Symposium 10
7th BCSCMsG International Symposium
on Grammatical Cosmos II,
dedicated to the Quantum Hologram
- Focus Session Intelligence, Consciousness & How The Laws
of Physics Become the Laws of Life
Organised by Peter J. Marcer
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Perplexity I. Logical Structures of Irregular Mathematics
Jerry LR Chandler
Research Professor, George Mason University, Fairfax, Virginia, USA. 22102.
Keywords: Irregular mathematics, perplex number systems, chemical valence, catalysis,
biomathematics, C. S. Peirce, L.J. Brouwer, G. Leibniz
Abstract
The irregularity of natural systems creates a challenge to applied mathematics. In recent
decades new mathematical theories of catastrophes, chaos, fractals and fuzzy sets developed
improved approaches to some irregularities. Philosophically, these theories invoke the
Aristotelian concepts of efficient and formal causality and the uniformity of the line. It was
recently demonstrated that the Aristotelian concepts of material, formal and (local) final
causality create a basis for a natural number system, the perplex number system (Dis. Appl.
Math. 157 (2009) 2296-2309). Electrical particles enumerate the sources of material causality.
The quality of electrical fields (Coulomb’s law, as attraction or repulsion) is used to
enumerate relations. The enumeration of particles and relations is sufficient to represent the
“categorical sketches” of chemical structures and the physical organization of the electrical
particles as labeled bipartite graphs.
This paper describes the logical and philosophical background supporting this scientific
number system. Although the logic of the perplex number system originates in the material
sciences, the roots of the mathematics of irregularity can be traced to the early Greek notions
of number and to the writings of G. Leibniz, C. S. Peirce and L. Brouwer. Leibniz offers
notions of substance and attributes; C. S. Peirce offers notions of relation and diagrammatic
logic; and L. E. J. Brouwer offers the role of two-ity as a syndeton between mathematical
semantics and philosophy.
… the concept of an individual substance involves all its changes and all its relations, even
those which are commonly called extrinsic. (G. Leibniz, Letter to Arnauld, 14 July 1686.)
An attribute is the predicate in a universal affirmative proposition (of which the subject is the
name of the thing. (G. Leibniz, in Couturat, OFI, p.241)
“Firstness is the mode of being of that which is such as it is, positively and without reference
to anything else.
Secondness is the mode of being of that which is such as it is, with respect to a second but
regardless of any third.
Thirdness is the mode of being of that which is such as it is, in bringing a second and third in
relation to each other.” (C. S. Peirce, Letter to Lady Welby, 1904 Oct 12, CP 8.328)
Completely separating mathematics from mathematical language and hence from the
phenomena of language described by theoretical logic, recognizing that intuitionistic
mathematics is an essentially languageless activity of the mind having its origin in the
perception of a motion of time. This perception of a move of time may be described as the
falling apart of a life moment into two distinct things, one of which gives way to the other,
but is retained by memory. If the twoity thus born is divested of all quality, it passes into the
empty form of the common substratum of all twoities. And it is this common substratum, this
empty form, which is the basic intuition of mathematics. (Brouwer, 1981, 4-5)
As they are unencumbered by the current hegemony of membership, containment, functions,
continuity, and infinity, these three notions contribute to the logical grounding of the
mathematics of local irregularity.
The perplex mathematics of irregularity requires units, integers, numerals, parity, triadic
identities, multisets and labeled bipartite graphs. Parity serves as an invariant for logical
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operations such that quantity is preserved as a weak symmetry between units and integers. A
new inductive inference termed synduction creates the graphic syndetons. Geometry and
arithmetic operations are secondary attributes of spatial graphs. A mutation of relations
between integers and units requires the introduction of the concept of time.
The perplex number system generates exact mathematical descriptions of material situations
that were previously intractable. The irregularity of chemical valence, chemical isomers and
chemical catalysis are readily expressed within the perplex number system. A notation for
chemical systems and chemical catalysis follow naturally from the principles of material
causality. An unbounded number of homologous irregular systems are easily shown.
The polysemic usage of the critical term “identity” conflates the historical discussion of
material and efficient causes and artificially induces many pseudo-conundrums. In fact, the
perplex number system conjoins logically with the real number system, both statically and
dynamically. The same material entity generates an abstract meso-group and the x-ray
diffraction pattern of a real crystal structure. The law of mass action connects the material,
temporal and thermodynamic relations between perplex multi-sets and sets. Spatial motion of
electrical particles is described by chemical QM.
Applications of irregular mathematics and synductive logic to the emergence of life, to
reproduction of an individual organism, to genomic medicine and to the origins of
consciousness are in progress.
