Computational Self Organized Emergence
as an explanation of Quantum
Physical laws and the Natural Hierarchy of 3D
dynamic Structural Complexity
including the architecture of the Human
Brain/Mind,
the Senses and Consciousness
BCS Cybernetics Machine Specialist Group
Remit – the physical foundations of computation
Founding speaker 1986 David Deutsch
Founding question – the brain’s architecture?
Why is it so different from that of the digital computer?
 Could physical law, explain this?
 and in particular, quantum mechanics (QM)?
Based on updated material prepared for the
Lionel Blue presentation 'Brain, mind and consciousness: is
there a quantum explanation for the operation of the brain?'
given at Durham University
Speaker Peter Marcer CEng, FBCS, CITP, DPhil
Contents
Natural 3D Structural Complexity

A summary of the Principal Findings

the Computational Methodology & Solutions


Einstein's Equation – the initial state of
primaeval dark energy
 Solving Einstein's Equation
 But now you will surely ask?
Recent Journal Evidence
 The Evidence in 1986
 A Summary
 Appendices
Additional Material and Perspectives.
The Natural Hierarchy of 3D structural Complexity
The scientific discovery of a natural hierarchy of 3D geometric dynamic
structural complexity on Earth
from the families of the elementary particles of quantum physics
through the periodic table of the elements which regulates their basic
chemistry,
upward to the molecular biology of life regulated by the DNA/RNA
genetic code
Culminating in the 3D molecular complexity of the neurophysiology
of the human brain, the connectivity of which is only surpassed by that
of the Universe itself.
And Just One Question
'
Does a scientific description which predicts this 3D
geometric hierarchy of complexity including that of
the brain/mind and the senses exist ?'
The well documented accumulating evidence,
 cited here & summarized on the BCSCMsG
homepages http://www.bcs.org.uk/cybergroup.htm
is that it does and is called the Nilpotent Universal
Computational Rewrite System (NUCRS)
Summary of
Principal Findings
The NUCRS Self Organised Tree of Emergent Knowledge
5. the 3D structure of brain/mind &
senses including
4. the laws of living systems in the form of
DNA/RNA genetic code
3. the laws of chemistry, valence &
6.the semantic laws of natural language &
the periodic table
thought in accord with Wittgenstein's principle
2. the nilpotent Dirac operator &
in the form of the Nilpotent Universal
Standard Model elementary particle
Computational Rewrite System itself
quantum physics
1. the laws of thermodynamics
& in particular Einstein's
conservation equation of
energy, momentum and mass
The NUCRS predicates a primaeval dark energy, from which 1-6 are emergent!
The 2007 source book of the NUCRS is Zero to Infinity
 http://www.worldscibooks.com/physics/
6544.html plus more
 recent refereed papers of the American
Institute of Physics CASYS and Vigier
conference proceedings of which
 Peter Rowlands, physicist ;Bernard Diaz
computer scientist, Vanessa Hill,
molecular biologist,Nature’s genetic Code
ch19, & myself, Nature’s Rules. ch20 for
the evolution of intelligence are coauthors
What the NUCRS says about the 3D structure of the
human brain or as it turns out
the physical brain mind.
the further evidence the NUCRS provides is, that there exists a
neural / glia (neuron / glial cell → ‘electronic / ionic’) dual 3D
geometric structure as the form of a self organized brain / mind
equipped with emergent symbolic/alphabetic semantic natural
language capabilities in accord with Wittgenstein's principle,
where the laws of natural semantic language have the NUCRS
universal grammar / alphabet
and the brain / mind is the control centre of each self organized
individual human body / self, nerve fibre / microtubule dual
The human brain mind


