Computational Self-Organized Emergence in Quantum Physics and the 3D Complexity of the Human Brain/Mind

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. 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 & the periodic table 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 2. the nilpotent Dirac operator & Standard Model elementary particle 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!

9. 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

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 wavefor the 3D structureat 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, 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.

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 = (ipx, jpy, kpz), 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 i2 +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 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.

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 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

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.