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Mathematics and Physics as Emergent Aspects of a Universal
Rewrite System
Peter Rowlands
Department of Physics, University of Liverpool,
Oliver Lodge Laboratory,
Oxford Street, Liverpool, L69 7ZE, UK.
e-mail [email protected]
Keywords: Universal rewrite system, symmetry breaking, quantum mechanics, gravity
Abstract
Mathematics and physics are shown to have a symbiotic relationship as emergent aspects of a
universal rewrite system. In addition to explaining the ‘unreasonable effectiveness’ of
mathematics in physics and the ‘unreasonable effectiveness’ of physics in mathematics, this
emergent nature of both subjects makes sense of the distinction between syntactic and
semantic approaches to logical reasoning. The system is also shown to generate constraints on
the kinds of mathematics and physics that are possible, explaining, in particular, why
symmetry is so significant in the subjects’ foundations, and specifying which symmetries are
most significant, as well as indicating their points of origin. Quantum mechanics emerges
from this structure in a very specific form which enables to understand the origin of symmetry
breaking in physics and many other aspects of fundamental physical theory. Gravity also has
special characteristics which explain its uniqueness among the four physical forces.
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An "Uncertainty Relation" Between Spatial and Temporal
Neuronal Coding as a Possible Reason for Phase Losses in
Amblyopia
Uwe Kämpf *, Igor Rabitchev **
* Dresden University of Technology
[email protected]
** Moscow Center of Investigation and Vision Correction
[email protected]
Keywords: Neuronal coding, vision, amblyopia, phase, uncertainty relation
Abstract
Amblyopia is a unilateral loss of visual performance associated, as a rule, with strabismus. A
typical disorder in the internal psychophysics of amblyopic vision is the pattern of so-called
spatial distortions (Hess et al., 1978). It is well-known that for low spatial frequencies the
spatial distortions imply no serious impairment of vision. However, they result in a serious
decay of visual performance for high spatial frequencies. This performance loss cannot be
attributed to a reduction of contrast sensitivity. Rather it is argued that the reason of the
disorder is a loss of coherence in the co-operative activity of the visual channels. As a result
we find an encoding impairment of the so-called spatial phase in the process which combines
the output of retinally distributed filter mechanisms. According to the presented view this
might be attributed to disorders in the coherence of temporal encoding.
To give an illustration: Spatial frequency on a TV image is generated as a “standing wave”
pattern by repetitive scanning with synchronized temporal frequency. If the integration
process in vision, operating probably on the base of so-called „synfire chains“ (Abeles, 1993),
might be compared – for illustrative purposes – with the repetitive scanning of a TV
monitor’s cathode ray tube, then a synchronism loss of this process has to be considered of
small impact on the phase coherence of the low spatial frequencies (ambient vision) but of
heavy impact on the high spatial frequencies (focal vision).
In order to prove the explanatory power of this idea for better understanding spatial
distortions in amblyopia, the predictions of such a hypothesis should be compared to the
assessment of neuronal synchronisation in the amblyopic cat’s visuo-cortical activity driven
by the normal vs. low vision eye (Roelfsema et al., 1993). The correlated single unit
recordings show a clear interrelation between the level of processing coherence and the
stimulation by low spatial frequency vs. high spatial frequency. Coherence peaks can be
found in cortical neurones driven by the normal eye as well as the amblyopic eye if their
receptive fields are stimulated by patterns of low spatial frequency. However, a stimulation
with patterns of high spatial frequency maintains processing coherence only in the synfire
chains driven by the normal eye but causes decoherence in that of the amblyopic eye. Thus, in
light of the discussed hypothesis, the loss of the spatial phase appears to be a result of
temporal processing decoherence due to a conflict between internal and external critical
timing constraints between spatial and temporal aspects of visual encoding in the sense of
what we want to call an „uncertainty relation“.
The term has been introduced by Werner Heisenberg in order to signify a basic measurement
problem. Such a problem arises if the more precise assessment of one of two complementary
aspects of an event impairs the precision of the contingent measurement of another aspect. Is
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there any direct psychophysical evidence in favour of an uncertainty relation in visual
processing?
It is a rather well-known fact that the spatial and temporal frequency filter bands of visual
channels are reciprocally tuned in relation to one another (Kelly, 1984). The frequency plot
shows the control parameters of two systems of reciprocally tuned spatial frequency
channels which support, on the one hand, ambient vision („motion channels“ of low spatial
and high temporal frequency) vs. focal vision („form channels“ of high spatial and low
temporal frequency) on the other hand. A reciprocal synergy of the both channel systems
grants for the coherence of the spatio-temporal interrelations between the optomotor and the
optosensory control of visual perception. In case of malfunction (amblyopia) this can lead to
losses of phase locking leading to spatial distortions as has been argued above. In the same
way, as has been shown for the optosensory domain, we find a psychophysical analogue to an
uncertainty relation in the optomotor domain too. According to their temporal characteristics
two kinds of saccadic eye movements can be differentiated (Velichkovsky et al., 2005):
1. Ambient saccadic eye movements of short duration (<180 msec), corresponding to high
temporal frequency of perceptual sampling with a great amplitude, i.e. low spatial frequency
of perceptual sampling.