There is an actual physical emergent human self, and an actual
physical emergent human mind, as part of the self organized human
body and the self organized human brain as a sensory whole.
so as, to result in, our evident 3D sensory self awareness, and
endow human semantic intelligence with the evident capability to
describe and understand the Universe from which as a species it is
emergent.
Because NUCRS self organization (envisaged here as a carrier
wave hierarchy) is of not just that of the Universe as a whole
but is also the way our brains are self organized too!
The human brain mind II
The NUCRS says that human sensory apparatus - eyes, ears,
nose and mouth, and skin i.e. touch, do not process
information in the form of words / symbols / bits but as
images of 3D geometric dynamic structure (i.e. of 3D
objects), using holography in the form of quantum
holograms as the means of 3D pattern recognition, which
the brain stores, self organized hierarchically, in the form of
a 3D associative memory/filter bank, described by the
Frobenius-Schur-Godement identity using holographic
phase/frequency transforms H(θ,ν) - the most efficient
organized means possible see notes,
The brain needs two hemispheres
It makes no evolutionary sense when 3D
information in the form amplitude and phase is
arriving at the senses to throw away the phase
information θ and just use the amplitude
information / bits, which are the NUCRC says in
use in the brain to encode semantic language in
the form of an alphabet with a universal grammar
and so results in two distinct brain hemispheres.
3D holographic image reconstruction
allows the information arriving at the senses as
amplitude and phase to be used /'seen' immediately
as a whole in the form of a single 3D wave front,
passed as a hologram directly to the brain (based on
a unique spectral / reference wave the brain
supplies) for use as memories and as filters,
beginning as empty slate (unless initial information
is supplied genetically). It says each sensory
apparatus is constituted of secondary sources of the
brain/body as a whole being/source
II
This shows a 3D object
image bearing acoustic
wave in water converted to
a 3D object image bearing
light wave in air, with the
water surface acting as a
hologram i.e. the means a
sensory apparatus uses to
transfer 3D sensory data to
the brain.
Quantum holography uses phase conjugation
where the 3D object image,
3D object and I / O signal
paths both coincide &
produce an adaptively
resonant signal.
This mechanism can be
conceived as a perfectly
focused lens, as is used to
acoustically remove gall
stones, or for Star Wars
technology!
Phase Conjugation is used to encode quantum holographic
diffraction patterns / holograms
in MRI Magnetic Resonance Imaging systems e.g.
produces real quantum holograms
where top left the entire diffraction
pattern A is converted to brain slice
B & in the middle and bottom only
the centre and outside of the centre
of A is converted to B.
All give a whole brain image at
different resolutions and not just a
part of the image.
Heisenberg uncertainty is the actual means of
3D geometric quantum computation!
The diagram shows quantum
signal decay losing amplitude
wrt z axis but simultaneously
regaining the energy
longitudinally as phase θ, so
that the brain slice selected for
measurement by the prepared
e-m pulse train applied in MRI,
is transformed thermodynamically into a wave
diffraction pattern/quantum
hologram of the brain slice.
An example of the holographic nature
of a NUCRS-like process
a self similar fractal
process is repeatedly
applied to the picture (top
left) until it appears
random (mid / right) and
the final return of the
picture (bottom right).
Other images obtained by MRI tensor diffusion
control in the form of a Levy stochastic process
Isn't it just amazing to be
able to see actual signal
paths in the human
brain that allow doctors
to diagnose illnesses
like Multiple Sclerosis
from 3D geometric
abnormalities. These
pictures are by courtesy
of Walter Schempp.
This is a new application of MRI
How best might the NUCRS be envisaged?




For me, it is as a quantum computational tower of 3D
dynamic structural complexity where
each bootstrapped emergent level of 3D structure
acts as the source of a fixed physical carrier wave for the
3D structure at the next level, ad infinitum and
where the 4 known fundamental laws of physics apply at
each level.
Wave particle duality is therefore essential to its
understanding.
A carrier wave field example is ...



gravity in the form of general relativity as the
carrier wave field for 3D celestial bodies,
where the NUCRS dynamic behaviour is
accordance with the principle of least action, i.e.
that of geodesic straight lines in 4 dimensions.
Often illustrated by a stretched rubber sheet under
the weight of a spherical object.
A proven example is



the spontaneous inclusion of a 3D object image in
any form of physical wave incident on the object!
The fact of which is testable holographically
Think of holography as the addition of a reference
wave phase θ to the incident wave θ' to form a
hologram. This encoding/interference pattern is
then decoded by subtracting the wave θ, to reveal
the incident object image bearing beam θ'.
The NUCRS methodology &
findings
The Nilpotent Universal Computational
Rewrite System I

is a universal self-organized computer science rewrite
methodology with an infinite alphabet, where
each letter symbolizes new emergent order, which must
incorporate the pre-existing order within it &

the simplest physical order to emerge is
that of Standard Model elementary particle physics
indivisible from a relativistic 3D space and time
as described by the conservation law of energy,
momentum and mass, which the NUCRS predicates

