1. 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

2. 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)?

3. 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

4.  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.

5. 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.

6. 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)

7. Summary of Principal Findings

8. 2. the nilpotent Dirac operator & Standard Model elementary particle quantum physics 3. the laws of chemistry, valence & the periodic table 4. the laws of living systems in the form of DNA/RNA genetic code 1. the laws of thermodynamics & in particular Einstein's conservation equation of energy, momentum and mass 5. the 3D structure of brain/mind & senses including 6.the semantic laws of natural language & thought in accord with Wittgenstein's principle in the form of the Nilpotent Universal Computational Rewrite System itself The NUCRS predicates a primaeval dark energy, from which 1-6 are emergent! The NUCRS Self Organised Tree of Emergent Knowledge

9.  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 The 2007 source book of the NUCRS is Zero to Infinity

10. 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

11. 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!

12. 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,

13. 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.

14. 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

15. 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.

16. 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!

17. 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.

18. 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 thermo- dynamically into a wave diffraction pattern/quantum hologram of the brain slice.

19. 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).

20. 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.

21. This is a new application of MRI

22. 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.

23. 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.

24. 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'.

25. The NUCRS methodology & findings

26. 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

27. 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

28. The Nilpotent Universal Computational Rewrite System The NUCRS predicates Einstein’s conservation equation of energy E, momentum p & mass m, E 2 – p 2 – m 2 = 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(ip x, jp y, kp z ), m) is a unique Pauli fermion state, paired with its own dual vacuum state as above.

29. 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.

30. 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

32. An actual picture of a coil of DNA and upwards

33. 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.

35. 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!

36. 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 = (ip x, jp y, kp z ), mass m expressed in terms of 3D coordinates (x, y, z) whatever dynamic behaviours satisfy the equation.

37. 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.

38. 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.

39. 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.

40. 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

41. 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.

42. 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 i 2 +1 = 0 is the nilpotent metric of quantum emergence with measure θ, which holds at every level of the NUCRS self organised emergence.

43. Finding the particular solutions thus concerns ‘phase’ gates and not simply 'bit' gates with metric i 2 + 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.

44. 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.

45. 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 i 2 + 1 = 0 ensuring that for every nilpotent solution quantum phase θ, cos 2 θ + sin 2 θ = 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

46. 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

47. 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)

48. 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!’

49. 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.

50. 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.

51. 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.

52. 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!

53. 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!

54. 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.

55. 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.

56. 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.

57. 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 10 4 molecules of neurotransmitter) (one of many in the synaptic bulb)] via the hexagonal vesicular grid of attachment sites to provide the synaptic gain!

58. 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.

59. 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

60. 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

61. 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.

62. 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.

63. The end Appendices

64. 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

65. 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.

66. 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.

67. 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.

68. 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.

69. 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.

70. 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

71. 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.

72. 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 E 8 symmetry.

73. The End II