2. Focal saccadic eye movements of long durations (> 180 msec), i.e. low temporal frequency
of perceptual sampling with small amplitude, i.e. high spatial frequency of perceptual
sampling.
Thus, the system’s synergy of the focal and ambient eye-movements’ control channels, which
manifests itself in an inversion of spatial and temporal frequency in the optomotor pattern, as
it has been recorded with an eye tracker, shows an analogue to what has been termed above as
an uncertainty relation (in correspondence to the one found in the optosensory domain). If so,
then a repetitive stimulation addressed at both the optomotor and the optosensory domain
might be considered to induce coherence in the coordinative processes between focal and
ambient vision, because it may be considered to improve focal visual processing via phase
coupling with ambient visual processing.
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Fractals, Coherence and Brain Dynamics
Giuseppe Vitiello
Dipartimento di Matematica e Informatica and INFN
Università di Salerno, I-84100 Salerno, Italy
[email protected] - http://www.sa.infn.it/giuseppe.vitiello
Keywords: Fractals; Coherent states; Entire analytical functions; Brain background activity;
the dissipative quantum model of brain
Abstract
In my talk I will consider fractals which are generated iteratively according to a prescribed
recipe, the so-called deterministic fractals. The self-similar fractal property is one of the
mathematical and phenomenological properties of fractals. It is a characterizing properties of
an extremely large class of fractals and therefore I focus my attention on it. My discussion of
fractals will point out some structural fractal aspects rather than features of specific fractals.
The connection will be made with the theory of the entire analytic functions and with the qdeformed algebra of the (Glauber) coherent states [1]. This results in the possibility of
incorporating fractal properties in the framework of the theory of entire analytical functions.
Conversely, it also allows to recognize, in some specific sense, fractal properties of coherent
states. This sheds some light on the understanding of the dynamical origin of fractals and of
their global nature emerging from local deformation processes. It also provides insights on the
geometrical (fractal) properties of coherent states. My conclusion is that fractals are global
systems arising from local deformation processes. Therefore they cannot be purely geometric
objects. Their connection with coherent states is in some sense expected, since coherence is
the available tool able to provide long range correlations out of the microscopic dynamics of
elementary components. The so called ``random fractals'', i.e. those fractals obtained by
randomization processes introduced in their iterative generation, will be not considered. Since
self-similarity is still a characterizing property in many of such random fractals, my
conjecture is that also in such cases there must exist a connection with the coherent state
algebraic structure.
The study of the fractal self-similarity property has been also motivated by the laboratory
observation of the brain background activity [2]. It results, indeed, that neocortical EEG phase
patterns have power-law distributions with no detectable minima. Moreover, the power
spectral densities in time and space of ECoGs from surface arrays conform to power-law
distributions, which suggests that the activity patterns generated by neocortical neuropil might
be scale-free with self-similarity in ECoGs patterns over distances ranging from
hypercolumns to an entire cerebral hemisphere. In my presentation I will frame these
observations in the context of the dissipative quantum model of brain [3].
1. G. Vitiello, Coherent states, fractals and brain waves, New Mathematics and Natural
Computing. 5, 245-264 (2009)
2. W. J. Freeman, A field-theoretic approach to understanding scale-free neocortical
dynamics, Biol. Cybern. 92/6 (2005) 350--359.
3. G. Vitiello, My Double Unveiled (John Benjamins, Amsterdam, 2001).
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Diffusion Tensor Magnetic Resonance Tomography and Cerebral
White Matter Tractography
Walter Schempp
Lehrstuhl fuer Mathematik I
University of Siegen
57068 Siegen
Germany
[email protected]
Keywords: Magnetic resonance tomography, diffusion tensor imaging, Lévy-Khintchin
integral representation, nilpotent harmonic analysis, symbolic calculus
Abstract
The technique of diffusion tensor imaging provides two unique insights into tissue
microstructure: It quantifies non--invasively diffusion anisotropy of proton motion, which is a
useful signum of cerebral white matter integrity, and provides an estimate of the principal
direction of axon fibers, which enables white matter tractography.
The paper presents a novel approach to the magnetic resonance modality of diffusion tensor
imaging which is based on the Lévy-Khintchin integral representation of the expectation
value of Lévy processes thought of as random walks in continuous time, that is they are
stochastic processes with independent and stationary increments. The proof is based on
nilpotent harmonic analysis, contact geometry and the symbolic calculus of quantum field
theory.
Diffusion tensor imaging provides indirect insights into the brain microstructural
characteristics of patients suffering of different forms of dementias, improving the
comprehension of the underlying pathophysiological processes that result in macroscopic
brain tissue loss over time.