Computational Self Organized Emergence
the computer science rewrite principle used in the
Nilpotent Universal Computational Rewrite
System (NUCRS)

concerns a 'logic of self organization'

based 0 and 0 rather than 0 and 1,

where this new logic, called nilpotent, is found to
be quantum mechanical (QM)

but includes the latter – digital computation
as shown in Deutsch’s 1985 Royal Society paper
The Nilpotent Universal Computational Rewrite System
The NUCRS predicates Einstein’s conservation equation of
energy E, momentum p & mass m,
E2 – p2 – m2 = 0 ( taking c = 1) factorized as
X.X = (ikE + ip + jm) (ikE + ip + jm) = 0
where p is a multivariate vector, k, i, j are quaternion units,
i = √–1, and c is the speed of light,
having an infinity of non trivial solutions/roots X ≠ 0
called nilpotent, each corresponding to a letter of the NUCRS
infinite alphabet, where each
X = (E, p(ipx, jpy, kpz), m) is a unique Pauli fermion state,
paired with its own dual vacuum state as above.
The Factorized Equation
describes a non trivial 'zero totality'
self organised emergent cosmology
with trace (its column vector x its row
vector) ∑ X.X = 0 at every stage n,
where each emergent stage is a unique
fermion state X(n) ≠ 0 defined by the
single generic Dirac rewrite operator
ikE + ip + jm .
The Dirac Rewrite Single Operator
'Nilpotent Machine Order Code'
The symbol signifying the NUCRS infinite alphabet
in the form of the symmetries of this single
operator (shown below to be those of Standard
Model Elementary particle quantum physics and
also of the genetic code) as the cosmology's
'machine order code' takes the form of the
hydrogen atom (i/e. an ion/electron dual & its
spectra) as the prelude to the periodic table &
chemical valence and a molecular rewrite of this
order code as the RNA/DNA genetic code
UNIFICATION OF PHYSICS AND BIOLOGY
BIOLOGY
5 - Fold Symmetry
Fibonacci, golden section etc
PHYSICS
5 - Fold Symmetry
Broken
20 Amino Acids
20 Algebraic Elements of
Fermionic+vacuum structure
Double stranded DNA : Double helix
One handedness
Van der Waals force
Fermion+vaccuum Spin ½ x 2 : Double helix
One handedness
Van der Waals force
64 Possible Triplet codons : 4³
64 Elements of Dirac Algebra
4 Bases : Adenine, Guanine
Cytosine, Thymine.
4 Parameters : Mass, Space,
Time, Charge
An actual picture of a coil of DNA
and upwards
Large-scale physical systems
‘Astronomers have discovered an
unusual helix-shaped nebula near
the centre of the Milky Way. This
peculiar nebula stretches 80 light
years, and looks like the classic
image of a DNA molecule. The
nebula formed because it’s so close
to the supermassive black hole at
the heart of the Milky Way, which
has a very powerful magnetic field,
powerful enough to reach out this
incredible distance and twist up
this gas cloud with its field lines.’
Nature March 16 2006.
##öý¶l®üAðSÄ_#´ïˆ:F•û"O¬?함ü
The NUCRS Dirac Order code
As the higher levels of 3D genetic molecular
hierarchical complexity, include those of the
human genome and the human brain, a
consequence of NUCRS Dirac rewrite
machine order code, will be the symbolic
semantic laws of language and thought in
the form of NUCRS itself!
As is evidentially the case!
Einstein's Equation-the Initial State
The equation itself defines an initial physical
totally 'degenerate' ground state where all the non
trivial solutions / roots X ≠ 0 are indistinguishable
from each other, i.e.

it specifies a 'primaeval dark energy' from which
each of the 'non degenerate' unique fermion states
X of the cosmology (its spectra) then emerge
with energy E, momentum p = (ipx, jpy, kpz), mass m
expressed in terms of 3D coordinates (x, y, z)
whatever dynamic behaviours satisfy the equation.