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Nature's Fundamental Symmetry-Breaking
Vanessa J. Hill *, Peter Rowlands **
* Lifeworks Foundation,
10 Meads Road, Seaford,
East Sussex, BN251S, UK.
e.mail [email protected]
** Department of Physics,
University of Liverpool,
Oliver Lodge Laboratory,
Oxford Street, Liverpool, L69 7ZE, UK.
e.mail [email protected]
Keywords: Universal rewrite system, symmetry breaking, geometry, genetic code,
fundamental particles
Abstract
The question we are concerned with is: how can the highly ordered replicating state which we
call ‘life’ form within a universe where the tendency of natural processes is towards a state of
increasing disorder? Life could not possibly emerge from a purely random arrangement of
physical and chemical interactions. There must therefore be some driving process, which, in
some way, maximizes information, an intrinsic information processing or machine order code,
which probably determines the behaviour of all ordered systems, physical and chemical as
well as biological, large scale as well as small scale. The existence of such a code seems to be
suggested by the generation of a universal rewrite system, with its own mathematical
structure, from the single assumption of a zero totality universe; and it would appear that the
successive stages which this system automatically generates correspond with the algebraic
and geometrical structures which are fundamental in physics and biology in particular. The
system has a number of significant aspects – cardinality, rather than ordinality, bifurcation at
each stage, and a key stage at which symmetry breaking first occurs. The progressive stages
are worked out here in both algebraic and geometrical terms and illustrated through detailed
applications to genetics and particle physics.
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The Numbers of Nature's Code
Vanessa J. Hill *, Peter Rowlands **
* Lifeworks Foundation,
10 Meads Road, Seaford,
East Sussex, BN251S, UK.
e.mail [email protected]
** Department of Physics,
University of Liverpool,
Oliver Lodge Laboratory,
Oxford Street, Liverpool, L69 7ZE, UK.
e.mail [email protected]
Keywords: Universal rewrite system, Nature’s code, fundamental particles, genetic code,
geometry
Abstract
Assuming that Nature is described by a universal rewrite system and operates according to a
process that we can refer to as Nature’s code, we define certain numbers as being crucial
indicators of how the code operates, whether in biology, chemistry or physics. We also show
how these numbers originate in the most extraordinarily simple way from two numbers which
correspond to the two distinct processes within the system – conserve and create – which can
in turn be related to the properties of duality and anticommutativity. The numbers emerge in a
number of distinct series which have distinct algebraic and geometrical representations. The
geometrical structures translate easily from 3- to higher-dimensional representations,
especially those of dimension 4 and 8, and also connect significantly with rotational
symmetries and with Lie groups, up to E8. The fundamental particles of physics are a classic
case of the operation of the number series, in which all the significant numbers are
represented, and no others. The structure leads to a complete classification of fermions and
bosons within an overall E8 representation. An almost parallel system emerges in the genetic
code, leading to the processes of transcription and translation.
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Rewriting Anticipatory Systems (RAS) in Chaos Map, Incursive
and Hyperincursive Systems, Self-Replicating Automata,
Self-Modifying Code, and Genetic Code
Daniel M. Dubois*, Peter J. Marcer** and Peter Rowlands***
* Centre for Hyperincursion and Anticipation in Ordered Systems (CHAOS ASBL),
Institute of Mathematics, B37, Grande Traverse 12, B-4000 Liège 1, Belgium,
and Department of Applied Informatics and Artificial Intelligence,
HEC-ULg, N1, rue Louvrex 14, B-4000 Liège, Belgium
email: [email protected] - http://www.sia.hec.ulg.ac.be
** 55 rue Jean Jaures, 83600, Frejus, Var, France
email [email protected]
*** Department of Physics, University of Liverpool,
Oliver Lodge Laboratory, Oxford Street, Liverpool, L69 7ZE, UK.
email [email protected]
Keywords: Rewriting Anticipatory Systems (RAS), chaos, incursion, self-replication, genetic
code
Abstract
The purpose of this paper consists in developing a theory of Rewriting Anticipatory Systems
(RAS) applied to chaos, incursion, hyperincursion, replicate automata, self-referential
program, and genetic code.
The first example will be the Verhulst map,
x(t +1) = ax(t)(1 − x(t)),
which gives rise to a deterministic chaos, for which the analytical solution shows that all the
future states of this map is a rewriting of all the infinite digits of the initial condition, and is
thus a strong anticipatory system.
The second example is the Dubois incursive system,
x(t + 1) = ax(t)(1 − x(t + 1)),
which is a self-referential system (an incursion is an inclusive recursion), and the infinite
regress of x(t+1) has an analytical stable solution.
The third example is the Dubois hyperincursive system,
x(t) = ax(t + 1)(1−x(t + 1)),
which gives rise to two states at each time step, and can be applied to build a memory that is
obviously a rewriting system.
The fourth example will deal with the theory of self-reproducing automata of von Neumann:
the important point here is the fact that the automata build replicates of themselves, what is
the main characteristics of living systems.
An elementary version is the Game of Life of Conway. Let us recall that simple cellular
automata show also self-replication of patterns.
The Quine self-reproducing programs deal also with replication.
Another type of rewrite system is the self-modifying code in computer science.
The main point is the fact that these systems are purely anticipatory and obey the paradigm of
Rewrite Systems.
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The last fifth example will be the genetic code in living systems, which is able to show selfreplication and self-modifying in relation with an evolution. The genetic code is an Alive
Rewriting Anticipatory System (ARAS).
An important last point is the fact that the living systems are programmed by the genetic code,
and due to this fact, all the dynamics of the living systems are governed by the instructions of
the genetic code where the information increases with the evolution, because entropy takes on
the role of an information metric, because living systems are anticipatory programmed
systems. The evolutionary process, however, remains in accord with the Second Law of
thermodynamics because the overall process of evolution in the universe, including the
emergence of new living and nonliving systems, is quantum mechanical and described by an
infinite rewrite system in the form of a universal (totality zero) attractor, which specifies a
unique irreversible birthordering for the emergence.
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Anticipating Real-Form Periodical System by Self-Templating
Expansion of Platonic and Archimedean Solids in Original Digital
Universe
Erik Y. Trell
Linköping University,
Se-58180, Linköping, Sweden
E-mail: [email protected]
Keywords: Digital Universe, Electron Distribution, Elementary Particles, Honeycombs,
Periodical System, Regular Solids, Self-aggregating, Self-templating, Truncated Octahedron.
Abstract
When, collage-style quoted, a recent authoritative “scientific data mining for conserved
quantitities and meaningful and nontrivial invariants that underlie physical phenomena in
nature, discovered Hamiltonians, Lagrangians and other concise analytical expressions”, such
“distilled conservation equations” are still analog since functions of the respective “system’s
partial derivatives”. These, in turn, are of course all equal and the real non-trivial conserved
quantity at the ground in any e.g. curve, intercept or identity/spin matrix therefore reduces to
a sole infinitesimal straight line bit so that at smallest scale the world is digital - like in
modern informatics and computing, the only sufficient letter and number and structural
element alike is the binary unit, I, which then forms the reality it may by the canvas and
lacework of its own. Showing that the current “digital revolution” is in fact the digital
Renaissance, this is the profound meaning of the ancient regular solids, too, opening up long
forgotten corridors also to the original Diophantine equations and onwards, e.g. to Keplerian
Cosmography, Renaissance Arithmetics, and Fermat’s Last Theorem and its offspring Beal’s
Conjecture. In fact, at the then available level of resolution, the anticipation of the possibly
underlying common alphabet of the physical systems and processes around came down to the
same ground invariant at hand, namely, anew, the straight line bit, I, from which a complete
Universe could be filled by the elements outlined by the infinitesimal digit distributed via
first-degree straight and square or diagonal wave sequences and second-degree self-closing
equilateral quadrate, triangle and pentagon planes to the maximally three-dimensional, in all
but five feasible regular solid expansions. As reported in the CASYS’07 meeting, a transfer to
modern elemental counterparts yields exact and exhaustive, both channel, angular and
electromagnetic quantum number, mass, and quark inclination reproduction of the meson
symmetries by the (assigned to) fire tetrahedron, baryons by the air octahedron, and
electrons/positrons by the only spacefilling, truncated octahedron distribution of the
continuous 2-tetrahedrons/1-octahedron lattice complex of their unit root vectors, while the
water icosahedron and the quintessential dodecahedron of cosmic advance relate to organic
matter; all embedded in the cube eigen-element manifold of geocentrically extrapolated
Euclidean space as well as original Diophantine equations. In principle, there is no difference
between an orbital and an axially twisting truncated octahedron distribution of the stepwise
path of the extra-nuclear electron domain, but the interesting advantage of the latter is its
direct root vector constitution with concomitantly defined lattice segment shape, enabling
further, virtually nanotechnological self-templating reduplication of its motif into serially
enlarged atomic and onwards modules. Moreover, when single truncated octahedron blocks of
lowest quantum state hydrogen at ultrahigh temperature and pressure might coerce they could
fuse to bi-modular Helium and from there to three-modular Lithium, four-modular Beryllium
etc. honeycombs of matching form and Bohr orbital shell layering with consequence that their
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spiralling pivot of axial twist widens correspondingly so that both electron and nuclear
aspects of the entire periodical system are reproduced with striking resemblance to its actual
features. Many other non-understood properties and conditions of matter from infinitesimal to
macroscopic size are replicated, too, as will be further discussed in the paper.
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The Science of Life
Otto van Nieuwenhuijze,
MSc, MD,
Independent Research Scientist
17-II Gerard Doustraat,
Amsterdam, NL-1072 VJ, The Netherlands
[email protected]
http://ottovannieuwenhuijze.googlepages.com
Keywords: Science of Life, consciousness, reverse engineering material science. reality
realisation
Abstract
Science is created by scientists: Reality is a Realisation. More and more, the models of
science determine the life of people. The following proposes that there are many healthy
reasons why we need a science of life. Health care and ecology is not helped by models of
dead matter. Economy is not helped by measures of objective quantities, instead of subjective
qualities. Peoples are not helped by being ruled as if machine parts.