Finding any particular solution I
The method for finding a particular nilpotent
solution of the self-organization is the
assignment of the specific operators
corresponding to the fermion state in
question such that this leads to a nilpotent
solution when the appropriate phase factor θ
is applied: e.g. as shown in the last figure.
θ takes the form of an invariant 3D
geometric/Berry phase of the wave function
of the cosmology.
Einstein's Equation Solutions 1
The separability of the 3D dynamic spatial quantum
degrees of freedom in the conservation equation,
says that the quaternion units i, k, j (which are
distinct square roots of –1!) and i = √-1 are those
which correspond to the electromagnetic, weak,
strong, and gravitational / inertial
parameterizations / quantizations of the physics of
the elementary particles, and therefore hold
throughout the universe.
Einstein's Equation Solutions 2
And evidentially, from the experimentally
determined results of the Standard Model, this is
indeed the case, since these known
quantizations/parametrizations correspond to the
symmetries U(1), SU(2), SU(3) and SU(4)
satisfying the requirement of the
NUCRS self-organized rewrite methodology
that each pre-existing order described
be incorporated in the new emergent order
.
Einstein's Equation Solutions 3
This electromagnetic, weak, strong and gravitational
vacuum/force separability with ikj = –1 so, as known,
CPT symmetry holds everywhere, says that
any subsequent fermion states X will incorporate
3D Standard Model elementary particle physics
as the pre-existing order &
that all the forces reduce and are equal to U(1) at the
Planck mass
Einstein's Equation Solutions X
Alternative Supporting Viewpoints
X are the non zero local stable critical points of the
cosmology, which from the renormalization group
viewpoint for predicting new states of matter, are
obtained by mapping it onto itself.
Or as its initial indistinguishable 'zero totality', the
complete symmetry Galois/permutation group of
automorphisms (mappings on itself), from which
the fermion states emerge by self organized
spontaneous symmetry breaking.
Finding any particular solution II
these nilpotent quantum relative phases θ (arbitrary
up to a fixed phase now taken as the measurement
standard!) which correspond to the NUCRS
infinite rewrite alphabet of fermion states; & to the
infinite square roots of -1(Rowlands and Diaz 2006
CASYS), uniquely determine each of the infinite
unit vectors of the unit disk, so that
i2 +1 = 0 is the nilpotent metric of quantum
emergence with measure θ, which holds at every
level of the NUCRS self organised emergence.
Finding the particular solutions thus concerns

‘phase’ gates and not simply 'bit' gates

with metric i2 + 1 = 0 i.e. i = √ –1 , an equation for

quantum chaos of fractal self similarity dimension 2 with

quantum ‘qubit’ logic of √[Not = –1 :truth value False]


i/the qubit is the basic computational primitive of the unit wire,
from which, Feynman showed, all the other primitives of : signal
exchange : signal fan out, fan in, XOR & the NAND gate, can be
constructed, for example, as is essential for any PC to be designed,
built and function digitally in terms of NAND primitives.
The NUCRS is thus computer constructor universal.
The nilpotent fractal self
similar universal
computational attractor,
where the changes of
phase θ all take place,
each resulting in an
entirely new emergent 2D
unit vector i.
Finding particular solutions III


as θ = π/2 defines orthogonality, the roots of this metric
correspond to the infinite unit vectors of the Hilbert space,
in which all the solutions / roots of QM are defined to lie
the metric i2 + 1 = 0 ensuring that for every nilpotent
solution quantum phase θ, cos2θ + sin2θ = 1
confirms the NUCRS predicated Einstein equation
quantum mechanical field solutions X are all finite &