At present we are very close to the onset of a science of life. Scientific modelling has already
led from a study of matter to a view on information. Quantum Theory already approached the
gap of the Heisenberg uncertainty. Alls that scientists need to do is to take the leap, step into
the gap, and realise their responsibility (and response-ability) in their creation. Tiller e.a.
already showed that energy follows thought: intent determines the effect of matter. Earlier
work has already described that every form of matter is a form of information. The universe is
a form of information, in formation. What is needed still is the realisation that every
description of science, describes the scientist's inner working. We in fact already have a
science of life, in inverse. Reverse engineering this we can realise that the models of science
are freeze-frame glimpses of our thinking. What is needed is a generalisation of the concept; a
formulation of conscience with its direct practical application: a Science of Life.
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Coherent Frequencies, Consciousness and the Laws of Life
Cyril W. Smith
Retired from the University of Salford, England.
36 Westminster Road, Ellesmere Park, Eccles, Manchester M30 9EA, England.
[email protected]
Keywords: Water, Coherence, Quantum Effects, Living Systems, Conscious Activity
Abstract
The language of communication within and between living systems is coherent frequencies.
Fröhlich first ntroduced the physics of coherent frequencies in respect of biological systems
and which is summarised in his two “Green Books”. Water is essential to life, Del Giudice
and Preparata showed that domains of coherence are a fundamental property of water. One
consequence is that frequency becomes a fractal quantity thereby linking the chemical to the
technological to the biological. The limit to the possible degree of this coherence is set by the
statistical fluctuations in the number of water molecules in a phase coherent state within a
domain; this is found experimentally.
In CASYS’01, it was shown that frequency imprints in water (RAM) could be subjected to all
the basic arithmetical operations and in CASYS’05 that all the basic reversible logic gates
could be devised whence, any reversible Boolean function could be computed.
In CASYS’07, it was shown that water imprinted with the patterns of frequencies from mononucleotides could be taken through the patterns of DNA and RNA to the amino acid. If the
same is done using traces of the mononucleotides one still gets the same frequency patterns
but these do not erase in mu-metal box so, it is possible that there been a chemical reaction
and frequency structured water can act like an enzyme. From work of Partheil, acoustic mode
frequencies through the Rydberg Constant enable living systems to identify atomic isotopes.
Rowlands has described a form of expression for the ‘Dirac Equation’ which contains purely
physical information so that mathematics becomes an intrinsic part of physical structure
furthermore, the equation contains three terms which separately express the “energy”,
“momentum” and “mass” in the physical system. This equation can also be expressed in
terms of three frequencies.
Living cells can respond to a single quantum of magnetic flux linking the cell and to the
Josephson effect, and are sensitive to the magnetic vector potential which affects the phase of
their wave function. A digital aspect of frequency in biocommunication may come in at the
quantum level through integer related quantum transitions between chemical states (ROM).
Water, H-bonded to chemicals, gives them characteristic frequency patterns. Marcer and
Schempp have shown the quantum coherence and phase conjugation conditions needed
holographic memory system. This is the only one which satisfies a living system’s need for an
image in the actual location of the object in space and time. The endogenous frequencies in
living systems must be ‘eigen’ states of these wave functions. Both can show chaotic
behaviour.
The human body’s endogenous coherent frequencies can be altered in anticipation by
application of aspects of consciousness and intention. All these possibilities for biocomputing have been built into the Laws of Life.
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The Grammatical Universe, and the Laws of Thermodynamics
and Quantum Entanglement
Peter J. Marcer * and Peter Rowlands **
* 55 rue Jean Jaures, 83600, Frejus, Var, France
email [email protected]
** Department of Physics, University of Liverpool,
Oliver Lodge Laboratory, Oxford Street, Liverpool, L69 7ZE, UK.
e-mail [email protected]
Keywords: Grammatical universe, universal nilpotent rewrite system, irreversibility, Laws of
Thermodynamics, Quantum entanglement, evolution
Abstract
The universal nilpotent computational rewrite system (UNCRS) (which delivers the whole
quantum mechanical (QM) language apparatus in terms of a single algebraic creation operator
(ikE + ip + jm), where k, i, j are quaternions units corresponding respectively to amplitude,
phase and reference phase and E, p, m are energy, momentum and rest mass) is shown to
formalize an irreversible process of emergence of new fermion states of matter in conformity
with the First, Second and Third Laws of Thermodynamics. This nilpotent evolution
describes ‘a dynamic zero totality quantum universe’ in terms of an infinite alphabet, where
(i) each emergent fermion state is by Pauli exclusion, is unique and non zero; (ii) with their
boson interactions, these states define physics at the fundamental level in terms of the
Standard Model of elementary particles ; (iii) all the novel states of matter retain some degree
of quantum coherence/entanglement and (iv) the mechanism of the emergent evolution
concerns the symmetry breaking of the Galois field of automorphisms of the complete
symmetric group of the infinite alphabet's symbol permutations, into its nilpotent 'fermion'
roots, so that these roots constitute a unique factorization of the QM language apparatus and
the quantum generalization of the fundamental theorem of arithmetic; where in one
dimension the primes provide the unique solutions on the real line and thus in 2 dimension the
nilpotent fermion states now provides this factorization on the line spin ½ in the form of
these unique states' quantum mechanical gauge invariant geometric phases***, so it can be
postulated that this factorization is that of the famous Riemann Zeta function into its non
trivial zeros. *** The proposed basis of a physical proof of the Riemann Hypothesis within
the UNCRS. In 2 dimensional plane (x,y), as the 3D nilpotent Heisenburg Lie Group G
shows, there exists a conformal mapping x + iy (where x,y constitute a Fourier duality pair)
with a one dimensional centre CG(0,0,z) where this leaves all the infinite dimensional
irreducible unitary linear representations of G, point wise fixed so that they concern a unique
phase 2πvz and where cin quantum holography be identified with a fixed frequency v. Ie take
ζ in the Zeta function to be x + iy. For in this case, the phase describes the basis of the means
by which the 3+1 D relativistic geometry of real world objects are encoded as gauge invariant
geometric phase - the process of which takes place entirely naturally whenever radiation is
incident on any object, the experimental proof of which is the existence of the holographic
process itself, since this process could not take place otherwise. In this evolutionary process:
(v) the Quantum Carnot Engine (QCE) extended model of thermo-dynamic irreversibility
applies and consists of a single heat bath of ensembles of Standard Model elementary
particles each retaining a small amount of quantum coherence / entanglement so as to
constitute the emergent fermion states of matter, and (vi) the metric (E2 – p2 – m2) = 0 ensures
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the First Law of the conservation of energy operates at each nilpotent stage, so that (vii) prior
to each creation (and implied corresponding annihilation / conserve operation), E and m can
be postulated to constitute dark energy and matter respectively. This says that the well known
natural language precepts of the Laws of Thermodynamics are formalized by the UNCRS, so
as to become (as already published at CASYS), firstly the Quantum Laws of Physics in the
form of the generalized Dirac equation and later at higher stages of QCE ensemble
complexity, the Laws of Life in the form of Nature’s (DNA / RNA genetic) Code and then
subsequently those of Intelligence and Consciousness (Nature’s Rules)..
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Riemann Hypothesis and Signal Processing Paradigm
Adrian James Rifat
6 Polebarn Road,
Trowbridge,
WILTS BA14 7EG, England, UK
Tel: +44 (01225) 762682
http://arifatmath.co.uk/
Keywords: Boltzmann Information Spike, Riemann Zeros, Replica Correlation, Dark Energy,
Mean Signal-to-Noise Ratio (SNR)
Abstract
A new physical paradigm is proposed based on signal processing. At the deepest level, the
only assumption is that reality is built on information without any other prior knowledge. This
is an alternative approach to extrapolating traditional physical models and first order
approximations of what constitutes the known ‘Laws of Physics’ to describe reality.
In 1859, Bernhard Riemann postulated what is known as the Riemann Hypothesis concerning
the distribution of prime numbers, the information building blocks of arithmetic. This has
both mystified researchers and frustrated attempts to prove/disprove it, but as mathematics is
often described as the language of Physics, the distribution of the Riemann Zeros may provide
an important insight to how the universe is constructed. This spectrum of scale goes from the
very small to the very large, and may help explain the fundamental nature of reality (using
Quantum Mechanics/Chaos Theory/Cosmology) that goes beyond the original Riemann
Number Theory problem, beyond the capacity of any known computer, at bit numbers that
may exceed the total number of atoms in the universe!
The Author’s interest in all of this is somewhat accidental. In 1987, Professor Sir Michael
Berry presented a paper to the Royal Society in his Bakerian Lecture (Ref [1]) where he
showed remarkable statistical correlations between the distribution of the zeros from
computations carried out by Odlyzko at AT&T and universal asymptotic ‘footprint’ of chaotic
billiards in average level spacings.
I was intrigued to see structural similarity with well known statistics used in signal processing
called Rice Distributions (or Rayleigh-Rice) that describe the distributions of Signal + Noise.
(By Signal, we mean containing coherent phase structure; the Noise being the complementary
non-periodic components). The Rice distribution was developed for Sonar [2] immediately
after The Second World War (named after S. O. Rice [3], who coincidently worked at Bell
Labs) for discriminating signal within noise limited backgrounds and there exists an extensive
body of literature on this subject. Some features of various graphs and observations from all
kinds of sources made with regard to the properties of the Zeta function can give us clues as
to its form. This is the eclectic approach I have taken to weave together a consistent physical
argument based on known facts such as Central Limit Theory (CLT) and the concept of
Universality viz. that the Riemann Zeta function can encode all possible Theorems.