similarly for the Galois/permutation group alternative
view where by definition every group element has an
inverse and each group a unit element & says
the solutions permute, & so are linearly independent
statistically
The NUCRS Hierarchy III
NUCRS waves imply brain neurons can be envisaged as
unit wires / wave guides for guided waves phase θ
equipped with a quantized amplifier for neural transmitters
– the synapse, see Eccles' hypothesis described later
able to explain 3D dreaming / awake or asleep and
hallucinations due transmitter imbalance
And of course of brainwaves in both senses
Or the chemical bond as unit wires at the lower level of
chemical complexity
Relative 3/4D sizes in Universe
This marvellous Scientific
American book gives a more
detailed picture.
By moving the decimal point
to change the scale from the
human scale we see, what our
scientific instruments tell us
is the case!
exp(ln θ) = θ = ln(exp θ)
But now you will surely ask
‘Is it really possible for a self organized Universe, as
illustrated by the single Tree, to consist at its inception
of a single inseparable heat bath of dark energy?’ and
‘what about ambient body temperature quantum
computation essential to the functioning of living
systems, like the human brain?’
The latest answer to both these questions from the
impeccable sources of the Journals of Science and
Nature is ‘yes, they can!’
The second law of thermodynamics and the question of ambient
body temperature quantum computation in living systems






A Nature paper recently published, confirms ambient body
temperature quantum computation is proven with respect to
Marine Algae Photosynthetic harvesting of photons by chlorophyll.
It allows us to postulate that it is ubiquitous to all plant life &
to all animal life, too! For if the magnesium atom in chlorophyll is
replaced with an iron atom, the result is a molecule very like
haemoglobin that harvests our oxygen.
So although science cannot currently perform quantum computation
of any significant complexity in the laboratory, nature, it appears,
does so all the time in all living systems, subsystems, &
unlike digital computation, is capable of solving natural problems of
exponential complexity in real time as the NUCRS describes.
As published in Science
The Carnot Engine, that idealises the workings of the Second Law of
Thermodynamics, is replaced by the Quantum Carnot Engine.
It describes the Second law’s extended functioning in a single ambient
temperature heat bath, where there is an ensemble of matter of quantum
coherence, parameter phase θ, as the measure of quantum entanglement!
It leads (as for the NUCRS) to the quantum emergence of new states of
matter, called in the Science article, a ‘phaseonium’ and
 as is well known in quantum mechanics in relation to the wave
function, θ concerns the 3D geometric gauge invariance of phase of the
wave function as would be required to specify the hierarchy of 3D
geometric complexity.
This is a very general confirmation 1
 the NUCRS methodology is what we are seeking; for example. if the human body departs even by a small amount from the ambient
blood temperature of 37 degrees, it loses consciousness, or can even
become ill and die.
That is to say, it can be postulated that
 dying implies the loss of quantum coherence / entanglement (qc/e) θ,
together with the subsequent breakdown of the body’s 3D structural
chemical complexity, and that
qc/e is central too, to the self organized working of the immune system
and the body’s mechanisms of self repair.
This is a very general confirmation 2
Equally the coherence/entanglement θ is then by implication essential
to the emergence of each entirely new human being!

so that, for example, when DNA enters, say a stem cell in the
appropriate way, the DNA acts as ‘the quantum thermodynamic
program' parameter θ for the spontaneous (self organized) emergence
of the being / organism in question.

a process the NUCRS system tells us happens by means of
spontaneous phase conjugate adaptive resonant emergence i.e. the
mapping of a 3D object onto itself, as in a previous figure

and phase conjugation appropriate to NUCRS self organization
would indeed produce our sense of bodily self awareness!

π = the Visual Cortex
It therefore comes as no surprise that in Nature a recent
paper entitled ‘π = the Visual Cortex’, which
experimentally examined the visual cortices of three
distinct mammals (one very distantly related to the others)
concludes that their 3D structure and dynamics are
remarkably all characterised by π as is the case for
quantum phase and that this coincidence could only
happen if mammalian brains were self organised, as
predicted earlier!
A demonstration of phase conjugation
sensory imaging
Just listen when I snap my fingers and ask
yourself where you hear the snap!
Its outside your head coincident ie phase
conjugate with the snap itself! Where too do you
see your left hand? Well, reach out your right
hand and touch it. Both sight and touch are 3D
phase conjugate images outside your head, too.
Key to the hard problem of consciousness?
The hard problem relates third person objectivity to first
person subjectivity. Yet while our whole experience of a
3D object is subjective, we can all communicate that
experience to one another, simply by pointing to the 3D
object in question, an image of it, or by saying the name of
it in a language we share. For as in the NUCRS it's the 3D
object itself, which defines quite literally its own
‘objectivity’ since no two objects on our level of scale can
be in the same place at the same time! For all the images
of a 3D object are phase conjugate, coincident with itself.
1986 Some Evidence



1985 Deutsch’s Royal Society seminal paper on
universal quantum computation
1983 Albert's finding that quantum and digital
automata are radically different
Sir John Eccles Royal Society paper’s quantum
brain hypothesis based on the neurophysiology for
which he was awarded the Nobel prize.
The basis of Eccles’ Hypothesis



The Nobel Laureate Ramon y Cajal’s 1911 hypothesis that
brain neurons act seemingly independently
the mind boggling structure & working of the synapse as a
‘phaser’ in Startrek terminology i.e.
the probabilistic exocytosis across the synaptic junction of
a single synaptic vesicle [(contents 104 molecules of
neurotransmitter) (one of many in the synaptic bulb)] via
the hexagonal vesicular grid of attachment sites to provide
the synaptic gain!
Eccles' Hypothesis II
Eccles Hypothesis
moots that if one can
explain the exact
nature of the working
of the synapse and
it is quantum
mechanical then the
brain must be too.
The likely explanation
The synapse (encased in a bulb of very high
dielectric constant) functions as a Quantum
Carnot Engine, where the synaptic vesicles
are the ensemble of matter from which a
new property of matter ie a neural
transmitter, emerges to provide the synaptic
gain via the SU6 ie hexagonal vesicular grid
A summary so far
That is to say, the NUCRS system has, with a high level of
certainty, the capability to describe the hierarchy of
cosmological complexity from the very smallest scale up to
the enormous variety of living systems that exists on Earth,
with the implication that our planet too is a self organised
unity, since the appropriate conditions still exist here to
support living systems of enormous complexity including our
own human species
& where the NUCRS postulates these living systems are all
themselves self organised and the result of the Earth's self
organization
However what of the cosmological complexity
from the 3D scale of the Earth upward?
Can it really be hypothesized that the NUCRS process
describes the cosmos as a self organized whole? And if
so, what does the NUCRS system have to say about
these higher scale 3D structures, such as our star, the sun
and the solar system? Could their behaviour be self
organized too?
The answer is yes it can as we have already established
General Relativity fits into the NUCRS scheme of things
too. But this is another story.
The object of another talk, on White (W)hole Physics,
where the cosmological Source of all / the Cosmos is the White
Whole and its secondary sources, are anti phase black holes / galaxies
on its surface S so as to constitute a zero totality. That is to say the
black holes act computationally as garbage collectors to allow defunct
matter and energy to be recycled into the newly emergent hierarchies
of higher 3D geometric structural complexity to come ad infinitum,
i.e. it is a sustainable metamorphic universe.
This self organised Cosmos as a whole constitutes at all times a ‘zero
totality’, but one where there are non zero local stable critical points:
as already described it is mathematically nilpotent ie there exist self
similar quantum computational operators X(n) ≠ 0 for all n = 1, 2, ...
such that X.X = 0 and the trace ∑X.X of the Cosmos i.e. its column
vector multiplied by its row vector is indeed zero for all n.
The end
Appendices
Rewrite systems – sidebar I



all digital computer programs are describable in terms
of conventional rewrite/production p systems with 4
fixed rules:an alphabet // the rewrite rules // a start ‘axiom’ or
symbol // and a stopping criteria
an example is Fibonacci nos, where these are a, b //
p1:a→b ; p2:b→ab // a // none respectively
Rewrite systems – sidebar II