The Rice distributions contain a Modified I0 Bessel functions (of the 1st kind – zero order)
multiplied by the Rayleigh density, and my modification extended to be further modulated by
a combinatorial sum which will be a sum of all possible signals to give an ‘Information Spike
of Everything’ (appropriately normalised with SNR=1) of infinite bandwidth.
This is the Sum of All Signals + Noise which the Author proposes, whose indirect
consequences are testable, and which describes the emergent properties of our Universe based
on a unique process.
If it holds true, it may help shed light on the following:
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Dark Energy and Dark Matter,
Cosmic Horizon and Inflation,
Black Hole and galaxy formation,
The Incorporation of Thermodynamics and Time Asymmetry,
Renormalisation, Feynman Integration over all Paths & The Casimir Effect,
The true nature of randomness and why our Universe evolved from ‘Nothing’.
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The Process Semantics of Time and Space as Anticipation
Michael Heather, Nick Rossiter
Address for correspondence: CEIS
Northumbria University
UK NE1 8ST
email: {[email protected]; [email protected]}
http://computing.unn.ac.uk/staff/cgnr1/
Keywords: process, time, space, category theory, adjointness
Abstract
Time and space in western culture whether intellectual or popular are treated as independent
and absolute. A common example is the notion of travel through time which treats time and
space at the start and finish of the journey. That space and time appear only relative in the
manner of their measurement was asserted by Newton in his first Scholium (at the beginning
of his Principia) even though the consequences of his work suggest otherwise as it led to
relativity and quantum mechanics.
Absolute implies permanence: relative implies variety. The distinction is often in a context
where time is implicit as in the comparison of the stationary and the non-stationary but the
distinction may be spatial just as well as temporal. Now the stationary and non-stationary
respectively of Parmenides and Heraclites are brought together by rising to the metaphysics of
the philosophy of process. Process has the two levels of a fixed intension and a diversity of
extensions. This intension-extension divide was possibly not made explicit until the 17th
century work of the Port Royal school of logic. Yet it is only with the emergence of category
theory in the second half of the 20th century that it is possible to express the distinction in a
single mathematical form. Category theory itself started with the category of sets from the
static view but with the development of the monad is now able to give the Process view of the
permanent, combining both the stationary and the non-stationary. The intension of any entity
is the entity itself; the extension of the entity are versions of itself and if proper only partial.
There is an adjointness Σ ┤Δ ┤ Π between the intension and any extension:
Σ: intension Æ extension; Δ: extension Æ intension; Π: intension Æ extension.
Σ identifies the existence and Δ the nature of the intension/extension relationship from the
permanent world view while Δ identifies the existence and Π the content of the
extension/intension relationship from the continuously varying logical world view. Σ is the
free functor representing contingent existence, Δ the underlying functor identifying the syntax
and Π the universal functor providing the whole semantics.
Time & Space are in the intension; Time || Space are in the extension where & and || are full
abstractions of the connectives AND and OR. Intension is the permanent Process, a preorder,
not distinguishing time from space nor space from time. Formally this is the monad induced
by the adjunction Σ ┤Δ ┤ Π. The extensions are the possible instantiations of process,
preorders in time and space, formally co-monads induced by the co-adjunction Π ┤Δ ┤ Σ.
The intension provides the unification of relativity and quantum theory. Their separate
classical representations respectively in Minkowski and Hilbert spaces are extensional
models. However, the property of a topos is that a contravariant extension is itself monadic.
An anticipatory system is a microcosm of the world and a monadic intension. Anticipation is
therefore more fundamental than either time or space. Anticipation is the natural preordering
on any system.
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Is Special Relativity Logically Prior to Quantum Mechanics?
Garnet N. Ord
Mathematics Dept.
Ryerson University
Toronto, Ontario, Canada.
416 979 5000 ext 6967
[email protected]
http://www.math.ryerson.ca/~gord/
Keywords: Relativity, Quantum Mechanics, Statistical Mechanics, Exactly Solvable Model
Abstract
The Dirac equation represents a marriage of quantum mechanics and special relativity. Highly
successful in its own right, it has proven difficult to extend the relationship to include general
relativity. Conventionally, special relativity inherits the concept of a smooth worldline from
Newtonian mechanics and as a result Minkowski space informs the motion of massive
particles. How this is done is not specified. In a two dimensional space it is easy to invent a
local rule about the fine-scale geometry of the worldline that enforces Lorentz covariance on
large scales. By looking at a very simple exactly solvable model of this we are able to see
that specification of the local rule for special relativity automatically implicates the Dirac
equation. As a result, in this model the phase of Feynman paths exists as a remnant of pathdependant proper time, and the superposition principle that separates quantum mechanics
from classical physics owes its existence to the odd signature of spacetime.