What are conventional rewrite systems for?
They provide an alphabet of symbols / algebraic
semantic language, a grammar, that enables a
programmer to proofread the logic of his / her
program
The NUCRS has an infinite alphabet, which
varying the production rules bootstraps itself into
place i.e. it is universal and self organising.
Independent Source works are
Weyl’s book The theory of groups and quantum mechanics, translated
by Robertson (Dover 1931), including Lie groups. This early source
work gives a full derivation of the periodic table, and chemical
valence in the chapters headed the 'Permutation Group', 'the Pauli
Exclusion Principle and the Periodic Table' and 'Spin and Valence – a
Group Theoretic Classification of Atomic Spectra' in complete
agreement the current NUCRS argument. As well as an independent
argument for the need of Einstein's General Relativity to hold so that
each point P of space time will consist of four mutually perpendicular
directions governed by local Lorentz transformations.
Plucker’s concept that the geometry of 3D space can be used for any
curve that is dependent on three parameters, which from Sophus Lie’s
1871 doctoral thesis lead him to his celebrated Lie Methodology, and
has allowed a colleague Erik Trell, to predict the relative masses of all
the Standard Model elementary particles.
Independent Source works are
The many papers (1) of Will Hoffman which treat the neuron as what
in Lie theory is called a ‘Lie group germ’; and (2) those of a further
colleague Walter Schempp, a specialist in the quantum holographic
working of MRI machinery based on the 3D Heisenberg Lie group
and the application of such signal processing to the neurocomputer
architecture of the brain. Walter is remarkably a descendent of Kepler!
Lie algebras play a pivotal role in Standard Model particle physics.
The Mathematical Group Perspective
The mathematical group perspective describes the NUCRS process
of hierarchical emergence as one of spontaneous symmetry breaking
of the complete symmetric group known as the Galois or
permutation** group (** i.e. its ‘statistical’ properties). That is, it is
universal in the mathematical group theoretic sense that it concerns
the complete field of mappings from one state of itself to another,
called automorphisms.
And there can be no quantum infinities (w.r.t. this NUCRS
interpretation) because every state of energy, matter and even 3D
space time corresponds to a group element where this has a dual /
inverse, and every group, of course, has a unit element (i.e. can be
normalised in quantum mechanical jargon)! For these requirements
are just the group axioms.
The Group construction part 2
It is ‘dark’ because with respect to any emergence, the dark energy constitutes
the global measurement standard for the next measurement / computational
output / emergence taking place for which all the previous emergences are the
input / quantum preparation and historical record.
That is to say it describes an irreversible quantum physical process of evolution,
where there can be no return to the initial state, and such that the totality of
energy and matter, light and dark, remains fixed but arbitrary in the sense that it
can never be directly measured (because it is the measurement standard against
which all future measurement takes place!): i.e. initially it is the point we call
the absolute zero of temperature, 0 degrees Kelvin.
That is, this Self Emergence satisfies all the Laws of Thermodynamics! i.e. the
trunk of the semantic Tree.
Automorphisms an example
As established by the famous mathematician J. H. Conway in his book On Numbers
and Games, any such field of automorphisms has a unique birth order or birth order
field automorphism ; and so in the case of the NUCRS this birth ordering can be
postulated to describe a quantum evolution.
A example, is number / the integers, where the next integer to emerge in the process of
generating the complete field of all the integers from the empty set, is unique and must
be consistent with all the previous integers generated earlier, ie it concerns an ordinal
number field i.e.
(1) (defined as the empty set ϕ compared to itself)
(1,2)
(1,2,3)
(1,2,3,4)
(1,2,3,4,5)
etc
So what does this group construction/description tell us?
Firstly it provides a mathematical explanation for the nature of the enigma of
quantum nonlocality / entanglement – as to why any 3D object / observer /
event / activity is inseparable from / part of the Universe itself as whole, in
agreement with the concept of automorphism and the dictionary definition of
the Universe as ‘all that exists (physically)’, and of a definition for so called
‘dark energy’, the primaeval form of which it describes as the complete
symmetric group.
That is to say, it is the totally degenerate (cosmological) ground state of
quantum energy (where no physical property can be distinguished from any
other!) such that each of its non degenerate (cosmological) states of energy and
matter make their appearance by spontaneous symmetry breaking leaving an
indistinguishable residue of dark energy from which the next emergence takes
place.
That is to say, it concerns the stages / staircase / spectra of the
metamorphosis of the dark energy.
Self-organization in solid-state matter
Coldea et al, Science, 327, 177,
January 2010, showed that linked
chains of magnetic atoms of cobalt,
one atom wide, transform, under a
magnetic field applied at right
angles to an aligned spin into a
quantum critical state – a quantum
version of a fractal pattern.
Resonances occurred in the golden
ratio of 1.618…, reflecting an
underlying E8 symmetry.
The End II